Finite Group Databasebeta

← #14925684

Subgroups — #14925684

Order 2816.

2290 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C212yesmaximal
2#13073650C211yesmaximal, characteristic, complemented
3#13073649C211yesmaximal, characteristic, complemented
4#13073644C211yesmaximal, characteristic, complemented
5#13073643C211yesmaximal, characteristic, complemented
6#13073636C212yesmaximal, complemented
7#13073634C212yesmaximal, complemented
8#13073626C212yesmaximal
9#13073625C212yesmaximal
10#13072321C211yesmaximal, characteristic
11#13072320C211yesmaximal, characteristic
12#13072316C211yesmaximal, characteristic
13#13072314C211yesmaximal, characteristic
14#13071910C212yesmaximal, complemented
15#13071907C212yesmaximal, complemented
16C4×#66922C211yesmaximal, characteristic, complemented
17C4×#66941C211yesmaximal, characteristic, complemented
18C4×#66941C211yesmaximal, characteristic, complemented
19#13071096C212yesmaximal
20#13071020C211yesmaximal, characteristic
21C4×#66925C211yesmaximal, characteristic
22C4×C4⋊C4×D11C211yesmaximal, characteristic
23C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2212yes—
26C2×#66999C2212yes—
27C2×#66997C2212yes—
28#10623109—216no—
29C2×#66950C2212yes—
30C2×#66949C2212yes—
31C2×#66949C2212yes—
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×#66942C2212yes—
35C2×#66942C2212yes—
36C2×#66941C2212yes—
37C2×#66941C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66925C2212yes—
40C2×#66925C2211yescharacteristic
41C2×#66925C2211yescharacteristic
42C2×C42×D11C2212yes—
43C2×C42×D11C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×C4×Dic22C2212yes—
46C2×C4×Dic22C2212yes—
47C2×C4×Dic22C2212yes—
48C11×#391C2212yes—
49C11×#389C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#389C2212yes—
52C11×#384C2211yescharacteristic
53C4×C11×C4⋊C4C2212yes—
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C43×C11C2211yescharacteristic
57#10622842C2212yes—
58#10622842C2212yes—
59#10622602C2212yes—
60#10622602C2212yes—
61#10622600C2211yescharacteristic
62#10622600C2211yescharacteristic
63#10622598C2211yescharacteristic
64#10622598C2211yescharacteristic
65#10622597C2212yes—
66#10622597C2212yes—
67#10622596C2212yes—
68#10622596C2212yes—
69#10622593C2212yes—
70#10622593C2212yes—
71#10622592C2212yes—
72#10622592C2212yes—
73#10622592C2212yes—
74#10622592C2212yes—
75#10622589C2211yescharacteristic
76#10622589C2211yescharacteristic
77#10622589C2211yescharacteristic
78#10622589C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80C4⋊C4×Dic11C2211yescharacteristic
81#10622586C2211yescharacteristic
82#10622586C2211yescharacteristic
83#10622585C2212yes—
84#10622585C2212yes—
85C4×(C2×D11)⋊C4C2211yescharacteristic
86C4×(C2×D11)⋊C4C2211yescharacteristic
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2211yescharacteristic
89#10622548C2211yescharacteristic
90C4×C4⋊Dic11C2212yes—
91C4×C4⋊Dic11C2211yescharacteristic
92C4×C4⋊Dic11C2211yescharacteristic
93#10622545C2211yescharacteristic
94#10622545C2211yescharacteristic
95C4×Dic11⋊C4C2212yes—
96C4×Dic11⋊C4C2212yes—
97C4×Dic11⋊C4C2212yes—
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2211yescharacteristic
100C4×Dic11⋊C4C2211yescharacteristic
101C4×Dic11⋊C4C2211yescharacteristic
102C4×Dic11⋊C4C2211yescharacteristic
103C42×Dic11C2211yescharacteristic
104#10622542C2212yes—
105#10622541C2211yescharacteristic
106#10622541C2211yescharacteristic
107#10622541C2212yes—
108#10622281C2212yes—
