Finite Group Databasebeta

← #14918262

Subgroups — #14918262

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×#10623232C211yesmaximal, characteristic
2#13071804C211yesmaximal, characteristic
3#13071800C211yesmaximal, characteristic, complemented
4#13071798C211yesmaximal, characteristic, complemented
5#13071776C211yesmaximal, characteristic
6#13071740C211yesmaximal, characteristic
7#13071733C211yesmaximal, characteristic
8#13071721C211yesmaximal, characteristic, complemented
9#13071719C211yesmaximal, characteristic, complemented
10#13071710C211yesmaximal, characteristic, complemented
11#13071707C211yesmaximal, characteristic, complemented
12#13071694C211yesmaximal, characteristic
13#13071577C211yesmaximal, characteristic, complemented
14#13071570C211yesmaximal, characteristic, complemented
15#13071498C211yesmaximal, characteristic
16#13071470C211yesmaximal, characteristic
17#13071418C211yesmaximal, characteristic, complemented
18#13071416C211yesmaximal, characteristic, complemented
19#13071398C211yesmaximal, characteristic
20#13071393C211yesmaximal, characteristic
21#13071393C211yesmaximal, characteristic
22#13071373C211yesmaximal, characteristic
23#13071363C211yesmaximal, characteristic, complemented
24#13071361C211yesmaximal, characteristic, complemented
25#13071353C211yesmaximal, characteristic, complemented
26#13071347C211yesmaximal, characteristic
27#13071262C211yesmaximal, characteristic, complemented
28C4×#66942C211yesmaximal, characteristic, complemented
29#13071170C211yesmaximal, characteristic
30#13071088C211yesmaximal, characteristic, complemented
31C11×#2373C211yesmaximal, characteristic
32C2×C11×#126C2211yescharacteristic
33#10623232C4116yescomplemented
34C2×#66943C2211yescharacteristic
35C2×#66942C2211yescharacteristic
36C2×#66942C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66932C2211yescharacteristic
41C2×#66932C2211yescharacteristic
42C2×#66932C2211yescharacteristic
43C2×#66931C2211yescharacteristic
44C2×#66931C2211yescharacteristic
45C2×#66930C2211yescharacteristic
46C2×#66923C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#388C2211yescharacteristic
50C11×#388C2211yescharacteristic
51C11×#388C2211yescharacteristic
52C11×#387C2211yescharacteristic
53C11×#387C2211yescharacteristic
54C11×#387C2211yescharacteristic
55C11×#385C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C4×C11×C4⋊C4C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C4×C11×C22⋊C4C2211yescharacteristic
60C4×C11×C22⋊C4C2211yescharacteristic
61C11×#376C2211yescharacteristic
62#10622823C2211yescharacteristic
63#10622823C2211yescharacteristic
64#10622823C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622598C2211yescharacteristic
67#10622594C2211yescharacteristic
68#10622594C2211yescharacteristic
69#10622594C2211yescharacteristic
70#10622591C2211yescharacteristic
71#10622591C2211yescharacteristic
72#10622591C2211yescharacteristic
73#10622591C2211yescharacteristic
74#10622591C2211yescharacteristic
75#10622591C2211yescharacteristic
76#10622590C2211yescharacteristic
77#10622590C2211yescharacteristic
78#10622589C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80C4⋊C4×Dic11C2211yescharacteristic
81C4⋊C4×Dic11C2211yescharacteristic
82#10622587C2211yescharacteristic
83#10622587C2211yescharacteristic
84#10622587C2211yescharacteristic
85#10622586C2211yescharacteristic
86#10622586C2211yescharacteristic
87#10622586C2211yescharacteristic
88#10622585C2211yescharacteristic
89#10622585C2211yescharacteristic
90#10622585C2211yescharacteristic
91#10622585C2211yescharacteristic
92#10622564C2211yescharacteristic
93#10622564C2211yescharacteristic
94#10622564C2211yescharacteristic
95#10622563C2211yescharacteristic
96#10622559C2211yescharacteristic
97#10622558C2211yescharacteristic
98#10622558C2211yescharacteristic
99#10622558C2211yescharacteristic
100#10622557C2211yescharacteristic
101#10622557C2211yescharacteristic
102#10622557C2211yescharacteristic
103#10622556C2211yescharacteristic
104#10622555C2211yescharacteristic
105C22⋊C4×Dic11C2211yescharacteristic
106C22⋊C4×Dic11C2211yescharacteristic
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C22⋊C4×Dic11C2211yescharacteristic
