Finite Group Databasebeta

← #14918263

Subgroups — #14918263

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623262C211yesmaximal, characteristic
2#13071807C211yesmaximal, characteristic
3#13071801C211yesmaximal, characteristic, complemented
4#13071800C211yesmaximal, characteristic, complemented
5#13071777C211yesmaximal, characteristic
6#13071735C211yesmaximal, characteristic
7#13071730C211yesmaximal, characteristic
8#13071729C211yesmaximal, characteristic
9#13071721C211yesmaximal, characteristic, complemented
10#13071719C211yesmaximal, characteristic, complemented
11#13071715C211yesmaximal, characteristic, complemented
12#13071707C211yesmaximal, characteristic, complemented
13#13071695C211yesmaximal, characteristic
14#13071580C211yesmaximal, characteristic, complemented
15#13071572C211yesmaximal, characteristic, complemented
16#13071502C211yesmaximal, characteristic
17#13071469C211yesmaximal, characteristic
18#13071418C211yesmaximal, characteristic, complemented
19#13071414C211yesmaximal, characteristic, complemented
20#13071396C211yesmaximal, characteristic
21#13071390C211yesmaximal, characteristic
22#13071385C211yesmaximal, characteristic
23#13071371C211yesmaximal, characteristic
24#13071365C211yesmaximal, characteristic, complemented
25#13071352C211yesmaximal, characteristic, complemented
26#13071348C211yesmaximal, characteristic
27#13071261C211yesmaximal, characteristic, complemented
28C4×#66942C211yesmaximal, characteristic, complemented
29#13071166C211yesmaximal, characteristic
30#13071091C211yesmaximal, characteristic, complemented
31C11×#2331C211yesmaximal, characteristic, complemented
32C2×C11×C4⋊Q8C2211yescharacteristic
33C2×#66999C2211yescharacteristic
34C2×#66999C2211yescharacteristic
35C2×Q8×Dic11C2211yescharacteristic
36C2×Q8×Dic11C2211yescharacteristic
37#10623262C4116yescomplemented
38C2×#66951C2211yescharacteristic
39C2×#66951C2211yescharacteristic
40C2×#66951C2211yescharacteristic
41C2×#66951C2211yescharacteristic
42C2×#66942C2211yescharacteristic
43C2×#66942C2211yescharacteristic
44C2×#66942C2211yescharacteristic
45C2×#66942C2211yescharacteristic
46C2×#66925C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#387C2211yescharacteristic
55C11×#387C2211yescharacteristic
56C11×#387C2211yescharacteristic
57C11×#387C2211yescharacteristic
58C11×#382C2211yescharacteristic
59C4×C11×C4⋊C4C2211yescharacteristic
60C4×C11×C4⋊C4C2211yescharacteristic
61C11×#376C2211yescharacteristic
62#10622843C2211yescharacteristic
63#10622843C2211yescharacteristic
64#10622843C2211yescharacteristic
65#10622843C2211yescharacteristic
66#10622603C2211yescharacteristic
67#10622603C2211yescharacteristic
68#10622602C2211yescharacteristic
69#10622602C2211yescharacteristic
70#10622602C2211yescharacteristic
71#10622602C2211yescharacteristic
72#10622598C2211yescharacteristic
73#10622598C2211yescharacteristic
74#10622594C2211yescharacteristic
75#10622594C2211yescharacteristic
76#10622594C2211yescharacteristic
77#10622594C2211yescharacteristic
78#10622591C2211yescharacteristic
79#10622591C2211yescharacteristic
80#10622591C2211yescharacteristic
81#10622591C2211yescharacteristic
82#10622591C2211yescharacteristic
83#10622591C2211yescharacteristic
84#10622590C2211yescharacteristic
85#10622589C2211yescharacteristic
86C4⋊C4×Dic11C2211yescharacteristic
87C4⋊C4×Dic11C2211yescharacteristic
88C4⋊C4×Dic11C2211yescharacteristic
89C4⋊C4×Dic11C2211yescharacteristic
90C4⋊C4×Dic11C2211yescharacteristic
91C4⋊C4×Dic11C2211yescharacteristic
92#10622586C2211yescharacteristic
93#10622586C2211yescharacteristic
94#10622585C2211yescharacteristic
95#10622585C2211yescharacteristic
96#10622585C2211yescharacteristic
97#10622585C2211yescharacteristic
98#10622553C2211yescharacteristic
99#10622553C2211yescharacteristic
100#10622553C2211yescharacteristic
101#10622553C2211yescharacteristic
