Finite Group Databasebeta

← #14925910

Subgroups — #14925910

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074229C212yesmaximal, complemented
4#13074223C212yesmaximal, complemented
5#13074092C211yesmaximal, characteristic, complemented
6#13073990C211yesmaximal, characteristic, complemented
7#13073799C211yesmaximal, characteristic, complemented
8#13073791C211yesmaximal, characteristic, complemented
9#13073768C211yesmaximal, characteristic, complemented
10#13073577C211yesmaximal, characteristic, complemented
11#13073573C211yesmaximal, characteristic, complemented
12#13073543C211yesmaximal, characteristic, complemented
13#13072005C212yesmaximal, complemented
14#13071985C212yesmaximal, complemented
15#13071873C211yesmaximal, characteristic, complemented
16#13071832C211yesmaximal, characteristic, complemented
17#13071831C211yesmaximal, characteristic, complemented
18C4×#66947C212yesmaximal, complemented
19C4×#66948C212yesmaximal, complemented
20C4×#66937C212yesmaximal, complemented
21C4×#66935C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2395C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic, complemented
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yescomplemented
34C4×D4×D11—28no—
35#10623055—28no—
36C2×#66950C2211yescharacteristic
37C2×#66950C2211yescharacteristic, complemented
38C2×#66948C2211yescharacteristic
39C2×#66948C2212yes—
40C2×#66948C2211yescharacteristic, complemented
41C2×#66947C2212yes—
42C2×#66946C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66939C2212yescomplemented
45C2×#66937C2212yes—
46C2×#66935C2212yes—
47C2×#66935C2212yes—
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2211yescharacteristic
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×C4×D44C2212yes—
54C2×C4×D44C2211yescharacteristic
55C2×C4×D44C2212yescomplemented
56C2×C4×D44C2212yescomplemented
57C2×C42×D11C2211yescharacteristic
58C2×C42×D11C2212yescomplemented
59C11×#400C2211yescharacteristic, complemented
60C11×#399C2211yescharacteristic, complemented
61C11×#398C2211yescharacteristic, complemented
62C11×#397C2212yescomplemented
63C11×#397C2211yescharacteristic, complemented
64C11×#394C2212yes—
65C4×C11×C4⋊C4C2212yescomplemented
66C4×C11×C22⋊C4C2212yescomplemented
67C4×C11×C22⋊C4C2211yescharacteristic, complemented
68#10622836C2212yes—
69C4×C22⋊Dic11C2211yescharacteristic, complemented
70#10622606C2211yescharacteristic, complemented
71#10622605C2211yescharacteristic, complemented
72#10622604C2211yescharacteristic, complemented
73#10622603C2212yescomplemented
74#10622602C2212yes—
75#10622601C2212yescomplemented
76#10622600C2212yescomplemented
77#10622598C2212yescomplemented
78#10622595C2211yescharacteristic, complemented
79#10622594C2212yescomplemented
80#10622593C2211yescharacteristic, complemented
81#10622592C2211yescharacteristic, complemented
82#10622574C2212yescomplemented
83#10622573C2212yes—
84#10622573C2211yescharacteristic, complemented
85#10622572C2212yes—
86#10622572C2212yescomplemented
87#10622571C2212yescomplemented
88#10622570C2212yescomplemented
89#10622569C2212yes—
90#10622568C2212yes—
91#10622565C2212yescomplemented
92#10622564C2212yescomplemented
93#10622563C2212yescomplemented
94#10622560C2211yescharacteristic, complemented
95C22⋊C4×Dic11C2212yescomplemented
96C4×(C2×D11)⋊C4C2212yes—
97C4×(C2×D11)⋊C4C2212yescomplemented
98C4×(C2×D11)⋊C4C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×Dic11⋊C4C2212yescomplemented
101#10622286C2211yescharacteristic, complemented
102#10622285C2211yescharacteristic, complemented
103#10622284C2211yescharacteristic, complemented
104#10622283C2212yescomplemented
105#10622283C2212yescomplemented
106#10622282C2212yescomplemented
107#10622282C2212yescomplemented
108#10622281C2212yes—
109#10622281C2212yescomplemented
110#10622280C2212yescomplemented
111#10622279C2211yescharacteristic
112#10622279C2211yescharacteristic
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622278C2212yescomplemented
119#10622277C2212yes—
120D11×#95C2211yescharacteristic, complemented
121D11×#95C2211yescharacteristic, complemented
122#10622269C2211yescharacteristic, complemented
123#10622268C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C2×D4×D11—24no—
