Finite Group Databasebeta

← #14925641

Subgroups — #14925641

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C212yesmaximal, complemented
2C2×#10623053C211yesmaximal, characteristic, complemented
3C2×C4×D4×D11C211yesmaximal, characteristic, complemented
4#13073533C212yesmaximal, complemented
5#13073528C212yesmaximal, complemented
6#13073522C211yesmaximal, characteristic, complemented
7#13073520C211yesmaximal, characteristic, complemented
8#13073514C211yesmaximal, characteristic, complemented
9#13073512C211yesmaximal, characteristic, complemented
10#13073507C212yesmaximal, complemented
11#13073501C212yesmaximal, complemented
12#13072919C211yesmaximal, characteristic, complemented
13#13072917C211yesmaximal, characteristic, complemented
14#13071967C211yesmaximal, characteristic, complemented
15#13071965C211yesmaximal, characteristic, complemented
16#13071856C211yesmaximal, characteristic, complemented
17#13071854C211yesmaximal, characteristic, complemented
18#13071852C211yesmaximal, characteristic, complemented
19C4×#66937C212yesmaximal, complemented
20C4×#66992C212yesmaximal, complemented
21#13071020C211yesmaximal, characteristic, complemented
22#13070997C212yesmaximal, complemented
23C11×#2392C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yescomplemented
29C2×C11×#117C2211yescharacteristic, complemented
30C2×#66992C2212yes—
31C2×#66992C2212yescomplemented
32C2×#66990C2212yes—
33C2×D4×Dic11C2211yescharacteristic
34C2×C4×C22⋊D11C2212yes—
35C2×C4×C22⋊D11C2212yescomplemented
36C2×C4×C22⋊D11C2212yescomplemented
37C22×C4×Dic11C2211yescharacteristic, complemented
38#10623078—216no—
39C4×D4×D11—28no—
40#10623053—28no—
41C2×#66949C2212yescomplemented
42C2×#66947C2212yes—
43C2×#66946C2211yescharacteristic
44C2×#66946C2211yescharacteristic
45C2×#66946C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×#66940C2211yescharacteristic, complemented
48C2×#66940C2211yescharacteristic, complemented
49C2×#66937C2212yes—
50C2×#66937C2212yescomplemented
51C2×#66936C2212yes—
52C2×#66935C2212yes—
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2211yescharacteristic
55C2×(C22⋊D11)⋊C4C2212yes—
56C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
57C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
58C2×C22⋊C4×D11C2212yes—
59C2×#66931C2212yescomplemented
60C2×C4×D44C2211yescharacteristic
61C2×C4×D44C2212yescomplemented
62C2×#66925C2212yes—
63C2×#66925C2211yescharacteristic
64C2×#66925C2211yescharacteristic, complemented
65C2×C42×D11C2211yescharacteristic
66C2×C42×D11C2211yescharacteristic, complemented
67C11×#398C2211yescharacteristic, complemented
68C11×#397C2211yescharacteristic, complemented
69C11×#396C2212yescomplemented
70C11×#394C2211yescharacteristic
71C11×#394C2212yescomplemented
72C11×#392C2211yescharacteristic
73C4×C11×C4⋊C4C2211yescharacteristic, complemented
74C4×C11×C22⋊C4C2212yescomplemented
75#10622836C2211yescharacteristic
76#10622835C2211yescharacteristic
77#10622833C2212yescomplemented
78C4×C22⋊Dic11C2212yescomplemented
79#10622607C2212yescomplemented
80#10622607C2212yescomplemented
81#10622606C2211yescharacteristic, complemented
82#10622604C2211yescharacteristic
83#10622604C2212yescomplemented
84#10622603C2212yescomplemented
85#10622600C2212yes—
86#10622596C2211yescharacteristic, complemented
87#10622593C2211yescharacteristic, complemented
88#10622589C2212yescomplemented
89#10622585C2212yescomplemented
90#10622574C2212yescomplemented
