Finite Group Databasebeta

← #14960533

Subgroups — #14960533

Order 2816.

3018 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623123C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3#13076910C211yesmaximal, characteristic, complemented
4#13076906C211yesmaximal, characteristic, complemented
5#13075058C212yesmaximal, complemented
6#13075054C212yesmaximal, complemented
7#13075028C212yesmaximal, complemented
8#13075024C212yesmaximal, complemented
9#13074888C212yesmaximal, complemented
10#13074884C212yesmaximal, complemented
11#13074858C212yesmaximal, complemented
12#13074854C212yesmaximal, complemented
13#13074328C211yesmaximal, characteristic, complemented
14#13072900C211yesmaximal, characteristic, complemented
15#13072887C211yesmaximal, characteristic, complemented
16#13072014C211yesmaximal, characteristic, complemented
17#13072008C211yesmaximal, characteristic, complemented
18#13071992C211yesmaximal, characteristic, complemented
19#13071986C211yesmaximal, characteristic, complemented
20#13071948C211yesmaximal, characteristic, complemented
21#13071932C211yesmaximal, characteristic, complemented
22#13071192C211yesmaximal, characteristic, complemented
23C11×#2613C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic
28C22×#4341C2211yescharacteristic
29C2×C11×#123C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C2×C11×#120C2211yescharacteristic
32C2×#67006C2211yescharacteristic
33C2×#67006C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66993C2211yescharacteristic, complemented
36C2×#66993C2211yescharacteristic, complemented
37C2×#66992—28no—
38C2×#66992C2212yes—
39C2×#66992C2212yes—
40C2×#66992C2212yes—
41C2×#66992C2212yes—
42C2×#66992C2211yescharacteristic, complemented
43C2×#66992C2211yescharacteristic, complemented
44C2×#66991C2212yescomplemented
45C2×#66990C2211yescharacteristic
46C2×#66988C2212yescomplemented
47C2×#66982C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50#10623123—28no—
51C2×#66939C2212yescomplemented
52C2×#66938C2211yescharacteristic, complemented
53C2×#66938C2211yescharacteristic, complemented
54C2×#66937C2211yescharacteristic, complemented
55C2×#66937C2211yescharacteristic, complemented
56C2×#66937C2212yescomplemented
57C2×#66935C2211yescharacteristic
58C2×C22⋊C4×D11C2211yescharacteristic
59C2×C22⋊C4×D11C2211yescharacteristic
60C2×#66930C2211yescharacteristic
61C11×#394C2212yescomplemented
62C11×#394C2212yescomplemented
63C11×#392C2212yescomplemented
64C11×#392C2212yescomplemented
65C11×#381C2211yescharacteristic
66C11×#379C2211yescharacteristic
67C11×#379C2211yescharacteristic
68#10622860C2211yescharacteristic
69#10622860C2211yescharacteristic
70#10622836C2212yescomplemented
71#10622836C2212yescomplemented
72#10622836C2212yescomplemented
73#10622836C2212yescomplemented
74#10622835C2212yescomplemented
75#10622835C2212yescomplemented
76#10622833C2211yescharacteristic
77#10622833C2211yescharacteristic
78#10622833C2212yescomplemented
79#10622833C2212yescomplemented
80#10622824C2211yescharacteristic
81#10622606C2212yescomplemented
82#10622602C2212yescomplemented
83#10622600C2212yescomplemented
84#10622592C2212yescomplemented
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622573C2212yescomplemented
88#10622572C2212yescomplemented
89#10622572C2212yescomplemented
90#10622571C2211yescharacteristic
91#10622571C2211yescharacteristic
92#10622571C2212yescomplemented
93#10622569C2212yescomplemented
94#10622569C2212yescomplemented
95#10622569C2212yescomplemented
96#10622569C2212yescomplemented
