Finite Group Databasebeta

← #14924839

Subgroups — #14924839

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#13074025C211yesmaximal, characteristic, complemented
2#13074024C211yesmaximal, characteristic, complemented
3#13074018C211yesmaximal, characteristic, complemented
4#13074017C211yesmaximal, characteristic, complemented
5#13073897C211yesmaximal, characteristic
6#13073896C211yesmaximal, characteristic
7#13073699C211yesmaximal, characteristic
8#13073698C211yesmaximal, characteristic
9#13073335C211yesmaximal, characteristic
10#13073334C211yesmaximal, characteristic
11#13073307C211yesmaximal, characteristic, complemented
12#13073306C211yesmaximal, characteristic, complemented
13#13072630C211yesmaximal, characteristic
14#13072593C211yesmaximal, characteristic, complemented
15#13072592C211yesmaximal, characteristic, complemented
16#13071906C211yesmaximal, characteristic, complemented
17#13071906C211yesmaximal, characteristic, complemented
18#13071891C211yesmaximal, characteristic
19#13071883C211yesmaximal, characteristic
20#13071175C211yesmaximal, characteristic, complemented
21#13071173C211yesmaximal, characteristic, complemented
22C22⋊Q8×Dic11C211yesmaximal, characteristic
23#13071148C211yesmaximal, characteristic
24#13071110C211yesmaximal, characteristic
25#13071110C211yesmaximal, characteristic
26#13071091C211yesmaximal, characteristic, complemented
27#13071089C211yesmaximal, characteristic, complemented
28#13071089C211yesmaximal, characteristic, complemented
29C4×Q8×Dic11C211yesmaximal, characteristic, complemented
30C4×#66930C211yesmaximal, characteristic
31C11×#2465C211yesmaximal, characteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×Q8×Dic11C2211yescharacteristic
35C2×Q8×Dic11C2211yescharacteristic
36C2×Q8×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66942C2211yescharacteristic
40C2×#66940C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×#66931C2211yescharacteristic
43C2×#66930C2211yescharacteristic
44C2×#66930C2211yescharacteristic
45C11×#396C2211yescharacteristic
46C11×#395C2211yescharacteristic
47C11×#395C2211yescharacteristic
48C11×#393C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#388C2211yescharacteristic
52C11×#388C2211yescharacteristic
53C11×#387C2211yescharacteristic
54C11×#387C2211yescharacteristic
55C11×#387C2211yescharacteristic
56C11×#385C2211yescharacteristic
57C4×C11×C22⋊C4C2211yescharacteristic
58#10622843C2211yescharacteristic
59#10622843C2211yescharacteristic
60#10622842C2211yescharacteristic
61#10622842C2211yescharacteristic
62#10622842C2211yescharacteristic
63#10622825C2211yescharacteristic
64#10622823C2211yescharacteristic
65C4×C22⋊Dic11C2211yescharacteristic
66#10622598C2211yescharacteristic
67#10622597C2211yescharacteristic
68#10622597C2211yescharacteristic
69#10622597C2211yescharacteristic
70#10622597C2211yescharacteristic
71#10622597C2211yescharacteristic
72#10622596C2211yescharacteristic
73#10622596C2211yescharacteristic
74#10622596C2211yescharacteristic
75#10622594C2211yescharacteristic
76#10622594C2211yescharacteristic
77#10622594C2211yescharacteristic
78#10622594C2211yescharacteristic
79#10622592C2211yescharacteristic
80#10622591C2211yescharacteristic
81#10622591C2211yescharacteristic
82#10622591C2211yescharacteristic
83#10622591C2211yescharacteristic
84#10622591C2211yescharacteristic
85#10622590C2211yescharacteristic
86C4⋊C4×Dic11C2211yescharacteristic
