Finite Group Databasebeta

← #14925567

Subgroups — #14925567

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×#10623048C212yesmaximal, complemented
2#13073707C212yesmaximal, complemented
3#13073699C212yesmaximal, complemented
4#13073644C211yesmaximal, characteristic, complemented
5#13073603C211yesmaximal, characteristic, complemented
6#13073567C211yesmaximal, characteristic
7#13073536C211yesmaximal, characteristic
8#13073135C211yesmaximal, characteristic, complemented
9#13073134C211yesmaximal, characteristic, complemented
10#13072987C212yesmaximal, complemented
11#13072469C211yesmaximal, characteristic
12#13072468C211yesmaximal, characteristic
13#13072212C212yesmaximal, complemented
14#13071890C212yesmaximal, complemented
15#13071884C212yesmaximal, complemented
16C4×#66922C211yesmaximal, characteristic, complemented
17C4×#66941C211yesmaximal, characteristic, complemented
18C4×#66941C211yesmaximal, characteristic, complemented
19C4×#66931C212yesmaximal, complemented
20#13071081C211yesmaximal, characteristic
21C42×Dic22C211yesmaximal, characteristic, complemented
22C4×D4×Dic11C211yesmaximal, characteristic
23C11×#2293C211yesmaximal, characteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2212yes—
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×#66979C2212yes—
29C22×C4×Dic11C2212yes—
30#10623048—216no—
31C2×#66943C2212yes—
32C2×#66943C2212yes—
33C2×#66941C2212yes—
34C2×#66941C2212yes—
35C2×#66941C2211yescharacteristic
36C2×#66941C2211yescharacteristic
37C2×#66931C2212yes—
38C2×#66931C2212yes—
39C2×#66931C2212yes—
40C2×#66931C2212yes—
41C2×#66931C2212yes—
42C2×#66922C2211yescharacteristic
43C2×C4×Dic22C2212yes—
44C2×C4×Dic22C2212yes—
45C2×C4×Dic22C2212yes—
46C2×C4×Dic22C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×C4×Dic22C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#389C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#388C2212yes—
54C11×#388C2212yes—
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2212yes—
57C43×C11C2211yescharacteristic
58#10622834C2211yescharacteristic
59#10622834C2211yescharacteristic
60C4×C22⋊Dic11C2212yes—
61C4×C22⋊Dic11C2212yes—
62#10622599C2212yes—
63#10622598C2211yescharacteristic
64#10622598C2211yescharacteristic
65#10622598C2211yescharacteristic
66#10622598C2211yescharacteristic
67#10622597C2212yes—
68#10622597C2212yes—
69#10622592C2212yes—
70#10622589C2211yescharacteristic
71#10622589C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73C4⋊C4×Dic11C2211yescharacteristic
74#10622586C2211yescharacteristic
75#10622586C2211yescharacteristic
76#10622564C2212yes—
77#10622564C2212yes—
78#10622563C2212yes—
79#10622562C2212yes—
80#10622562C2212yes—
81#10622561C2212yes—
82#10622561C2212yes—
83#10622561C2212yes—
84#10622561C2212yes—
85#10622560C2212yes—
86#10622560C2212yes—
87#10622559C2212yes—
88#10622555C2212yes—
89C22⋊C4×Dic11C2212yes—
90C22⋊C4×Dic11C2212yes—
91#10622548C2211yescharacteristic
92C4×C4⋊Dic11C2211yescharacteristic
93C4×C4⋊Dic11C2212yes—
94C4×C4⋊Dic11C2211yescharacteristic
95C4×C4⋊Dic11C2211yescharacteristic
96C4×C4⋊Dic11C2211yescharacteristic
97C4×C4⋊Dic11C2211yescharacteristic
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2212yes—
100C4×Dic11⋊C4C2211yescharacteristic
101C4×Dic11⋊C4C2211yescharacteristic
102C4×Dic11⋊C4C2211yescharacteristic
103C4×Dic11⋊C4C2211yescharacteristic