91#10622574C2212yescomplemented
92#10622573C2211yescharacteristic
93#10622571C2212yescomplemented
94#10622570C2212yes—
95#10622570C2212yes—
96#10622569C2212yescomplemented
97#10622568C2212yes—
98#10622568C2212yes—
99#10622566C2211yescharacteristic, complemented
100#10622564C2212yescomplemented
101#10622561C2212yescomplemented
102#10622558C2212yescomplemented
103#10622555C2212yescomplemented
104#10622555C2212yescomplemented
105#10622555C2212yescomplemented
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×(C2×D11)⋊C4C2212yescomplemented
108C4×C4⋊Dic11C2211yescharacteristic, complemented
109C4×Dic11⋊C4C2212yescomplemented
110#10622287C2211yescharacteristic, complemented
111#10622285C2211yescharacteristic
112#10622284C2211yescharacteristic
113#10622282C2212yescomplemented
114#10622280C2211yescharacteristic
115#10622280C2211yescharacteristic
116#10622280C2212yescomplemented
117#10622280C2212yescomplemented
118#10622280C2212yescomplemented
119#10622278C2212yescomplemented
120#10622277C2212yes—
121#10622277C2212yes—
122#10622274C2211yescharacteristic, complemented
123#10622263C2211yescharacteristic, complemented
124#10622263C2211yescharacteristic, complemented
125#10622260C2212yescomplemented
126C24×D11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2312yes—
136C23×Dic11C2312yes—
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C2×D4×D11—28no—
140C2×D4×D11—24no—
141C2×#4339—24no—
142C2×#4339—24no—
143C2×#4339D418yescomplemented
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×D44C2311yescharacteristic
147C22×C4×D11—28no—
148C22×C4×D11—28no—
149C22×C4×D11—28no—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×Dic22C2311yescharacteristic
160C4×D4×C11—28no—
161C4×D4×C11—24no—
162C11×#117—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2312yes—
177C2×C42×C11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183#66992—28no—
184#66992—28no—
185#66990—28no—
186D4×Dic11—24no—
187C4×C22⋊D11—28no—
188C4×C22⋊D11—28no—
189C4×C22⋊D11—28no—
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
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⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×C4×Dic11—24no—
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230#66949—28no—
231#66947—28no—
232#66946—24no—
233#66946—24no—
234#66946—24no—
235C4⋊C4×D11—24no—
236#66940—24no—
237#66940—24no—
238#66937—28no—
239#66937—28no—
240#66936—28no—
241#66935—28no—
242(C22⋊D11)⋊C4—24no—
243(C22⋊D11)⋊C4—24no—
244(C22⋊D11)⋊C4—28no—
245(C22⋊D11)⋊C4—24no—
246(C22⋊D11)⋊C4—24no—
247C22⋊C4×D11—28no—
248#66931—28no—
249C4×D44—28no—
250C4×D44—24no—
251#66925—24no—
252#66925—28no—
253#66925—24no—
254C42×D11—24no—
255C42×D11D418yescomplemented
256C11×#95C2312yes—
257C11×#95C2311yescharacteristic
258C11×#95C2311yescharacteristic
259C11×#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2311yescharacteristic
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2312yes—
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270#34935—111nomaximal, Sylow
271C24×C11C2411yescharacteristic
272C24×C11C2412yes—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—24no—
276C23×D11—24no—
277C23×D11—24no—
278C23×D11—42no—
279C23×D11—42no—
280C23×D11C2411yescharacteristic
281C23×D11C2412yes—
282C23×D11C2411yescharacteristic
283C2×D4×C11—24no—
284C2×D4×C11—24no—
285C2×D4×C11—24no—
286C2×D4×C11—22no—
287C2×D4×C11—42no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—24no—
293C22×C4×C11C2×D414yescomplemented
