Finite Group Databasebeta

← #14924849

Subgroups — #14924849

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074026C211yesmaximal, characteristic, complemented
2#13074026C211yesmaximal, characteristic, complemented
3#13074010C211yesmaximal, characteristic, complemented
4#13074009C211yesmaximal, characteristic, complemented
5#13073895C211yesmaximal, characteristic
6#13073894C211yesmaximal, characteristic
7#13073697C211yesmaximal, characteristic
8#13073696C211yesmaximal, characteristic
9#13073337C211yesmaximal, characteristic
10#13073336C211yesmaximal, characteristic
11#13073305C211yesmaximal, characteristic, complemented
12#13073304C211yesmaximal, characteristic, complemented
13#13072632C211yesmaximal, characteristic
14#13072631C211yesmaximal, characteristic
15#13072591C211yesmaximal, characteristic, complemented
16#13071908C211yesmaximal, characteristic, complemented
17#13071906C211yesmaximal, characteristic, complemented
18#13071893C211yesmaximal, characteristic
19#13071887C211yesmaximal, characteristic
20#125×Dic11C211yesmaximal, characteristic, complemented
21#13071173C211yesmaximal, characteristic, complemented
22#13071150C211yesmaximal, characteristic
23#13071146C211yesmaximal, characteristic
24#13071108C211yesmaximal, characteristic
25#13071108C211yesmaximal, characteristic
26#13071089C211yesmaximal, characteristic, complemented
27#13071089C211yesmaximal, characteristic, complemented
28#13071087C211yesmaximal, characteristic, complemented
29C4×Q8×Dic11C211yesmaximal, characteristic, complemented
30C4×#66945C211yesmaximal, characteristic
31C11×#2462C211yesmaximal, characteristic, complemented
32C2×C11×#125C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×Q8×Dic11C2211yescharacteristic
35C2×Q8×Dic11C2211yescharacteristic
36C2×#66950C2211yescharacteristic
37C2×#66949C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66942C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C11×#398C2211yescharacteristic
46C11×#398C2211yescharacteristic
47C11×#395C2211yescharacteristic
48C11×#395C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#387C2211yescharacteristic
52C11×#387C2211yescharacteristic
53C11×#387C2211yescharacteristic
54C11×#387C2211yescharacteristic
55C11×#387C2211yescharacteristic
56C11×#387C2211yescharacteristic
57C4×C11×C4⋊C4C2211yescharacteristic
58#10622844C2211yescharacteristic
59#10622842C2211yescharacteristic
60#10622607C2211yescharacteristic
61#10622607C2211yescharacteristic
62#10622607C2211yescharacteristic
63#10622607C2211yescharacteristic
64#10622605C2211yescharacteristic
65#10622603C2211yescharacteristic
66#10622603C2211yescharacteristic
67#10622602C2211yescharacteristic
68#10622602C2211yescharacteristic
69#10622602C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622599C2211yescharacteristic
72#10622598C2211yescharacteristic
73#10622598C2211yescharacteristic
74#10622598C2211yescharacteristic
75#10622597C2211yescharacteristic
76#10622597C2211yescharacteristic
77#10622597C2211yescharacteristic
78#10622596C2211yescharacteristic
79#10622594C2211yescharacteristic
80#10622594C2211yescharacteristic
81#10622594C2211yescharacteristic
82#10622594C2211yescharacteristic
83#10622594C2211yescharacteristic