110C4×C4⋊Dic11C2211yescharacteristic
111C4×C4⋊Dic11C2211yescharacteristic
112C4×C4⋊Dic11C2211yescharacteristic
113C4×C4⋊Dic11C2211yescharacteristic
114#10622546C2211yescharacteristic
115#10622546C2211yescharacteristic
116#10622546C2211yescharacteristic
117#10622546C2211yescharacteristic
118#10622546C2211yescharacteristic
119#10622546C2211yescharacteristic
120#10622546C2211yescharacteristic
121#10622546C2211yescharacteristic
122#10622546C2211yescharacteristic
123#10622545C2211yescharacteristic
124#10622545C2211yescharacteristic
125#10622545C2211yescharacteristic
126#10622545C2211yescharacteristic
127C4×Dic11⋊C4C2211yescharacteristic
128C4×Dic11⋊C4C2211yescharacteristic
129C4×Dic11⋊C4C2211yescharacteristic
130C4×Dic11⋊C4C2211yescharacteristic
131C4×Dic11⋊C4C2211yescharacteristic
132C4×Dic11⋊C4C2211yescharacteristic
133C4×Dic11⋊C4C2211yescharacteristic
134C4×Dic11⋊C4C2211yescharacteristic
135C42×Dic11C2211yescharacteristic
136#10622542C2211yescharacteristic
137#10622541C2211yescharacteristic
138#10622541C2211yescharacteristic
139#10622541C2211yescharacteristic
140#10622268C2211yescharacteristic
141#10622268C2211yescharacteristic
142#10622268C2211yescharacteristic
143#10622268C2211yescharacteristic
144#10622267C2211yescharacteristic
145#10622267C2211yescharacteristic
146#10622267C2211yescharacteristic
147#10622267C2211yescharacteristic
148#10622267C2211yescharacteristic
149#10622267C2211yescharacteristic
150#10622266C2211yescharacteristic
151#10622266C2211yescharacteristic
152#10622266C2211yescharacteristic
153#10622266C2211yescharacteristic
154#10622265C2211yescharacteristic
155#10622265C2211yescharacteristic
156#10622265C2211yescharacteristic
157#10622265C2211yescharacteristic
158#10622265C2211yescharacteristic
159#10622265C2211yescharacteristic
160#10622265C2211yescharacteristic
161#10622265C2211yescharacteristic
162#10622265C2211yescharacteristic
163#10622264C2211yescharacteristic
164#10622264C2211yescharacteristic
165#10622264C2211yescharacteristic
166#10622263C2211yescharacteristic
167#10622263C2211yescharacteristic
168#10622263C2211yescharacteristic
169#10622263C2211yescharacteristic
170#10622262C2211yescharacteristic
171#10622262C2211yescharacteristic
172#10622262C2211yescharacteristic
173#10622262C2211yescharacteristic
174#10622262C2211yescharacteristic
175#10622262C2211yescharacteristic
176#10622262C2211yescharacteristic
177#10622261C2211yescharacteristic
178#10622260C2211yescharacteristic
179#10622260C2211yescharacteristic
180#10622260C2211yescharacteristic
181#10622260C2211yescharacteristic
182#10622260C2211yescharacteristic
183#10622260C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187#10622259C2211yescharacteristic
188C23×C4×C11C2311yescharacteristic
189C23×Dic11C2311yescharacteristic
190C23×Dic11C2311yescharacteristic
191C22×Dic22C2311yescharacteristic
192C22×Dic22C2311yescharacteristic
193C11×#126C2×C418yes—
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×C22⋊C4C2311yescharacteristic
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C22⋊Dic11C2311yescharacteristic
217C2×C22⋊Dic11C2311yescharacteristic
218C2×C22⋊Dic11C2311yescharacteristic
219C2×C22⋊Dic11C2311yescharacteristic
220C2×C22⋊Dic11C2311yescharacteristic
221C2×C22⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223C2×C4⋊Dic11C2311yescharacteristic
224C2×C4⋊Dic11C2311yescharacteristic
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
227C2×C4⋊Dic11C2311yescharacteristic
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2311yescharacteristic
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2311yescharacteristic
232C2×Dic11⋊C4C2311yescharacteristic
233C2×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2311yescharacteristic
235C2×Dic11⋊C4C2311yescharacteristic
236C2×Dic11⋊C4C2311yescharacteristic
237C2×Dic11⋊C4C2311yescharacteristic
238C2×Dic11⋊C4C2311yescharacteristic
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×C4×Dic11C2311yescharacteristic
261C2×C4×Dic11C2311yescharacteristic
262C2×C4×Dic11C2311yescharacteristic
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