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C2×C22⋊D11—22no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11C2×D414yes—
316C2×C22⋊D11C2×D414yescomplemented
317C2×C22⋊D11#4118yescomplemented
318C22×Dic11—24no—
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11—24no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—42no—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2412yes—
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334D4×D11—232no—
335#4339—232no—
336C2×D44—22no—
337C2×D44—24no—
338C2×D44—22no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—22no—
342C2×D44—42no—
343C2×D44C2×D414yes—
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—24no—
354C2×C4×D11—22no—
355C2×C4×D11—24no—
356C2×C4×D11—24no—
357C2×C4×D11—22no—
358C2×C4×D11—24no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—432no—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×C4×D11C2×D414yes—
366C2×C4×D11C2×D414yescomplemented
367C2×C4×D11#4114yes—
368C2×Dic22—22no—
369C2×Dic22—22no—
370C2×Dic22C2×D414yescomplemented
371C11×C4⋊C4—22no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—24no—
375C11×C4⋊C4—42no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—24no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—24no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—42no—
383C42×C11—22no—
384C42×C11—24no—
385C42×C11C2×D414yes—
386C22⋊Dic11—24no—
387C22⋊Dic11—24no—
388C22⋊Dic11—24no—
389C22⋊Dic11—24no—
390C22⋊Dic11—42no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—22no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—22no—
402(C2×D11)⋊C4—22no—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—42no—
406(C2×D11)⋊C4—42no—
407C4⋊Dic11—24no—
408C4⋊Dic11—22no—
409C4⋊Dic11—42no—
410Dic11⋊C4—24no—
411Dic11⋊C4—22no—
412Dic11⋊C4—22no—
413Dic11⋊C4—24no—
414Dic11⋊C4—24no—
415Dic11⋊C4—24no—
416Dic11⋊C4—24no—
417Dic11⋊C4—24no—
418Dic11⋊C4—22no—
419Dic11⋊C4—22no—
420Dic11⋊C4—24no—
421C4×Dic11—22no—
422C4×Dic11—22no—
423C4×Dic11—22no—
424C4×Dic11—22no—
425C4×Dic11—22no—
426C4×Dic11—24no—
427C4×Dic11C2×D414yes—
428C4×Dic11C2×D414yes—
429C4×Dic11C2×D414yes—
430C2×#525—112no—
431C2×C4×#41—111no—
432C22×C4×D4—111no—
433#2538—112no—
434#2537—112no—
435#2536—111no—
436#2536—111no—
437#2535—111no—
438#2535—111no—
439#2534—112no—
440#2534—112no—
441#2486—111no—
442#2486—111no—
443#2408—111no—
444#2408—111no—
445#2392—111no—
446#2392—111no—
447#2392—111no—
448#2392D1111yescharacteristic, complemented
449C4×#121—112no—
450C4×#121—112no—
451#2285—111no—
452#2280—112no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—21no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11C22×D412yes—
464C23×C11C2×#4114yes—
465C23×C11C2511yescharacteristic
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—216no—
469C22×D11—21no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—21no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—48no—
480C22×D11—48no—
481C22×D11—48no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11C22×D412yes—
486C22×D11C22×D412yes—
487C22×D11C22×D412yes—
488C22×D11C2×#4114yes—
489C22×D11C2×#4112yes—
490D4×C11—28no—
491D4×C11—48no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—28no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
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—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—48no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D412yes—