97#10622569C2212yescomplemented
98#10622569C2212yescomplemented
99#10622569C2212yescomplemented
100#10622569C2212yescomplemented
101#10622565C2212yescomplemented
102#10622564C2212yescomplemented
103#10622563C2211yescharacteristic
104#10622563C2211yescharacteristic
105#10622563C2212yescomplemented
106#10622562C2212yescomplemented
107#10622560C2212yescomplemented
108#10622559C2211yescharacteristic
109#10622559C2211yescharacteristic
110#10622559C2212yescomplemented
111#10622559C2212yescomplemented
112#10622558C2212yescomplemented
113#10622556C2211yescharacteristic
114#10622556C2211yescharacteristic
115#10622556C2212yescomplemented
116#10622556C2212yescomplemented
117#10622288C2212yescomplemented
118#10622285C2212yescomplemented
119#10622280C2212yescomplemented
120#10622278C2212yescomplemented
121#10622271C2212yescomplemented
122#10622270C2212yescomplemented
123#10622267C2212yescomplemented
124#10622265C2212yescomplemented
125C25×C11C2311yescharacteristic
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11—24no—
129C22×D4×C11—42no—
130C22×D4×C11—42no—
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2312yes—
134C22×D4×C11C2312yes—
135C22×D4×C11C2311yescharacteristic
136C22×D4×C11C2312yes—
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—24no—
139C22×C22⋊D11—44no—
140C22×C22⋊D11—42no—
141C22×C22⋊D11—42no—
142C22×C22⋊D11D418yescomplemented
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2312yes—
146C22×C22⋊D11C2311yescharacteristic
147C22×C22⋊D11C2311yescharacteristic
148C22×C22⋊D11C2311yescharacteristic
149C22×C22⋊D11C2311yescharacteristic
150C22×C22⋊D11C2311yescharacteristic
151C22×C22⋊D11C2312yes—
152C22×C22⋊D11C2311yescharacteristic
153C22×C22⋊D11C2311yescharacteristic
154C22×C22⋊D11C2311yescharacteristic
155C22×C22⋊D11C2311yescharacteristic
156C23×Dic11—24no—
157C23×Dic11—44no—
158C23×Dic11C2311yescharacteristic
159C23×Dic11C2312yes—
160C23×Dic11C2312yes—
161C23×Dic11C2311yescharacteristic
162C23×Dic11C2311yescharacteristic
163C23×Dic11C2311yescharacteristic
164C2×#4341—24no—
165C2×#4341—42no—
166C2×#4341—42no—
167C22×D44C2311yescharacteristic
168C22×D44C2311yescharacteristic
169C22×C4×D11C2311yescharacteristic
170C22×C4×D11C2312yes—
171C22×C4×D11C2312yes—
172C22×Dic22C2311yescharacteristic
173C11×#123—42no—
174C11×#120—24no—
175C11×#120—42no—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188#67006—24no—
189#67006—42no—
190C2×C22⋊Dic11—24no—
191C2×C22⋊Dic11C2311yescharacteristic
192C2×C22⋊Dic11C2311yescharacteristic
193C2×C22⋊Dic11C2311yescharacteristic
194C2×C22⋊Dic11C2311yescharacteristic
195C2×C22⋊Dic11C2311yescharacteristic
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203C2×C22⋊Dic11C2312yes—
204C2×C22⋊Dic11C2312yes—
205#66993—24no—
206#66993—24no—
207#66992—28no—
208#66992—28no—
209#66992—28no—
210#66992—28no—
211#66992—24no—
212#66992—24no—
213#66991—44no—
214#66990—24no—
215#66988—44no—
216#66982—42no—
217C2×(C2×D11)⋊C4—24no—
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×(C2×D11)⋊C4C2311yescharacteristic
221C2×(C2×D11)⋊C4C2311yescharacteristic
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224C2×(C2×D11)⋊C4C2312yes—
225C2×(C2×D11)⋊C4C2312yes—
226C2×(C2×D11)⋊C4C2312yes—
227C2×(C2×D11)⋊C4C2312yes—
228C2×(C2×D11)⋊C4C2312yes—
229C2×C4⋊Dic11C2312yes—
230C2×C4⋊Dic11C2312yes—
231C2×Dic11⋊C4—24no—
232C2×Dic11⋊C4C2311yescharacteristic
233C2×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2312yes—
235C2×Dic11⋊C4C2312yes—
236C2×Dic11⋊C4C2312yes—
237C2×Dic11⋊C4C2312yes—