104C4×Dic11⋊C4C2211yescharacteristic
105C4×Dic11⋊C4C2211yescharacteristic
106C42×Dic11C2211yescharacteristic
107C42×Dic11C2211yescharacteristic
108#10622542C2212yes—
109#10622541C2212yes—
110#10622541C2211yescharacteristic
111#10622541C2211yescharacteristic
112#10622274C2212yes—
113#10622273C2212yes—
114#10622270C2212yes—
115#10622269C2212yes—
116#10622268C2212yes—
117#10622267C2212yes—
118#10622260C2212yes—
119#10622260C2212yes—
120#10622260C2212yes—
121#10622259C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×D4×C11C2311yescharacteristic
125C23×C4×C11C2312yes—
126C23×Dic11C2312yes—
127C23×Dic11C2312yes—
128C22×Dic22C2312yes—
129C22×Dic22C2312yes—
130C22×Dic22C2312yes—
131C22×Dic22C2311yescharacteristic
132C4×D4×C11Q818yescomplemented
133C11×#117—28no—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C42×C11C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158D4×Dic11—24no—
159D4×Dic11—24no—
160#66979—28no—
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2312yes—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2311yescharacteristic
191C2×C4×Dic11—28no—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208#66943—28no—
209#66943—28no—
210#66941—28no—
211#66941—24no—
212#66941—28no—
213#66941—24no—
214#66931—28no—
215#66931—28no—
216#66931—28no—
217#66931—28no—
218#66931—28no—
219#66922—24no—
220C4×Dic22—28no—
221C4×Dic22—24no—
222C4×Dic22—28no—
223C4×Dic22—28no—
224C4×Dic22—24no—
225C4×Dic22D418yescomplemented
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247#34929—111nomaximal, Sylow
248C24×C11C2412yes—
249C2×D4×C11—22no—
250C2×D4×C11—22no—
251C2×D4×C11C2×Q814yes—
252C22×C4×C11—24no—
253C22×C4×C11—24no—
254C22×C4×C11C2×Q818yes—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2412yes—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×Dic11—24no—
266C22×Dic11—24no—
267C22×Dic11—24no—
268C22×Dic11—24no—
269C22×Dic11—24no—
270C22×Dic11—42no—
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2412yes—
282C22×Dic11C2411yescharacteristic
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—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4C2×Q814yes—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—42no—
304C11×C22⋊C4C2×Q818yes—
305C42×C11—24no—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—41no—
311C42×C11C2×D414yes—
312C42×C11C2×Q814yes—
313C22⋊Dic11—24no—
314C22⋊Dic11—24no—
315C22⋊Dic11—24no—
316C22⋊Dic11—24no—
317C22⋊Dic11—24no—
318C22⋊Dic11—42no—
319C4⋊Dic11—24no—
320C4⋊Dic11—24no—
321C4⋊Dic11—24no—
322C4⋊Dic11—24no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—24no—
326C4⋊Dic11—24no—
327C4⋊Dic11—22no—
328C4⋊Dic11—24no—
329C4⋊Dic11—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11C2×D414yes—
332C4⋊Dic11#4114yes—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336Dic11⋊C4—24no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—24no—
342Dic11⋊C4—24no—
343Dic11⋊C4—24no—
344Dic11⋊C4—22no—
345Dic11⋊C4—42no—
346Dic11⋊C4C2×D414yes—
347Dic11⋊C4C2×D414yes—
348Dic11⋊C4#4114yes—
349C4×Dic11—24no—
350C4×Dic11—24no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—24no—
354C4×Dic11—24no—
355C4×Dic11—22no—
356C4×Dic11—22no—
357C4×Dic11—22no—
358C4×Dic11—22no—
359C4×Dic11—22no—
360C4×Dic11—41no—
361C4×Dic11—41no—
362C4×Dic11C2×D414yes—
363C4×Dic11C2×D414yes—