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×#4339—24no—
140C2×#4339—44no—
141C22×D44C2312yes—
142C22×D44C2312yes—
143C22×D44C2312yes—
144C22×D44C2311yescharacteristic
145C22×D44C2311yescharacteristic
146C22×C4×D11—24no—
147C22×C4×D11—44no—
148C22×C4×D11—44no—
149C22×C4×D11D418yescomplemented
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×Dic22C2311yescharacteristic
163C4×D4×C11—24no—
164C11×#117—24no—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C42×C11C2311yescharacteristic
177C2×C42×C11C2312yes—
178C2×C42×C11C2312yes—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183D4×Dic11—24no—
184C4×C22⋊D11—24no—
185C4×C22⋊D11—24no—
186C4×C22⋊D11—44no—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221#66950—24no—
222#66950—24no—
223#66948—28no—
224#66948—24no—
225#66948—24no—
226#66947—28no—
227#66946—24no—
228C4⋊C4×D11—24no—
229#66939—28no—
230#66937—28no—
231#66935—28no—
232#66935—28no—
233(C22⋊D11)⋊C4—24no—
234(C22⋊D11)⋊C4—24no—
235C22⋊C4×D11—24no—
236C22⋊C4×D11—24no—
237C22⋊C4×D11—28no—
238C4×D44—28no—
239C4×D44—24no—
240C4×D44—28no—
241C4×D44—44no—
242C42×D11—24no—
243C42×D11—44no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2311yescharacteristic
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262#34957—111nomaximal, Sylow
263C24×C11C2411yescharacteristic
264C24×C11C2411yescharacteristic
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—24no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—24no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11C2×D414yes—
275C23×D11C2412yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11C2×D414yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—22no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11#4114yescomplemented
307C22×Dic11—22no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C2×D414yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319D4×D11—232no—
320#4339—416no—
321C2×D44—22no—
322C2×D44—24no—
323C2×D44—24no—
324C2×D44—22no—
325C2×D44—24no—
326C2×D44—24no—
327C2×D44—24no—
328C2×D44—24no—
329C2×D44—24no—
330C2×D44—22no—
331C2×D44—24no—
332C2×D44—42no—
333C2×D44—42no—
334C2×D44#4114yescomplemented
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—416no—
360C2×C4×D11—416no—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×Dic22—22no—
366C2×Dic22—42no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—24no—
371C11×C4⋊C4—24no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—24no—
378C42×C11—22no—
379C42×C11—24no—
380C42×C11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—24no—
383C22⋊Dic11—22no—
384C22⋊Dic11—42no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—22no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4—42no—
402(C2×D11)⋊C4—42no—
403(C2×D11)⋊C4#4118yescomplemented
404C4⋊Dic11—24no—
405C4⋊Dic11—24no—
406C4⋊Dic11—22no—
407C4⋊Dic11—42no—
408Dic11⋊C4—22no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—22no—
412Dic11⋊C4—42no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C4×Dic11—24no—
417C4×Dic11—42no—
418C4×Dic11—42no—
419C2×#525—111no—
420C22×C4×D4—111no—
421#2602—112no—
422#2602—112no—
423#2591—111no—
424#2583—111no—
425#2564—111no—
426#2564—111no—
427#2561—111no—
428#2543—111no—
429#2543—111no—
430#2539—111no—
431#2412—112no—
432#2410—112no—
433#2395—111no—
434#2395D1111yescharacteristic, complemented
435#2388—111no—
436#2388—111no—
437C4×#123—112no—
438C4×#121—112no—
439C4×#121—112no—
440C4×#120—112no—
441C2×C4×C22⋊C4—111no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11C22×D412yes—
451C23×C11C2×#4112yes—
452C23×C11C2511yescharacteristic
453C22×D11—22no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—28no—
459C22×D11—21no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—44no—
473C22×D11—48no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—44no—
478C22×D11—44no—
479C22×D11C22×D412yes—
480C22×D11C22×D412yes—
481C22×D11C2×#4112yes—
482C22×D11C2×#4112yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4114yes—
485D4×C11—28no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—28no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