87C4⋊C4×Dic11C2211yescharacteristic
88C4⋊C4×Dic11C2211yescharacteristic
89C4⋊C4×Dic11C2211yescharacteristic
90C4⋊C4×Dic11C2211yescharacteristic
91C4⋊C4×Dic11C2211yescharacteristic
92C4⋊C4×Dic11C2211yescharacteristic
93C4⋊C4×Dic11C2211yescharacteristic
94C4⋊C4×Dic11C2211yescharacteristic
95C4⋊C4×Dic11C2211yescharacteristic
96C4⋊C4×Dic11C2211yescharacteristic
97#10622586C2211yescharacteristic
98#10622585C2211yescharacteristic
99#10622585C2211yescharacteristic
100#10622585C2211yescharacteristic
101#10622585C2211yescharacteristic
102#10622564C2211yescharacteristic
103#10622564C2211yescharacteristic
104#10622563C2211yescharacteristic
105#10622563C2211yescharacteristic
106#10622562C2211yescharacteristic
107#10622562C2211yescharacteristic
108#10622561C2211yescharacteristic
109#10622561C2211yescharacteristic
110#10622561C2211yescharacteristic
111#10622560C2211yescharacteristic
112#10622558C2211yescharacteristic
113#10622558C2211yescharacteristic
114#10622557C2211yescharacteristic
115#10622557C2211yescharacteristic
116#10622555C2211yescharacteristic
117C22⋊C4×Dic11C2211yescharacteristic
118C22⋊C4×Dic11C2211yescharacteristic
119C22⋊C4×Dic11C2211yescharacteristic
120C22⋊C4×Dic11C2211yescharacteristic
121C22⋊C4×Dic11C2211yescharacteristic
122C22⋊C4×Dic11C2211yescharacteristic
123C4×C4⋊Dic11C2211yescharacteristic
124C4×C4⋊Dic11C2211yescharacteristic
125C4×C4⋊Dic11C2211yescharacteristic
126#10622546C2211yescharacteristic
127#10622546C2211yescharacteristic
128#10622546C2211yescharacteristic
129#10622546C2211yescharacteristic
130#10622546C2211yescharacteristic
131C4×Dic11⋊C4C2211yescharacteristic
132C4×Dic11⋊C4C2211yescharacteristic
133C42×Dic11C2211yescharacteristic
134C42×Dic11C2211yescharacteristic
135C42×Dic11C2211yescharacteristic
136C42×Dic11C2211yescharacteristic
137#10622541C2211yescharacteristic
138#10622541C2211yescharacteristic
139#10622274C2211yescharacteristic
140#10622274C2211yescharacteristic
141#10622272C2211yescharacteristic
142#10622271C2211yescharacteristic
143#10622270C2211yescharacteristic
144#10622270C2211yescharacteristic
145#10622269C2211yescharacteristic
146#10622269C2211yescharacteristic
147#10622269C2211yescharacteristic
148#10622269C2211yescharacteristic
149#10622268C2211yescharacteristic
150#10622268C2211yescharacteristic
151#10622268C2211yescharacteristic
152#10622267C2211yescharacteristic
153#10622267C2211yescharacteristic
154#10622267C2211yescharacteristic
155#10622266C2211yescharacteristic
156#10622266C2211yescharacteristic
157#10622266C2211yescharacteristic
158#10622266C2211yescharacteristic
159#10622266C2211yescharacteristic
160#10622265C2211yescharacteristic
161#10622265C2211yescharacteristic
162#10622265C2211yescharacteristic
163#10622265C2211yescharacteristic
164#10622263C2211yescharacteristic
165#10622262C2211yescharacteristic
166#10622262C2211yescharacteristic
167#10622262C2211yescharacteristic
168#10622262C2211yescharacteristic
169#10622262C2211yescharacteristic
170#10622262C2211yescharacteristic
171#10622262C2211yescharacteristic
172#10622262C2211yescharacteristic
173#10622262C2211yescharacteristic
174#10622262C2211yescharacteristic
175#10622261C2211yescharacteristic
176#10622261C2211yescharacteristic
177#10622261C2211yescharacteristic
178#10622261C2211yescharacteristic
179#10622260C2211yescharacteristic
180#10622260C2211yescharacteristic
181#10622260C2211yescharacteristic