238C2×Dic11⋊C4C2312yes—
239C2×C4×Dic11C2311yescharacteristic
240C2×C4×Dic11C2311yescharacteristic
241#66939—44no—
242#66938—24no—
243#66938—24no—
244#66937—24no—
245#66937—24no—
246#66937—44no—
247#66935—24no—
248C22⋊C4×D11—42no—
249C22⋊C4×D11—42no—
250#66930—24no—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267#36704—111nomaximal, Sylow
268C24×C11—22no—
269C24×C11—22no—
270C24×C11—22no—
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—42no—
274C24×C11—42no—
275C24×C11—42no—
276C24×C11—42no—
277C24×C11C2×D414yes—
278C24×C11C2412yes—
279C24×C11C2411yescharacteristic
280C24×C11C2411yescharacteristic
281C24×C11C2411yescharacteristic
282C24×C11C2411yescharacteristic
283C23×D11—22no—
284C23×D11—22no—
285C23×D11—42no—
286C23×D11—42no—
287C23×D11C2×D414yes—
288C23×D11C2411yescharacteristic
289C23×D11C2411yescharacteristic
290C23×D11C2411yescharacteristic
291C2×D4×C11—22no—
292C2×D4×C11—24no—
293C2×D4×C11—24no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—22no—
297C2×D4×C11—22no—
298C2×D4×C11—42no—
299C2×D4×C11—42no—
300C2×D4×C11—42no—
301C2×D4×C11—42no—
302C2×D4×C11—42no—
303C2×D4×C11—42no—
304C2×D4×C11—42no—
305C2×D4×C11—42no—
306C2×D4×C11—42no—
307C2×D4×C11—416no—
308C22×C4×C11—22no—
309C22×C4×C11—22no—
310C22×C4×C11—22no—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2412yes—
313C22×C4×C11C2412yes—
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2412yes—
316C22×C4×C11C2411yescharacteristic
317C2×C22⋊D11—22no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—22no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—22no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—24no—
326C2×C22⋊D11—24no—
327C2×C22⋊D11—22no—
328C2×C22⋊D11—22no—
329C2×C22⋊D11—41no—
330C2×C22⋊D11—41no—
331C2×C22⋊D11—416no—
332C2×C22⋊D11—41no—
333C2×C22⋊D11—41no—
334C2×C22⋊D11—41no—
335C2×C22⋊D11—41no—
336C2×C22⋊D11—41no—
337C2×C22⋊D11—41no—
338C2×C22⋊D11—41no—
339C2×C22⋊D11—41no—
340C2×C22⋊D11—42no—
341C2×C22⋊D11—42no—
342C2×C22⋊D11—42no—
343C2×C22⋊D11—42no—
344C2×C22⋊D11—42no—
345C2×C22⋊D11—42no—
346C2×C22⋊D11—42no—
347C2×C22⋊D11—42no—
348C2×C22⋊D11—42no—
349C2×C22⋊D11—416no—
350C2×C22⋊D11C2×D414yes—
351C2×C22⋊D11C2×D414yes—
352C2×C22⋊D11C2×D414yes—
353C2×C22⋊D11C2×D414yes—
354C22×Dic11—24no—
355C22×Dic11—22no—
356C22×Dic11—24no—
357C22×Dic11—24no—
358C22×Dic11—22no—
359C22×Dic11—22no—
360C22×Dic11—24no—
361C22×Dic11—24no—
362C22×Dic11—22no—
363C22×Dic11—22no—
364C22×Dic11—41no—
365C22×Dic11—41no—
366C22×Dic11—42no—
367C22×Dic11—42no—
368C22×Dic11—42no—
369C22×Dic11—416no—
370C22×Dic11C2×D414yes—
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2412yes—
373C22×Dic11C2412yes—
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2412yes—
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2412yes—
380#4341—416no—
381C2×D44—22no—
382C2×D44—22no—
383C2×D44—42no—
384C2×D44—42no—
385C2×C4×D11—22no—
386C2×C4×D11—41no—
387C2×C4×D11—41no—
388C2×C4×D11—42no—
389C2×C4×D11—42no—
390C2×C4×D11—42no—
391C2×C4×D11—42no—
392C2×C4×D11—42no—
393C2×C4×D11—42no—
394C2×Dic22—22no—
395C2×Dic22—41no—
396C2×Dic22—41no—
397C11×C4⋊C4—42no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—42no—
404C11×C22⋊C4—42no—
405C11×C22⋊C4—42no—
406C11×C22⋊C4—42no—
407C11×C22⋊C4—42no—
408C11×C22⋊C4—42no—
409C22⋊Dic11—24no—
410C22⋊Dic11—24no—
411C22⋊Dic11—24no—
412C22⋊Dic11—22no—
413C22⋊Dic11—22no—
414C22⋊Dic11—22no—
415C22⋊Dic11—22no—
416C22⋊Dic11—22no—
417C22⋊Dic11—42no—
418C22⋊Dic11—42no—
419C22⋊Dic11—42no—
420C22⋊Dic11—42no—
421C22⋊Dic11—42no—