109#10622281C2212yes—
110#10622280C2212yes—
111D11×#95C2212yes—
112#10622270C2212yes—
113#10622270C2212yes—
114#10622269C2212yes—
115#10622269C2212yes—
116#10622263C2212yes—
117#10622262C2212yes—
118#10622260C2212yes—
119#10622260C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×Q8×C11C2312yes—
125C22×C4×D11C2312yes—
126C22×C4×D11C2312yes—
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×Dic22C2312yes—
131C22×Dic22C2312yes—
132C22×Dic22C2312yes—
133C11×C4⋊Q8—24no—
134C4×Q8×C11—28no—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C42×C11C2312yes—
145C2×C42×C11C2312yes—
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153#66999—28no—
154#66997—28no—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2311yescharacteristic
158C2×(C2×D11)⋊C4C2311yescharacteristic
159C2×(C2×D11)⋊C4C2311yescharacteristic
160C2×(C2×D11)⋊C4C2311yescharacteristic
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2312yes—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2312yes—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2311yescharacteristic
187C2×Dic11⋊C4C2311yescharacteristic
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2311yescharacteristic
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
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#66950—28no—
204#66949—28no—
205#66949—28no—
206C4⋊C4×D11—24no—
207C4⋊C4×D11—24no—
208#66942—28no—
209#66942—28no—
210#66941—24no—
211#66941—24no—
212#66941—28no—
213#66925—28no—
214#66925D418yes—
215#66925Q818yescomplemented
216C42×D11—28no—
217C42×D11Q818yescomplemented
218#66922—24no—
219C4×Dic22—28no—
220C4×Dic22—28no—
221C4×Dic22—28no—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2312yes—
225C11×#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246#34938—111nomaximal, Sylow
247C23×D11C2411yescharacteristic
248C2×Q8×C11—24no—
249C2×Q8×C11—24no—
250C2×Q8×C11—42no—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2412yes—
272C22×Dic11C2411yescharacteristic
273C2×C4×D11—24no—
274C2×C4×D11—24no—
275C2×C4×D11—24no—
276C2×C4×D11—22no—
277C2×C4×D11—22no—
278C2×C4×D11—24no—
279C2×C4×D11—41no—
280C2×C4×D11—41no—
281C2×C4×D11—42no—
282C2×C4×D11—42no—
283C2×C4×D11C2×D414yes—
284C2×C4×D11C2×Q814yes—
285C2×C4×D11C2×Q814yes—
286C2×C4×D11C2×Q814yes—
287C2×C4×D11C2×Q814yes—
288C2×Dic22—24no—
289C2×Dic22—24no—
290C2×Dic22—24no—
291C2×Dic22—24no—
292C2×Dic22—24no—
293C2×Dic22—24no—
294C2×Dic22—42no—
295C2×Dic22—42no—
296C2×Dic22—42no—
297C11×C4⋊C4—24no—
298C11×C4⋊C4—24no—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—22no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—42no—
305C11×C4⋊C4#4114yes—
306C42×C11—24no—
307C42×C11—24no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—41no—
311C42×C11—41no—
312C42×C11C2×D414yes—
313C42×C11C2×Q814yes—
314C42×C11C2×Q814yes—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4C2×D414yes—
318(C2×D11)⋊C4C2×D414yes—
319(C2×D11)⋊C4C2×Q814yes—
320(C2×D11)⋊C4C2×Q814yes—
321C4⋊Dic11—24no—
322C4⋊Dic11—24no—
323C4⋊Dic11—24no—
324C4⋊Dic11—24no—
325C4⋊Dic11—22no—
326C4⋊Dic11—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—42no—
329C4⋊Dic11#4114yes—
330Dic11⋊C4—24no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338Dic11⋊C4—24no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—24no—
342Dic11⋊C4—42no—
343Dic11⋊C4—42no—
344Dic11⋊C4—42no—
345Dic11⋊C4—42no—
346Dic11⋊C4C2×D414yes—
347Dic11⋊C4C2×D414yes—
348Dic11⋊C4C2×Q814yes—
349Dic11⋊C4C2×Q814yes—
350C4×Dic11—24no—