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#2506—111no—
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#2293D1111yescharacteristic
386C42×Q8—111no—
387C42×D4—111no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11C22×Q814yes—
395C23×C11C2511yescharacteristic
396D4×C11—28no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—22no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—216no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
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—21no—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D412yes—
419C2×C4×C11C22×D412yes—
420C2×C4×C11C22×Q812yes—
421C2×C4×C11C22×Q814yes—
422C2×C4×C11C22×Q812yes—
423C2×C4×C11C22×Q812yes—
424C2×C4×C11C2×#4112yes—
425C2×C4×C11C2×#4112yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C112−1+412yes—
428C2×Dic11—22no—
429C2×Dic11—21no—
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—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—48no—
456C2×Dic11—48no—
457C2×Dic11C22×D412yes—
458C2×Dic11C22×D412yes—
459C2×Dic11C22×D412yes—
460C2×Dic11C22×D412yes—
461C2×Dic11C2×#4112yes—
462C2×Dic11C2×#4112yes—
463C2×Dic11C2×#4114yes—
464C2×Dic11C2×#4112yes—
465C2×Dic11C2×#4112yes—
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×#125—112no—
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×D4C2×D1111yescharacteristic
492C2×#117—112no—
493C2×#117C2×D1112yes—
494C22×C42—112no—
495#400—112no—
496#400—112no—
497#399—112no—
498#399—112no—
499#398—112no—
500#398—112no—
501#398—112no—
502#398—112no—
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#390C2×D1111yescharacteristic
518#390C2×D1111yescharacteristic
519#389—111no—
520#389—111no—
521#389—111no—
522#389—111no—
523#389—111no—
524#389—111no—
525#389—112no—
526#389—111no—
527#389—111no—
528#389—112no—
529#389—112no—
530#389—112no—
531#389C2×D1111yescharacteristic
532#389C2×D1111yescharacteristic
533#388—112no—
534#388—112no—
535#388C2×D1112yes—
536#388C2×D1112yes—
537#387—112no—
538#387—112no—
539#385—112no—
540#385—112no—
541#384—111no—
542#384—111no—
543#384—111no—
544#380—112no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—111no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—112no—
550C4×C4⋊C4—112no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—111no—
553C4×C4⋊C4—111no—
554C4×C4⋊C4—111no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—111no—
558C4×C4⋊C4—111no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4—111no—
561C4×C4⋊C4C2×D1111yescharacteristic
562C4×C22⋊C4—112no—
563C4×C22⋊C4—112no—
564C4×C22⋊C4—112no—
565C4×C22⋊C4—112no—
566C4×C22⋊C4C2×D1112yes—
567C43—111no—
568C43—111no—
569C43C2×D1111yescharacteristic
570C22×C11—24no—
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11C23×D411yescharacteristic
578C22×C11C23×Q811yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C22×#4111yescharacteristic
582C22×C11C2×2−1+411yescharacteristic
583C22×C11#58511yescharacteristic
584C4×C11—22no—
585C4×C11—24no—
586C4×C11—22no—
587C4×C11—22no—
588C4×C11—22no—
589C4×C11—42no—
590C4×C11—41no—
591C4×C11—42no—
592C4×C11#53314yescomplemented
593C4×C11D4×Q814yes—
594Dic11—22no—
595Dic11—22no—
596Dic11—24no—
597Dic11—22no—
598Dic11—22no—
599Dic11—22no—
600Dic11—42no—
601Dic11—42no—
602Dic11—41no—
603Dic11—42no—
604Dic11—41no—
605Dic11#53214yes—
606C22×Q8—111no—
607C22×Q8—112no—