84#10622594C2211yescharacteristic
85#10622594C2211yescharacteristic
86#10622594C2211yescharacteristic
87#10622593C2211yescharacteristic
88#10622592C2211yescharacteristic
89#10622592C2211yescharacteristic
90#10622592C2211yescharacteristic
91#10622591C2211yescharacteristic
92#10622591C2211yescharacteristic
93C4⋊C4×Dic11C2211yescharacteristic
94C4⋊C4×Dic11C2211yescharacteristic
95C4⋊C4×Dic11C2211yescharacteristic
96C4⋊C4×Dic11C2211yescharacteristic
97C4⋊C4×Dic11C2211yescharacteristic
98C4⋊C4×Dic11C2211yescharacteristic
99C4⋊C4×Dic11C2211yescharacteristic
100C4⋊C4×Dic11C2211yescharacteristic
101C4⋊C4×Dic11C2211yescharacteristic
102C4⋊C4×Dic11C2211yescharacteristic
103C4⋊C4×Dic11C2211yescharacteristic
104C4⋊C4×Dic11C2211yescharacteristic
105C4⋊C4×Dic11C2211yescharacteristic
106C4⋊C4×Dic11C2211yescharacteristic
107C4⋊C4×Dic11C2211yescharacteristic
108#10622587C2211yescharacteristic
109#10622585C2211yescharacteristic
110#10622585C2211yescharacteristic
111#10622585C2211yescharacteristic
112#10622553C2211yescharacteristic
113#10622553C2211yescharacteristic
114C4×(C2×D11)⋊C4C2211yescharacteristic
115C4×(C2×D11)⋊C4C2211yescharacteristic
116#10622549C2211yescharacteristic
117C4×C4⋊Dic11C2211yescharacteristic
118C4×C4⋊Dic11C2211yescharacteristic
119C4×C4⋊Dic11C2211yescharacteristic
120C4×C4⋊Dic11C2211yescharacteristic
121#10622546C2211yescharacteristic
122#10622546C2211yescharacteristic
123#10622546C2211yescharacteristic
124#10622546C2211yescharacteristic
125C42×Dic11C2211yescharacteristic
126C42×Dic11C2211yescharacteristic
127C42×Dic11C2211yescharacteristic
128C42×Dic11C2211yescharacteristic
129#10622542C2211yescharacteristic
130#10622542C2211yescharacteristic
131#10622290C2211yescharacteristic
132#10622286C2211yescharacteristic
133#10622283C2211yescharacteristic
134#10622283C2211yescharacteristic
135#10622282C2211yescharacteristic
136#10622282C2211yescharacteristic
137#10622281C2211yescharacteristic
138#10622280C2211yescharacteristic
139#10622279C2211yescharacteristic
140#10622279C2211yescharacteristic
141#10622279C2211yescharacteristic
142#10622279C2211yescharacteristic
143#10622279C2211yescharacteristic
144#10622279C2211yescharacteristic
145#10622274C2211yescharacteristic
146#10622274C2211yescharacteristic
147#10622274C2211yescharacteristic
148#10622273C2211yescharacteristic
149#10622270C2211yescharacteristic
150#10622270C2211yescharacteristic
151#10622269C2211yescharacteristic
152#10622269C2211yescharacteristic
153#10622269C2211yescharacteristic
154#10622269C2211yescharacteristic
155#10622268C2211yescharacteristic
156#10622268C2211yescharacteristic
157#10622268C2211yescharacteristic
158#10622267C2211yescharacteristic
159#10622267C2211yescharacteristic
160#10622267C2211yescharacteristic
161#10622267C2211yescharacteristic
162#10622267C2211yescharacteristic
163#10622266C2211yescharacteristic
164#10622266C2211yescharacteristic
165#10622265C2211yescharacteristic
166#10622265C2211yescharacteristic
167#10622263C2211yescharacteristic
168#10622262C2211yescharacteristic
169#10622262C2211yescharacteristic
170#10622262C2211yescharacteristic
171#10622262C2211yescharacteristic
172#10622262C2211yescharacteristic
173#10622262C2211yescharacteristic
