Finite Group Databasebeta

← #14925574

Subgroups — #14925574

Order 2816.

2308 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C212yesmaximal, complemented
2#13073704C212yesmaximal, complemented
3#13073696C212yesmaximal, complemented
4#13073644C211yesmaximal, characteristic, complemented
5#13073603C211yesmaximal, characteristic, complemented
6#13073568C211yesmaximal, characteristic
7#13073537C211yesmaximal, characteristic
8#13073126C211yesmaximal, characteristic, complemented
9#13072985C212yesmaximal, complemented
10#13072467C211yesmaximal, characteristic
11#13072466C211yesmaximal, characteristic
12#13072210C212yesmaximal, complemented
13#13071893C212yesmaximal, complemented
14#13071889C212yesmaximal, complemented
15#13071187C211yesmaximal, characteristic, complemented
16#13071187C211yesmaximal, characteristic, complemented
17#13071183C211yesmaximal, characteristic, complemented
18#13071150C212yesmaximal, complemented
19#13071074C211yesmaximal, characteristic
20#13071074C211yesmaximal, characteristic
21C4×#66940C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic
23C11×#2506C211yesmaximal, characteristic, complemented
24C2×C11×#125C2212yes—
25#10623219—216no—
26C2×#66949C2212yes—
27C2×#66949C2212yes—
28C2×#66949C2212yes—
29C2×#66949C2212yes—
30C2×#66949C2212yes—
31C2×#66946C2211yescharacteristic
32C2×#66946C2211yescharacteristic
33C2×#66945C2212yes—
34C2×#66945C2212yes—
35C2×#66941C2212yes—
36C2×#66941C2212yes—
37C2×#66941C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66940C2212yes—
40C2×#66940C2212yes—
41C2×#66940C2212yes—
42C2×#66940C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C42×D11C2212yes—
46C2×#66923C2212yes—
47C2×#66922C2211yescharacteristic
48C2×C4×Dic22C2211yescharacteristic
49C11×#400C2212yes—
50C11×#398C2212yes—
51C11×#389C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#389C2211yescharacteristic
55C11×#387C2212yes—
56C11×#384C2211yescharacteristic
57C4×C11×C4⋊C4C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59#10622607C2212yes—
60#10622607C2212yes—
61#10622605C2212yes—
62#10622605C2212yes—
63#10622603C2212yes—
64#10622603C2212yes—
65#10622602C2212yes—
66#10622601C2211yescharacteristic
67#10622601C2211yescharacteristic
68#10622598C2211yescharacteristic
69#10622598C2211yescharacteristic
70#10622597C2212yes—
71#10622592C2212yes—
72#10622589C2211yescharacteristic
73#10622589C2211yescharacteristic
74C4⋊C4×Dic11C2211yescharacteristic
75C4⋊C4×Dic11C2212yes—
76C4⋊C4×Dic11C2211yescharacteristic
77C4⋊C4×Dic11C2211yescharacteristic
78C4⋊C4×Dic11C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80C4⋊C4×Dic11C2211yescharacteristic
81#10622587C2212yes—
82#10622586C2212yes—
83#10622586C2211yescharacteristic
84#10622586C2211yescharacteristic
85#10622585C2212yes—
86#10622585C2212yes—
87#10622552C2211yescharacteristic
88#10622552C2211yescharacteristic
89C4×(C2×D11)⋊C4C2212yes—
90#10622546C2212yes—
91C4×Dic11⋊C4C2211yescharacteristic
92C4×Dic11⋊C4C2211yescharacteristic
93C42×Dic11C2211yescharacteristic
94C42×Dic11C2211yescharacteristic
95C42×Dic11C2211yescharacteristic
96#10622541C2211yescharacteristic
97#10622541C2211yescharacteristic
98#10622289C2212yes—
99#10622289C2212yes—
100#10622286C2212yes—
101#10622286C2212yes—
102#10622283C2212yes—
103#10622283C2212yes—
104#10622281C2212yes—
105#10622280C2212yes—
106#10622279C2212yes—
107#10622279C2212yes—
108#10622279C2212yes—
109#10622279C2212yes—
110#10622273C2212yes—
111#10622270C2212yes—