608C22×Q8—112no—
609C22×Q8—112no—
610C22×D4C22×D1111yescharacteristic
611C23×C4—112no—
612C23×C4—112no—
613C23×C4C22×D1112yes—
614C4⋊Q8—224no—
615C4⋊Q8—224no—
616C4⋊Q8—228no—
617C4⋊Q8—224no—
618C4⋊Q8—228no—
619#125—228no—
620#125—228no—
621C22⋊Q8—228no—
622C22⋊Q8—228no—
623C22⋊Q8—228no—
624C22⋊Q8—228no—
625C22⋊Q8—228no—
626C4×Q8—118no—
627C4×Q8—228no—
628C4×Q8—228no—
629C4×Q8—224no—
630C4×Q8—224no—
631C4×Q8—228no—
632C4×D4—224no—
633C4×D4—224no—
634C4×D4Dic2218yescomplemented
635#117—28no—
636#117—228no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—111no—
657C2×C4⋊C4—111no—
658C2×C4⋊C4—111no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—111no—
663C2×C4⋊C4—112no—
664C2×C4⋊C4—112no—
665C2×C4⋊C4—112no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4C22×D1112yes—
668C2×C4⋊C4C22×D1112yes—
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⋊C4C22×D1112yes—
679C2×C22⋊C4C22×D1112yes—
680C2×C22⋊C4C22×D1112yes—
681C2×C22⋊C4C22×D1112yes—
682C2×C22⋊C4C22×D1112yes—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—112no—
691C2×C42—112no—
692C2×C42—111no—
693C2×C42—112no—
694C2×C42—112no—
695C2×C42—111no—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—228no—
700C2×C42C22×D1111yescharacteristic
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703C2×C42C22×D1112yes—
704C2×C42C22×D1111yescharacteristic
705C2×C42C22×D1111yescharacteristic
706C2×C42C22×D1111yescharacteristic
707C2×C42C22×D1111yescharacteristic
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95—111no—
714#95—111no—
715#95—111no—
716#95—111no—
717#95—111no—
718#95—111no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95C22×D1112yes—
727#95C22×D1112yes—
728#95C22×D1112yes—
729C2×C11—44no—
730C2×C11C2×#53211yescharacteristic
731C2×C11C2×#53311yescharacteristic
732C2×C11#346111yescharacteristic
733C2×C11C2×D4×Q811yescharacteristic
734C2×C11D4×#4111yescharacteristic
735C2×C11Q8×#4111yescharacteristic
736C2×C11#348211yescharacteristic
737C24C23×D1112yes—
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—22no—
751C2×D4—22no—
752C2×D4C2×Dic2214yes—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—111no—
756C22×C4—111no—
757C22×C4—111no—
758C22×C4—112no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—111no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—224no—
768C22×C4—224no—
769C22×C4—224no—
770C22×C4—224no—
771C22×C4—224no—
772C22×C4—442no—
773C22×C4C2×Dic2218yes—
774C22×C4C23×D1111yescharacteristic
775C22×C4C23×D1112yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1111yescharacteristic
778C22×C4C23×D1112yes—
779C22×C4C23×D1111yescharacteristic
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—114no—
789C4⋊C4—114no—
790C4⋊C4—114no—
791C4⋊C4—114no—
792C4⋊C4—114no—
793C4⋊C4—224no—
794C4⋊C4—224no—
795C4⋊C4—224no—
796C4⋊C4—224no—
797C4⋊C4—224no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—224no—
801C4⋊C4—222no—
802C4⋊C4—222no—
803C4⋊C4—222no—
804C4⋊C4—222no—
805C4⋊C4—224no—
806C4⋊C4—224no—
807C4⋊C4—224no—
808C4⋊C4—224no—
809C4⋊C4—224no—
810C4⋊C4—224no—
811C4⋊C4—224no—
812C4⋊C4—222no—
813C4⋊C4—222no—
814C4⋊C4—224no—
815C4⋊C4—222no—
816C4⋊C4—222no—
817C4⋊C4—442no—
818C4⋊C4C2×Dic2214yes—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—42no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—224no—
828C22⋊C4—442no—
829C22⋊C4C2×Dic2218yes—