284#66943C2×C418yescomplemented
285#66942C2×C418yescomplemented
286#66942C2×C418yescomplemented
287#66942C2×C418yescomplemented
288#66941C2×C418yescomplemented
289#66940C2×C418yescomplemented
290#66932C2×C418yes—
291#66932C2×C418yes—
292#66932C2×C418yes—
293#66931C2×C418yes—
294#66931C2×C418yes—
295#66930C2×C418yes—
296#66923C2×C418yescomplemented
297C4×Dic22C2×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
359C24×C11C2411yescharacteristic
360C22×C4×C11—41no—
361C22×C4×C11—41no—
362C22×C4×C11—41no—
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
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×Dic11—22no—
378C22×Dic11—41no—
379C22×Dic11—41no—
380C22×Dic11—41no—
381C22×Dic11—41no—
382C22×Dic11C22×C414yes—
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
396C22×Dic11C2411yescharacteristic
397C22×Dic11C2411yescharacteristic
398C22×Dic11C2411yescharacteristic
399C2×Dic22—41no—
400C2×Dic22—41no—
401C2×Dic22—41no—
402C2×Dic22—41no—
403C2×Dic22C22×C414yes—
404C2×Dic22C22×C414yes—
405C11×C4⋊C4—41no—
406C11×C4⋊C4—41no—
407C11×C4⋊C4—41no—
408C11×C4⋊C4—41no—
409C11×C4⋊C4—41no—
410C11×C4⋊C4C22×C414yes—
411C11×C4⋊C4C22×C414yes—
412C11×C4⋊C4C22×C414yes—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—41no—
415C11×C22⋊C4—41no—
416C11×C22⋊C4C22×C414yes—
417C11×C22⋊C4C22×C414yes—
418C11×C22⋊C4C22×C414yes—
419C42×C11—22no—
420C42×C11—22no—
421C42×C11—41no—
422C42×C11—41no—
423C42×C11—41no—
424C42×C11—41no—
425C42×C11—41no—
426C42×C11C22×C414yes—
427C22⋊Dic11—41no—
428C22⋊Dic11—41no—
429C22⋊Dic11—41no—
430C22⋊Dic11C22×C414yes—
431C22⋊Dic11C22×C414yes—
432C22⋊Dic11C22×C414yes—
433C4⋊Dic11—22no—
434C4⋊Dic11—41no—
435C4⋊Dic11—41no—
436C4⋊Dic11—41no—
437C4⋊Dic11—41no—
438C4⋊Dic11C22×C414yes—
439C4⋊Dic11C22×C414yes—
440C4⋊Dic11C22×C414yes—
441C4⋊Dic11C22×C414yes—
442C4⋊Dic11C22×C414yes—
443Dic11⋊C4—22no—
444Dic11⋊C4—22no—
445Dic11⋊C4—41no—
446Dic11⋊C4—41no—
447Dic11⋊C4—41no—
448Dic11⋊C4—41no—
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⋊C4C22×C414yes—
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—
470Dic11⋊C4C22×C414yes—
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#2373D1111yescharacteristic
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#2331—111no—
520#2330—111no—
521#2329—111no—
522#2320—111no—
523C4×#125—111no—
524C4×#126—111no—
525#2295—111no—
526C23×C11—21no—
527C23×C11—21no—
528C23×C11—21no—
529C23×C11—21no—
530C23×C11—21no—
531C23×C11—21no—
532C23×C11C23×C412yes—
533C23×C11C2511yescharacteristic
534C2×C4×C11—21no—
535C2×C4×C11—21no—
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—82no—
570C2×C4×C11C23×C412yes—
571C2×C4×C11C23×C412yes—
572C2×C4×C11C23×C412yes—
573C2×C4×C11C23×C412yes—
574C2×C4×C11C23×C412yes—
575C2×C4×C11C23×C412yes—
576C2×C4×C112−1+412yes—
577C2×Dic11—21no—
578C2×Dic11—21no—
579C2×Dic11—21no—
580C2×Dic11—21no—
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—44no—
617C2×Dic11—82no—
618C2×Dic11C23×C412yes—
619C2×Dic11C23×C412yes—
620C2×Dic11C23×C412yes—
621C2×Dic11C23×C412yes—
622C2×Dic11C23×C412yes—
623C2×Dic11C23×C412yes—
624C2×Dic11C23×C412yes—
625C2×Dic11C23×C412yes—
626C2×Dic112−1+412yes—
627Dic22—44no—
628Dic22—44no—
629#541—1116no—
630C2×C4⋊Q8—111no—
631C2×#126—111no—
632C2×#126—111no—
633C2×#126—111no—
634C2×#126C2×D1111yescharacteristic
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#391—111no—
650#391—111no—
651#391—111no—
652#391—111no—
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#389—111no—
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#388C2×D1111yescharacteristic
681#388C2×D1111yescharacteristic
682#388C2×D1111yescharacteristic
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#387—111no—
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#385C2×D1111yescharacteristic
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#382—111no—
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⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
776C4×C22⋊C4C2×D1111yescharacteristic
777#376—111no—
778#376—111no—
779#376—111no—
780#376—111no—
781#376—111no—
782#376C2×D1111yescharacteristic
783C2×#95—111no—
784C43—111no—
785C22×C11—22no—
