Finite Group Databasebeta

← #14925736

Subgroups — #14925736

Order 2816.

2036 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073864C212yesmaximal, complemented
2#13073863C212yesmaximal, complemented
3#13073857C211yesmaximal, characteristic, complemented
4#13073788C211yesmaximal, characteristic, complemented
5#13073786C211yesmaximal, characteristic, complemented
6#13073531C211yesmaximal, characteristic
7#13073022C212yesmaximal, complemented
8#13073021C211yesmaximal, characteristic, complemented
9#13072109C211yesmaximal, characteristic, complemented
10#13072108C211yesmaximal, characteristic, complemented
11#13072103C212yesmaximal, complemented
12#13071905C212yesmaximal, complemented
13#13071901C212yesmaximal, complemented
14#13071187C211yesmaximal, characteristic, complemented
15#13071128C212yesmaximal, complemented
16#13071124C211yesmaximal, characteristic, complemented
17#13071122C211yesmaximal, characteristic, complemented
18#13071013C212yesmaximal, complemented
19#13071011C211yesmaximal, characteristic, complemented
20#13071009C211yesmaximal, characteristic, complemented
21C4×#66946C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2495C211yesmaximal, characteristic, complemented
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×#66948C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×#66946C2212yes—
31C2×#66941C2211yescharacteristic
32C2×#66940C2212yes—
33C2×#66937C2212yes—
34C2×(C22⋊D11)⋊C4C2211yescharacteristic
35C2×(C22⋊D11)⋊C4C2211yescharacteristic
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×C4×D44C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2212yes—
40C11×#400C2212yes—
41C11×#397C2212yes—
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#388C2212yes—
45C11×#383C2212yes—
46C11×#382C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51#10622825C2211yescharacteristic
52#10622606C2212yes—
53#10622604C2212yes—
54#10622603C2212yes—
55#10622601C2211yescharacteristic
56#10622600C2211yescharacteristic
57#10622600C2211yescharacteristic
58#10622600C2211yescharacteristic
59#10622595C2212yes—
60#10622590C2211yescharacteristic
61#10622590C2211yescharacteristic
62#10622589C2211yescharacteristic
63C4⋊C4×Dic11C2211yescharacteristic
64C4⋊C4×Dic11C2211yescharacteristic
65C4⋊C4×Dic11C2211yescharacteristic
66C4⋊C4×Dic11C2211yescharacteristic
67#10622586C2211yescharacteristic
68#10622585C2212yes—
69#10622585C2212yes—
70#10622572C2212yes—
71#10622572C2212yes—
72#10622571C2212yes—
73#10622570C2212yes—
74#10622569C2212yes—
75#10622560C2212yes—
76#10622556C2212yes—
77C22⋊C4×Dic11C2212yes—
78C22⋊C4×Dic11C2211yescharacteristic
79C22⋊C4×Dic11C2211yescharacteristic
80#10622553C2212yes—
81#10622552C2211yescharacteristic
82C4×(C2×D11)⋊C4C2211yescharacteristic
83C4×(C2×D11)⋊C4C2212yes—
84#10622550C2212yes—
85#10622549C2211yescharacteristic
86C4×Dic11⋊C4C2211yescharacteristic
87C42×Dic11C2211yescharacteristic
88#10622541C2211yescharacteristic
89#10622288C2212yes—
90#10622288C2212yes—
91#10622286C2212yes—
92#10622286C2212yes—
93#10622286C2212yes—
94#10622285C2212yes—
95#10622282C2212yes—
96#10622280C2212yes—
97#10622280C2212yes—
98#10622280C2212yes—
99#10622279C2212yes—
100#10622279C2212yes—
101#10622279C2212yes—
102#10622279C2212yes—
103#10622279C2211yescharacteristic
104#10622279C2211yescharacteristic
105#10622279C2212yes—
106#10622278C2212yes—
107#10622278C2212yes—
108#10622277C2212yes—
109#10622277C2212yes—
110#10622277C2212yes—
111#10622271C2212yes—
112#10622271C2212yes—
113#10622264C2212yes—
114#10622264C2212yes—
115#10622263C2212yes—
116#10622263C2212yes—
117#10622262C2212yes—
118#10622262C2211yescharacteristic
119#10622262C2211yescharacteristic
120#10622261C2212yes—
121#10622261C2212yes—
122#10622259C2212yes—
123C23×C4×C11C2311yescharacteristic