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic
104#10622549C2211yescharacteristic
105C4×C4⋊Dic11C2211yescharacteristic
106C4×C4⋊Dic11C2211yescharacteristic
107#10622546C2211yescharacteristic
108#10622546C2211yescharacteristic
109#10622546C2211yescharacteristic
110#10622546C2211yescharacteristic
111#10622545C2211yescharacteristic
112#10622545C2211yescharacteristic
113C4×Dic11⋊C4C2211yescharacteristic
114C4×Dic11⋊C4C2211yescharacteristic
115C4×Dic11⋊C4C2211yescharacteristic
116C4×Dic11⋊C4C2211yescharacteristic
117C4×Dic11⋊C4C2211yescharacteristic
118C4×Dic11⋊C4C2211yescharacteristic
119C4×Dic11⋊C4C2211yescharacteristic
120C4×Dic11⋊C4C2211yescharacteristic
121C42×Dic11C2211yescharacteristic
122#10622541C2211yescharacteristic
123#10622541C2211yescharacteristic
124#10622283C2211yescharacteristic
125#10622283C2211yescharacteristic
126#10622283C2211yescharacteristic
127#10622283C2211yescharacteristic
128#10622282C2211yescharacteristic
129#10622282C2211yescharacteristic
130#10622281C2211yescharacteristic
131#10622281C2211yescharacteristic
132#10622280C2211yescharacteristic
133#10622279C2211yescharacteristic
134#10622279C2211yescharacteristic
135#10622279C2211yescharacteristic
136#10622279C2211yescharacteristic
137#10622279C2211yescharacteristic
138#10622277C2211yescharacteristic
139D11×#95C2211yescharacteristic
140#10622268C2211yescharacteristic
141#10622268C2211yescharacteristic
142#10622268C2211yescharacteristic
143#10622268C2211yescharacteristic
144#10622267C2211yescharacteristic
145#10622267C2211yescharacteristic
146#10622267C2211yescharacteristic
147#10622267C2211yescharacteristic
148#10622267C2211yescharacteristic
149#10622267C2211yescharacteristic
150#10622267C2211yescharacteristic
151#10622267C2211yescharacteristic
152#10622266C2211yescharacteristic
153#10622266C2211yescharacteristic
154#10622266C2211yescharacteristic
155#10622266C2211yescharacteristic
156#10622266C2211yescharacteristic
157#10622266C2211yescharacteristic
158#10622266C2211yescharacteristic
159#10622266C2211yescharacteristic
160#10622265C2211yescharacteristic
161#10622265C2211yescharacteristic
162#10622265C2211yescharacteristic
163#10622265C2211yescharacteristic
164#10622265C2211yescharacteristic
165#10622265C2211yescharacteristic
166#10622264C2211yescharacteristic
167#10622264C2211yescharacteristic
168#10622264C2211yescharacteristic
169#10622263C2211yescharacteristic
170#10622263C2211yescharacteristic
171#10622263C2211yescharacteristic
172#10622262C2211yescharacteristic
173#10622262C2211yescharacteristic
174#10622262C2211yescharacteristic
175#10622262C2211yescharacteristic
176#10622262C2211yescharacteristic
177#10622262C2211yescharacteristic
178#10622262C2211yescharacteristic
179#10622261C2211yescharacteristic
180#10622261C2211yescharacteristic
181#10622261C2211yescharacteristic
182#10622260C2211yescharacteristic
183#10622260C2211yescharacteristic
184#10622260C2211yescharacteristic
185#10622260C2211yescharacteristic
186#10622260C2211yescharacteristic
187#10622260C2211yescharacteristic
188C22×Q8×C11C2311yescharacteristic
189C22×Q8×C11C2311yescharacteristic
190C22×C4×D11C2311yescharacteristic
191C22×C4×D11C2311yescharacteristic
192C22×C4×D11C2311yescharacteristic
193C11×C4⋊Q8C2×C418yescomplemented
194C2×C11×C4⋊C4C2311yescharacteristic
195C2×C11×C4⋊C4C2311yescharacteristic
196C2×C11×C4⋊C4C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2311yescharacteristic
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C4⋊C4C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2311yescharacteristic
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211#66999C2×C418yes—
212#66999C2×C418yes—
213Q8×Dic11C2×C418yescomplemented
214Q8×Dic11C2×C418yescomplemented
215C2×(C2×D11)⋊C4C2311yescharacteristic
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×(C2×D11)⋊C4C2311yescharacteristic
221C2×(C2×D11)⋊C4C2311yescharacteristic