422C22⋊Dic11—42no—
423(C2×D11)⋊C4—24no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—22no—
428(C2×D11)⋊C4—24no—
429(C2×D11)⋊C4—24no—
430(C2×D11)⋊C4—42no—
431(C2×D11)⋊C4—42no—
432(C2×D11)⋊C4—42no—
433(C2×D11)⋊C4—42no—
434C4⋊Dic11—24no—
435C4⋊Dic11—42no—
436Dic11⋊C4—22no—
437Dic11⋊C4—22no—
438Dic11⋊C4—24no—
439Dic11⋊C4—24no—
440Dic11⋊C4—24no—
441Dic11⋊C4—42no—
442Dic11⋊C4—42no—
443C4×Dic11—22no—
444C4×Dic11—22no—
445C2×#535—111no—
446C22×#121—111no—
447#2849—111no—
448#2849—111no—
449#2688—112no—
450#2688—112no—
451#2686—112no—
452#2686—112no—
453#2673—112no—
454#2673—112no—
455#2671—112no—
456#2671—112no—
457#2613—111no—
458#2613D1111yescharacteristic, complemented
459#2484—111no—
460#2482—111no—
461#2412—111no—
462#2412—111no—
463#2410—111no—
464#2410—111no—
465#2406—111no—
466#2404—111no—
467#2308—111no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—28no—
471C23×C11—22no—
472C23×C11—22no—
473C23×C11—21no—
474C23×C11—21no—
475C23×C11—21no—
476C23×C11—21no—
477C23×C11—22no—
478C23×C11—22no—
479C23×C11—22no—
480C23×C11—21no—
481C23×C11—22no—
482C23×C11—22no—
483C23×C11—22no—
484C23×C11—21no—
485C23×C11—22no—
486C23×C11—22no—
487C23×C11—21no—
488C23×C11—22no—
489C23×C11—22no—
490C23×C11—22no—
491C23×C11—44no—
492C23×C11—44no—
493C23×C11—48no—
494C23×C11—48no—
495C23×C11—44no—
496C23×C11—44no—
497C23×C11—44no—
498C23×C11—84no—
499C23×C11—84no—
500C23×C11C22×D412yes—
501C23×C11C22×D412yes—
502C23×C11C22×D412yes—
503C23×C11H(5,𝔽2)12yes—
504C23×C11H(5,𝔽2)12yes—
505C23×C11C2511yescharacteristic
506C22×D11—21no—
507C22×D11—21no—
508C22×D11—21no—
509C22×D11—21no—
510C22×D11—22no—
511C22×D11—22no—
512C22×D11—22no—
513C22×D11—22no—
514C22×D11—28no—
515C22×D11—21no—
516C22×D11—22no—
517C22×D11—21no—
518C22×D11—21no—
519C22×D11—22no—
520C22×D11—44no—
521C22×D11—44no—
522C22×D11—84no—
523C22×D11—84no—
524C22×D11C22×D412yes—
525C22×D11C22×D412yes—
526D4×C11—48no—
527D4×C11—48no—
528D4×C11—44no—
529D4×C11—82no—
530D4×C11—82no—
531D4×C11—84no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—22no—
544C2×C4×C11—21no—
545C2×C4×C11—22no—
546C2×C4×C11—22no—
547C2×C4×C11—22no—
548C2×C4×C11—44no—
549C22⋊D11—44no—
550C22⋊D11—44no—
551C22⋊D11—44no—
552C22⋊D11—44no—
553C22⋊D11—48no—
554C22⋊D11—48no—
555C22⋊D11—44no—
556C22⋊D11—44no—
557C22⋊D11—82no—
558C22⋊D11—82no—
559C22⋊D11—82no—
560C22⋊D11—82no—
561C22⋊D11—84no—
562C2×Dic11—28no—
563C2×Dic11—28no—
564C2×Dic11—22no—
565C2×Dic11—21no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—22no—
570C2×Dic11—21no—
571C2×Dic11—21no—
572C2×Dic11—21no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—21no—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
579C2×Dic11—22no—
580C2×Dic11—22no—
581C2×Dic11—22no—
582C2×Dic11—21no—
583C2×Dic11—22no—
584C2×Dic11—22no—
585C2×Dic11—22no—
586C2×Dic11—48no—
587C2×Dic11—48no—
588C2×Dic11—44no—
589C2×Dic11—44no—
590C2×Dic11C22×D412yes—
591C2×Dic11C22×D412yes—
592C2×Dic11H(5,𝔽2)14yes—
593D44—82no—
594D44—82no—
595C4×D11—44no—
596C4×D11—84no—
597C4×D11—84no—
598Dic22—44no—
599C22×#41—111no—
600C23×D4—111no—
601C23×D4—111no—
602C23×D4C2×D1111yescharacteristic
603C24×C4—111no—
604#535—228no—
605C2×#127—111no—
606C2×#127—111no—
607C2×#124—111no—
608C2×#124—111no—
609C2×#123—112no—
610C2×#123—111no—
611C2×#123—112no—
612C2×#123C2×D1111yescharacteristic
613C2×#121—112no—
614C2×#121—112no—
615C2×#121—112no—
616C2×#121—112no—
617C2×#121—111no—
618C2×#121—111no—
619C2×#121—112no—
620C2×#121—111no—
621C2×#121—111no—
622C2×#121—112no—
623C2×#121—228no—