112#10622270C2212yes—
113#10622269C2212yes—
114#10622262C2211yescharacteristic
115#10622262C2212yes—
116#10622262C2212yes—
117#10622262C2211yescharacteristic
118#10622262C2211yescharacteristic
119#10622262C2211yescharacteristic
120#10622260C2212yes—
121#10622259C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×D44C2311yescharacteristic
125C22×C4×D11C2312yes—
126C22×C4×D11C2312yes—
127C22×C4×D11C2312yes—
128C22×Dic22C2312yes—
129C22×Dic22C2312yes—
130C22×Dic22C2312yes—
131C22×Dic22C2311yescharacteristic
132C11×#125—28no—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2312yes—
148C2×C42×C11C2311yescharacteristic
149C2×(C2×D11)⋊C4C2312yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2311yescharacteristic
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2312yes—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167C2×Dic11⋊C4C2311yescharacteristic
168C2×Dic11⋊C4C2311yescharacteristic
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203#66949—28no—
204#66949—28no—
205#66949—28no—
206#66949—28no—
207#66949—28no—
208#66946—24no—
209#66946Q818yescomplemented
210#66945—28no—
211#66945—28no—
212#66941—28no—
213#66941—24no—
214#66941—28no—
215#66941—24no—
216#66940—24no—
217#66940—28no—
218#66940—28no—
219#66940—28no—
220#66940D418yescomplemented
221C4×D44—24no—
222C42×D11—28no—
223#66923—28no—
224#66922—24no—
225C4×Dic22—24no—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247#34929—111nomaximal, Sylow
248C23×D11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2412yes—
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2411yescharacteristic
271C2×D44—22no—
272C2×D44—22no—
273C2×D44C2×Q814yes—
274C2×C4×D11—24no—
275C2×C4×D11—24no—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—42no—
282C2×C4×D11C2×Q818yes—
283C2×Dic22—22no—
284C2×Dic22—22no—
285C2×Dic22—24no—
286C2×Dic22—24no—
287C2×Dic22—24no—
288C2×Dic22—24no—
289C2×Dic22—24no—
290C2×Dic22—24no—
291C2×Dic22—24no—
292C2×Dic22—42no—
293C2×Dic22—42no—
294C2×Dic22C2×D414yes—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—24no—
297C11×C4⋊C4—24no—
298C11×C4⋊C4—24no—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—22no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—24no—
305C11×C4⋊C4C2×D414yes—
306C11×C4⋊C4C2×Q814yes—
307C42×C11—24no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—22no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—42no—
320(C2×D11)⋊C4—42no—
321(C2×D11)⋊C4C2×Q818yes—
322C4⋊Dic11—24no—
323C4⋊Dic11—24no—
324C4⋊Dic11—22no—
325C4⋊Dic11—24no—
326C4⋊Dic11—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11#4114yes—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338Dic11⋊C4—24no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—42no—
342Dic11⋊C4C2×D414yes—
343Dic11⋊C4C2×D414yes—
344Dic11⋊C4#4114yes—
345C4×Dic11—24no—
346C4×Dic11—24no—
347C4×Dic11—24no—
348C4×Dic11—24no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—22no—
355C4×Dic11—22no—
356C4×Dic11—22no—
357C4×Dic11—41no—
358C4×Dic11—41no—
359C4×Dic11—41no—
360C4×Dic11C2×D414yes—
361C4×Dic11C2×D414yes—
362C4×Dic11C2×D414yes—
363C4×Dic11C2×Q814yes—
364C4×Dic11#4114yes—
365C2×#533—112no—
366#2556—112no—
367#2556—112no—
368#2551—111no—
369#2546—111no—
370#2542—111no—
371#2538—111no—
372#2506—111no—
373#2506D1111yescharacteristic, complemented
374#2492—112no—
375#2452—111no—
376#2452—111no—
377#2429—112no—
378#2396—112no—
379#2396—112no—
380C4×C4⋊Q8—111no—
381C4×C4⋊Q8—111no—
382C4×C4⋊Q8—111no—