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2311yescharacteristic
126C23×Dic11C2311yescharacteristic
127C23×Dic11C2311yescharacteristic
128C22×D44C2312yes—
129C22×D44C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2312yes—
132C22×C4×D11C2312yes—
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2312yes—
135C22×C4×D11C2311yescharacteristic
136C22×Dic22C2312yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C22⋊Dic11C2311yescharacteristic
151C2×C22⋊Dic11C2312yes—
152#66983—24no—
153C4×C22⋊D11—24no—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2311yescharacteristic
156C2×(C2×D11)⋊C4C2311yescharacteristic
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×Dic11⋊C4C2311yescharacteristic
173C2×Dic11⋊C4C2311yescharacteristic
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2311yescharacteristic
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×C4×Dic11—24no—
181C2×C4×Dic11C2311yescharacteristic
182C2×C4×Dic11C2312yes—
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196#66948—24no—
197#66946—24no—
198#66946—24no—
199#66946—44no—
200#66941—24no—
201#66940—44no—
202#66937—28no—
203(C22⋊D11)⋊C4—24no—
204(C22⋊D11)⋊C4—24no—
205(C22⋊D11)⋊C4—44no—
206C4×D44—24no—
207C42×D11—28no—
208C42×D11—24no—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2311yescharacteristic
213C11×#95C2311yescharacteristic
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238#34943—111nomaximal, Sylow
239C24×C11C2411yescharacteristic
240C23×D11C2412yes—
241C23×D11C2411yescharacteristic
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2412yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—42no—
260C2×C22⋊D11#4114yes—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—41no—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C2×D44—24no—
278C2×D44—24no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—42no—
282C2×D44#4114yes—
283C2×C4×D11—22no—
284C2×C4×D11—24no—
285C2×C4×D11—22no—
286C2×C4×D11—24no—
287C2×C4×D11—22no—
288C2×C4×D11—24no—
289C2×C4×D11—24no—
290C2×C4×D11—24no—
291C2×C4×D11—24no—
292C2×C4×D11—22no—
293C2×C4×D11—24no—
294C2×C4×D11—22no—
295C2×C4×D11—24no—
296C2×C4×D11—22no—
297C2×C4×D11—22no—
298C2×C4×D11—22no—
299C2×C4×D11—42no—
300C2×C4×D11—41no—
301C2×Dic22—24no—
302C2×Dic22—42no—
303C2×Dic22—42no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4—42no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—24no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—42no—
314C42×C11—24no—
315C42×C11—22no—
316C42×C11—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—42no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—42no—
329(C2×D11)⋊C4—42no—
330(C2×D11)⋊C4—42no—
331(C2×D11)⋊C4—42no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4—42no—
334C4⋊Dic11—22no—
335C4⋊Dic11—22no—
336C4⋊Dic11—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—22no—
342Dic11⋊C4—42no—
343Dic11⋊C4—42no—
344Dic11⋊C4—42no—
345C4×Dic11—22no—
346C4×Dic11—24no—
347C4×Dic11—22no—
348C4×Dic11—24no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—24no—
353C4×Dic11—22no—
354C4×Dic11—24no—
355C4×Dic11—22no—
356C4×Dic11—41no—
357C4×Dic11#4114yes—
358C4×Dic11#4114yes—
359C4×Dic11#4114yes—
360#2572—112no—
361#2572—112no—
362#2571—111no—
363#2563—111no—
364#2563—111no—
365#2537—111no—
366#2495—112no—
367#2495—111no—
368#2495D1111yescharacteristic, complemented
369#2420—112no—
370#2420—111no—
371#2420—111no—
372#2398—112no—
373#2398—112no—
374C4×C4⋊Q8—111no—
375C4×#121—111no—
376C4×#121—112no—
377C4×#121—111no—
378#2283—112no—
379#2283—111no—
380#2283—111no—
381C42×D4—111no—
382C42×D4—111no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11C2×#4112yes—
390C23×C11C2511yescharacteristic
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11—21no—
396C22×D11—22no—
397C22×D11—21no—
398C22×D11—22no—
399C22×D11—21no—
