Finite Group Databasebeta

← #14920188

Subgroups — #14920188

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623117C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13074532C212yesmaximal, complemented
4#13074499C212yesmaximal, complemented
5#13074454C212yesmaximal, complemented
6#13074452C212yesmaximal, complemented
7#13074433C211yesmaximal, characteristic, complemented
8#13074425C211yesmaximal, characteristic, complemented
9#13074392C211yesmaximal, characteristic, complemented
10#13074391C211yesmaximal, characteristic, complemented
11#13074362C211yesmaximal, characteristic, complemented
12#13074354C211yesmaximal, characteristic, complemented
13#13074328C211yesmaximal, characteristic, complemented
14#13071872C212yesmaximal, complemented
15#13071859C212yesmaximal, complemented
16#13071851C212yesmaximal, complemented
17#13071828C212yesmaximal, complemented
18#123×Dic11C211yesmaximal, characteristic, complemented
19#13071133C211yesmaximal, characteristic, complemented
20#120×Dic11C211yesmaximal, characteristic, complemented
21#13071115C211yesmaximal, characteristic, complemented
22#13070994C211yesmaximal, characteristic, complemented
23C11×#2613C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C22×#4341C2211yescharacteristic, complemented
28C2×C11×#123C2211yescharacteristic
29C2×C11×#120C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C2×#67006C2211yescharacteristic
32C2×#67006C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992C2211yescharacteristic
36C2×#66992C2211yescharacteristic, complemented
37C2×#66988C2211yescharacteristic, complemented
38C2×D4×Dic11—28no—
39C2×D4×Dic11C2212yes—
40C2×D4×Dic11C2211yescharacteristic
41C2×D4×Dic11C2212yes—
42C2×D4×Dic11C2212yes—
43C2×D4×Dic11C2212yes—
44C2×D4×Dic11C2211yescharacteristic, complemented
45C2×D4×Dic11C2212yescomplemented
46C2×#66982C2211yescharacteristic
47C22×C4⋊Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49#10623117—28no—
50C2×#66939C2211yescharacteristic, complemented
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
53C2×(C22⋊D11)⋊C4C2212yescomplemented
54C2×#66931C2211yescharacteristic
55C2×#66931C2211yescharacteristic, complemented
56C2×#66930C2211yescharacteristic, complemented
57C2×#66930C2212yescomplemented
58C11×#394C2212yes—
59C11×#394C2212yes—
60C11×#392C2212yes—
61C11×#392C2212yes—
62C11×#381C2211yescharacteristic
63C11×#379C2211yescharacteristic
64C11×#379C2211yescharacteristic
65#10622860C2211yescharacteristic
66#10622860C2211yescharacteristic
67#10622836C2212yes—
68#10622836C2212yes—
69#10622836C2212yescomplemented
70#10622835C2212yes—
71#10622835C2212yes—
72#10622835C2212yescomplemented
73#10622835C2212yescomplemented
74#10622835C2212yescomplemented
75#10622833C2211yescharacteristic
76#10622833C2211yescharacteristic
77#10622833C2212yescomplemented
78#10622824C2211yescharacteristic
79#10622607C2212yescomplemented
80#10622597C2212yescomplemented
81#10622594C2212yescomplemented
82C4⋊C4×Dic11C2212yescomplemented
83#10622574C2212yescomplemented
84#10622574C2212yescomplemented
85#10622574C2212yescomplemented
86#10622572C2212yescomplemented
87#10622571C2211yescharacteristic
88#10622571C2211yescharacteristic
89#10622571C2212yescomplemented
90#10622566C2212yescomplemented
91#10622566C2212yescomplemented
92#10622565C2212yescomplemented
93#10622565C2212yescomplemented
94#10622565C2212yescomplemented
95#10622564C2212yescomplemented
96#10622563C2211yescharacteristic
97#10622563C2211yescharacteristic
98#10622563C2212yescomplemented