624C2×#120—111no—
625C2×#120—111no—
626C2×#120—111no—
627C2×#120—111no—
628C2×#120C2×D1111yescharacteristic
629C2×#120C2×D1111yescharacteristic
630C2×#117—111no—
631C22×C4⋊C4—111no—
632C22×C22⋊C4—111no—
633C22×C22⋊C4—111no—
634C22×C22⋊C4—111no—
635C22×C22⋊C4—111no—
636#400—112no—
637#399—112no—
638#398—112no—
639#397—112no—
640#397—112no—
641#397—112no—
642#395—112no—
643#394—112no—
644#394—112no—
645#394—112no—
646#394—112no—
647#394—112no—
648#394—112no—
649#394—112no—
650#394C2×D1112yescomplemented
651#394C2×D1112yescomplemented
652#393—112no—
653#392—112no—
654#392—112no—
655#392—112no—
656#392—112no—
657#392—112no—
658#392C2×D1112yescomplemented
659#392C2×D1112yescomplemented
660#388—112no—
661#388—112no—
662#387—112no—
663#387—112no—
664#386—111no—
665#386—111no—
666#386—112no—
667#386—112no—
668#386—112no—
669#386—112no—
670#386—112no—
671#386—112no—
672#386—111no—
673#386—111no—
674#386—112no—
675#386—112no—
676#386—112no—
677#386—112no—
678#386—112no—
679#386—112no—
680#385—112no—
681#385—111no—
682#385—111no—
683#385—112no—
684#385—111no—
685#385—111no—
686#385—112no—
687#385—112no—
688#381—111no—
689#381—111no—
690#381—111no—
691#381—112no—
692#381—112no—
693#381C2×D1111yescharacteristic
694#380—112no—
695#380—112no—
696#379—111no—
697#379—111no—
698#379C2×D1111yescharacteristic
699#379C2×D1111yescharacteristic
700C22×C11—22no—
701C22×C11—22no—
702C22×C11—24no—
703C22×C11—24no—
704C22×C11—22no—
705C22×C11—22no—
706C22×C11—22no—
707C22×C11—22no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—416no—
711C22×C11—42no—
712C22×C11—42no—
713C22×C11—42no—
714C22×C11—42no—
715C22×C11—42no—
716C22×C11—41no—
717C22×C11—41no—
718C22×C11—42no—
719C22×C11—41no—
720C22×C11—42no—
721C22×C11—42no—
722C22×C11—42no—
723C22×C11—42no—
724C22×C11—42no—
725C22×C11—42no—
726C22×C11—42no—
727C22×C11—88no—
728C22×C11#53414yes—
729C22×C11C23×D411yescharacteristic
730C22×C11C2×H(5,𝔽2)11yescharacteristic
731C22×C11C2×H(5,𝔽2)11yescharacteristic
732C22×C11C2×H(5,𝔽2)12yes—
733C22×C11#58512yes—
734C2×D11—22no—
735C2×D11—22no—
736C2×D11—22no—
737C2×D11—22no—
738C2×D11—22no—
739C2×D11—22no—
740C2×D11—42no—
741C2×D11—42no—
742C2×D11—42no—
743C2×D11—42no—
744C2×D11—41no—
745C2×D11—41no—
746C2×D11—41no—
747C2×D11—42no—
748C2×D11—42no—
749C2×D11—88no—
750C4×C11—42no—
751C4×C11—41no—
752C4×C11—41no—
753C4×C11—41no—
754C4×C11—42no—
755C4×C11—42no—
756Dic11—22no—
757Dic11—22no—
758Dic11—24no—
759Dic11—41no—
760Dic11—42no—
761Dic11—41no—
762Dic11—41no—
763Dic11—42no—
764Dic11—42no—
765C25—111no—
766C25C22×D1111yescharacteristic
767C25C22×D1111yescharacteristic
768C2×#41—224no—
769C2×#41—442no—
770C2×#41—442no—
771C22×Q8—111no—
772C22×D4—24no—
773C22×D4—42no—
774C22×D4—42no—
775C22×D4—118no—
776C22×D4—111no—
777C22×D4—111no—
778C22×D4—111no—
779C22×D4—111no—
780C22×D4—111no—
781C22×D4—112no—
782C22×D4—112no—
783C22×D4—111no—
784C22×D4—111no—
785C22×D4—111no—
786C22×D4—111no—
787C22×D4—111no—
788C22×D4—112no—
789C22×D4—111no—
790C22×D4—111no—
791C22×D4—224no—
792C22×D4—444no—
793C22×D4—442no—
794C22×D4—442no—
795C22×D4C22×D1111yescharacteristic
796C22×D4C22×D1111yescharacteristic
797C22×D4C22×D1111yescharacteristic
798C22×D4C22×D1112yes—
799C22×D4C22×D1112yes—
800C22×D4C22×D1112yes—
801C23×C4—111no—
802C23×C4—111no—
803C23×C4—112no—
804C23×C4—112no—
805C23×C4—111no—
806C23×C4—111no—
807C23×C4—111no—
808C23×C4—112no—
809C23×C4—112no—
810C23×C4—224no—
811C23×C4—444no—
812C23×C4C22×D1111yescharacteristic
813#127—224no—
814#127—224no—
815#124—224no—