786C22×C11—22no—
787C22×C11—22no—
788C22×C11—41no—
789C22×C11—41no—
790C22×C11—41no—
791C22×C11—41no—
792C22×C11C24×C411yescharacteristic
793C22×C11C2×2−1+411yescharacteristic
794C22×C11C2×2−1+411yescharacteristic
795C22×C11#58511yescharacteristic
796C22×C11#58511yescharacteristic
797C22×C11#58511yescharacteristic
798C22×C11#58511yescharacteristic
799C4×C11—22no—
800C4×C11—22no—
801C4×C11—22no—
802C4×C11—22no—
803C4×C11—22no—
804C4×C11—22no—
805C4×C11—22no—
806C4×C11—41no—
807C4×C11—41no—
808C4×C11—41no—
809C4×C11—41no—
810C4×C11—41no—
811C4×C11—41no—
812C4×C11—41no—
813Dic11—22no—
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×Q8—111no—
830C22×Q8—111no—
831C23×C4—111no—
832C23×C4—111no—
833C23×C4C22×D1111yescharacteristic
834C4⋊Q8—118no—
835#126—118no—
836#126—118no—
837#126—118no—
838#126C4×D1118yes—
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⋊C4—111no—
886C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
902C2×C22⋊C4C22×D1111yescharacteristic
903C2×C22⋊C4C22×D1111yescharacteristic
904C2×C22⋊C4C22×D1111yescharacteristic
905C2×C22⋊C4C22×D1111yescharacteristic
906C2×C22⋊C4C22×D1111yescharacteristic
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×C42C22×D1111yescharacteristic
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#95—111no—
984#95—111no—
985#95—111no—
986#95—111no—
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—42no—
1000C2×C11#342811yescharacteristic
1001C2×C11C4×2−1+411yescharacteristic
1002C2×C11C4×2−1+411yescharacteristic
1003C2×C11#356311yescharacteristic
1004C2×C11#356411yescharacteristic
1005C2×C11#356511yescharacteristic
1006C2×C11#356611yescharacteristic
1007C24C23×D1111yescharacteristic
1008C2×Q8—114no—
1009C2×Q8—114no—
1010C2×Q8—441no—
1011C2×Q8—441no—
1012C2×Q8—441no—
1013C2×Q8—441no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—111no—
1018C22×C4—111no—
1019C22×C4—111no—
1020C22×C4—111no—
1021C22×C4—111no—
1022C22×C4—111no—
1023C22×C4—111no—
1024C22×C4—111no—
1025C22×C4—111no—
1026C22×C4—114no—
1027C22×C4—111no—
1028C22×C4—111no—
1029C22×C4—111no—
1030C22×C4—111no—
1031C22×C4—111no—
1032C22×C4—111no—
1033C22×C4—111no—
1034C22×C4—222no—
1035C22×C4—441no—
1036C22×C4—441no—
1037C22×C4—441no—
1038C22×C4—441no—
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—114no—
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⋊C4—441no—
1096C4⋊C4C2×C4×D1114yes—
1097C4⋊C4C2×C4×D1114yes—
1098C4⋊C4C2×C4×D1114yes—
1099C22⋊C4—22no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—114no—
1103C22⋊C4—114no—
1104C22⋊C4—114no—
1105C22⋊C4—441no—
1106C22⋊C4—441no—
1107C22⋊C4—441no—
1108C22⋊C4C2×C4×D1114yes—
1109C22⋊C4C2×C4×D1114yes—
1110C22⋊C4C2×C4×D1114yes—
1111C42—22no—
1112C42—22no—
1113C42—41no—
1114C42—41no—
1115C42—41no—
1116C42—41no—
1117C42—41no—
1118C42—114no—
1119C42—114no—
1120C42—114no—
1121C42—114no—
1122C42—114no—
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—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23C22×C4×D1112yes—
1151C23C24×D1111yescharacteristic
1152Q8—444no—
1153Q8—444no—
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—82no—
1190C2×C4—112no—
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—221no—
1237C2×C4—221no—
1238C2×C4—444no—
1239C2×C4—882no—
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#6704312yes—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22C23×C4×D1111yescharacteristic
1255C22C2×#6704311yescharacteristic
1256C22#1062345311yescharacteristic
1257C22#1062345311yescharacteristic
1258C22#1062345311yescharacteristic
1259C22#1062345511yescharacteristic
1260C22D11×2−1+411yescharacteristic
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—222no—
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—42no—
1292C2#1308181511yescharacteristic
1293C2C4×#6704311yescharacteristic
1294C2#1308182711yescharacteristic
1295C2#1308321311yescharacteristic
1296C2#1308323511yescharacteristic
1297C2#1308326211yescharacteristic
1298C2#1308327811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2373C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2373D11
hypocenterC11#34455
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2373