99#10622562C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622561C2212yescomplemented
103#10622560C2212yescomplemented
104#10622559C2211yescharacteristic
105#10622559C2211yescharacteristic
106#10622559C2212yescomplemented
107#10622556C2212yescomplemented
108#10622555C2211yescharacteristic
109#10622555C2211yescharacteristic
110#10622555C2212yescomplemented
111C22⋊C4×Dic11C2211yescharacteristic
112C22⋊C4×Dic11C2211yescharacteristic
113C22⋊C4×Dic11C2212yescomplemented
114C22⋊C4×Dic11C2212yescomplemented
115C22⋊C4×Dic11C2212yescomplemented
116C22⋊C4×Dic11C2212yescomplemented
117#10622282C2212yescomplemented
118#10622279C2212yescomplemented
119#10622274C2212yescomplemented
120#10622273C2212yescomplemented
121#10622270C2212yescomplemented
122#10622269C2212yescomplemented
123#10622265C2212yescomplemented
124#10622262C2212yescomplemented
125C25×C11C2311yescharacteristic
126C25×C11C2311yescharacteristic
127C22×D4×C11—24no—
128C22×D4×C11—24no—
129C22×D4×C11—24no—
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2312yes—
135C22×D4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C23×Dic11—24no—
143C23×Dic11—44no—
144C23×Dic11—44no—
145C23×Dic11D418yescomplemented
146C23×Dic11C2312yes—
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2311yescharacteristic
150C23×Dic11C2311yescharacteristic
151C23×Dic11C2311yescharacteristic
152C23×Dic11C2311yescharacteristic
153C23×Dic11C2312yes—
154C23×Dic11C2311yescharacteristic
155C23×Dic11C2311yescharacteristic
156C23×Dic11C2311yescharacteristic
157C2×#4341—24no—
158C2×#4341—44no—
159C22×C4×D11C2311yescharacteristic
160C22×Dic22C2311yescharacteristic
161C11×#123—24no—
162C11×#120—24no—
163C11×#120—24no—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176#67006—24no—
177#67006—24no—
178C2×C22⋊Dic11—24no—
179C2×C22⋊Dic11—24no—
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2311yescharacteristic
192C2×C22⋊Dic11C2312yes—
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2312yes—
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198#66992—24no—
199#66992—24no—
200#66988—24no—
201D4×Dic11—28no—
202D4×Dic11—28no—
203D4×Dic11—28no—
204D4×Dic11—28no—
205D4×Dic11—24no—
206D4×Dic11—24no—
207D4×Dic11—44no—
208#66982—24no—
209C2×(C2×D11)⋊C4C2311yescharacteristic
210C2×(C2×D11)⋊C4C2311yescharacteristic
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×C4⋊Dic11—24no—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2311yescharacteristic
217C2×C4⋊Dic11C2312yes—
218C2×C4⋊Dic11C2312yes—
219C2×C4⋊Dic11C2312yes—
220C2×C4⋊Dic11C2312yes—
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2311yescharacteristic
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×C4×Dic11—24no—
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2312yes—
235C2×C4×Dic11C2312yes—
236C2×C4×Dic11C2312yes—
237#66939—24no—
238(C22⋊D11)⋊C4—24no—
239(C22⋊D11)⋊C4—24no—
240(C22⋊D11)⋊C4—44no—
241#66931—24no—
242#66931—24no—
243#66930—24no—
244#66930—44no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#34562—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—22no—
264C24×C11—22no—
265C24×C11—22no—
266C24×C11—42no—
267C24×C11—42no—
268C24×C11—42no—
269C24×C11—42no—
270C24×C11C2×D414yes—
271C24×C11#4114yescomplemented
272C24×C11C2411yescharacteristic
273C24×C11C2411yescharacteristic
274C24×C11C2411yescharacteristic
275C24×C11C2412yes—
276C24×C11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C2×D4×C11—232no—
279C2×D4×C11—24no—
280C2×D4×C11—24no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—22no—