174#10622261C2211yescharacteristic
175#10622261C2211yescharacteristic
176#10622261C2211yescharacteristic
177#10622261C2211yescharacteristic
178#10622260C2211yescharacteristic
179#10622260C2211yescharacteristic
180#10622260C2211yescharacteristic
181#10622260C2211yescharacteristic
182#10622259C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×Q8×C11C2311yescharacteristic
188C22×C4×D11C2311yescharacteristic
189C22×C4×D11C2311yescharacteristic
190C22×C4×D11C2311yescharacteristic
191C22×Dic22C2311yescharacteristic
192C22×Dic22C2311yescharacteristic
193C22×Dic22C2311yescharacteristic
194C11×#125—24no—
195C4×Q8×C11—24no—
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×C11×C4⋊C4C2311yescharacteristic
205C2×C11×C4⋊C4C2311yescharacteristic
206C2×C11×C4⋊C4C2311yescharacteristic
207C2×C11×C4⋊C4C2311yescharacteristic
208C2×C11×C4⋊C4C2311yescharacteristic
209C2×C11×C4⋊C4C2311yescharacteristic
210C2×C11×C4⋊C4C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216Q8×Dic11—24no—
217Q8×Dic11—24no—
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×(C2×D11)⋊C4C2311yescharacteristic
228C2×(C2×D11)⋊C4C2311yescharacteristic
229C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
240C2×C4⋊Dic11C2311yescharacteristic
241C2×C4⋊Dic11C2311yescharacteristic
242C2×C4⋊Dic11C2311yescharacteristic
243C2×C4⋊Dic11C2311yescharacteristic
244C2×C4⋊Dic11C2311yescharacteristic
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
288C2×C4×Dic11C2311yescharacteristic
289C2×C4×Dic11C2311yescharacteristic
290#66950—24no—
291#66949—24no—
292#66945—24no—
293#66945Q818yescomplemented
294#66942—24no—
295#66940—24no—
296#66940—24no—
297#66940—24no—
298C42×D11—24no—
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
355#34882—111nomaximal, Sylow
356C23×D11C2411yescharacteristic
357C2×Q8×C11—22no—
358C2×Q8×C11—22no—
359C2×Q8×C11—22no—
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2411yescharacteristic
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×Dic11C2411yescharacteristic
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C22×Dic11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C22×Dic11C2411yescharacteristic
387C22×Dic11C2411yescharacteristic
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2411yescharacteristic
390C2×C4×D11—22no—
391C2×C4×D11—22no—
392C2×C4×D11—22no—
393C2×C4×D11—22no—
394C2×C4×D11—22no—
395C2×C4×D11—22no—
396C2×C4×D11—41no—
397C2×C4×D11—41no—
398C2×C4×D11C2×Q814yes—
399C2×Dic22—22no—
400C2×Dic22—22no—
401C2×Dic22—22no—
402C2×Dic22—22no—
403C2×Dic22—22no—
404C2×Dic22—41no—
405C2×Dic22—41no—
406C2×Dic22—41no—
407C2×Dic22—41no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4—22no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4—22no—
418C11×C4⋊C4—22no—
419C11×C4⋊C4—22no—
420C11×C4⋊C4—22no—
421C11×C4⋊C4C2×Q814yes—
422C11×C4⋊C4#4114yes—
423C42×C11—22no—
424C42×C11—22no—
425C42×C11—22no—
426C42×C11—22no—
427C42×C11—22no—
428(C2×D11)⋊C4—22no—
429(C2×D11)⋊C4—22no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—41no—
435(C2×D11)⋊C4—41no—
436(C2×D11)⋊C4—41no—
437(C2×D11)⋊C4—41no—
438(C2×D11)⋊C4C2×Q814yes—
439(C2×D11)⋊C4C2×Q814yes—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—22no—
447C4⋊Dic11—41no—
448C4⋊Dic11—41no—