515C2×C4×C11C22×D412yes—
516C2×C4×C11C2×#4112yes—
517C22⋊D11—28no—
518C22⋊D11—28no—
519C22⋊D11—216no—
520C22⋊D11—48no—
521C22⋊D11—48no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—44no—
539C2×Dic11—48no—
540C2×Dic11—44no—
541C2×Dic11C22×D412yes—
542C2×Dic11C22×D412yes—
543C2×Dic11C22×D412yes—
544C2×Dic11C22×D412yes—
545C2×Dic11C22×D412yes—
546C2×Dic11C2×#4112yes—
547C2×Dic11C2×#4114yes—
548D44—28no—
549D44—28no—
550D44—48no—
551C4×D11—28no—
552C4×D11—28no—
553C4×D11—44no—
554C4×D11—44no—
555C4×D11—48no—
556C4×D11—48no—
557C4×D11—48no—
558C4×D11—44no—
559C4×D11#121116yescomplemented
560Dic22—28no—
561C22×#41—111no—
562C23×D4—111no—
563C24×C4—112no—
564#525—2216no—
565C2×#123—112no—
566C2×#123—112no—
567C2×C22⋊Q8—112no—
568C2×C22⋊Q8—112no—
569C2×#121—112no—
570C2×#121—112no—
571C2×#121—112no—
572C2×#121—112no—
573C2×#120—112no—
574C2×#120—112no—
575C4×#41—228no—
576C2×C4×Q8—111no—
577C2×C4×Q8—111no—
578C2×C4×D4—111no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—111no—
583C2×C4×D4—111no—
584C2×C4×D4—111no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4—111no—
590C2×C4×D4—111no—
591C2×C4×D4—112no—
592C2×C4×D4—228no—
593C2×C4×D4C2×D1111yescharacteristic
594C2×C4×D4C2×D1112yescomplemented
595C2×#117—111no—
596C2×#117—112no—
597C2×#117—111no—
598C2×#117C2×D1111yescharacteristic, complemented
599C22×C4⋊C4—111no—
600C22×C22⋊C4—112no—
601C22×C42—111no—
602C22×C42—111no—
603C22×C42—111no—
604#398—111no—
605#398—111no—
606#398—111no—
607#398C2×D1111yescharacteristic, complemented
608#397—111no—
609#397—111no—
610#397—111no—
611#397C2×D1111yescharacteristic, complemented
612#396—112no—
613#396—112no—
614#396—112no—
615#396C2×D1112yescomplemented
616#394—111no—
617#394—111no—
618#394—112no—
619#394—112no—
620#394—112no—
621#394—111no—
622#394C2×D1111yescharacteristic
623#394C2×D1112yescomplemented
624#392—111no—
625#392—111no—
626#392—111no—
627#392C2×D1111yescharacteristic
628#390—112no—
629#390—112no—
630#389—112no—
631#389—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#386—112no—
637#386—112no—
638#386—112no—
639#386—112no—
640#384—112no—
641#382—111no—
642#382—111no—
643#381—112no—
644#381—112no—
645#380—112no—
646#380—112no—
647#380—112no—
648#380—112no—
649#380—111no—
650#380—111no—
651#380—112no—
652#380—112no—
653#380—112no—
654#379—112no—
655#379—112no—
656C4×C4⋊C4—112no—
657C4×C4⋊C4—111no—
658C4×C4⋊C4C2×D1111yescharacteristic, complemented
659C4×C22⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4—112no—
662C4×C22⋊C4C2×D1112yescomplemented
663C22×C11—22no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—24no—
667C22×C11—24no—
668C22×C11—42no—
669C22×C11—41no—
670C22×C11—42no—
671C22×C11—41no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11C23×D411yescharacteristic
676C22×C11C23×D411yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C22×#4112yes—
679C22×C11#58512yes—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—24no—
683C2×D11—24no—
684C2×D11—22no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—24no—
688C2×D11—24no—
689C2×D11—432no—
690C2×D11—42no—
691C2×D11—41no—
692C2×D11—42no—
693C2×D11—41no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11C2×#12114yes—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—22no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11—41no—
704C4×C11—42no—
705C4×C11—42no—
706C4×C11C2×#12114yes—
707Dic11—22no—
708Dic11—22no—
709Dic11—42no—
710Dic11—41no—
711Dic11—41no—
712Dic11—42no—