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—24no—
287C2×D4×C11—22no—
288C2×D4×C11—22no—
289C2×D4×C11—24no—
290C2×D4×C11—24no—
291C2×D4×C11—42no—
292C2×D4×C11—42no—
293C2×D4×C11—42no—
294C2×D4×C11—42no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11#4114yescomplemented
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2412yes—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C22×Dic11—24no—
317C22×Dic11—24no—
318C22×Dic11—24no—
319C22×Dic11—22no—
320C22×Dic11—24no—
321C22×Dic11—24no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—24no—
325C22×Dic11—22no—
326C22×Dic11—22no—
327C22×Dic11—42no—
328C22×Dic11—42no—
329C22×Dic11—42no—
330C22×Dic11—42no—
331C22×Dic11—42no—
332C22×Dic11—42no—
333C22×Dic11—42no—
334C22×Dic11—416no—
335C22×Dic11—416no—
336C22×Dic11C2×D414yes—
337C22×Dic11C2×D414yes—
338C22×Dic11C2×D414yes—
339C22×Dic11C2×D414yes—
340C22×Dic11C2×D414yes—
341C22×Dic11C2×D414yes—
342C22×Dic11C2412yes—
343C22×Dic11C2412yes—
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2412yes—
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2412yes—
348C22×Dic11C2411yescharacteristic
349C22×Dic11C2411yescharacteristic
350C22×Dic11C2411yescharacteristic
351C22×Dic11C2411yescharacteristic
352C22×Dic11C2411yescharacteristic
353#4341—416no—
354C2×C4×D11—22no—
355C2×C4×D11—24no—
356C2×Dic22—22no—
357C2×Dic22—42no—
358C11×C4⋊C4—24no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—22no—
373C22⋊Dic11—22no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—22no—
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—22no—
380C22⋊Dic11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—42no—
383C22⋊Dic11—42no—
384C22⋊Dic11—42no—
385C22⋊Dic11—42no—
386C22⋊Dic11—42no—
387C22⋊Dic11—42no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—24no—
396C4⋊Dic11—24no—
397C4⋊Dic11—42no—
398C4⋊Dic11—42no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—24no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C2×#525—111no—
415C22×C4×D4—111no—
416#2638—112no—
417#2635—112no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—111no—
423#2622—111no—
424#2618—111no—
425#2617—111no—
426#2613—111no—
427#2613D1111yescharacteristic, complemented
428#2395—112no—
429#2392—112no—
430#2392—112no—
431#2388—112no—
432C4×#123—111no—
433C4×#123—111no—
434C4×#120—111no—
435C4×#120—111no—
436#2280—111no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—28no—
440C23×C11—28no—
441C23×C11—22no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—21no—
457C23×C11—21no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—44no—
461C23×C11—44no—
462C23×C11—48no—
463C23×C11—44no—
464C23×C11—44no—
465C23×C11—48no—
466C23×C11—48no—
467C23×C11—48no—
468C23×C11C22×D412yes—
469C23×C11C22×D412yes—
470C23×C11C22×D412yes—
471C23×C11C2×#4114yes—
472C23×C11C2×#4112yes—
473C23×C11C2×#4112yes—
474C23×C11C2511yescharacteristic
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—22no—
479C22×D11—22no—
480D4×C11—216no—
481D4×C11—216no—
482D4×C11—44no—
483D4×C11—44no—
484D4×C11—48no—
485D4×C11—44no—
486C2×C4×C11—28no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11C2×#4114yes—
503C22⋊D11—44no—
504C22⋊D11—44no—
505C22⋊D11—44no—
506C22⋊D11—48no—
507C22⋊D11—44no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—28no—
512C2×Dic11—28no—
513C2×Dic11—28no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—44no—
534C2×Dic11—44no—
535C2×Dic11—44no—
536C2×Dic11—48no—
537C2×Dic11—44no—
538C2×Dic11—44no—
539C2×Dic11—44no—
540C2×Dic11—48no—
541C2×Dic11C22×D412yes—