449C4⋊Dic11—41no—
450C4⋊Dic11—41no—
451C4⋊Dic11—41no—
452C4⋊Dic11—41no—
453C4⋊Dic11C2×Q814yes—
454C4⋊Dic11#4114yes—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465Dic11⋊C4—22no—
466Dic11⋊C4—22no—
467Dic11⋊C4—41no—
468Dic11⋊C4—41no—
469Dic11⋊C4—41no—
470Dic11⋊C4—41no—
471Dic11⋊C4—41no—
472Dic11⋊C4—41no—
473C4×Dic11—22no—
474C4×Dic11—22no—
475C4×Dic11—22no—
476C4×Dic11—22no—
477C4×Dic11—22no—
478C4×Dic11—22no—
479C4×Dic11—22no—
480C4×Dic11—22no—
481C4×Dic11—22no—
482C4×Dic11—22no—
483C4×Dic11—22no—
484C4×Dic11—22no—
485C4×Dic11—22no—
486C4×Dic11—22no—
487C4×Dic11—22no—
488C4×Dic11—41no—
489C4×Dic11—41no—
490C4×Dic11—41no—
491C4×Dic11—41no—
492C4×Dic11—41no—
493C4×Dic11—41no—
494C4×Dic11—41no—
495C4×Dic11—41no—
496C4×Dic11C2×Q814yes—
497C4×Dic11C2×Q814yes—
498C4×Dic11#4114yes—
499C4×Dic11#4114yes—
500#2586—111no—
501#2586—111no—
502#2585—111no—
503#2585—111no—
504#2574—111no—
505#2574—111no—
506#2556—111no—
507#2556—111no—
508#2522—111no—
509#2522—111no—
510#2520—111no—
511#2520—111no—
512#2465—111no—
513#2465—111no—
514#2462—111no—
515#2462D1111yescharacteristic, complemented
516#2399—111no—
517#2399—111no—
518#2396—111no—
519#2396—111no—
520C4×#125—111no—
521C4×#125—111no—
522C4×C22⋊Q8—111no—
523C4×C22⋊Q8—111no—
524#2298—111no—
525#2298—111no—
526#2295—111no—
527#2295—111no—
528#2295—111no—
529C42×Q8—111no—
530C4×#117—111no—
531C23×C11C2511yescharacteristic
532C22×D11—21no—
533C22×D11—21no—
534C22×D11—21no—
535C22×D11—21no—
536C22×D11—21no—
537C22×D11—21no—
538C22×D11C22×Q812yes—
539Q8×C11—28no—
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×C11—21no—
574C2×C4×C11—21no—
575C2×C4×C11—21no—
576C2×C4×C11C22×Q812yes—
577C2×C4×C11C22×Q812yes—
578C2×C4×C11C22×Q812yes—
579C2×C4×C11C2×#4112yes—
580C2×C4×C11C2×#4112yes—
581C2×C4×C11C2×#4112yes—
582C2×C4×C11C2×#4112yes—
583C2×C4×C11C2×#4112yes—
584C2×C4×C11C2×#4112yes—
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×Dic11—21no—
619C2×Dic11—21no—
620C2×Dic11—21no—
621C2×Dic11C22×Q812yes—
622C2×Dic11C22×Q812yes—
623C2×Dic11C22×Q812yes—
624C2×Dic11C2×#4112yes—
625C2×Dic11C2×#4112yes—
626C2×Dic11C2×#4112yes—
627C2×Dic11C2×#4112yes—
628C2×Dic11C2×#4112yes—
629C2×Dic11C2×#4112yes—
630C4×D11—28no—
631C4×D11—44no—
632C4×D11—44no—
633Dic22—44no—
634Dic22—44no—
635Dic22—44no—
636C2×#125—111no—
637C2×#125C2×D1111yescharacteristic
638C2×C22⋊Q8—111no—
639C2×C22⋊Q8—111no—
640C2×C4×Q8—111no—
641C2×C4×Q8—111no—
642C2×C4×Q8—111no—
643C2×C4×Q8—111no—
644C2×C4×Q8—111no—
645C2×C4×Q8C2×D1111yescharacteristic
646C2×#117—111no—
647C2×#117—111no—
648C22×C42—111no—
649#400—111no—
650#400—111no—
651#399—111no—
652#399—111no—
653#398—111no—
654#398—111no—
655#398—111no—
656#398—111no—
657#398—111no—
658#398—111no—
659#398—111no—
660#398—111no—
661#398—111no—
662#398—111no—
663#398C2×D1111yescharacteristic
664#398C2×D1111yescharacteristic
665#396—111no—
666#396—111no—
667#396—111no—
668#396—111no—
669#395—111no—
670#395—111no—
671#395—111no—
672#395—111no—
673#395—111no—
674#395—111no—
675#395—111no—
676#395—111no—
677#395C2×D1111yescharacteristic
678#395C2×D1111yescharacteristic
679#393—111no—
680#393—111no—
681#391—111no—
682#391—111no—
683#391—111no—
684#391—111no—
685#391—111no—
686#391—111no—