400C22×D11—22no—
401C22×D11—21no—
402C22×D11—22no—
403C22×D11C2×#4112yes—
404C22×D11C2×#4114yes—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—21no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—21no—
429C2×C4×C11—22no—
430C2×C4×C11—21no—
431C2×C4×C11—44no—
432C2×C4×C11C2×#4112yes—
433C2×C4×C11C2×#4112yes—
434C2×C4×C11C2×#4112yes—
435C2×C4×C11C2×#4112yes—
436C22⋊D11—28no—
437C22⋊D11—48no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—22no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—22no—
447C2×Dic11—21no—
448C2×Dic11—21no—
449C2×Dic11—22no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—21no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—44no—
461C2×Dic11—44no—
462C2×Dic11C2×#4112yes—
463C2×Dic11C2×#4112yes—
464C2×Dic11C2×#4112yes—
465C2×Dic11C2×#4112yes—
466C2×Dic11C2×#4112yes—
467C2×Dic11C2×#4112yes—
468C2×Dic11C2×#4112yes—
469C2×Dic11H(5,𝔽2)12yes—
470D44—28no—
471D44—48no—
472C4×D11—44no—
473C4×D11—48no—
474C4×D11—44no—
475C4×D11—48no—
476C4×D11—44no—
477C4×D11—48no—
478Dic22—48no—
479C2×C4⋊Q8—111no—
480C2×#121—111no—
481C2×#121—111no—
482C2×#121—112no—
483C2×C4×Q8—112no—
484C2×C4×D4—111no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487C2×C4×D4—112no—
488C2×C4×D4—111no—
489C2×C4×D4—111no—
490C2×C4×D4—112no—
491C2×C4×D4—111no—
492C22×C42—111no—
493C22×C42—112no—
494C22×C42—111no—
495#400—112no—
496#400—112no—
497#400—112no—
498#400C2×D1112yes—
499#397—112no—
500#397—112no—
501#397—112no—
502#397C2×D1112yes—
503#394—112no—
504#394—112no—
505#394—112no—
506#394—112no—
507#393—112no—
508#393—112no—
509#393—112no—
510#393—112no—
511#391—112no—
512#390—111no—
513#390—112no—
514#390—111no—
515#389—112no—
516#389—112no—
517#389—111no—
518#389—111no—
519#389C2×D1111yescharacteristic
520#389C2×D1111yescharacteristic
521#388—112no—
522#388—112no—
523#388—112no—
524#388C2×D1112yes—
525#386—112no—
526#386—112no—
527#386—112no—
528#386—112no—
529#384—111no—
530#383—112no—
531#383—112no—
532#383—112no—
533#383C2×D1112yes—
534#382—111no—
535#382—111no—
536#382—111no—
537#382—112no—
538#382—112no—
539#382C2×D1111yescharacteristic
540#381—112no—
541#381—112no—
542#381—112no—
543#381—112no—
544#380—111no—
545#380—111no—
546#380—111no—
547#380—111no—
548#380—112no—
549#380—112no—
550#380—112no—
551#380C2×D1111yescharacteristic
552#380C2×D1111yescharacteristic
553C4×C4⋊C4—111no—
554C4×C4⋊C4—111no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—111no—
558C4×C4⋊C4—112no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4—111no—
561C4×C4⋊C4C2×D1111yescharacteristic
562C4×C22⋊C4—111no—
563C4×C22⋊C4—111no—
564C4×C22⋊C4—112no—
565C4×C22⋊C4—112no—
566C4×C22⋊C4—111no—
567C4×C22⋊C4—111no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—111no—
570C4×C22⋊C4—112no—
571C4×C22⋊C4—112no—
572C4×C22⋊C4—112no—
573C4×C22⋊C4—112no—
574C4×C22⋊C4C2×D1111yescharacteristic
575#376—112no—
576#376—112no—
577C43—111no—
578C22×C11—22no—
579C22×C11—22no—
580C22×C11—22no—
581C22×C11—41no—
582C22×C11—41no—
583C22×C11—41no—
584C22×C11—41no—
585C22×C11C22×#4111yescharacteristic
586C22×C11C22×#4111yescharacteristic
587C22×C11C22×#4111yescharacteristic
588C22×C11C22×#4111yescharacteristic
589C22×C11C22×#4111yescharacteristic
590C22×C11C2×H(5,𝔽2)11yescharacteristic
591C22×C11#58511yescharacteristic
592C2×D11—24no—
593C2×D11—22no—
594C2×D11—22no—
595C2×D11—24no—
596C2×D11—22no—
597C2×D11—24no—
598C2×D11—42no—
599C2×D11—41no—
600C2×D11—42no—
601C2×D11—41no—
602C2×D11—42no—
603C2×D11—41no—
604C2×D11—42no—
605C2×D11—41no—
606C4×C11—22no—
607C4×C11—41no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—41no—
611C4×C11—42no—
612C4×C11—41no—
613C4×C11—41no—
614C4×C11—42no—
615C4×C11#52914yes—
616Dic11—22no—
617Dic11—22no—
618Dic11—41no—
619Dic11—42no—
620Dic11—41no—
621Dic11—42no—
622Dic11—41no—