830C42—24no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—22no—
835C42—41no—
836C42—114no—
837C42—114no—
838C42—114no—
839C42—224no—
840C42—224no—
841C42—222no—
842C42—222no—
843C42—224no—
844C42—224no—
845C42—222no—
846C42—222no—
847C42—222no—
848C42—222no—
849C42—222no—
850C42—441no—
851C42—441no—
852C42C2×Dic2214yes—
853C42D4×D1114yes—
854C11#3492911yescharacteristic, complemented, Sylow
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23C22×Dic2214yes—
862C23C24×D1111yescharacteristic
863Q8—228no—
864Q8—448no—
865Q8—448no—
866Q8—448no—
867D4—28no—
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—216no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—112no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—112no—
892C2×C4—112no—
893C2×C4—112no—
894C2×C4—112no—
895C2×C4—112no—
896C2×C4—114no—
897C2×C4—222no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—221no—
905C2×C4—221no—
906C2×C4—221no—
907C2×C4—221no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—221no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—221no—
921C2×C4—221no—
922C2×C4—221no—
923C2×C4—222no—
924C2×C4—448no—
925C2×C4—448no—
926C2×C4C22×Dic2212yes—
927C2×C4C22×Dic2214yes—
928C2×C4C22×Dic2212yes—
929C2×C4C22×Dic2212yes—
930C2×C4C2×D4×D1112yes—
931C2×C4C2×D4×D1112yes—
932C2×C4C2×D4×D1112yes—
933C2×C4#41×D1112yes—
934C2×C4#41×D1112yes—
935C2×C4#41×D1112yes—
936C2×C4#6704312yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C23×Dic2211yescharacteristic
945C22C22×D4×D1111yescharacteristic
946C22C2×#41×D1111yescharacteristic
947C22C2×#41×D1111yescharacteristic
948C22C2×#41×D1111yescharacteristic
949C22C2×#6704311yescharacteristic
950C22#1062345311yescharacteristic
951C4—22no—
952C4—22no—
953C4—22no—
954C4—24no—
955C4—22no—
956C4—42no—
957C4—41no—
958C4—42no—
959C4—114no—
960C4—222no—
961C4—222no—
962C4—222no—
963C4—222no—
964C4—224no—
965C4—222no—
966C4—442no—
967C4—442no—
968C4—441no—
969C4—441no—
970C4—442no—
971C4#1062304814yescomplemented
972C4D4×Dic2214yes—
973C2—44no—
974C2D11×#53211yescharacteristic
975C2C2×#1062304811yescharacteristic
976C2#1308204111yescharacteristic
977C2C2×D4×Dic2211yescharacteristic
978C2#1308210211yescharacteristic
979C2#41×Dic2211yescharacteristic
980C2#1308222911yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2293C2
prime radicalC22×D4×C11C23
hypercenter#2293D11
hypocenterC11#34929
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2293

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
2. #13073707C2semidirect
3. #13073699C2semidirect
4. #13073644C2semidirect
5. #13073603C2semidirect
8. #13073135C2semidirect
9. #13073134C2semidirect
10. #13072987C2semidirect
13. #13072212C2semidirect
14. #13071890C2semidirect
15. #13071884C2semidirect
16. C4×#66922C2semidirect
17. C4×#66941C2semidirect
18. C4×#66941C2semidirect
19. C4×#66931C2semidirect
21. C42×Dic22C2semidirect
132. C4×D4×C11Q8semidirect
225. C4×Dic22D4semidirect
592. C4×C11#533semidirect
634. C4×D4Dic22semidirect
854. C11#34929semidirect
971. C4#10623048semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
#130737072
#130736992
#130736442
#130736032
#130735672
#130735362
#130731352
#130731342
#130729872
#130724692
#130724682
#130722122
#130718902
#130718842
C4×#669222
C4×#669412
C4×#669312
#130710812
C42×Dic222
C4×D4×Dic112
C11×#22932
#3492911