222C2×(C2×D11)⋊C4C2311yescharacteristic
223C2×(C2×D11)⋊C4C2311yescharacteristic
224C2×(C2×D11)⋊C4C2311yescharacteristic
225C2×(C2×D11)⋊C4C2311yescharacteristic
226C2×(C2×D11)⋊C4C2311yescharacteristic
227C2×C4⋊Dic11C2311yescharacteristic
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2311yescharacteristic
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2311yescharacteristic
232C2×C4⋊Dic11C2311yescharacteristic
233C2×C4⋊Dic11C2311yescharacteristic
234C2×C4⋊Dic11C2311yescharacteristic
235C2×C4⋊Dic11C2311yescharacteristic
236C2×C4⋊Dic11C2311yescharacteristic
237C2×C4⋊Dic11C2311yescharacteristic
238C2×C4⋊Dic11C2311yescharacteristic
239C2×Dic11⋊C4C2311yescharacteristic
240C2×Dic11⋊C4C2311yescharacteristic
241C2×Dic11⋊C4C2311yescharacteristic
242C2×Dic11⋊C4C2311yescharacteristic
243C2×Dic11⋊C4C2311yescharacteristic
244C2×Dic11⋊C4C2311yescharacteristic
245C2×Dic11⋊C4C2311yescharacteristic
246C2×Dic11⋊C4C2311yescharacteristic
247C2×Dic11⋊C4C2311yescharacteristic
248C2×Dic11⋊C4C2311yescharacteristic
249C2×Dic11⋊C4C2311yescharacteristic
250C2×Dic11⋊C4C2311yescharacteristic
251C2×Dic11⋊C4C2311yescharacteristic
252C2×Dic11⋊C4C2311yescharacteristic
253C2×Dic11⋊C4C2311yescharacteristic
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2311yescharacteristic
256C2×Dic11⋊C4C2311yescharacteristic
257C2×Dic11⋊C4C2311yescharacteristic
258C2×Dic11⋊C4C2311yescharacteristic
259C2×Dic11⋊C4C2311yescharacteristic
260C2×Dic11⋊C4C2311yescharacteristic
261C2×Dic11⋊C4C2311yescharacteristic
262C2×Dic11⋊C4C2311yescharacteristic
263C2×C4×Dic11C2311yescharacteristic
264C2×C4×Dic11C2311yescharacteristic
265C2×C4×Dic11C2311yescharacteristic
266C2×C4×Dic11C2311yescharacteristic
267C2×C4×Dic11C2311yescharacteristic
268C2×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2311yescharacteristic
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
277C2×C4×Dic11C2311yescharacteristic
278C2×C4×Dic11C2311yescharacteristic
279C2×C4×Dic11C2311yescharacteristic
280C2×C4×Dic11C2311yescharacteristic
281C2×C4×Dic11C2311yescharacteristic
282C2×C4×Dic11C2311yescharacteristic
283C2×C4×Dic11C2311yescharacteristic
284C2×C4×Dic11C2311yescharacteristic
285C2×C4×Dic11C2311yescharacteristic
286C2×C4×Dic11C2311yescharacteristic
287C2×C4×Dic11C2311yescharacteristic
288#66951C2×C418yes—
289#66951C2×C418yes—
290#66951C2×C418yes—
291#66951C2×C418yes—
292#66942C2×C418yescomplemented
293#66942C2×C418yescomplemented
294#66942C2×C418yescomplemented
295#66942C2×C418yescomplemented
296#66925C2×C418yes—
297#66923C2×C418yescomplemented
298C11×#95C2311yescharacteristic
299C11×#95C2311yescharacteristic
300C11×#95C2311yescharacteristic
301C11×#95C2311yescharacteristic
302C11×#95C2311yescharacteristic
303C11×#95C2311yescharacteristic
304C11×#95C2311yescharacteristic
305C11×#95C2311yescharacteristic
306C11×#95C2311yescharacteristic
307C11×#95C2311yescharacteristic
308C11×#95C2311yescharacteristic
309C11×#95C2311yescharacteristic
310C11×#95C2311yescharacteristic
311C11×#95C2311yescharacteristic
312C11×#95C2311yescharacteristic
313C11×#95C2311yescharacteristic
314C11⋊#95C2311yescharacteristic
315C11⋊#95C2311yescharacteristic
316C11⋊#95C2311yescharacteristic
317C11⋊#95C2311yescharacteristic
318C11⋊#95C2311yescharacteristic
319C11⋊#95C2311yescharacteristic
320C11⋊#95C2311yescharacteristic
321C11⋊#95C2311yescharacteristic
322C11⋊#95C2311yescharacteristic
323C11⋊#95C2311yescharacteristic
324C11⋊#95C2311yescharacteristic
325C11⋊#95C2311yescharacteristic
326C11⋊#95C2311yescharacteristic
327C11⋊#95C2311yescharacteristic
328C11⋊#95C2311yescharacteristic
329C11⋊#95C2311yescharacteristic
330C11⋊#95C2311yescharacteristic
331C11⋊#95C2311yescharacteristic
332C11⋊#95C2311yescharacteristic
333C11⋊#95C2311yescharacteristic
334C11⋊#95C2311yescharacteristic
335C11⋊#95C2311yescharacteristic
336C11⋊#95C2311yescharacteristic
337C11⋊#95C2311yescharacteristic