351C4×Dic11—24no—
352C4×Dic11—24no—
353C4×Dic11—24no—
354C4×Dic11—22no—
355C4×Dic11—22no—
356C4×Dic11—41no—
357C4×Dic11—41no—
358C4×Dic11C2×D414yes—
359C4×Dic11C2×Q814yes—
360C4×Dic11C2×Q814yes—
361C4×Dic11C2×Q814yes—
362C4×Dic11C2×Q814yes—
363C2×#533—112no—
364#2552—111no—
365#2552—111no—
366#2551—111no—
367#2551—111no—
368#2550—112no—
369#2550—112no—
370#2549—112no—
371#2549—112no—
372#2440—111no—
373#2440—111no—
374#2440—111no—
375#2440—111no—
376#2399—112no—
377#2399—112no—
378C4×C4⋊Q8—111no—
379C4×C4⋊Q8—111no—
380C4×C4⋊Q8—111no—
381C4×C4⋊Q8D1111yescharacteristic, complemented
382#2296—112no—
383#2285—111no—
384C4×#117—111no—
385C2×C4×C4⋊C4—111no—
386C23×C11C2511yescharacteristic
387C22×D11—21no—
388C22×D11—21no—
389C22×D11—21no—
390C22×D11—21no—
391C22×D11C22×D412yes—
392C22×D11C22×Q812yes—
393C22×D11C22×Q812yes—
394Q8×C11—48no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
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—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D412yes—
419C2×C4×C11C22×Q812yes—
420C2×C4×C11C22×Q812yes—
421C2×C4×C11C22×Q812yes—
422C2×C4×C11C22×Q812yes—
423C2×C4×C11C22×Q812yes—
424C2×C4×C11C22×Q812yes—
425C2×C4×C11C2×#4114yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C11C2×#4112yes—
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—21no—
440C2×Dic11—21no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11C22×D412yes—
452C2×Dic11C22×D412yes—
453C2×Dic11C22×D412yes—
454C2×Dic11C22×Q812yes—
455C2×Dic11C22×Q812yes—
456C2×Dic11C22×Q812yes—
457C2×Dic11C22×Q812yes—
458C2×Dic11C22×Q812yes—
459C2×Dic11C22×Q812yes—
460C2×Dic11C2×#4114yes—
461C4×D11—28no—
462C4×D11—44no—
463C4×D11—48no—
464C4×D11—48no—
465C4×D11C4⋊Q8116yescomplemented
466Dic22—48no—
467Dic22—48no—
468Dic22—48no—
469#533—2216no—
470C2×C4⋊Q8—112no—
471C2×C4⋊Q8—111no—
472C2×C4⋊Q8—111no—
473C2×C4⋊Q8—112no—
474C2×C4⋊Q8—111no—
475C2×C4⋊Q8C2×D1111yescharacteristic
476C2×#125—112no—
477C2×#125—112no—
478C2×C22⋊Q8—112no—
479C2×C22⋊Q8—112no—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—112no—
484C2×C4×Q8—112no—
485C2×C4×Q8C2×D1112yes—
486C2×#117—111no—
487C2×#117—111no—
488C2×#117—112no—
489C22×C4⋊C4—111no—
490C22×C4⋊C4—111no—
491C22×C42—111no—
492C22×C42—112no—
493#398—112no—
494#398—112no—
495#398—112no—
496#398—112no—
497#398—112no—
498#398—112no—
499#398—112no—
500#398—112no—
501#395—112no—
502#395—112no—
503#395—112no—
504#395—112no—
505#395—112no—
506#395—112no—
507#395—112no—
508#395—112no—
509#391—112no—
510#391—112no—
511#391—112no—
512#391C2×D1112yes—
513#389—111no—
514#389—111no—
515#389—111no—
516#389—111no—
517#389—112no—
518#389—112no—
519#389—111no—
520#389—111no—
521#389—112no—
522#389—112no—
523#389—112no—
524#389—112no—
525#389—112no—
526#389C2×D1111yescharacteristic
527#389C2×D1111yescharacteristic
528#389C2×D1112yes—
529#385—112no—
530#385—112no—
531#385—112no—
532#385—112no—
533#384—111no—
534#384—111no—
535#384—111no—
536#384—111no—
537#384—111no—
538#384C2×D1111yescharacteristic
539#382—112no—
540#380—111no—
541#380—111no—
542#380—112no—
543C4×C4⋊C4—111no—
544C4×C4⋊C4—111no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—112no—
548C4×C4⋊C4—112no—
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—112no—
557C4×C4⋊C4C2×D1111yescharacteristic
558C4×C4⋊C4C2×D1111yescharacteristic
559C4×C4⋊C4C2×D1112yes—
560C4×C22⋊C4—111no—
561C4×C22⋊C4—111no—
562C4×C22⋊C4—111no—
563C4×C22⋊C4—111no—
564#376—111no—
565#376—111no—
566C2×#95—112no—