182#10622259C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×Q8×C11C2311yescharacteristic
188C22×Q8×C11C2311yescharacteristic
189C23×C4×C11C2311yescharacteristic
190C23×Dic11C2311yescharacteristic
191C23×Dic11C2311yescharacteristic
192C22×Dic22C2311yescharacteristic
193C22×Dic22C2311yescharacteristic
194C11×C22⋊Q8—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×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2311yescharacteristic
208C2×C11×C22⋊C4C2311yescharacteristic
209C2×C11×C22⋊C4C2311yescharacteristic
210C2×C11×C22⋊C4C2311yescharacteristic
211C2×C11×C22⋊C4C2311yescharacteristic
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
222Q8×Dic11—24no—
223Q8×Dic11—24no—
224Q8×Dic11—24no—
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
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×Dic11—24no—
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
290C2×C4×Dic11C2311yescharacteristic
291C2×C4×Dic11C2311yescharacteristic
292#66943—24no—
293#66942—24no—
294#66940—24no—
295#66940—24no—
296#66931—24no—
297#66930—24no—
298#66930Q818yescomplemented
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
356C24×C11C2411yescharacteristic
357C2×Q8×C11—22no—
358C2×Q8×C11—22no—
359C2×Q8×C11—22no—
360C2×Q8×C11—22no—
361C2×Q8×C11—22no—
362C2×Q8×C11—41no—
363C22×C4×C11—22no—
364C22×C4×C11—22no—
365C22×C4×C11—41no—
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×Dic11—22no—
381C22×Dic11—22no—
382C22×Dic11—22no—
383C22×Dic11—22no—
384C22×Dic11—41no—
385C22×Dic11C2×Q814yes—
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
399C22×Dic11C2411yescharacteristic
400C22×Dic11C2411yescharacteristic
401C22×Dic11C2411yescharacteristic
402C2×Dic22—22no—
403C2×Dic22—22no—
404C2×Dic22—22no—
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—41no—
416C11×C4⋊C4—41no—
417C11×C4⋊C4#4114yes—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—41no—
423C11×C22⋊C4C2×Q814yes—
424C42×C11—22no—
425C42×C11—22no—
426C42×C11—22no—
427C42×C11—41no—
428C22⋊Dic11—22no—
429C22⋊Dic11—22no—
430C22⋊Dic11—41no—
431C22⋊Dic11—41no—
432C22⋊Dic11—41no—
433C22⋊Dic11C2×Q814yes—
434C4⋊Dic11—22no—
435C4⋊Dic11—22no—
436C4⋊Dic11—22no—
437C4⋊Dic11—22no—
438C4⋊Dic11—22no—
439C4⋊Dic11—22no—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—41no—
446C4⋊Dic11—41no—
447C4⋊Dic11#4114yes—
448Dic11⋊C4—22no—
449Dic11⋊C4—22no—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—41no—
463Dic11⋊C4—41no—
464Dic11⋊C4—41no—
465Dic11⋊C4—41no—
466Dic11⋊C4—41no—
467Dic11⋊C4—41no—
468Dic11⋊C4—41no—
469Dic11⋊C4—41no—
470Dic11⋊C4C2×Q814yes—
471Dic11⋊C4C2×Q814yes—
472C4×Dic11—22no—
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—22no—
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#2465D1111yescharacteristic
514#2462—111no—
515#2462—111no—
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×C11—21no—
532C23×C11—21no—
533C23×C11—21no—
534C23×C11—21no—
535C23×C11—21no—
536C23×C11—21no—
537C23×C11C22×Q812yes—
538C23×C11C2511yescharacteristic
539Q8×C11—28no—
540Q8×C11—44no—
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—44no—
576C2×C4×C11C22×Q812yes—
577C2×C4×C11C22×Q812yes—
578C2×C4×C11C2×#4112yes—
579C2×C4×C11C2×#4112yes—
580C2×C4×C11C2×#4112yes—
581C2×C4×C11C2×#4112yes—
582C2×C4×C11C2×#4112yes—
583C2×C4×C11C2×#4112yes—
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—28no—
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×Dic11—21no—
622C2×Dic11—21no—
623C2×Dic11—44no—
624C2×Dic11C22×Q812yes—