338C11⋊#95C2311yescharacteristic
339C11⋊#95C2311yescharacteristic
340C11⋊#95C2311yescharacteristic
341C11⋊#95C2311yescharacteristic
342C11⋊#95C2311yescharacteristic
343C11⋊#95C2311yescharacteristic
344C11⋊#95C2311yescharacteristic
345C11⋊#95C2311yescharacteristic
346C11⋊#95C2311yescharacteristic
347C11⋊#95C2311yescharacteristic
348C11⋊#95C2311yescharacteristic
349C11⋊#95C2311yescharacteristic
350C11⋊#95C2311yescharacteristic
351C11⋊#95C2311yescharacteristic
352C11⋊#95C2311yescharacteristic
353C11⋊#95C2311yescharacteristic
354C11⋊#95C2311yescharacteristic
355C11⋊#95C2311yescharacteristic
356C11⋊#95C2311yescharacteristic
357C11⋊#95C2311yescharacteristic
358#34455—111nomaximal, Sylow
359C23×D11C2411yescharacteristic
360C2×Q8×C11—41no—
361C2×Q8×C11—41no—
362C2×Q8×C11—41no—
363C2×Q8×C11—41no—
364C2×Q8×C11C22×C414yes—
365C2×Q8×C11C22×C414yes—
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2411yescharacteristic
372C22×C4×C11C2411yescharacteristic
373C22×C4×C11C2411yescharacteristic
374C22×C4×C11C2411yescharacteristic
375C22×C4×C11C2411yescharacteristic
376C22×C4×C11C2411yescharacteristic
377C22×C4×C11C2411yescharacteristic
378C22×C4×C11C2411yescharacteristic
379C22×C4×C11C2411yescharacteristic
380C22×C4×C11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C22×Dic11C2411yescharacteristic
387C22×Dic11C2411yescharacteristic
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2411yescharacteristic
390C22×Dic11C2411yescharacteristic
391C22×Dic11C2411yescharacteristic
392C22×Dic11C2411yescharacteristic
393C22×Dic11C2411yescharacteristic
394C22×Dic11C2411yescharacteristic
395C22×Dic11C2411yescharacteristic
396C2×C4×D11—22no—
397C2×C4×D11—41no—
398C2×C4×D11—41no—
399C2×C4×D11—41no—
400C2×C4×D11—41no—
401C2×C4×D11—41no—
402C2×C4×D11—41no—
403C2×C4×D11—41no—
404C2×C4×D11C22×C414yes—
405C11×C4⋊C4—41no—
406C11×C4⋊C4—41no—
407C11×C4⋊C4—41no—
408C11×C4⋊C4—41no—
409C11×C4⋊C4—41no—
410C11×C4⋊C4—41no—
411C11×C4⋊C4C22×C414yes—
412C11×C4⋊C4C22×C414yes—
413C11×C4⋊C4C22×C414yes—
414C11×C4⋊C4C22×C414yes—
415C42×C11—22no—
416C42×C11—41no—
417C42×C11—41no—
418C42×C11—41no—
419C42×C11—41no—
420C42×C11—41no—
421C42×C11C22×C414yes—
422(C2×D11)⋊C4—22no—
423(C2×D11)⋊C4—41no—
424(C2×D11)⋊C4—41no—
425(C2×D11)⋊C4—41no—
426(C2×D11)⋊C4—41no—
427(C2×D11)⋊C4—41no—
428(C2×D11)⋊C4C22×C414yes—
429(C2×D11)⋊C4C22×C414yes—
430(C2×D11)⋊C4C22×C414yes—
431(C2×D11)⋊C4C22×C414yes—
432(C2×D11)⋊C4C22×C414yes—
433(C2×D11)⋊C4C22×C414yes—
434C4⋊Dic11—41no—
435C4⋊Dic11—41no—
436C4⋊Dic11—41no—
437C4⋊Dic11—41no—
438C4⋊Dic11—41no—
439C4⋊Dic11—41no—
440C4⋊Dic11C22×C414yes—
441C4⋊Dic11C22×C414yes—
442C4⋊Dic11C22×C414yes—
443C4⋊Dic11C22×C414yes—
444C4⋊Dic11C22×C414yes—
445C4⋊Dic11C22×C414yes—
446Dic11⋊C4—22no—
447Dic11⋊C4—22no—
448Dic11⋊C4—22no—
449Dic11⋊C4—41no—
450Dic11⋊C4—41no—
451Dic11⋊C4—41no—
452Dic11⋊C4—41no—
453Dic11⋊C4—41no—
454Dic11⋊C4—41no—
455Dic11⋊C4—41no—
456Dic11⋊C4—41no—
457Dic11⋊C4—41no—
458Dic11⋊C4—41no—
459Dic11⋊C4—41no—
460Dic11⋊C4C22×C414yes—
461Dic11⋊C4C22×C414yes—
462Dic11⋊C4C22×C414yes—
463Dic11⋊C4C22×C414yes—
464Dic11⋊C4C22×C414yes—
465Dic11⋊C4C22×C414yes—
466Dic11⋊C4C22×C414yes—
467Dic11⋊C4C22×C414yes—
468Dic11⋊C4C22×C414yes—
469Dic11⋊C4C22×C414yes—
470C4×Dic11—22no—
471C4×Dic11—22no—
472C4×Dic11—22no—
473C4×Dic11—22no—
474C4×Dic11—41no—
475C4×Dic11—41no—
476C4×Dic11—41no—
477C4×Dic11—41no—
478C4×Dic11—41no—
479C4×Dic11—41no—
480C4×Dic11—41no—
481C4×Dic11—41no—
482C4×Dic11—41no—
483C4×Dic11—41no—
484C4×Dic11—41no—
485C4×Dic11—41no—
486C4×Dic11—41no—
487C4×Dic11—41no—
488C4×Dic11—41no—
489C4×Dic11—41no—
490C4×Dic11C22×C414yes—
491C4×Dic11C22×C414yes—
492C4×Dic11C22×C414yes—
493C4×Dic11C22×C414yes—
494C4×Dic11C22×C414yes—
495C2×#541—111no—
496#2383—111no—
497#2382—111no—
498#2382—111no—
499#2378—111no—
500#2373—111no—
501#2373—111no—
502#2373—111no—
503#2371—111no—
504#2371—111no—
505#2370—111no—
506#2370—111no—