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×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—44no—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C2×#4112yes—
509C2×C4×C11C2×#4114yes—
510C2×C4×C11H(5,𝔽2)14yes—
511C22⋊D11—28no—
512C22⋊D11—28no—
513C22⋊D11—48no—
514C22⋊D11—48no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—21no—
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—44no—
532C2×Dic11—44no—
533C2×Dic11C22×D412yes—
534C2×Dic11C22×D412yes—
535C2×Dic11C2×#4112yes—
536C2×Dic11C2×#4114yes—
537D44—28no—
538D44—48no—
539D44—44no—
540D44—48no—
541D44—48no—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—28no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—48no—
548C4×D11—44no—
549C4×D11—48no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11—48no—
554Dic22—44no—
555C22×#41—111no—
556C23×D4—111no—
557C24×C4—111no—
558C24×C4—111no—
559#525—228no—
560C2×#123—112no—
561C2×#123—112no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8—111no—
564C2×#121—111no—
565C2×#121—112no—
566C2×#121—111no—
567C2×#121—112no—
568C2×#120—112no—
569C2×#120—112no—
570C2×C4×D4—111no—
571C2×C4×D4—111no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—111no—
575C2×C4×D4—111no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—228no—
582C2×C4×D4C2×D1111yescharacteristic
583C2×#117C2×D1111yescharacteristic, complemented
584C22×C4⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—112no—
588C22×C42—111no—
589C22×C42—112no—
590#400—111no—
591#400C2×D1111yescharacteristic, complemented
592#399—111no—
593#399C2×D1111yescharacteristic, complemented
594#398—111no—
595#398C2×D1111yescharacteristic, complemented
596#397—111no—
597#397—112no—
598#397C2×D1111yescharacteristic, complemented
599#397C2×D1112yescomplemented
600#395—111no—
601#395—111no—
602#394—111no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—111no—
607#394C2×D1112yes—
608#393—111no—
609#393—111no—
610#392—112no—
611#392—112no—
612#392—111no—
613#392—111no—
614#390—112no—
615#390—112no—
616#389—112no—
617#389—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#387—112no—
625#387—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#385—112no—
635#385—112no—
636#385—112no—
637#385—112no—
638#381—112no—
639#380—112no—
640#380—112no—
641#379—112no—
642C4×C4⋊C4—112no—
643C4×C4⋊C4C2×D1112yescomplemented
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4C2×D1112yescomplemented
654C2×#95—111no—
655C2×#95—111no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—24no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11C23×D411yescharacteristic
667C22×C11C22×#4111yescharacteristic
668C22×C11C22×#4111yescharacteristic
669C22×C11C22×#4112yes—
670C22×C11C2×H(5,𝔽2)12yes—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—24no—
678C2×D11—24no—
679C2×D11—22no—
680C2×D11—24no—
681C2×D11—416no—
682C2×D11—416no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11#52514yes—
694C2×D11#53214yes—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—42no—
699C4×C11—41no—
700C4×C11—42no—
701C4×C11—41no—
702C4×C11—42no—
703C4×C11#53414yes—
704Dic11—22no—
705Dic11—22no—
706Dic11—22no—
707Dic11—24no—
708Dic11—41no—
709Dic11—42no—
710Dic11—41no—
711Dic11—42no—
712C25—111no—
713C25—111no—
714C2×#41—224no—
715C2×#41—444no—
716C22×Q8—111no—
717C22×D4—111no—
718C22×D4—111no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—111no—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—111no—
726C22×D4—224no—
727C22×D4—224no—
728C22×D4—224no—
729C22×D4C22×D1111yescharacteristic
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—118no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—112no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—224no—
746C23×C4—444no—
747C23×C4—444no—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic
750#123—228no—
751#123—228no—
752C22⋊Q8—224no—
753C22⋊Q8—224no—
754#121—228no—
755#121—224no—
756#121—224no—
757#121—228no—
758#120—228no—
759#120—228no—
760C4×D4—24no—
761C4×D4—224no—
762C4×D4—228no—
763C4×D4—228no—
764C4×D4—224no—
765C4×D4—224no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—224no—
769C4×D4—224no—
770C4×D4—444no—
771C4×D4—444no—
772#117—24no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—224no—
783C2×C4⋊C4C22×D1111yescharacteristic