816#124—224no—
817#123—42no—
818#123—444no—
819#123—444no—
820#123—442no—
821#121—224no—
822#121—224no—
823#121—228no—
824#121—228no—
825#121—228no—
826#121—228no—
827#121—224no—
828#121—224no—
829#121—444no—
830#121—444no—
831#120—24no—
832#120—42no—
833#120—224no—
834#120—224no—
835#120—224no—
836#120—442no—
837#117—224no—
838C2×C4⋊C4—112no—
839C2×C4⋊C4—112no—
840C2×C4⋊C4—111no—
841C2×C4⋊C4—111no—
842C2×C4⋊C4—112no—
843C2×C4⋊C4—112no—
844C2×C4⋊C4—112no—
845C2×C4⋊C4—112no—
846C2×C4⋊C4—112no—
847C2×C4⋊C4—224no—
848C2×C4⋊C4C22×D1112yes—
849C2×C22⋊C4—111no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—112no—
852C2×C22⋊C4—111no—
853C2×C22⋊C4—111no—
854C2×C22⋊C4—111no—
855C2×C22⋊C4—111no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—111no—
860C2×C22⋊C4—111no—
861C2×C22⋊C4—111no—
862C2×C22⋊C4—111no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—112no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—112no—
872C2×C22⋊C4—112no—
873C2×C22⋊C4—112no—
874C2×C22⋊C4—224no—
875C2×C22⋊C4—224no—
876C2×C22⋊C4—442no—
877C2×C22⋊C4—442no—
878C2×C22⋊C4C22×D1111yescharacteristic
879C2×C22⋊C4C22×D1111yescharacteristic
880C2×C22⋊C4C22×D1111yescharacteristic
881C2×C22⋊C4C22×D1111yescharacteristic
882C2×C22⋊C4C22×D1111yescharacteristic
883C2×C22⋊C4C22×D1112yes—
884C2×C22⋊C4C22×D1112yes—
885C2×C22⋊C4C22×D1112yes—
886C2×C22⋊C4C22×D1112yes—
887C2×C22⋊C4C22×D1112yes—
888C2×C22⋊C4C22×D1112yes—
889C2×C42—111no—
890C2×C42—111no—
891#95—112no—
892#95—112no—
893#95—112no—
894#95—112no—
895#95—112no—
896#95—112no—
897#95—112no—
898#95—112no—
899#95—112no—
900#95—112no—
901#95—112no—
902#95—112no—
903#95—112no—
904#95—112no—
905#95C22×D1112yes—
906#95C22×D1112yes—
907C2×C11—24no—
908C2×C11—42no—
909C2×C11—42no—
910C2×C11—81no—
911C2×C11—82no—
912C2×C11C2×#53411yescharacteristic
913C2×C11#348411yescharacteristic
914C2×C11#348511yescharacteristic
915C2×C11#354212yes—
916C2×C11#354212yes—
917D11—42no—
918D11—42no—
919D11—81no—
920C24—22no—
921C24—22no—
922C24—22no—
923C24—22no—
924C24—22no—
925C24—42no—
926C24—42no—
927C24—42no—
928C24—42no—
929C24—111no—
930C24—111no—
931C24—114no—
932C24—111no—
933C24—222no—
934C24—222no—
935C24—442no—
936C24—442no—
937C24D4×D1114yes—
938C24C23×D1112yes—
939C24C23×D1111yescharacteristic
940C24C23×D1111yescharacteristic
941C24C23×D1111yescharacteristic
942C24C23×D1111yescharacteristic
943#41—4416no—
944C2×Q8—222no—
945C2×Q8—441no—
946C2×Q8—441no—
947C2×D4—22no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4—22no—
953C2×D4—22no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—416no—
964C2×D4—114no—
965C2×D4—114no—
966C2×D4—114no—
967C2×D4—114no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—224no—
971C2×D4—224no—
972C2×D4—222no—
973C2×D4—224no—
974C2×D4—224no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—222no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—222no—
982C2×D4—442no—
983C2×D4—442no—
984C2×D4—4416no—
985C2×D4—441no—
986C2×D4—441no—
987C2×D4—441no—
988C2×D4—441no—
989C2×D4—441no—
990C2×D4—441no—
991C2×D4—441no—
992C2×D4—441no—
993C2×D4—442no—
994C2×D4—442no—
995C2×D4—441no—
996C2×D4—441no—
997C2×D4—4416no—
998C2×D4—442no—
999C2×D4—442no—
1000C2×D4—442no—
1001C2×D4—442no—
1002C2×D4—442no—
1003C2×D4—442no—
1004C2×D4—442no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—22no—
1008C22×C4—114no—
1009C22×C4—111no—
1010C22×C4—111no—
1011C22×C4—112no—
1012C22×C4—111no—
1013C22×C4—112no—
1014C22×C4—112no—
1015C22×C4—112no—
1016C22×C4—111no—
1017C22×C4—111no—
1018C22×C4—222no—