507#2368—111no—
508#2356—111no—
509#2355—111no—
510#2346—111no—
511#2343—111no—
512#2336—111no—
513#2336—111no—
514#2334—111no—
515#2334—111no—
516#2334—111no—
517#2332—111no—
518#2331—111no—
519#2331D1111yescharacteristic, complemented
520#2330—111no—
521#2329—111no—
522#2320—111no—
523C4×#125—111no—
524C4×#126—111no—
525#2295—111no—
526C23×C11C2511yescharacteristic
527C22×D11—21no—
528C22×D11—21no—
529C22×D11—21no—
530C22×D11—21no—
531C22×D11—21no—
532C22×D11—21no—
533C22×D11C23×C412yes—
534Q8×C11—44no—
535Q8×C11—44no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—21no—
554C2×C4×C11—21no—
555C2×C4×C11—21no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—21no—
568C2×C4×C11—21no—
569C2×C4×C11—21no—
570C2×C4×C11—21no—
571C2×C4×C11—21no—
572C2×C4×C11—21no—
573C2×C4×C11C23×C412yes—
574C2×C4×C11C23×C412yes—
575C2×C4×C11C23×C412yes—
576C2×C4×C11C23×C412yes—
577C2×C4×C11C23×C412yes—
578C2×C4×C11C23×C412yes—
579C2×C4×C11C23×C412yes—
580C2×C4×C112−1+412yes—
581C2×Dic11—21no—
582C2×Dic11—21no—
583C2×Dic11—21no—
584C2×Dic11—21no—
585C2×Dic11—21no—
586C2×Dic11—21no—
587C2×Dic11—21no—
588C2×Dic11—21no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—21no—
592C2×Dic11—21no—
593C2×Dic11—21no—
594C2×Dic11—21no—
595C2×Dic11—21no—
596C2×Dic11—21no—
597C2×Dic11—21no—
598C2×Dic11—21no—
599C2×Dic11—21no—
600C2×Dic11—21no—
601C2×Dic11—21no—
602C2×Dic11—21no—
603C2×Dic11—21no—
604C2×Dic11—21no—
605C2×Dic11—21no—
606C2×Dic11—21no—
607C2×Dic11—21no—
608C2×Dic11—21no—
609C2×Dic11—21no—
610C2×Dic11—21no—
611C2×Dic11—21no—
612C2×Dic11—21no—
613C2×Dic11—21no—
614C2×Dic11—21no—
615C2×Dic11—21no—
616C2×Dic11—21no—
617C2×Dic11—21no—
618C2×Dic11C23×C412yes—
619C2×Dic11C23×C412yes—
620C2×Dic11C23×C412yes—
621C2×Dic11C23×C412yes—
622C2×Dic11C23×C412yes—
623C2×Dic11C23×C412yes—
624C2×Dic11C23×C412yes—
625C2×Dic112−1+412yes—
626C4×D11—44no—
627C4×D11—82no—
628C4×D11—82no—
629#541—1116no—
630C2×C4⋊Q8C2×D1111yescharacteristic
631C2×#126—111no—
632C2×#126—111no—
633C2×#126—111no—
634C2×#126—111no—
635C2×#125—111no—
636C2×#125—111no—
637C2×#125—111no—
638C2×#125—111no—
639C2×#125—111no—
640C2×C22⋊Q8—111no—
641C2×C22⋊Q8—111no—
642C2×C4×Q8—111no—
643C2×C4×Q8—111no—
644C2×#117—111no—
645#391—111no—
646#391—111no—
647#391—111no—
648#391—111no—
649#391C2×D1111yescharacteristic
650#391C2×D1111yescharacteristic
651#391C2×D1111yescharacteristic
652#391C2×D1111yescharacteristic
653#389—111no—
654#389—111no—
655#389—111no—
656#389—111no—
657#389—111no—
658#389—111no—
659#389—111no—
660#389—111no—
661#389—111no—
662#389—111no—
663#389—111no—
664#389—111no—
665#389—111no—
666#389—111no—
667#389—111no—
668#389—111no—
669#389C2×D1111yescharacteristic
670#389C2×D1111yescharacteristic
671#388—111no—
672#388—111no—
673#388—111no—
674#388—111no—
675#388—111no—
676#388—111no—
677#388—111no—
678#388—111no—
679#388—111no—
680#388—111no—
681#388—111no—
682#388—111no—
683#387—111no—
684#387—111no—
685#387—111no—
686#387—111no—
687#387—111no—
688#387—111no—
689#387—111no—
690#387—111no—
691#387—111no—
692#387—111no—
693#387—111no—
694#387—111no—
695#387—111no—
696#387—111no—
697#387—111no—
698#387—111no—
699#387—111no—
700#387—111no—
701#387—111no—
702#387—111no—
703#387—111no—
704#387—111no—
705#387—111no—
706#387—111no—
707#387—111no—
708#387—111no—
709#387—111no—
710#387—111no—
711#387—111no—
712#387—111no—
713#387—111no—
714#387—111no—
715#387—111no—
716#387—111no—
717#387—111no—
718#387—111no—
719#387—111no—
720#387—111no—
721#387—111no—
722#387—111no—
723#387C2×D1111yescharacteristic
724#387C2×D1111yescharacteristic
725#387C2×D1111yescharacteristic
726#387C2×D1111yescharacteristic
727#385—111no—
728#385—111no—
729#385—111no—
730#385—111no—
731#385—111no—
732#385—111no—
733#384—111no—
734#383—111no—
735#383—111no—
736#383—111no—
737#382—111no—
738#382—111no—
739#382—111no—
740#382—111no—
741#382—111no—