542C2×Dic11C22×D412yes—
543C2×Dic11C22×D412yes—
544C2×Dic11C22×D412yes—
545C2×Dic11H(5,𝔽2)14yes—
546C4×D11—44no—
547Dic22—44no—
548C22×#41—111no—
549C23×D4C2×D1111yescharacteristic
550C24×C4—111no—
551C24×C4—111no—
552#525—228no—
553C2×#123—111no—
554C2×#123—111no—
555C2×#123—111no—
556C2×#123C2×D1111yescharacteristic
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×#121—111no—
560C2×#121—111no—
561C2×#120—111no—
562C2×#120—111no—
563C2×#120C2×D1111yescharacteristic
564C2×#120C2×D1111yescharacteristic
565C2×C4×D4—112no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—111no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—228no—
576C2×#117—111no—
577C2×#117—112no—
578C22×C4⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C42—111no—
582#400—112no—
583#399—112no—
584#398—112no—
585#398—112no—
586#398—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397—112no—
591#397—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394C2×D1112yes—
607#394C2×D1112yes—
608#393—112no—
609#392—112no—
610#392—112no—
611#392—112no—
612#392C2×D1112yes—
613#392C2×D1112yes—
614#388—112no—
615#388—112no—
616#387—112no—
617#387—112no—
618#386—111no—
619#386—111no—
620#386—112no—
621#386—111no—
622#386—111no—
623#386—112no—
624#385—111no—
625#385—111no—
626#385—111no—
627#385—111no—
628#385—112no—
629#385—112no—
630#381—111no—
631#381—112no—
632#381C2×D1111yescharacteristic
633#380—111no—
634#380—111no—
635#380—112no—
636#379—111no—
637#379—111no—
638#379C2×D1111yescharacteristic
639#379C2×D1111yescharacteristic
640C4×C4⋊C4—112no—
641C4×C4⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—112no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—24no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—416no—
663C22×C11—416no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11#52514yes—
678C22×C11C23×D411yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C22×#4111yescharacteristic
681C22×C11C2×H(5,𝔽2)12yes—
682C22×C11#58512yes—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—42no—
687C2×D11—42no—
688C4×C11—24no—
689C4×C11—41no—
690C4×C11—41no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—42no—
694Dic11—22no—
695Dic11—22no—
696Dic11—22no—
697Dic11—41no—
698Dic11—41no—
699Dic11—42no—
700Dic11—42no—
701Dic11—41no—
702Dic11—42no—
703Dic11—42no—
704Dic11#53414yes—
705C25C22×D1111yescharacteristic
706C25C22×D1111yescharacteristic
707C2×#41—224no—
708C2×#41—444no—
709C22×Q8—111no—
710C22×D4—24no—
711C22×D4—24no—
712C22×D4—24no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—111no—
718C22×D4C22×D1112yes—
719C22×D4C22×D1112yes—
720C22×D4C22×D1111yescharacteristic
721C22×D4C22×D1111yescharacteristic
722C22×D4C22×D1112yes—
723C22×D4C22×D1111yescharacteristic
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—118no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—112no—
736C23×C4—111no—
737C23×C4—224no—
738C23×C4—444no—
739C23×C4—444no—
740C23×C4C22×D1111yescharacteristic
741#123—24no—
742#123—224no—
743#123—224no—
744#123—224no—
745C22⋊Q8—224no—
746C22⋊Q8—224no—
747#121—224no—
748#121—224no—
749#120—24no—
750#120—24no—
751#120—224no—
752#120—224no—
753C4×D4—224no—
754C4×D4—224no—
755C4×D4—228no—
756C4×D4—228no—
757C4×D4—228no—
758C4×D4—228no—
759C4×D4—224no—
760C4×D4—224no—
761C4×D4—444no—
762C4×D4—444no—
763#117—224no—
764#117—444no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—224no—
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—224no—
806C2×C22⋊C4—224no—
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1111yescharacteristic