383C4×C22⋊Q8—112no—
384#2293—111no—
385#2293—111no—
386C42×Q8—111no—
387C42×D4—111no—
388C23×C11C2511yescharacteristic
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11C22×Q814yes—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11C22×D412yes—
422C2×C4×C11C22×D412yes—
423C2×C4×C11C22×D412yes—
424C2×C4×C11C22×Q814yes—
425C2×C4×C11C22×Q812yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C2×Dic11—22no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—21no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—21no—
448C2×Dic11—21no—
449C2×Dic11—22no—
450C2×Dic11C22×D412yes—
451C2×Dic11C22×D412yes—
452C2×Dic11C22×D412yes—
453C2×Dic11C22×D412yes—
454C2×Dic11C22×Q812yes—
455C2×Dic11C22×Q812yes—
456C2×Dic11C2×#4112yes—
457C2×Dic11C2×#4112yes—
458C2×Dic11C2×#4114yes—
459C2×Dic11C2×#4112yes—
460C2×Dic11C2×#4112yes—
461C2×Dic112−1+412yes—
462D44—28no—
463C4×D11—216no—
464C4×D11—48no—
465C4×D11—48no—
466Dic22—28no—
467Dic22—48no—
468Dic22—48no—
469Dic22—48no—
470#533—2216no—
471C2×C4⋊Q8—111no—
472C2×C4⋊Q8—111no—
473C2×C4⋊Q8—112no—
474C2×C4⋊Q8—112no—
475C2×C4⋊Q8—111no—
476C2×#125—112no—
477C2×#125C2×D1112yes—
478C2×C22⋊Q8—112no—
479C2×C22⋊Q8—112no—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—112no—
482C2×C22⋊Q8—112no—
483C2×C4×Q8—111no—
484C2×C4×Q8—112no—
485C2×C4×Q8—112no—
486C2×C4×Q8—112no—
487C2×C4×Q8—111no—
488C2×C4×Q8—111no—
489C2×C4×D4—111no—
490C2×C4×D4—111no—
491C2×C4×D4—111no—
492C2×#117—112no—
493C2×#117—112no—
494C22×C42—112no—
495#400—112no—
496#400C2×D1112yes—
497#399—112no—
498#399—112no—
499#398—112no—
500#398—112no—
501#398—112no—
502#398C2×D1112yes—
503#396—112no—
504#396—112no—
505#396—112no—
506#396—112no—
507#395—112no—
508#395—112no—
509#393—112no—
510#393—112no—
511#391—112no—
512#391—112no—
513#391—112no—
514#391—112no—
515#390—111no—
516#390—111no—
517#390—111no—
518#390—111no—
519#389—112no—
520#389—112no—
521#389—112no—
522#389—111no—
523#389—111no—
524#389—111no—
525#389—111no—
526#389—111no—
527#389—111no—
528#389—112no—
529#389C2×D1111yescharacteristic
530#389C2×D1111yescharacteristic
531#389C2×D1111yescharacteristic
532#389C2×D1111yescharacteristic
533#388—112no—
534#388—112no—
535#388—112no—
536#388—112no—
537#387—112no—
538#387C2×D1112yes—
539#385—112no—
540#385—112no—
541#384—111no—
542#384—111no—
543#384C2×D1111yescharacteristic
544#380—112no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—111no—
548C4×C4⋊C4—112no—
549C4×C4⋊C4—111no—
550C4×C4⋊C4—111no—
551C4×C4⋊C4—111no—
552C4×C4⋊C4—111no—
553C4×C4⋊C4—111no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—112no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—111no—
558C4×C4⋊C4—111no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4C2×D1111yescharacteristic
561C4×C4⋊C4C2×D1111yescharacteristic
562C4×C22⋊C4—112no—
563C4×C22⋊C4—112no—
564C4×C22⋊C4—112no—
565C4×C22⋊C4—112no—
566C4×C22⋊C4—112no—
567C43—111no—
568C43—111no—
569C43—111no—
570C22×C11C23×D411yescharacteristic
571C22×C11C23×Q811yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C22×#4111yescharacteristic
574C22×C11C22×#4111yescharacteristic
575C22×C11C2×2−1+411yescharacteristic
576C22×C11#58511yescharacteristic
577C2×D11—24no—
578C2×D11—24no—
579C2×D11—24no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C4×C11—22no—
585C4×C11—24no—
586C4×C11—22no—
587C4×C11—22no—
588C4×C11—22no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—41no—
592C4×C11—42no—
593C4×C11—41no—
594C4×C11#53314yescomplemented
595Dic11—22no—