742#382C2×D1111yescharacteristic
743#381—111no—
744#380—111no—
745C4×C4⋊C4—111no—
746C4×C4⋊C4—111no—
747C4×C4⋊C4—111no—
748C4×C4⋊C4—111no—
749C4×C4⋊C4—111no—
750C4×C4⋊C4—111no—
751C4×C4⋊C4—111no—
752C4×C4⋊C4—111no—
753C4×C4⋊C4—111no—
754C4×C4⋊C4—111no—
755C4×C4⋊C4—111no—
756C4×C4⋊C4—111no—
757C4×C4⋊C4—111no—
758C4×C4⋊C4—111no—
759C4×C4⋊C4—111no—
760C4×C4⋊C4—111no—
761C4×C4⋊C4—111no—
762C4×C4⋊C4—111no—
763C4×C4⋊C4—111no—
764C4×C4⋊C4—111no—
765C4×C4⋊C4—111no—
766C4×C4⋊C4—111no—
767C4×C4⋊C4—111no—
768C4×C4⋊C4C2×D1111yescharacteristic
769C4×C4⋊C4C2×D1111yescharacteristic
770C4×C22⋊C4—111no—
771C4×C22⋊C4—111no—
772C4×C22⋊C4—111no—
773C4×C22⋊C4—111no—
774C4×C22⋊C4—111no—
775C4×C22⋊C4—111no—
776C4×C22⋊C4—111no—
777#376—111no—
778#376—111no—
779#376—111no—
780#376—111no—
781#376—111no—
782#376C2×D1111yescharacteristic
783C2×#95—111no—
784C43—111no—
785C22×C11C24×C411yescharacteristic
786C22×C11C2×2−1+411yescharacteristic
787C22×C11C2×2−1+411yescharacteristic
788C22×C11#58511yescharacteristic
789C22×C11#58511yescharacteristic
790C22×C11#58511yescharacteristic
791C22×C11#58511yescharacteristic
792C2×D11—22no—
793C2×D11—22no—
794C2×D11—22no—
795C2×D11—41no—
796C2×D11—41no—
797C2×D11—41no—
798C2×D11—41no—
799C4×C11—22no—
800C4×C11—22no—
801C4×C11—22no—
802C4×C11—22no—
803C4×C11—22no—
804C4×C11—22no—
805C4×C11—22no—
806C4×C11—22no—
807C4×C11—41no—
808C4×C11—41no—
809C4×C11—41no—
810C4×C11—41no—
811C4×C11—41no—
812C4×C11—41no—
813C4×C11—41no—
814Dic11—22no—
815Dic11—22no—
816Dic11—22no—
817Dic11—22no—
818Dic11—22no—
819Dic11—22no—
820Dic11—22no—
821Dic11—22no—
822Dic11—41no—
823Dic11—41no—
824Dic11—41no—
825Dic11—41no—
826Dic11—41no—
827Dic11—41no—
828Dic11—41no—
829C22×Q8C22×D1111yescharacteristic
830C22×Q8C22×D1111yescharacteristic
831C23×C4—111no—
832C23×C4—111no—
833C23×C4—111no—
834C4⋊Q8C4×D1118yescomplemented
835#126—118no—
836#126—118no—
837#126—118no—
838#126—118no—
839#125—118no—
840#125—118no—
841#125—118no—
842#125—118no—
843#125—118no—
844C22⋊Q8—118no—
845C22⋊Q8—118no—
846C4×Q8—118no—
847C4×Q8—118no—
848#117—118no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—111no—
851C2×C4⋊C4—111no—
852C2×C4⋊C4—111no—
853C2×C4⋊C4—111no—
854C2×C4⋊C4—111no—
855C2×C4⋊C4—111no—
856C2×C4⋊C4—111no—
857C2×C4⋊C4—111no—
858C2×C4⋊C4—111no—
859C2×C4⋊C4—111no—
860C2×C4⋊C4—111no—
861C2×C4⋊C4—111no—
862C2×C4⋊C4—111no—
863C2×C4⋊C4—111no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—111no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—111no—
870C2×C4⋊C4—111no—
871C2×C4⋊C4—111no—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—111no—
874C2×C4⋊C4—111no—
875C2×C4⋊C4—111no—
876C2×C4⋊C4—111no—
877C2×C4⋊C4—111no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—111no—
881C2×C4⋊C4—111no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4C22×D1111yescharacteristic
886C2×C4⋊C4C22×D1111yescharacteristic
887C2×C4⋊C4C22×D1111yescharacteristic
888C2×C4⋊C4C22×D1111yescharacteristic
889C2×C4⋊C4C22×D1111yescharacteristic
890C2×C4⋊C4C22×D1111yescharacteristic
891C2×C4⋊C4C22×D1111yescharacteristic
892C2×C4⋊C4C22×D1111yescharacteristic
893C2×C4⋊C4C22×D1111yescharacteristic
894C2×C4⋊C4C22×D1111yescharacteristic
895C2×C22⋊C4—111no—
896C2×C22⋊C4—111no—
897C2×C22⋊C4—111no—
898C2×C22⋊C4—111no—
899C2×C22⋊C4—111no—
900C2×C22⋊C4—111no—
901C2×C22⋊C4—111no—
902C2×C22⋊C4—111no—
903C2×C22⋊C4—111no—
904C2×C22⋊C4—111no—
905C2×C22⋊C4—111no—
906C2×C22⋊C4—111no—
907C2×C42—111no—
908C2×C42—111no—
909C2×C42—111no—
910C2×C42—111no—
911C2×C42—111no—
912C2×C42—111no—
913C2×C42—111no—
914C2×C42—111no—
915C2×C42—111no—
916C2×C42—111no—
917C2×C42—111no—
918C2×C42—111no—
919C2×C42—111no—
920C2×C42—111no—
921C2×C42—111no—
922C2×C42—111no—
923C2×C42—111no—
924C2×C42—111no—
925C2×C42—111no—
926C2×C42—111no—
927C2×C42—111no—
928C2×C42—111no—
929C2×C42—111no—
930C2×C42—111no—
931C2×C42—111no—
932C2×C42C22×D1111yescharacteristic