687#391—111no—
688#391—111no—
689#389—111no—
690#389—111no—
691#389—111no—
692#389—111no—
693#389—111no—
694#389—111no—
695#389—111no—
696#389—111no—
697#389—111no—
698#389—111no—
699#389C2×D1111yescharacteristic
700#389C2×D1111yescharacteristic
701#388—111no—
702#388—111no—
703#388—111no—
704#388—111no—
705#388—111no—
706#388—111no—
707#388—111no—
708#388—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#387—111no—
725#387—111no—
726#387—111no—
727#387—111no—
728#387—111no—
729#387—111no—
730#387—111no—
731#387—111no—
732#387—111no—
733#387—111no—
734#387—111no—
735#387C2×D1111yescharacteristic
736#387C2×D1111yescharacteristic
737#387C2×D1111yescharacteristic
738#387C2×D1111yescharacteristic
739#387C2×D1111yescharacteristic
740#387C2×D1111yescharacteristic
741#385—111no—
742#385—111no—
743#385—111no—
744#385—111no—
745#382—111no—
746#382—111no—
747#380—111no—
748#380—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⋊C4—111no—
769C4×C4⋊C4—111no—
770C4×C4⋊C4—111no—
771C4×C4⋊C4—111no—
772C4×C4⋊C4—111no—
773C4×C4⋊C4—111no—
774C4×C4⋊C4C2×D1111yescharacteristic
775C4×C22⋊C4—111no—
776C4×C22⋊C4—111no—
777C4×C22⋊C4—111no—
778C4×C22⋊C4—111no—
779C4×C22⋊C4—111no—
780C4×C22⋊C4—111no—
781C4×C22⋊C4—111no—
782C4×C22⋊C4—111no—
783#376—111no—
784#376—111no—
785#376—111no—
786#376—111no—
787C43—111no—
788C43—111no—
789C43—111no—
790C43—111no—
791C22×C11C23×Q811yescharacteristic
792C22×C11C22×#4111yescharacteristic
793C22×C11C22×#4111yescharacteristic
794C22×C11C22×#4111yescharacteristic
795C22×C11C22×#4111yescharacteristic
796C22×C11#58511yescharacteristic
797C22×C11#58511yescharacteristic
798C2×D11—22no—
799C2×D11—22no—
800C2×D11—22no—
801C2×D11—41no—
802C2×D11—41no—
803C2×D11—41no—
804C2×D11—41no—
805C4×C11—22no—
806C4×C11—22no—
807C4×C11—22no—
808C4×C11—22no—
809C4×C11—22no—
810C4×C11—22no—
811C4×C11—22no—
812C4×C11—22no—
813C4×C11—22no—
814C4×C11—41no—
815C4×C11—41no—
816C4×C11—41no—
817C4×C11—41no—
818C4×C11—41no—
819C4×C11—41no—
820Dic11—22no—
821Dic11—22no—
822Dic11—22no—
823Dic11—22no—
824Dic11—22no—
825Dic11—22no—
826Dic11—41no—
827Dic11—41no—
828Dic11—41no—
829Dic11—41no—
830Dic11—41no—
831Dic11—41no—
832Dic11—41no—
833Dic11—41no—
834Dic11#53314yes—
835C22×Q8—111no—
836C22×Q8—111no—
837C22×Q8—111no—
838C22×Q8C22×D1111yescharacteristic
839C23×C4—111no—
840C23×C4—111no—
841C23×C4—111no—
842#125—24no—
843#125—224no—
844C22⋊Q8—224no—
845C22⋊Q8—224no—
846C4×Q8—24no—
847C4×Q8—224no—
848C4×Q8—224no—
849C4×Q8—224no—
850C4×Q8—224no—
851C4×Q8—224no—
852#117—118no—
853#117—224no—
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×C4⋊C4C22×D1111yescharacteristic
896C2×C4⋊C4C22×D1111yescharacteristic
897C2×C4⋊C4C22×D1111yescharacteristic
898C2×C4⋊C4C22×D1111yescharacteristic
899C2×C4⋊C4C22×D1111yescharacteristic
900C2×C4⋊C4C22×D1111yescharacteristic
901C2×C4⋊C4C22×D1111yescharacteristic
902C2×C22⋊C4—111no—
903C2×C22⋊C4—111no—
904C2×C22⋊C4—111no—
905C2×C22⋊C4—111no—
906C2×C22⋊C4—111no—
907C2×C22⋊C4—111no—
908C2×C22⋊C4—111no—
909C2×C22⋊C4—111no—
910C2×C22⋊C4—111no—
911C2×C22⋊C4—111no—
912C2×C22⋊C4—111no—
913C2×C22⋊C4—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×C42—111no—
933C2×C42—111no—
934C2×C42—111no—
935C2×C42—111no—
936C2×C42—111no—