625C2×Dic11C22×Q812yes—
626C2×Dic11C22×Q812yes—
627C2×Dic11C22×Q812yes—
628C2×Dic11C2×#4112yes—
629C2×Dic11C2×#4112yes—
630C2×Dic11C2×#4112yes—
631C2×Dic11C2×#4112yes—
632C2×Dic11C2×#4112yes—
633C2×Dic11C2×#4112yes—
634Dic22—44no—
635Dic22—44no—
636C2×#125—111no—
637C2×#125—111no—
638C2×C22⋊Q8—111no—
639C2×C22⋊Q8C2×D1111yescharacteristic
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#398—111no—
664#398—111no—
665#396—111no—
666#396—111no—
667#396—111no—
668#396C2×D1111yescharacteristic
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#393C2×D1111yescharacteristic
681#391—111no—
682#391—111no—
683#391—111no—
684#391—111no—
685#391—111no—
686#391—111no—
687#391—111no—
688#391C2×D1111yescharacteristic
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#389—111no—
700#389C2×D1111yescharacteristic
701#388—111no—
702#388—111no—
703#388—111no—
704#388—111no—
705#388—111no—
706#388—111no—
707#388C2×D1111yescharacteristic
708#388C2×D1111yescharacteristic
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#387—111no—
736#387—111no—
737#387—111no—
738#387C2×D1111yescharacteristic
739#387C2×D1111yescharacteristic
740#387C2×D1111yescharacteristic
741#385—111no—
742#385—111no—
743#385—111no—
744#385C2×D1111yescharacteristic
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⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
783#376—111no—
784#376—111no—
785#376—111no—
786#376—111no—
787C43—111no—
788C43—111no—
789C43—111no—
790C43—111no—
791C22×C11—22no—
792C22×C11—22no—
793C22×C11—22no—
794C22×C11—41no—
795C22×C11—41no—
796C22×C11—41no—
797C22×C11—41no—
798C22×C11C23×Q811yescharacteristic
799C22×C11C22×#4111yescharacteristic
800C22×C11C22×#4111yescharacteristic
801C22×C11C22×#4111yescharacteristic
802C22×C11C22×#4111yescharacteristic
803C22×C11#58511yescharacteristic
804C22×C11#58511yescharacteristic
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—41no—
814C4×C11—41no—
815C4×C11—41no—
816C4×C11—41no—
817C4×C11—41no—
818C4×C11—41no—
819Dic11—22no—
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×Q8C22×D1111yescharacteristic
838C22×Q8C22×D1111yescharacteristic
839C23×C4—111no—
840C23×C4—111no—
841C23×C4C22×D1111yescharacteristic
842#125—224no—
843#125—224no—
844C22⋊Q8—24no—
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⋊C4—111no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
909C2×C22⋊C4C22×D1111yescharacteristic
910C2×C22⋊C4C22×D1111yescharacteristic
911C2×C22⋊C4C22×D1111yescharacteristic
912C2×C22⋊C4C22×D1111yescharacteristic
913C2×C22⋊C4C22×D1111yescharacteristic
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—111no—
942C2×C42—224no—
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#95—111no—
990#95—111no—
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×C11—42no—
1004C2×C11C2×#53311yescharacteristic
1005C2×C11#344411yescharacteristic
1006C2×C11#345511yescharacteristic
1007C2×C11#347511yescharacteristic
1008C2×C11#347511yescharacteristic
1009C2×C11Q8×#4111yescharacteristic
1010C2×C11Q8×#4111yescharacteristic
1011C24C23×D1111yescharacteristic
1012C2×Q8—22no—
1013C2×Q8—22no—
1014C2×Q8—22no—
1015C2×Q8—22no—
1016C2×Q8—22no—
1017C2×Q8—41no—
1018C2×Q8—222no—
1019C2×Q8—222no—
1020C2×Q8—222no—
1021C2×Q8—441no—
1022C2×Q8—441no—
1023C2×Q8—441no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—41no—
1027C22×C4—111no—
1028C22×C4—114no—
1029C22×C4—111no—
1030C22×C4—111no—
1031C22×C4—111no—