1019C22×C4—224no—
1020C22×C4—222no—
1021C22×C4—224no—
1022C22×C4—224no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—222no—
1027C22×C4—224no—
1028C22×C4—224no—
1029C22×C4—441no—
1030C22×C4—441no—
1031C22×C4—442no—
1032C22×C4—442no—
1033C22×C4—442no—
1034C22×C4—442no—
1035C22×C4—442no—
1036C22×C4—442no—
1037C22×C4—442no—
1038C22×C4—442no—
1039C22×C4—442no—
1040C22×C4—441no—
1041C22×C4—441no—
1042C22×C4—4416no—
1043C22×C4C23×D1111yescharacteristic
1044C22×C4C23×D1112yes—
1045C22×C4C23×D1112yes—
1046C22×C4C23×D1111yescharacteristic
1047C22×C4C23×D1112yes—
1048C22×C4C23×D1111yescharacteristic
1049C4⋊C4—42no—
1050C4⋊C4—224no—
1051C4⋊C4—224no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—224no—
1055C4⋊C4—224no—
1056C4⋊C4—442no—
1057C4⋊C4—442no—
1058C4⋊C4—442no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—224no—
1071C22⋊C4—224no—
1072C22⋊C4—224no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—222no—
1077C22⋊C4—224no—
1078C22⋊C4—224no—
1079C22⋊C4—224no—
1080C22⋊C4—222no—
1081C22⋊C4—222no—
1082C22⋊C4—222no—
1083C22⋊C4—222no—
1084C22⋊C4—222no—
1085C22⋊C4—442no—
1086C22⋊C4—442no—
1087C22⋊C4—442no—
1088C22⋊C4—442no—
1089C22⋊C4—442no—
1090C22⋊C4—442no—
1091C22⋊C4—442no—
1092C22⋊C4—442no—
1093C22⋊C4—442no—
1094C22⋊C4—442no—
1095C42—222no—
1096C42—222no—
1097C11#3670411yescharacteristic, complemented, Sylow
1098C23—22no—
1099C23—22no—
1100C23—28no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—21no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—44no—
1122C23—44no—
1123C23—48no—
1124C23—48no—
1125C23—44no—
1126C23—44no—
1127C23—44no—
1128C23—84no—
1129C23—84no—
1130C23—112no—
1131C23—112no—
1132C23—221no—
1133C23—221no—
1134C23—221no—
1135C23—221no—
1136C23—222no—
1137C23—222no—
1138C23—222no—
1139C23—222no—
1140C23—228no—
1141C23—221no—
1142C23—221no—
1143C23—221no—
1144C23—222no—
1145C23—222no—
1146C23—444no—
1147C23—444no—
1148C23—884no—
1149C23—884no—
1150C23C2×D4×D1112yes—
1151C23C2×D4×D1112yes—
1152C23C2×D4×D1112yes—
1153C23#6703712yes—
1154C23#6703712yes—
1155C23C24×D1111yescharacteristic
1156Q8—444no—
1157D4—48no—
1158D4—48no—
1159D4—44no—
1160D4—82no—
1161D4—82no—
1162D4—84no—
1163D4—444no—
1164D4—444no—
1165D4—444no—
1166D4—444no—
1167D4—448no—
1168D4—448no—
1169D4—444no—
1170D4—444no—
1171D4—882no—
1172D4—882no—
1173D4—882no—
1174D4—882no—
1175D4—882no—
1176D4—882no—
1177D4—884no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—44no—
1195C2×C4—112no—
1196C2×C4—112no—
1197C2×C4—114no—
1198C2×C4—228no—
1199C2×C4—228no—
1200C2×C4—222no—
1201C2×C4—221no—
1202C2×C4—221no—
1203C2×C4—221no—
1204C2×C4—221no—
1205C2×C4—222no—
1206C2×C4—221no—
1207C2×C4—221no—
1208C2×C4—222no—
1209C2×C4—221no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—221no—
1213C2×C4—221no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—444no—
1223C2×C4—448no—
1224C2×C4—448no—
1225C2×C4—444no—
1226C2×C4—444no—
1227C2×C4—884no—
1228C2×C4—884no—
1229C22—24no—
1230C22—24no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—416no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—41no—
1251C22—42no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—42no—
1256C22—88no—
1257C22—222no—
1258C22—222no—
1259C22—222no—
1260C22—222no—
1261C22—222no—
1262C22—222no—
1263C22—442no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—442no—
1269C22—441no—
1270C22—441no—
1271C22—441no—
1272C22—888no—
1273C22#1062312014yes—
1274C22C22×D4×D1111yescharacteristic
1275C22C2×#6703711yescharacteristic