567C43—111no—
568C43C2×D1111yescharacteristic
569C22×C11C23×D411yescharacteristic
570C22×C11C23×Q811yescharacteristic
571C22×C11C23×Q811yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C22×#4111yescharacteristic
574C22×C11#58511yescharacteristic
575C22×C11#58511yescharacteristic
576C2×D11—22no—
577C2×D11—22no—
578C2×D11—22no—
579C2×D11—22no—
580C2×D11—22no—
581C2×D11—22no—
582C2×D11C2×C4⋊Q814yes—
583C4×C11—22no—
584C4×C11—22no—
585C4×C11—22no—
586C4×C11—24no—
587C4×C11—22no—
588C4×C11—22no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11C2×C4⋊Q814yes—
593C4×C11#53314yescomplemented
594Dic11—22no—
595Dic11—22no—
596Dic11—24no—
597Dic11—22no—
598Dic11—22no—
599Dic11—22no—
600Dic11—22no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11C2×C4⋊Q814yes—
605C22×Q8—112no—
606C22×Q8—112no—
607C22×Q8—112no—
608C22×Q8C22×D1112yes—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—112no—
613C23×C4—112no—
614C4⋊Q8—24no—
615C4⋊Q8—224no—
616C4⋊Q8—228no—
617C4⋊Q8—224no—
618C4⋊Q8—228no—
619C4⋊Q8—224no—
620#125—228no—
621#125—228no—
622C22⋊Q8—228no—
623C22⋊Q8—228no—
624C22⋊Q8—228no—
625C22⋊Q8—228no—
626C4×Q8—28no—
627C4×Q8—228no—
628C4×Q8—228no—
629C4×Q8—228no—
630#117—118no—
631#117—118no—
632#117—228no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
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—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—224no—
663C2×C4⋊C4—224no—
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1112yes—
666C2×C4⋊C4C22×D1112yes—
667C2×C4⋊C4C22×D1112yes—
668C2×C4⋊C4C22×D1111yescharacteristic
669C2×C4⋊C4C22×D1111yescharacteristic
670C2×C4⋊C4C22×D1112yes—
671C2×C4⋊C4C22×D1112yes—
672C2×C4⋊C4C22×D1111yescharacteristic
673C2×C22⋊C4—111no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C42—111no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—118no—
685C2×C42—112no—
686C2×C42—112no—
687C2×C42—111no—
688C2×C42—111no—
689C2×C42—112no—
690C2×C42—112no—
691C2×C42—111no—
692C2×C42—111no—
693C2×C42—228no—
694C2×C42C22×D1111yescharacteristic
695C2×C42C22×D1111yescharacteristic
696C2×C42C22×D1112yes—
697C2×C42C22×D1112yes—
698C2×C42C22×D1111yescharacteristic
699C2×C42C22×D1111yescharacteristic
700C2×C42C22×D1111yescharacteristic
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703#95—112no—
704#95—112no—
705#95—112no—
706#95—111no—
707#95—111no—
708#95—111no—
709#95—111no—
710#95—111no—
711#95—111no—
712#95—111no—
713#95—111no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95C22×D1112yes—
724#95C22×D1112yes—
725#95C22×D1112yes—
726#95C22×D1112yes—
727C2×C11C22×C4⋊Q811yescharacteristic
728C2×C11C2×#53311yescharacteristic
729C2×C11#345811yescharacteristic
730C2×C11D4×#4111yescharacteristic
731C2×C11D4×#4111yescharacteristic
732C2×C11Q8×#4111yescharacteristic
733C2×C11Q8×#4111yescharacteristic
734D11—24no—
735C24—111no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—42no—
739C2×Q8—224no—
740C2×Q8—224no—
741C2×Q8—224no—
742C2×Q8—224no—
743C2×Q8—224no—
744C2×Q8—224no—
745C2×Q8—442no—
746C2×Q8—442no—
747C2×Q8—442no—
748C22×C4—111no—
749C22×C4—114no—
750C22×C4—114no—
751C22×C4—114no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—112no—
757C22×C4—111no—
758C22×C4—111no—
759C22×C4—114no—
760C22×C4—114no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—224no—
765C22×C4—224no—
766C22×C4—224no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—224no—
770C22×C4—441no—
771C22×C4—441no—
772C22×C4—442no—