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—111no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—111no—
1044C22×C4—222no—
1045C22×C4—222no—
1046C22×C4—222no—
1047C22×C4—222no—
1048C22×C4—441no—
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—41no—
1071C4⋊C4—41no—
1072C4⋊C4—114no—
1073C4⋊C4—114no—
1074C4⋊C4—114no—
1075C4⋊C4—222no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
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—222no—
1098C4⋊C4—222no—
1099C4⋊C4—222no—
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—441no—
1110C4⋊C4#434114yes—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—41no—
1116C22⋊C4—114no—
1117C22⋊C4—222no—
1118C22⋊C4—222no—
1119C22⋊C4—441no—
1120C22⋊C4—441no—
1121C22⋊C4—441no—
1122C22⋊C4Q8×D1114yes—
1123C42—22no—
1124C42—22no—
1125C42—22no—
1126C42—41no—
1127C42—114no—
1128C42—114no—
1129C42—114no—
1130C42—114no—
1131C42—222no—
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—222no—
1148C42—441no—
1149C42—441no—
1150C42—441no—
1151C42—441no—
1152C42—441no—
1153C42—441no—
1154C42—441no—
1155C11#3488211yescharacteristic, complemented, Sylow
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23C2×Q8×D1112yes—
1163C23C24×D1111yescharacteristic
1164Q8—28no—
1165Q8—44no—
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—44no—
1203C2×C4—112no—
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—221no—
1251C2×C4—221no—
1252C2×C4—444no—
1253C2×C4C2×#434112yes—
1254C2×C4C2×#434112yes—
1255C2×C4C2×#434112yes—
1256C2×C4C2×Q8×D1112yes—
1257C2×C4C2×Q8×D1112yes—
1258C2×C4#41×D1112yes—
1259C2×C4#41×D1112yes—
1260C2×C4#41×D1112yes—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22C22×#434111yescharacteristic
1269C22C22×Q8×D1111yescharacteristic
1270C22C2×#41×D1111yescharacteristic
1271C22C2×#41×D1111yescharacteristic
1272C22C2×#41×D1111yescharacteristic
1273C22#1062345511yescharacteristic
1274C22#1062345711yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—114no—
1290C4—222no—
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—42no—
1306C2D11×#53311yescharacteristic
1307C2#1308190811yescharacteristic
1308C2#1308200311yescharacteristic
1309C2#1308216711yescharacteristic
1310C2#1308217711yescharacteristic
1311C2Q8×#434111yescharacteristic
1312C2#1308219511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2465C2
prime radicalC24×C11C24
hypercenter#2465D11
hypocenterC11#34882
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2465

Complements

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

NH ≅ G/Ntype
1. #13074025C2semidirect
2. #13074024C2semidirect
3. #13074018C2semidirect
4. #13074017C2semidirect
11. #13073307C2semidirect
12. #13073306C2semidirect
14. #13072593C2semidirect
15. #13072592C2semidirect
16. #13071906C2semidirect
17. #13071906C2semidirect
20. #13071175C2semidirect
21. #13071173C2semidirect
26. #13071091C2semidirect
27. #13071089C2semidirect
28. #13071089C2semidirect
29. C4×Q8×Dic11C2semidirect
298. #66930Q8semidirect
1155. C11#34882semidirect

Maximal subgroups

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

subgroupindex
#130740252
#130740242
#130740182
#130740172
#130738972
#130738962
#130736992
#130736982
#130733352
#130733342
#130733072
#130733062
#130726302
#130725932
#130725922
#130719062
#130718912
#130718832
#130711752
#130711732
C22⋊Q8×Dic112
#130711482
#130711102
#130710912
#130710892
C4×Q8×Dic112
C4×#669302
C11×#24652
#3488211