937C2×C42—111no—
938C2×C42—111no—
939C2×C42—111no—
940C2×C42—111no—
941C2×C42—224no—
942C2×C42C22×D1111yescharacteristic
943C2×C42C22×D1111yescharacteristic
944C2×C42C22×D1111yescharacteristic
945C2×C42C22×D1111yescharacteristic
946C2×C42C22×D1111yescharacteristic
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#95—111no—
988#95—111no—
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
999#95C22×D1111yescharacteristic
1000#95C22×D1111yescharacteristic
1001#95C22×D1111yescharacteristic
1002#95C22×D1111yescharacteristic
1003C2×C11C2×#53311yescharacteristic
1004C2×C11#344411yescharacteristic
1005C2×C11#345511yescharacteristic
1006C2×C11#347511yescharacteristic
1007C2×C11#347511yescharacteristic
1008C2×C11Q8×#4111yescharacteristic
1009C2×C11Q8×#4111yescharacteristic
1010D11—42no—
1011C24—111no—
1012C2×Q8—22no—
1013C2×Q8—22no—
1014C2×Q8—22no—
1015C2×Q8—222no—
1016C2×Q8—222no—
1017C2×Q8—222no—
1018C2×Q8—222no—
1019C2×Q8—222no—
1020C2×Q8—441no—
1021C2×Q8—441no—
1022C2×Q8—441no—
1023C2×Q8—441no—
1024C22×C4—111no—
1025C22×C4—111no—
1026C22×C4—111no—
1027C22×C4—111no—
1028C22×C4—111no—
1029C22×C4—111no—
1030C22×C4—111no—
1031C22×C4—114no—
1032C22×C4—111no—
1033C22×C4—111no—
1034C22×C4—111no—
1035C22×C4—111no—
1036C22×C4—111no—
1037C22×C4—111no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—222no—
1041C22×C4—222no—
1042C22×C4—222no—
1043C22×C4—222no—
1044C22×C4—222no—
1045C22×C4—222no—
1046C22×C4—441no—
1047C22×C4—441no—
1048C22×C4C23×D1111yescharacteristic
1049C22×C4C23×D1111yescharacteristic
1050C22×C4C23×D1111yescharacteristic
1051C22×C4C23×D1111yescharacteristic
1052C22×C4C23×D1111yescharacteristic
1053C22×C4C23×D1111yescharacteristic
1054C22×C4C23×D1111yescharacteristic
1055C22×C4C23×D1111yescharacteristic
1056C22×C4C23×D1111yescharacteristic
1057C22×C4C23×D1111yescharacteristic
1058C22×C4C23×D1111yescharacteristic
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1111yescharacteristic
1061C22×C4C23×D1111yescharacteristic
1062C22×C4C23×D1111yescharacteristic
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—114no—
1077C4⋊C4—114no—
1078C4⋊C4—222no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4—222no—
1082C4⋊C4—222no—
1083C4⋊C4—222no—
1084C4⋊C4—222no—
1085C4⋊C4—222no—
1086C4⋊C4—222no—
1087C4⋊C4—222no—
1088C4⋊C4—222no—
1089C4⋊C4—222no—
1090C4⋊C4—222no—
1091C4⋊C4—222no—
1092C4⋊C4—222no—
1093C4⋊C4—222no—
1094C4⋊C4—222no—
1095C4⋊C4—222no—
1096C4⋊C4—222no—
1097C4⋊C4—441no—
1098C4⋊C4—441no—
1099C4⋊C4—441no—
1100C4⋊C4—441no—
1101C4⋊C4—441no—
1102C4⋊C4—441no—
1103C4⋊C4—441no—
1104C4⋊C4—441no—
1105C4⋊C4—441no—
1106C4⋊C4—441no—
1107C4⋊C4—441no—
1108C4⋊C4—441no—
1109C4⋊C4#434114yes—
1110C4⋊C4Q8×D1114yes—
1111C22⋊C4—114no—
1112C22⋊C4—114no—
1113C22⋊C4—222no—
1114C22⋊C4—222no—
1115C22⋊C4—222no—
1116C22⋊C4—222no—
1117C22⋊C4—222no—
1118C22⋊C4—222no—
1119C22⋊C4—441no—
1120C22⋊C4—441no—
1121C22⋊C4—441no—
1122C22⋊C4—441no—
1123C42—22no—
1124C42—22no—
1125C42—22no—
1126C42—22no—
1127C42—22no—
1128C42—114no—
1129C42—114no—
1130C42—114no—
1131C42—114no—
1132C42—222no—
1133C42—222no—
1134C42—222no—
1135C42—222no—
1136C42—222no—
1137C42—222no—
1138C42—222no—
1139C42—222no—
1140C42—222no—
1141C42—222no—
1142C42—222no—
1143C42—222no—