596Dic11—22no—
597Dic11—24no—
598Dic11—22no—
599Dic11—22no—
600Dic11—22no—
601Dic11—42no—
602Dic11—41no—
603Dic11—42no—
604Dic11#53214yes—
605Dic11D4×Q814yes—
606C22×Q8—111no—
607C22×Q8—112no—
608C22×Q8—112no—
609C22×Q8—112no—
610C22×D4—111no—
611C23×C4—112no—
612C23×C4—112no—
613C23×C4—112no—
614C4⋊Q8—224no—
615C4⋊Q8—224no—
616C4⋊Q8—228no—
617C4⋊Q8—224no—
618C4⋊Q8—228no—
619#125—28no—
620#125—228no—
621C22⋊Q8—228no—
622C22⋊Q8—228no—
623C22⋊Q8—228no—
624C22⋊Q8—228no—
625C22⋊Q8—228no—
626C4×Q8—118no—
627C4×Q8—224no—
628C4×Q8—228no—
629C4×Q8—228no—
630C4×Q8—228no—
631C4×Q8—224no—
632C4×D4—118no—
633C4×D4—224no—
634C4×D4—224no—
635#117—228no—
636#117—228no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4C22×D1112yes—
661C2×C4⋊C4C22×D1112yes—
662C2×C4⋊C4C22×D1111yescharacteristic
663C2×C4⋊C4C22×D1112yes—
664C2×C4⋊C4C22×D1112yes—
665C2×C4⋊C4C22×D1112yes—
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1112yes—
668C2×C4⋊C4C22×D1111yescharacteristic
669C2×C4⋊C4C22×D1111yescharacteristic
670C2×C4⋊C4C22×D1111yescharacteristic
671C2×C4⋊C4C22×D1111yescharacteristic
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
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×C42—111no—
684C2×C42—111no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—112no—
689C2×C42—112no—
690C2×C42—112no—
691C2×C42—111no—
692C2×C42—111no—
693C2×C42—111no—
694C2×C42—111no—
695C2×C42—112no—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—111no—
700C2×C42—111no—
701C2×C42—111no—
702C2×C42—111no—
703C2×C42—228no—
704C2×C42C22×D1111yescharacteristic
705C2×C42C22×D1111yescharacteristic
706C2×C42C22×D1112yes—
707C2×C42C22×D1111yescharacteristic
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—111no—
713#95—111no—
714#95—111no—
715#95—111no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95C22×D1112yes—
723#95C22×D1112yes—
724#95C22×D1112yes—
725#95C22×D1111yescharacteristic
726#95C22×D1111yescharacteristic
727#95C22×D1112yes—
728#95C22×D1112yes—
729C2×C11C2×#53211yescharacteristic
730C2×C11C2×#53311yescharacteristic
731C2×C11#346111yescharacteristic
732C2×C11C2×D4×Q811yescharacteristic
733C2×C11D4×#4111yescharacteristic
734C2×C11Q8×#4111yescharacteristic
735C2×C11#348211yescharacteristic
736D11—44no—
737C24—112no—
738C2×Q8—114no—
739C2×Q8—222no—
740C2×Q8—222no—
741C2×Q8—224no—
742C2×Q8—224no—
743C2×Q8—224no—
744C2×Q8—224no—
745C2×Q8—224no—
746C2×Q8—224no—
747C2×Q8—224no—
748C2×Q8—442no—
749C2×Q8—442no—
750C2×D4—114no—
751C2×D4—222no—
752C2×D4—222no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—111no—
757C22×C4—111no—
758C22×C4—112no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—118no—
762C22×C4—111no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—224no—
766C22×C4—224no—
767C22×C4—224no—
768C22×C4—224no—
769C22×C4—224no—
770C22×C4—224no—
771C22×C4—224no—
772C22×C4—442no—
773C22×C4C23×D1111yescharacteristic
774C22×C4C23×D1111yescharacteristic
775C22×C4C23×D1112yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1112yes—
778C22×C4C23×D1111yescharacteristic
779C22×C4C23×D1111yescharacteristic
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1112yes—
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—24no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—114no—
795C4⋊C4—114no—
796C4⋊C4—114no—
797C4⋊C4—114no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C4⋊C4—222no—
805C4⋊C4—222no—
806C4⋊C4—222no—
807C4⋊C4—222no—
808C4⋊C4—224no—
809C4⋊C4—224no—