713Dic11—42no—
714Dic11C2×#12114yes—
715Dic11#52514yescomplemented
716C25—112no—
717C2×#41—118no—
718C2×#41—224no—
719C2×#41—224no—
720C22×Q8—111no—
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—111no—
727C22×D4—111no—
728C22×D4—112no—
729C22×D4—224no—
730C22×D4—228no—
731C22×D4C22×D1111yescharacteristic
732C22×D4C22×D1112yes—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—112no—
739C23×C4—111no—
740C23×C4—112no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4—111no—
745C23×C4—228no—
746C23×C4—228no—
747C23×C4—228no—
748C23×C4C22×D1112yes—
749C23×C4C22×D1111yescharacteristic
750#123—228no—
751#123—228no—
752C22⋊Q8—228no—
753C22⋊Q8—228no—
754#121—228no—
755#121—228no—
756#121—228no—
757#121—228no—
758#120—228no—
759#120—228no—
760C4×Q8—224no—
761C4×Q8—224no—
762C4×D4—28no—
763C4×D4—24no—
764C4×D4—228no—
765C4×D4—228no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—224no—
769C4×D4—228no—
770C4×D4—224no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—224no—
775C4×D4—228no—
776C4×D4—228no—
777C4×D4—224no—
778#117—24no—
779#117—224no—
780#117—228no—
781#117—224no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—111no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4—112no—
796C2×C4⋊C4—224no—
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C4⋊C4C22×D1111yescharacteristic
799C2×C4⋊C4C22×D1111yescharacteristic
800C2×C4⋊C4C22×D1112yes—
801C2×C4⋊C4C22×D1112yes—
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—111no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—228no—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1111yescharacteristic
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C22⋊C4C22×D1112yes—
828C2×C22⋊C4C22×D1112yes—
829C2×C22⋊C4C22×D1112yes—
830C2×C22⋊C4C22×D1112yes—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—118no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—111no—
839C2×C42—111no—
840C2×C42—112no—
841C2×C42—224no—
842C2×C42—224no—
843C2×C42C22×D1111yescharacteristic
844C2×C42C22×D1112yes—
845C2×C42C22×D1111yescharacteristic
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—111no—
855#95—111no—
856#95C22×D1112yes—
857#95C22×D1112yes—
858#95C22×D1111yescharacteristic
859#95C22×D1111yescharacteristic
860C2×C11—44no—
861C2×C11—42no—
862C2×C11C22×#12111yescharacteristic
863C2×C11C2×#52511yescharacteristic
864C2×C11#344911yescharacteristic
865C2×C11D4×#4112yes—
866C2×C11#347512yes—
867D11—24no—
868D11—42no—
869D11—44no—
870C24—111no—
871C24—112no—
872C24—111no—
873C24—224no—
874C24—224no—
875C24—224no—
876C24—224no—
877C24—224no—
878C24—442no—
879C24—442no—
880C24C23×D1111yescharacteristic
881C24C23×D1112yes—
882#41—2232no—
883C2×Q8—114no—
884C2×Q8—222no—
885C2×Q8—222no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—22no—
890C2×D4—42no—
891C2×D4—114no—
892C2×D4—114no—
893C2×D4—118no—
894C2×D4—114no—
895C2×D4—222no—
896C2×D4—224no—
897C2×D4—222no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—224no—
903C2×D4—222no—
904C2×D4—2232no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—224no—
908C2×D4—224no—
909C2×D4—224no—
910C2×D4—224no—
911C2×D4—222no—
912C2×D4—442no—
913C2×D4—442no—
914C2×D4—442no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—111no—
921C22×C4—111no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—114no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—224no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—222no—
952C22×C4—222no—