1276C22C2×#6703711yescharacteristic
1277C22D11×H(5,𝔽2)12yes—
1278C22#1062345512yes—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—222no—
1286C4—222no—
1287C4—224no—
1288C4—442no—
1289C4—442no—
1290C4—441no—
1291C4—442no—
1292C4—441no—
1293C4—441no—
1294C2—24no—
1295C2—42no—
1296C2—42no—
1297C2—82no—
1298C2—81no—
1299C2—442no—
1300C2—442no—
1301C2—881no—
1302C2C2×#1062312011yescharacteristic
1303C2#1308224811yescharacteristic
1304C2#1308225711yescharacteristic
1305C2#1308291912yes—
1306C2#1308292712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2613C2
hypercenter#2613D11
hypocenterC11#36704
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2613

Complements

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

NH ≅ G/Ntype
1. C2×#10623123C2semidirect
2. C22×#66992C2semidirect
3. #13076910C2semidirect
4. #13076906C2semidirect
5. #13075058C2semidirect
6. #13075054C2semidirect
7. #13075028C2semidirect
8. #13075024C2semidirect
9. #13074888C2semidirect
10. #13074884C2semidirect
11. #13074858C2semidirect
12. #13074854C2semidirect
13. #13074328C2semidirect
14. #13072900C2semidirect
15. #13072887C2semidirect
16. #13072014C2semidirect
17. #13072008C2semidirect
18. #13071992C2semidirect
19. #13071986C2semidirect
20. #13071948C2semidirect
21. #13071932C2semidirect
22. #13071192C2semidirect
23. C11×#2613C2semidirect
35. C2×#66993C22semidirect
36. C2×#66993C22semidirect
42. C2×#66992C22semidirect
43. C2×#66992C22semidirect
44. C2×#66991C22semidirect
46. C2×#66988C22semidirect
51. C2×#66939C22semidirect
52. C2×#66938C22semidirect
53. C2×#66938C22semidirect
54. C2×#66937C22semidirect
55. C2×#66937C22semidirect
56. C2×#66937C22semidirect
61. C11×#394C22semidirect
62. C11×#394C22semidirect
63. C11×#392C22semidirect
64. C11×#392C22semidirect
70. #10622836C22semidirect
71. #10622836C22semidirect
72. #10622836C22semidirect
73. #10622836C22semidirect
74. #10622835C22semidirect
75. #10622835C22semidirect
78. #10622833C22semidirect
79. #10622833C22semidirect
81. #10622606C22semidirect
82. #10622602C22semidirect
83. #10622600C22semidirect
84. #10622592C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
87. #10622573C22semidirect
88. #10622572C22semidirect
89. #10622572C22semidirect
92. #10622571C22semidirect
93. #10622569C22semidirect
94. #10622569C22semidirect
95. #10622569C22semidirect
96. #10622569C22semidirect
97. #10622569C22semidirect
98. #10622569C22semidirect
99. #10622569C22semidirect
100. #10622569C22semidirect
101. #10622565C22semidirect
102. #10622564C22semidirect
105. #10622563C22semidirect
106. #10622562C22semidirect
107. #10622560C22semidirect
110. #10622559C22semidirect
111. #10622559C22semidirect
112. #10622558C22semidirect
115. #10622556C22semidirect
116. #10622556C22semidirect
117. #10622288C22semidirect
118. #10622285C22semidirect
119. #10622280C22semidirect
120. #10622278C22semidirect
121. #10622271C22semidirect
122. #10622270C22semidirect
123. #10622267C22semidirect
124. #10622265C22semidirect
142. C22×C22⋊D11D4semidirect
458. #2613D11semidirect
650. #394C2×D11semidirect
651. #394C2×D11semidirect
658. #392C2×D11semidirect
659. #392C2×D11semidirect
1097. C11#36704semidirect

Maximal subgroups

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

subgroupindex
C2×#106231232
C22×#669922
#130769102
#130769062
#130750582
#130750542
#130750282
#130750242
#130748882
#130748842
#130748582
#130748542
#130743282
#130729002
#130728872
#130720142
#130720082
#130719922
#130719862
#130719482
#130719322
#130711922
C11×#26132
#3670411