933C2×C42C22×D1111yescharacteristic
934C2×C42C22×D1111yescharacteristic
935C2×C42C22×D1111yescharacteristic
936C2×C42C22×D1111yescharacteristic
937C2×C42C22×D1111yescharacteristic
938C2×C42C22×D1111yescharacteristic
939#95—111no—
940#95—111no—
941#95—111no—
942#95—111no—
943#95—111no—
944#95—111no—
945#95—111no—
946#95—111no—
947#95—111no—
948#95—111no—
949#95—111no—
950#95—111no—
951#95—111no—
952#95—111no—
953#95—111no—
954#95—111no—
955#95—111no—
956#95—111no—
957#95—111no—
958#95—111no—
959#95—111no—
960#95—111no—
961#95—111no—
962#95—111no—
963#95—111no—
964#95—111no—
965#95—111no—
966#95—111no—
967#95—111no—
968#95—111no—
969#95—111no—
970#95—111no—
971#95—111no—
972#95—111no—
973#95—111no—
974#95—111no—
975#95—111no—
976#95—111no—
977#95—111no—
978#95—111no—
979#95—111no—
980#95—111no—
981#95—111no—
982#95—111no—
983#95C22×D1111yescharacteristic
984#95C22×D1111yescharacteristic
985#95C22×D1111yescharacteristic
986#95C22×D1111yescharacteristic
987#95C22×D1111yescharacteristic
988#95C22×D1111yescharacteristic
989#95C22×D1111yescharacteristic
990#95C22×D1111yescharacteristic
991#95C22×D1111yescharacteristic
992#95C22×D1111yescharacteristic
993#95C22×D1111yescharacteristic
994#95C22×D1111yescharacteristic
995#95C22×D1111yescharacteristic
996#95C22×D1111yescharacteristic
997#95C22×D1111yescharacteristic
998#95C22×D1111yescharacteristic
999C2×C11#342811yescharacteristic
1000C2×C11C4×2−1+411yescharacteristic
1001C2×C11C4×2−1+411yescharacteristic
1002C2×C11#356311yescharacteristic
1003C2×C11#356411yescharacteristic
1004C2×C11#356511yescharacteristic
1005C2×C11#356611yescharacteristic
1006D11—42no—
1007C24—111no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8C2×C4×D1114yes—
1013C2×Q8C2×C4×D1114yes—
1014C22×C4—111no—
1015C22×C4—111no—
1016C22×C4—111no—
1017C22×C4—111no—
1018C22×C4—111no—
1019C22×C4—111no—
1020C22×C4—111no—
1021C22×C4—111no—
1022C22×C4—114no—
1023C22×C4—111no—
1024C22×C4—111no—
1025C22×C4—111no—
1026C22×C4—111no—
1027C22×C4—111no—
1028C22×C4—111no—
1029C22×C4—111no—
1030C22×C4—222no—
1031C22×C4—441no—
1032C22×C4—441no—
1033C22×C4—441no—
1034C22×C4—441no—
1035C22×C4—441no—
1036C22×C4—441no—
1037C22×C4—441no—
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1111yescharacteristic
1040C22×C4C23×D1111yescharacteristic
1041C22×C4C23×D1111yescharacteristic
1042C22×C4C23×D1111yescharacteristic
1043C22×C4C23×D1111yescharacteristic
1044C22×C4C23×D1111yescharacteristic
1045C22×C4C23×D1111yescharacteristic
1046C22×C4C23×D1111yescharacteristic
1047C22×C4C23×D1111yescharacteristic
1048C22×C4C23×D1111yescharacteristic
1049C22×C4C23×D1111yescharacteristic
1050C22×C4C23×D1111yescharacteristic
1051C22×C4C23×D1111yescharacteristic
1052C22×C4C23×D1111yescharacteristic
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—114no—
1060C4⋊C4—114no—
1061C4⋊C4—114no—
1062C4⋊C4—114no—
1063C4⋊C4—114no—
1064C4⋊C4—114no—
1065C4⋊C4—114no—
1066C4⋊C4—114no—
1067C4⋊C4—114no—
1068C4⋊C4—114no—
1069C4⋊C4—114no—
1070C4⋊C4—114no—
1071C4⋊C4—114no—
1072C4⋊C4—114no—
1073C4⋊C4—114no—
1074C4⋊C4—114no—
1075C4⋊C4—222no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—441no—
1079C4⋊C4—441no—
1080C4⋊C4—441no—
1081C4⋊C4—441no—
1082C4⋊C4—441no—
1083C4⋊C4—441no—
1084C4⋊C4—441no—
1085C4⋊C4—441no—
1086C4⋊C4—441no—
1087C4⋊C4—441no—
1088C4⋊C4—441no—
1089C4⋊C4—441no—
1090C4⋊C4—441no—
1091C4⋊C4—441no—
1092C4⋊C4—441no—
1093C4⋊C4—441no—
1094C4⋊C4—441no—
1095C4⋊C4C2×C4×D1114yes—
1096C4⋊C4C2×C4×D1114yes—
1097C4⋊C4C2×C4×D1114yes—
1098C4⋊C4C2×C4×D1114yes—
1099C22⋊C4—114no—
1100C22⋊C4—114no—
1101C22⋊C4—114no—
1102C22⋊C4—114no—
1103C22⋊C4—114no—
1104C22⋊C4—114no—
1105C22⋊C4—222no—
1106C22⋊C4—441no—
1107C22⋊C4—441no—
1108C22⋊C4—441no—
1109C22⋊C4—441no—
1110C22⋊C4—441no—
1111C42—22no—
1112C42—41no—
1113C42—41no—
1114C42—41no—
1115C42—41no—
1116C42—41no—
1117C42—114no—
1118C42—114no—
1119C42—114no—
1120C42—114no—