953C22×C4—224no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—442no—
957C22×C4—442no—
958C22×C4—4432no—
959C22×C4—442no—
960C22×C4D4×D1114yescomplemented
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1112yes—
964C22×C4C23×D1112yes—
965C22×C4C23×D1112yes—
966C22×C4C23×D1111yescharacteristic
967C22×C4C23×D1111yescharacteristic
968C22×C4C23×D1111yescharacteristic
969C22×C4C23×D1111yescharacteristic
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—24no—
974C4⋊C4—42no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—224no—
979C4⋊C4—224no—
980C4⋊C4—224no—
981C4⋊C4—224no—
982C4⋊C4—224no—
983C4⋊C4—224no—
984C4⋊C4—222no—
985C4⋊C4—222no—
986C4⋊C4—222no—
987C4⋊C4—224no—
988C4⋊C4—442no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—24no—
995C22⋊C4—42no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—222no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—224no—
1009C22⋊C4—224no—
1010C22⋊C4—224no—
1011C22⋊C4—222no—
1012C22⋊C4—222no—
1013C22⋊C4—224no—
1014C22⋊C4—442no—
1015C22⋊C4—442no—
1016C22⋊C4—442no—
1017C42—22no—
1018C42—24no—
1019C42—114no—
1020C42—114no—
1021C42—114no—
1022C42—222no—
1023C42—222no—
1024C42—222no—
1025C42—222no—
1026C42—222no—
1027C42—224no—
1028C42D4×D1114yes—
1029C11#3493511yescharacteristic, complemented, Sylow
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—112no—
1041C23—112no—
1042C23—112no—
1043C23—112no—
1044C23—114no—
1045C23—2216no—
1046C23—222no—
1047C23—222no—
1048C23—221no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—221no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—448no—
1059C23—448no—
1060C23—448no—
1061C23—448no—
1062C23—448no—
1063C23—448no—
1064C23C2×D4×D1112yes—
1065C23#41×D1114yes—
1066C23C24×D1111yescharacteristic
1067Q8—228no—
1068D4—28no—
1069D4—48no—
1070D4—228no—
1071D4—228no—
1072D4—2216no—
1073D4—228no—
1074D4—228no—
1075D4—448no—
1076D4—448no—
1077D4—448no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—28no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—48no—
1097C2×C4—112no—
1098C2×C4—112no—
1099C2×C4—112no—
1100C2×C4—114no—
1101C2×C4—112no—
1102C2×C4—1116no—
1103C2×C4—112no—
1104C2×C4—112no—
1105C2×C4—228no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—228no—
1110C2×C4—221no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—444no—
1124C2×C4—448no—
1125C2×C4—444no—
1126C2×C4—444no—
1127C2×C4—448no—
1128C2×C4—448no—
1129C2×C4—444no—
1130C2×C4—444no—
1131C2×C4—448no—
1132C2×C4C2×D4×D1112yes—
1133C2×C4C2×D4×D1112yes—
1134C2×C4C2×D4×D1112yes—
1135C2×C4C2×D4×D1112yes—
1136C2×C4C2×D4×D1112yes—
1137C2×C4#41×D1112yes—
1138C22—24no—
1139C22—22no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—42no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—41no—
1150C22—114no—
1151C22—224no—
1152C22—222no—
1153C22—224no—
1154C22—222no—
1155C22—224no—
1156C22—222no—
1157C22—224no—
1158C22—224no—
1159C22—224no—
1160C22—4432no—
1161C22—442no—
1162C22—442no—
1163C22—441no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—441no—
1168C22C22×D4×D1111yescharacteristic
1169C22C22×D4×D1111yescharacteristic
1170C22C2×#41×D1111yescharacteristic
1171C22C2×#41×D1112yes—
1172C22#1062345312yes—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—41no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—41no—
1181C4—114no—
1182C4—114no—
1183C4—222no—
1184C4—222no—
1185C4—441no—
1186C4—442no—
1187C4—442no—
1188C4—442no—
1189C4—441no—
1190C4D11×#12114yes—
1191C2—44no—
1192C2—42no—