Complements

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

NH ≅ G/Ntype
3. #13071800C2semidirect
4. #13071798C2semidirect
8. #13071721C2semidirect
9. #13071719C2semidirect
10. #13071710C2semidirect
11. #13071707C2semidirect
13. #13071577C2semidirect
14. #13071570C2semidirect
17. #13071418C2semidirect
18. #13071416C2semidirect
23. #13071363C2semidirect
24. #13071361C2semidirect
25. #13071353C2semidirect
27. #13071262C2semidirect
28. C4×#66942C2semidirect
30. #13071088C2semidirect
33. #10623232C4semidirect
284. #66943C2×C4semidirect
285. #66942C2×C4semidirect
286. #66942C2×C4semidirect
287. #66942C2×C4semidirect
288. #66941C2×C4semidirect
289. #66940C2×C4semidirect
296. #66923C2×C4semidirect
297. C4×Dic22C2×C4semidirect
1143. C11#34455semidirect

Maximal subgroups

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

subgroupindex
C2×#106232322
#130718042
#130718002
#130717982
#130717762
#130717402
#130717332
#130717212
#130717192
#130717102
#130717072
#130716942
#130715772
#130715702
#130714982
#130714702
#130714182
#130714162
#130713982
#130713932
#130713732
#130713632
#130713612
#130713532
#130713472
#130712622
C4×#669422
#130711702
#130710882
C11×#23732
#3445511