810C4⋊C4—224no—
811C4⋊C4—224no—
812C4⋊C4—224no—
813C4⋊C4—224no—
814C4⋊C4—222no—
815C4⋊C4—222no—
816C4⋊C4—442no—
817C4⋊C4D4×D1114yes—
818C4⋊C4Q8×D1114yes—
819C22⋊C4—118no—
820C22⋊C4—224no—
821C22⋊C4—224no—
822C22⋊C4—224no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—224no—
828C22⋊C4—442no—
829C22⋊C4—442no—
830C42—24no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—114no—
835C42—114no—
836C42—114no—
837C42—114no—
838C42—114no—
839C42—224no—
840C42—224no—
841C42—224no—
842C42—224no—
843C42—222no—
844C42—222no—
845C42—222no—
846C42—222no—
847C42—222no—
848C42—222no—
849C42—222no—
850C42—222no—
851C42—441no—
852C42—441no—
853C42—441no—
854C11#3492911yescharacteristic, complemented, Sylow
855C23—114no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23C24×D1111yescharacteristic
863Q8—228no—
864Q8—448no—
865Q8—448no—
866Q8—448no—
867D4—228no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—112no—
894C2×C4—112no—
895C2×C4—112no—
896C2×C4—112no—
897C2×C4—112no—
898C2×C4—112no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—114no—
905C2×C4—2216no—
906C2×C4—222no—
907C2×C4—221no—
908C2×C4—221no—
909C2×C4—221no—
910C2×C4—221no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—221no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—221no—
925C2×C4—221no—
926C2×C4—222no—
927C2×C4—448no—
928C2×C4—448no—
929C2×C4C2×D4×D1112yes—
930C2×C4C2×D4×D1112yes—
931C2×C4C2×D4×D1112yes—
932C2×C4C2×Q8×D1114yes—
933C2×C4C2×Q8×D1112yes—
934C2×C4#41×D1112yes—
935C2×C4#41×D1112yes—
936C2×C4#41×D1112yes—
937C22—224no—
938C22—224no—
939C22—224no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22C22×D4×D1111yescharacteristic
945C22C22×Q8×D1111yescharacteristic
946C22C2×#41×D1111yescharacteristic
947C22C2×#41×D1111yescharacteristic
948C22C2×#41×D1111yescharacteristic
949C22D11×2−1+411yescharacteristic
950C22#1062345711yescharacteristic
951C4—22no—
952C4—22no—
953C4—24no—
954C4—22no—
955C4—22no—
956C4—42no—
957C4—42no—
958C4—41no—
959C4—41no—
960C4—42no—
961C4—114no—
962C4—114no—
963C4—222no—
964C4—222no—
965C4—222no—
966C4—222no—
967C4—224no—
968C4—222no—
969C4—442no—
970C4—441no—
971C4—442no—
972C4#1062321914yescomplemented
973C2—444no—
974C2D11×#53211yescharacteristic
975C2C2×#1062321911yescharacteristic
976C2#1308204811yescharacteristic
977C2D4×Q8×D1111yescharacteristic
978C2#1308210311yescharacteristic
979C2#1308219811yescharacteristic
980C2#1308223011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2506C2
prime radicalC22×D44C23
hypercenter#2506D11
hypocenterC11#34929
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2506

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
2. #13073704C2semidirect
3. #13073696C2semidirect
4. #13073644C2semidirect
5. #13073603C2semidirect
8. #13073126C2semidirect
9. #13072985C2semidirect
12. #13072210C2semidirect
13. #13071893C2semidirect
14. #13071889C2semidirect
15. #13071187C2semidirect
16. #13071187C2semidirect
17. #13071183C2semidirect
18. #13071150C2semidirect
21. C4×#66940C2semidirect
23. C11×#2506C2semidirect
209. #66946Q8semidirect
220. #66940D4semidirect
373. #2506D11semidirect
594. C4×C11#533semidirect
854. C11#34929semidirect
972. C4#10623219semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
#130737042
#130736962
#130736442
#130736032
#130735682
#130735372
#130731262
#130729852
#130724672
#130724662
#130722102
#130718932
#130718892
#130711872
#130711832
#130711502
#130710742
C4×#669402
C4×#669462
C11×#25062
#3492911