623Dic11—42no—
624Dic11#52914yes—
625Dic11#55514yes—
626C22×Q8—112no—
627C22×D4—111no—
628C22×D4—112no—
629C22×D4—111no—
630C22×D4—112no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—112no—
634C23×C4—111no—
635C23×C4—112no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—112no—
639C23×C4C22×D1111yescharacteristic
640C4⋊Q8—224no—
641#121—228no—
642#121—224no—
643#121—224no—
644C4×Q8—444no—
645C4×D4—224no—
646C4×D4—224no—
647C4×D4—224no—
648C4×D4—224no—
649C4×D4—224no—
650C4×D4—224no—
651C4×D4—444no—
652C4×D4—444no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—111no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—111no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4—112no—
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—111no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—112no—
680C2×C22⋊C4—112no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—112no—
683C2×C22⋊C4—112no—
684C2×C22⋊C4—112no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4C22×D1111yescharacteristic
688C2×C22⋊C4C22×D1111yescharacteristic
689C2×C22⋊C4C22×D1112yes—
690C2×C22⋊C4C22×D1112yes—
691C2×C42—111no—
692C2×C42—111no—
693C2×C42—111no—
694C2×C42—112no—
695C2×C42—112no—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—112no—
699C2×C42—111no—
700C2×C42—111no—
701C2×C42—112no—
702C2×C42—111no—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—228no—
707C2×C42—224no—
708C2×C42—224no—
709C2×C42C22×D1111yescharacteristic
710C2×C42C22×D1112yes—
711C2×C42C22×D1111yescharacteristic
712#95—112no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—111no—
720#95—112no—
721#95—111no—
722#95—111no—
723#95—111no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95C22×D1112yes—
733#95C22×D1112yes—
734#95C22×D1112yes—
735#95C22×D1111yescharacteristic
736#95C22×D1111yescharacteristic
737#95C22×D1112yes—
738#95C22×D1112yes—
739#95C22×D1112yes—
740#95C22×D1112yes—
741C2×C11—42no—
742C2×C11C2×#52911yescharacteristic
743C2×C11C2×#52911yescharacteristic
744C2×C11#346011yescharacteristic
745C2×C11C2×#55511yescharacteristic
746C2×C11#347511yescharacteristic
747C2×C11#347511yescharacteristic
748C2×C11#348111yescharacteristic
749D11—44no—
750D11—42no—
751C24—111no—
752C24—112no—
753C24C23×D1111yescharacteristic
754C2×Q8—224no—
755C2×Q8—442no—
756C2×Q8—442no—
757C2×D4—114no—
758C2×D4—114no—
759C2×D4—224no—
760C2×D4—224no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—224no—
764C2×D4—224no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—442no—
768C2×D4—442no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—111no—
777C22×C4—112no—
778C22×C4—111no—
779C22×C4—111no—
780C22×C4—112no—
781C22×C4—112no—
782C22×C4—224no—
783C22×C4—224no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—224no—
788C22×C4—224no—
789C22×C4—224no—
790C22×C4—222no—
791C22×C4—224no—
792C22×C4—224no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—224no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—442no—
804C22×C4—441no—
805C22×C4—441no—
806C22×C4C23×D1112yes—
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1112yes—
810C22×C4C23×D1112yes—
811C22×C4C23×D1111yescharacteristic
812C22×C4C23×D1112yes—
813C22×C4C23×D1111yescharacteristic
814C22×C4C23×D1111yescharacteristic
815C22×C4C23×D1111yescharacteristic
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—42no—
821C4⋊C4—42no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—224no—
826C4⋊C4—224no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—442no—
831C4⋊C4—442no—
832C4⋊C4—442no—
833C22⋊C4—22no—
834C22⋊C4—24no—
835C22⋊C4—22no—
836C22⋊C4—42no—
837C22⋊C4—224no—
838C22⋊C4—224no—
839C22⋊C4—222no—
840C22⋊C4—224no—
841C22⋊C4—222no—
842C22⋊C4—224no—
843C22⋊C4—224no—
844C22⋊C4—224no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C22⋊C4—442no—