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1111yescharacteristic
786C2×C4⋊C4C22×D1112yes—
787C2×C4⋊C4C22×D1112yes—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—111no—
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—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—228no—
812C2×C22⋊C4—224no—
813C2×C22⋊C4—224no—
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1111yescharacteristic
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—112no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—224no—
827C2×C42—444no—
828C2×C42C22×D1112yes—
829C2×C42C22×D1111yescharacteristic
830C2×C42C22×D1112yes—
831#95—112no—
832#95—112no—
833#95—111no—
834#95—111no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95C22×D1111yescharacteristic
844#95C22×D1111yescharacteristic
845#95C22×D1112yes—
846#95C22×D1112yes—
847#95C22×D1112yes—
848#95C22×D1112yes—
849C2×C11—42no—
850C2×C11—42no—
851C2×C11C2×#52511yescharacteristic
852C2×C11C2×#53211yescharacteristic
853C2×C11C2×#53411yescharacteristic
854C2×C11#348112yes—
855C2×C11#348112yes—
856D11—24no—
857D11—24no—
858D11—42no—
859D11—82no—
860C24—111no—
861C24—111no—
862C24—111no—
863C24—114no—
864C24—112no—
865C24—222no—
866C24—224no—
867C24—222no—
868C24—222no—
869C24—222no—
870C24—224no—
871C24—222no—
872C24—442no—
873C24—442no—
874C24C23×D1111yescharacteristic
875C24C23×D1111yescharacteristic
876#41—4416no—
877C2×Q8—222no—
878C2×Q8—442no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—114no—
883C2×D4—114no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—222no—
894C2×D4—224no—
895C2×D4—2232no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—222no—
903C2×D4—224no—
904C2×D4—442no—
905C2×D4—442no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—442no—
909C22×C4—24no—
910C22×C4—22no—
911C22×C4—24no—
912C22×C4—112no—
913C22×C4—111no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—114no—
917C22×C4—114no—
918C22×C4—114no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—112no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—112no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—224no—
944C22×C4—4416no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—4416no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4D4×D1114yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1112yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1112yes—
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—442no—
977C4⋊C4—442no—
978C22⋊C4—22no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—22no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—118no—
985C22⋊C4—222no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—222no—
992C22⋊C4—222no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—222no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C42—22no—
1008C42—24no—
1009C42—24no—
1010C42—222no—
1011C42—222no—
1012C42—222no—
1013C42—224no—
1014C42—442no—
1015C42—442no—
1016C11#3495711yescharacteristic, complemented, Sylow
1017C23—21no—
1018C23—22no—
1019C23—22no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—22no—
1024C23—22no—
1025C23—112no—
1026C23—112no—
1027C23—114no—
1028C23—112no—
1029C23—112no—
1030C23—112no—
1031C23—228no—
1032C23—228no—
1033C23—228no—
1034C23—222no—
1035C23—221no—
1036C23—221no—
1037C23—222no—
1038C23—222no—
1039C23—221no—
1040C23—222no—
1041C23—221no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—444no—
1051C23—448no—
1052C23—444no—
1053C23—448no—
1054C23—448no—
1055C23—448no—
1056C23—444no—
1057C23C2×D4×D1112yes—
1058C23#41×D1112yes—
1059C23C24×D1111yescharacteristic
1060Q8—444no—
1061D4—28no—
1062D4—228no—
1063D4—228no—
1064D4—228no—
1065D4—448no—
1066D4—444no—
1067D4—448no—
1068D4—448no—
1069D4—448no—
1070D4—448no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—28no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—44no—
1091C2×C4—112no—
1092C2×C4—112no—
1093C2×C4—114no—
1094C2×C4—112no—
1095C2×C4—228no—
1096C2×C4—221no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—228no—
1103C2×C4—228no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—444no—
1115C2×C4—444no—
1116C2×C4—448no—
1117C2×C4—448no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—448no—