809C2×C22⋊C4C22×D1111yescharacteristic
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1112yes—
814C2×C22⋊C4C22×D1112yes—
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—112no—
823C2×C42—112no—
824C2×C42—224no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95C22×D1112yes—
840#95C22×D1112yes—
841C2×C11—24no—
842C2×C11—42no—
843C2×C11—42no—
844C2×C11—44no—
845C2×C11—81no—
846C2×C11C2×#52511yescharacteristic
847C2×C11C2×#53411yescharacteristic
848C2×C11#344911yescharacteristic
849C2×C11#345912yes—
850C2×C11#346012yes—
851D11—81no—
852C24—22no—
853C24—22no—
854C24—22no—
855C24—22no—
856C24—42no—
857C24—42no—
858C24—42no—
859C24—42no—
860C24—111no—
861C24D4×D1114yes—
862C24#434114yescomplemented
863C24C23×D1111yescharacteristic
864C24C23×D1111yescharacteristic
865C24C23×D1111yescharacteristic
866C24C23×D1112yes—
867C24C23×D1111yescharacteristic
868#41—4416no—
869C2×Q8—222no—
870C2×Q8—442no—
871C2×D4—232no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—24no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—222no—
889C2×D4—222no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—224no—
893C2×D4—222no—
894C2×D4—222no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—114no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—112no—
913C22×C4—112no—
914C22×C4—112no—
915C22×C4—111no—
916C22×C4—111no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—222no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—4416no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—4416no—
941C22×C4#434114yescomplemented
942C22×C4C23×D1112yes—
943C22×C4C23×D1112yes—
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1112yes—
948C4⋊C4—24no—
949C4⋊C4—224no—
950C4⋊C4—224no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—224no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—24no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—224no—
982C22⋊C4—224no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—222no—
986C22⋊C4—224no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C42—224no—
999C42—224no—
1000C42—222no—
1001C42—222no—
1002C42—224no—
1003C42—224no—
1004C11#3456211yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—28no—
1009C23—22no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—22no—
1027C23—22no—
1028C23—44no—
1029C23—44no—
1030C23—48no—
1031C23—44no—
1032C23—44no—
1033C23—48no—
1034C23—48no—
1035C23—48no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—222no—
1040C23—222no—
1041C23C2×D4×D1112yes—
1042C23C2×D4×D1112yes—
1043C23C2×D4×D1112yes—
1044C23C2×#434114yes—
1045C23C2×#434112yes—
1046C23C2×#434112yes—
1047C23C24×D1111yescharacteristic
1048Q8—444no—
1049D4—216no—
1050D4—216no—
1051D4—44no—
1052D4—48no—
1053D4—44no—
1054D4—44no—
1055D4—444no—
1056D4—444no—
1057D4—444no—
1058D4—448no—
1059D4—444no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—112no—
1077C2×C4—114no—
1078C2×C4—112no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—228no—
1082C2×C4—228no—
1083C2×C4—228no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—221no—
1090C2×C4—222no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—444no—
1107C2×C4—448no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—444no—
1111C2×C4—444no—
1112C2×C4—448no—
1113C2×C4—444no—
1114C2×C4—444no—
1115C2×C4C2×#434114yes—
1116C22—22no—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—24no—
1125C22—24no—
1126C22—22no—
1127C22—22no—
1128C22—24no—
1129C22—416no—
1130C22—416no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—41no—