1121C42—114no—
1122C42—222no—
1123C42—222no—
1124C42—222no—
1125C42—222no—
1126C42—441no—
1127C42—441no—
1128C42—441no—
1129C42—441no—
1130C42—441no—
1131C42—441no—
1132C42—441no—
1133C42—441no—
1134C42—441no—
1135C42—441no—
1136C42—441no—
1137C42—441no—
1138C42—441no—
1139C42—441no—
1140C42—441no—
1141C42—441no—
1142C42C2×C4×D1114yes—
1143C11#3445511yescharacteristic, complemented, Sylow
1144C23—112no—
1145C23—221no—
1146C23—221no—
1147C23—221no—
1148C23—221no—
1149C23—221no—
1150C23—221no—
1151C23C24×D1111yescharacteristic
1152Q8—44no—
1153Q8—44no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—112no—
1192C2×C4—112no—
1193C2×C4—112no—
1194C2×C4—112no—
1195C2×C4—112no—
1196C2×C4—112no—
1197C2×C4—112no—
1198C2×C4—112no—
1199C2×C4—221no—
1200C2×C4—221no—
1201C2×C4—221no—
1202C2×C4—221no—
1203C2×C4—221no—
1204C2×C4—221no—
1205C2×C4—221no—
1206C2×C4—221no—
1207C2×C4—221no—
1208C2×C4—221no—
1209C2×C4—221no—
1210C2×C4—221no—
1211C2×C4—221no—
1212C2×C4—221no—
1213C2×C4—221no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—221no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—221no—
1220C2×C4—221no—
1221C2×C4—221no—
1222C2×C4—221no—
1223C2×C4—221no—
1224C2×C4—221no—
1225C2×C4—221no—
1226C2×C4—221no—
1227C2×C4—221no—
1228C2×C4—221no—
1229C2×C4—221no—
1230C2×C4—221no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—221no—
1236C2×C4—444no—
1237C2×C4—882no—
1238C2×C4—882no—
1239C2×C4C22×C4×D1112yes—
1240C2×C4C22×C4×D1112yes—
1241C2×C4C22×C4×D1112yes—
1242C2×C4C22×C4×D1112yes—
1243C2×C4C22×C4×D1112yes—
1244C2×C4C22×C4×D1112yes—
1245C2×C4C22×C4×D1112yes—
1246C2×C4#6704012yes—
1247C22—222no—
1248C22—222no—
1249C22—222no—
1250C22—441no—
1251C22—441no—
1252C22—441no—
1253C22—441no—
1254C22C23×C4×D1111yescharacteristic
1255C22C2×#6704011yescharacteristic
1256C22#1062345311yescharacteristic
1257C22#1062345511yescharacteristic
1258C22#1062345511yescharacteristic
1259C22D11×2−1+411yescharacteristic
1260C22#1062345711yescharacteristic
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—222no—
1277C4—222no—
1278C4—222no—
1279C4—222no—
1280C4—222no—
1281C4—222no—
1282C4—222no—
1283C4—222no—
1284C4—441no—
1285C4—441no—
1286C4—441no—
1287C4—441no—
1288C4—441no—
1289C4—441no—
1290C4—441no—
1291C2—442no—
1292C2#1308181411yescharacteristic
1293C2#1308182511yescharacteristic
1294C2C4×#6704011yescharacteristic
1295C2#1308321511yescharacteristic
1296C2#1308324111yescharacteristic
1297C2#1308325711yescharacteristic
1298C2#1308329611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2331C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2331D11
hypocenterC11#34455
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2331

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13071801C2semidirect
4. #13071800C2semidirect
9. #13071721C2semidirect
10. #13071719C2semidirect
11. #13071715C2semidirect
12. #13071707C2semidirect
14. #13071580C2semidirect
15. #13071572C2semidirect
18. #13071418C2semidirect
19. #13071414C2semidirect
24. #13071365C2semidirect
25. #13071352C2semidirect
27. #13071261C2semidirect
28. C4×#66942C2semidirect
30. #13071091C2semidirect
31. C11×#2331C2semidirect
37. #10623262C4semidirect
193. C11×C4⋊Q8C2×C4semidirect
213. Q8×Dic11C2×C4semidirect
214. Q8×Dic11C2×C4semidirect
292. #66942C2×C4semidirect
293. #66942C2×C4semidirect
294. #66942C2×C4semidirect
295. #66942C2×C4semidirect
297. #66923C2×C4semidirect
519. #2331D11semidirect
834. C4⋊Q8C4×D11semidirect
1143. C11#34455semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106232622
#130718072
#130718012
#130718002
#130717772
#130717352
#130717302
#130717292
#130717212
#130717192
#130717152
#130717072
#130716952
#130715802
#130715722
#130715022
#130714692
#130714182
#130714142
#130713962
#130713902
#130713852
#130713712
#130713652
#130713522
#130713482
#130712612
C4×#669422
#130711662
#130710912
C11×#23312
#3445511