1125C2×C4C2×D4×D1112yes—
1126C2×C4C2×D4×D1112yes—
1127C2×C4#41×D1114yes—
1128C2×C4#41×D1112yes—
1129C2×C4#6704214yes—
1130C22—22no—
1131C22—22no—
1132C22—24no—
1133C22—22no—
1134C22—22no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—114no—
1141C22—114no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—224no—
1146C22—224no—
1147C22—224no—
1148C22—224no—
1149C22—222no—
1150C22—224no—
1151C22—222no—
1152C22—4416no—
1153C22—4416no—
1154C22—441no—
1155C22—441no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22C22×D4×D1111yescharacteristic
1165C22C2×#41×D1112yes—
1166C22C2×#41×D1111yescharacteristic
1167C22C2×#41×D1111yescharacteristic
1168C22C2×#6704212yes—
1169C4—22no—
1170C4—24no—
1171C4—22no—
1172C4—41no—
1173C4—42no—
1174C4—41no—
1175C4—42no—
1176C4—42no—
1177C4—222no—
1178C4—222no—
1179C4—224no—
1180C4—222no—
1181C4—441no—
1182C4—441no—
1183C4—442no—
1184C4—442no—
1185C4#1062318414yes—
1186C2—42no—
1187C2—42no—
1188C2—224no—
1189C2—224no—
1190C2—442no—
1191C2—882no—
1192C2D11×#52511yescharacteristic
1193C2D11×#53211yescharacteristic
1194C2C2×#1062318411yescharacteristic
1195C2#1308222212yes—
1196C2#1308222212yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2395C2
hypercenter#2395D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
1. C2×#10623055C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074229C2semidirect
4. #13074223C2semidirect
5. #13074092C2semidirect
6. #13073990C2semidirect
7. #13073799C2semidirect
8. #13073791C2semidirect
9. #13073768C2semidirect
10. #13073577C2semidirect
11. #13073573C2semidirect
12. #13073543C2semidirect
13. #13072005C2semidirect
14. #13071985C2semidirect
15. #13071873C2semidirect
16. #13071832C2semidirect
17. #13071831C2semidirect
18. C4×#66947C2semidirect
19. C4×#66948C2semidirect
20. C4×#66937C2semidirect
21. C4×#66935C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2395C2semidirect
25. C22×#4339C22semidirect
29. C2×C11×#117C22semidirect
33. C2×C4×C22⋊D11C22semidirect
37. C2×#66950C22semidirect
40. C2×#66948C22semidirect
44. C2×#66939C22semidirect
55. C2×C4×D44C22semidirect
56. C2×C4×D44C22semidirect
58. C2×C42×D11C22semidirect
59. C11×#400C22semidirect
60. C11×#399C22semidirect
61. C11×#398C22semidirect
62. C11×#397C22semidirect
63. C11×#397C22semidirect
65. C4×C11×C4⋊C4C22semidirect
66. C4×C11×C22⋊C4C22semidirect
67. C4×C11×C22⋊C4C22semidirect
69. C4×C22⋊Dic11C22semidirect
70. #10622606C22semidirect
71. #10622605C22semidirect
72. #10622604C22semidirect
73. #10622603C22semidirect
75. #10622601C22semidirect
76. #10622600C22semidirect
77. #10622598C22semidirect
78. #10622595C22semidirect
79. #10622594C22semidirect
80. #10622593C22semidirect
81. #10622592C22semidirect
82. #10622574C22semidirect
84. #10622573C22semidirect
86. #10622572C22semidirect
87. #10622571C22semidirect
88. #10622570C22semidirect
91. #10622565C22semidirect
92. #10622564C22semidirect
93. #10622563C22semidirect
94. #10622560C22semidirect
95. C22⋊C4×Dic11C22semidirect
97. C4×(C2×D11)⋊C4C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. #10622286C22semidirect
102. #10622285C22semidirect
103. #10622284C22semidirect
104. #10622283C22semidirect
105. #10622283C22semidirect
106. #10622282C22semidirect
107. #10622282C22semidirect
109. #10622281C22semidirect
110. #10622280C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
118. #10622278C22semidirect
120. D11×#95C22semidirect
121. D11×#95C22semidirect
122. #10622269C22semidirect
123. #10622268C22semidirect
124. #10622260C22semidirect
149. C22×C4×D11D4semidirect
306. C2×C22⋊D11#41semidirect
334. C2×D44#41semidirect
403. (C2×D11)⋊C4#41semidirect
434. #2395D11semidirect
583. C2×#117C2×D11semidirect
591. #400C2×D11semidirect
593. #399C2×D11semidirect
595. #398C2×D11semidirect
598. #397C2×D11semidirect
599. #397C2×D11semidirect
643. C4×C4⋊C4C2×D11semidirect
652. C4×C22⋊C4C2×D11semidirect
653. C4×C22⋊C4C2×D11semidirect
1016. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×C4×D4×D112
#130742292
#130742232
#130740922
#130739902
#130737992
#130737912
#130737682
#130735772
#130735732
#130735432
#130720052
#130719852
#130718732
#130718322
#130718312
C4×#669472
C4×#669482
C4×#669372
C4×#669352
C4×C22⋊C4×D112
C11×#23952
#3495711