1193C2—224no—
1194C2—444no—
1195C2—442no—
1196C2C2×D11×#12111yescharacteristic
1197C2D11×#52511yescharacteristic
1198C2#1308194311yescharacteristic
1199C2#1308209912yes—
1200C2#1308216812yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2392C2
hypercenter#2392D11
hypocenterC11#34935
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C2×#10623078C2semidirect
2. C2×#10623053C2semidirect
3. C2×C4×D4×D11C2semidirect
4. #13073533C2semidirect
5. #13073528C2semidirect
6. #13073522C2semidirect
7. #13073520C2semidirect
8. #13073514C2semidirect
9. #13073512C2semidirect
10. #13073507C2semidirect
11. #13073501C2semidirect
12. #13072919C2semidirect
13. #13072917C2semidirect
14. #13071967C2semidirect
15. #13071965C2semidirect
16. #13071856C2semidirect
17. #13071854C2semidirect
18. #13071852C2semidirect
19. C4×#66937C2semidirect
20. C4×#66992C2semidirect
21. #13071020C2semidirect
22. #13070997C2semidirect
23. C11×#2392C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C11×#117C22semidirect
31. C2×#66992C22semidirect
35. C2×C4×C22⋊D11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C22×C4×Dic11C22semidirect
41. C2×#66949C22semidirect
47. C2×#66940C22semidirect
48. C2×#66940C22semidirect
50. C2×#66937C22semidirect
56. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×(C22⋊D11)⋊C4C22semidirect
59. C2×#66931C22semidirect
61. C2×C4×D44C22semidirect
64. C2×#66925C22semidirect
66. C2×C42×D11C22semidirect
67. C11×#398C22semidirect
68. C11×#397C22semidirect
69. C11×#396C22semidirect
71. C11×#394C22semidirect
73. C4×C11×C4⋊C4C22semidirect
74. C4×C11×C22⋊C4C22semidirect
77. #10622833C22semidirect
78. C4×C22⋊Dic11C22semidirect
79. #10622607C22semidirect
80. #10622607C22semidirect
81. #10622606C22semidirect
83. #10622604C22semidirect
84. #10622603C22semidirect
86. #10622596C22semidirect
87. #10622593C22semidirect
88. #10622589C22semidirect
89. #10622585C22semidirect
90. #10622574C22semidirect
91. #10622574C22semidirect
93. #10622571C22semidirect
96. #10622569C22semidirect
99. #10622566C22semidirect
100. #10622564C22semidirect
101. #10622561C22semidirect
102. #10622558C22semidirect
103. #10622555C22semidirect
104. #10622555C22semidirect
105. #10622555C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×C4⋊Dic11C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. #10622287C22semidirect
113. #10622282C22semidirect
116. #10622280C22semidirect
117. #10622280C22semidirect
118. #10622280C22semidirect
119. #10622278C22semidirect
122. #10622274C22semidirect
123. #10622263C22semidirect
124. #10622263C22semidirect
125. #10622260C22semidirect
143. C2×#4339D4semidirect
255. C42×D11D4semidirect
293. C22×C4×C11C2×D4semidirect
316. C2×C22⋊D11C2×D4semidirect
317. C2×C22⋊D11#41semidirect
366. C2×C4×D11C2×D4semidirect
370. C2×Dic22C2×D4semidirect
448. #2392D11semidirect
559. C4×D11#121semidirect
594. C2×C4×D4C2×D11semidirect
598. C2×#117C2×D11semidirect
607. #398C2×D11semidirect
611. #397C2×D11semidirect
615. #396C2×D11semidirect
623. #394C2×D11semidirect
658. C4×C4⋊C4C2×D11semidirect
662. C4×C22⋊C4C2×D11semidirect
715. Dic11#525semidirect
960. C22×C4D4×D11semidirect
1029. C11#34935semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×#106230532
C2×C4×D4×D112
#130735332
#130735282
#130735222
#130735202
#130735142
#130735122
#130735072
#130735012
#130729192
#130729172
#130719672
#130719652
#130718562
#130718542
#130718522
C4×#669372
C4×#669922
#130710202
#130709972
C11×#23922
#3493511