1144C42—222no—
1145C42—222no—
1146C42—222no—
1147C42—441no—
1148C42—441no—
1149C42—441no—
1150C42—441no—
1151C42—441no—
1152C42—441no—
1153C42—441no—
1154C42—441no—
1155C11#3488211yescharacteristic, complemented, Sylow
1156C23—112no—
1157C23—221no—
1158C23—221no—
1159C23—221no—
1160C23—221no—
1161C23—221no—
1162C23—221no—
1163C23C24×D1111yescharacteristic
1164Q8—28no—
1165Q8—444no—
1166Q8—444no—
1167Q8—444no—
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—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—112no—
1205C2×C4—112no—
1206C2×C4—112no—
1207C2×C4—112no—
1208C2×C4—112no—
1209C2×C4—112no—
1210C2×C4—112no—
1211C2×C4—112no—
1212C2×C4—112no—
1213C2×C4—228no—
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—221no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—221no—
1242C2×C4—221no—
1243C2×C4—221no—
1244C2×C4—221no—
1245C2×C4—221no—
1246C2×C4—221no—
1247C2×C4—221no—
1248C2×C4—221no—
1249C2×C4—221no—
1250C2×C4—444no—
1251C2×C4—444no—
1252C2×C4C2×#434112yes—
1253C2×C4C2×#434112yes—
1254C2×C4C2×#434112yes—
1255C2×C4C2×Q8×D1112yes—
1256C2×C4C2×Q8×D1112yes—
1257C2×C4C2×Q8×D1112yes—
1258C2×C4#41×D1112yes—
1259C2×C4#41×D1112yes—
1260C2×C4#41×D1112yes—
1261C22—222no—
1262C22—222no—
1263C22—222no—
1264C22—441no—
1265C22—441no—
1266C22—441no—
1267C22—441no—
1268C22C22×#434111yescharacteristic
1269C22C22×Q8×D1111yescharacteristic
1270C22C2×#41×D1111yescharacteristic
1271C22C2×#41×D1111yescharacteristic
1272C22C2×#41×D1111yescharacteristic
1273C22#1062345711yescharacteristic
1274C22#1062345711yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—114no—
1291C4—222no—
1292C4—222no—
1293C4—222no—
1294C4—222no—
1295C4—222no—
1296C4—222no—
1297C4—441no—
1298C4—441no—
1299C4—441no—
1300C4—441no—
1301C4—441no—
1302C4—441no—
1303C4—441no—
1304C4—441no—
1305C2—442no—
1306C2D11×#53311yescharacteristic
1307C2#1308190811yescharacteristic
1308C2#1308200711yescharacteristic
1309C2#1308217911yescharacteristic
1310C2#1308218111yescharacteristic
1311C2Q8×#434111yescharacteristic
1312C2#1308219811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2462C2
prime radicalC23×D11C24
hypercenter#2462D11
hypocenterC11#34882
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2462

Complements

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

NH ≅ G/Ntype
1. #13074026C2semidirect
2. #13074026C2semidirect
3. #13074010C2semidirect
4. #13074009C2semidirect
11. #13073305C2semidirect
12. #13073304C2semidirect
15. #13072591C2semidirect
16. #13071908C2semidirect
17. #13071906C2semidirect
20. #125×Dic11C2semidirect
21. #13071173C2semidirect
26. #13071089C2semidirect
27. #13071089C2semidirect
28. #13071087C2semidirect
29. C4×Q8×Dic11C2semidirect
31. C11×#2462C2semidirect
293. #66945Q8semidirect
515. #2462D11semidirect
1155. C11#34882semidirect

Maximal subgroups

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

subgroupindex
#130740262
#130740102
#130740092
#130738952
#130738942
#130736972
#130736962
#130733372
#130733362
#130733052
#130733042
#130726322
#130726312
#130725912
#130719082
#130719062
#130718932
#130718872
#125×Dic112
#130711732
#130711502
#130711462
#130711082
#130710892
#130710872
C4×Q8×Dic112
C4×#669452
C11×#24622
#3488211