1140C22—41no—
1141C22—42no—
1142C22—42no—
1143C22—41no—
1144C22—441no—
1145C22—441no—
1146C22—442no—
1147C22—442no—
1148C22—441no—
1149C22#1062311714yes—
1150C22C22×D4×D1111yescharacteristic
1151C22C22×#434111yescharacteristic
1152C22C22×#434111yescharacteristic
1153C22D11×H(5,𝔽2)12yes—
1154C22#1062345512yes—
1155C4—24no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—42no—
1160C4—41no—
1161C4—114no—
1162C4—222no—
1163C4—222no—
1164C4—222no—
1165C4—442no—
1166C4—441no—
1167C4—442no—
1168C4—441no—
1169C4—442no—
1170C4—442no—
1171C4—441no—
1172C2—24no—
1173C2—42no—
1174C2—42no—
1175C2—44no—
1176C2—81no—
1177C2—881no—
1178C2C2×#1062311711yescharacteristic
1179C2D11×#53411yescharacteristic
1180C2#1308194211yescharacteristic
1181C2#1308202212yes—
1182C2#1308202912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2613C2
hypercenter#2613D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2613

Complements

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

NH ≅ G/Ntype
1. C2×#10623117C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13074532C2semidirect
4. #13074499C2semidirect
5. #13074454C2semidirect
6. #13074452C2semidirect
7. #13074433C2semidirect
8. #13074425C2semidirect
9. #13074392C2semidirect
10. #13074391C2semidirect
11. #13074362C2semidirect
12. #13074354C2semidirect
13. #13074328C2semidirect
14. #13071872C2semidirect
15. #13071859C2semidirect
16. #13071851C2semidirect
17. #13071828C2semidirect
18. #123×Dic11C2semidirect
19. #13071133C2semidirect
20. #120×Dic11C2semidirect
21. #13071115C2semidirect
22. #13070994C2semidirect
23. C11×#2613C2semidirect
27. C22×#4341C22semidirect
36. C2×#66992C22semidirect
37. C2×#66988C22semidirect
44. C2×D4×Dic11C22semidirect
45. C2×D4×Dic11C22semidirect
50. C2×#66939C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×#66931C22semidirect
56. C2×#66930C22semidirect
57. C2×#66930C22semidirect
69. #10622836C22semidirect
72. #10622835C22semidirect
73. #10622835C22semidirect
74. #10622835C22semidirect
77. #10622833C22semidirect
79. #10622607C22semidirect
80. #10622597C22semidirect
81. #10622594C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. #10622574C22semidirect
84. #10622574C22semidirect
85. #10622574C22semidirect
86. #10622572C22semidirect
89. #10622571C22semidirect
90. #10622566C22semidirect
91. #10622566C22semidirect
92. #10622565C22semidirect
93. #10622565C22semidirect
94. #10622565C22semidirect
95. #10622564C22semidirect
98. #10622563C22semidirect
99. #10622562C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622561C22semidirect
103. #10622560C22semidirect
106. #10622559C22semidirect
107. #10622556C22semidirect
110. #10622555C22semidirect
113. C22⋊C4×Dic11C22semidirect
114. C22⋊C4×Dic11C22semidirect
115. C22⋊C4×Dic11C22semidirect
116. C22⋊C4×Dic11C22semidirect
117. #10622282C22semidirect
118. #10622279C22semidirect
119. #10622274C22semidirect
120. #10622273C22semidirect
121. #10622270C22semidirect
122. #10622269C22semidirect
123. #10622265C22semidirect
124. #10622262C22semidirect
145. C23×Dic11D4semidirect
271. C24×C11#41semidirect
297. C22×C4×C11#41semidirect
427. #2613D11semidirect
862. C24#4341semidirect
941. C22×C4#4341semidirect
1004. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106231172
C22×D4×Dic112
#130745322
#130744992
#130744542
#130744522
#130744332
#130744252
#130743922
#130743912
#130743622
#130743542
#130743282
#130718722
#130718592
#130718512
#130718282
#123×Dic112
#130711332
#120×Dic112
#130711152
#130709942
C11×#26132
#3456211