848C22⋊C4—442no—
849C22⋊C4—442no—
850C22⋊C4—442no—
851C22⋊C4—442no—
852C22⋊C4—442no—
853C22⋊C4—442no—
854C42—24no—
855C42—22no—
856C42—22no—
857C42—114no—
858C42—114no—
859C42—114no—
860C42—224no—
861C42—224no—
862C42—222no—
863C42—222no—
864C42—222no—
865C42—222no—
866C42—222no—
867C42—224no—
868C42—224no—
869C42—222no—
870C42—222no—
871C42—441no—
872C11#3494311yescharacteristic, complemented, Sylow
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—112no—
880C23—114no—
881C23—221no—
882C23—221no—
883C23—222no—
884C23—222no—
885C23—221no—
886C23—222no—
887C23—222no—
888C23—221no—
889C23—221no—
890C23—222no—
891C23—221no—
892C23—222no—
893C23#41×D1112yes—
894C23C24×D1111yescharacteristic
895Q8—448no—
896D4—228no—
897D4—228no—
898D4—448no—
899D4—448no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—44no—
927C2×C4—112no—
928C2×C4—112no—
929C2×C4—112no—
930C2×C4—112no—
931C2×C4—112no—
932C2×C4—112no—
933C2×C4—112no—
934C2×C4—112no—
935C2×C4—221no—
936C2×C4—221no—
937C2×C4—221no—
938C2×C4—221no—
939C2×C4—221no—
940C2×C4—221no—
941C2×C4—221no—
942C2×C4—222no—
943C2×C4—221no—
944C2×C4—221no—
945C2×C4—221no—
946C2×C4—221no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—221no—
954C2×C4—221no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—448no—
958C2×C4—448no—
959C2×C4—444no—
960C2×C4—448no—
961C2×C4—444no—
962C2×C4—444no—
963C2×C4—444no—
964C2×C4—444no—
965C2×C4#41×D1112yes—
966C2×C4#41×D1112yes—
967C2×C4#41×D1112yes—
968C2×C4#41×D1112yes—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—41no—
976C22—222no—
977C22—224no—
978C22—222no—
979C22—224no—
980C22—222no—
981C22—224no—
982C22—442no—
983C22—441no—
984C22—441no—
985C22—442no—
986C22—442no—
987C22—441no—
988C22—441no—
989C22—442no—
990C22C2×#41×D1111yescharacteristic
991C22C2×#41×D1111yescharacteristic
992C22C2×#41×D1111yescharacteristic
993C22C2×#41×D1111yescharacteristic
994C22C2×#41×D1111yescharacteristic
995C22D11×H(5,𝔽2)11yescharacteristic
996C22#1062345711yescharacteristic
997C4—22no—
998C4—42no—
999C4—41no—
1000C4—41no—
1001C4—42no—
1002C4—41no—
1003C4—42no—
1004C4—41no—
1005C4—42no—
1006C4—114no—
1007C4—114no—
1008C4—222no—
1009C4—222no—
1010C4—441no—
1011C4—441no—
1012C4—441no—
1013C4—442no—
1014C4—442no—
1015C4—442no—
1016C4#1062323714yes—
1017C2—42no—
1018C2—442no—
1019C2—444no—
1020C2D11×#52911yescharacteristic
1021C2C2×#1062323711yescharacteristic
1022C2#1308203611yescharacteristic
1023C2D11×#55511yescharacteristic
1024C2#1308216911yescharacteristic
1025C2#1308218111yescharacteristic
1026C2#1308222311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2495C2
prime radical#13073531C2
hypercenter#2495D11
hypocenterC11#34943
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2495

Complements

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

NH ≅ G/Ntype
1. #13073864C2semidirect
2. #13073863C2semidirect
3. #13073857C2semidirect
4. #13073788C2semidirect
5. #13073786C2semidirect
7. #13073022C2semidirect
8. #13073021C2semidirect
9. #13072109C2semidirect
10. #13072108C2semidirect
11. #13072103C2semidirect
12. #13071905C2semidirect
13. #13071901C2semidirect
14. #13071187C2semidirect
15. #13071128C2semidirect
16. #13071124C2semidirect
17. #13071122C2semidirect
18. #13071013C2semidirect
19. #13071011C2semidirect
20. #13071009C2semidirect
21. C4×#66946C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2495C2semidirect
368. #2495D11semidirect
872. C11#34943semidirect

Maximal subgroups

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

subgroupindex
#130738642
#130738632
#130738572
#130737882
#130737862
#130735312
#130730222
#130730212
#130721092
#130721082
#130721032
#130719052
#130719012
#130711872
#130711282
#130711242
#130711222
#130710132
#130710112
#130710092
C4×#669462
C4×(C22⋊D11)⋊C42
C11×#24952
#3494311