773C22×C4—442no—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1112yes—
778C22×C4C23×D1111yescharacteristic
779C22×C4C23×D1111yescharacteristic
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1111yescharacteristic
785C4⋊C4—24no—
786C4⋊C4—22no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—42no—
793C4⋊C4—114no—
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—224no—
805C4⋊C4—224no—
806C4⋊C4—224no—
807C4⋊C4—224no—
808C4⋊C4—224no—
809C4⋊C4—224no—
810C4⋊C4—222no—
811C4⋊C4—224no—
812C4⋊C4—222no—
813C4⋊C4—224no—
814C4⋊C4—224no—
815C4⋊C4—224no—
816C4⋊C4—222no—
817C4⋊C4—442no—
818C4⋊C4—442no—
819C4⋊C4—442no—
820C4⋊C4—442no—
821C4⋊C4—442no—
822C4⋊C4#433914yes—
823C22⋊C4—114no—
824C22⋊C4—114no—
825C22⋊C4—114no—
826C22⋊C4—114no—
827C22⋊C4—224no—
828C22⋊C4—224no—
829C42—22no—
830C42—24no—
831C42—24no—
832C42—22no—
833C42—41no—
834C42—41no—
835C42—114no—
836C42—114no—
837C42—114no—
838C42—114no—
839C42—114no—
840C42—224no—
841C42—224no—
842C42—222no—
843C42—224no—
844C42—224no—
845C42—222no—
846C42—441no—
847C42—441no—
848C42D4×D1114yes—
849C42Q8×D1114yes—
850C42Q8×D1114yes—
851C11#3493811yescharacteristic, complemented, Sylow
852C23—112no—
853C23—112no—
854C23—112no—
855C23—221no—
856C23—221no—
857C23—221no—
858C23—221no—
859C23C24×D1111yescharacteristic
860Q8—48no—
861Q8—448no—
862Q8—448no—
863Q8—448no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—112no—
886C2×C4—112no—
887C2×C4—112no—
888C2×C4—1116no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—112no—
892C2×C4—112no—
893C2×C4—112no—
894C2×C4—112no—
895C2×C4—114no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—222no—
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—221no—
909C2×C4—222no—
910C2×C4—228no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—444no—
921C2×C4—448no—
922C2×C4—448no—
923C2×C4C2×#433914yes—
924C2×C4C2×#433912yes—
925C2×C4C2×D4×D1112yes—
926C2×C4C2×D4×D1112yes—
927C2×C4C2×D4×D1112yes—
928C2×C4C2×Q8×D1112yes—
929C2×C4C2×Q8×D1112yes—
930C2×C4C2×Q8×D1112yes—
931C2×C4C2×Q8×D1112yes—
932C2×C4C2×Q8×D1112yes—
933C2×C4C2×Q8×D1112yes—
934C2×C4#41×D1112yes—
935C22—114no—
936C22—222no—
937C22—222no—
938C22—222no—
939C22—222no—
940C22—222no—
941C22—222no—
942C22C22×#433911yescharacteristic
943C22C22×D4×D1111yescharacteristic
944C22C22×Q8×D1111yescharacteristic
945C22C22×Q8×D1111yescharacteristic
946C22C2×#41×D1111yescharacteristic
947C22#1062345311yescharacteristic
948C22#1062345311yescharacteristic
949C4—22no—
950C4—22no—
951C4—22no—
952C4—22no—
953C4—24no—
954C4—22no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—114no—
959C4—222no—
960C4—222no—
961C4—222no—
962C4—222no—
963C4—224no—
964C4—222no—
965C4—222no—
966C4—442no—
967C4—442no—
968C4—442no—
969C4#1062310914yescomplemented
970C4D11×C4⋊Q814yes—
971C2—224no—
972C2C2×D11×C4⋊Q811yescharacteristic
973C2C2×#1062310911yescharacteristic
974C2#1308201911yescharacteristic
975C2#1308210211yescharacteristic
976C2D4×#433911yescharacteristic
977C2#1308219411yescharacteristic
978C2Q8×#433911yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×C4⋊Q8C2
prime radicalC23×D11C24
hypercenterC4×C4⋊Q8D11
hypocenterC11#34938
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13073650C2semidirect
3. #13073649C2semidirect
4. #13073644C2semidirect
5. #13073643C2semidirect
6. #13073636C2semidirect
7. #13073634C2semidirect
14. #13071910C2semidirect
15. #13071907C2semidirect
16. C4×#66922C2semidirect
17. C4×#66941C2semidirect
18. C4×#66941C2semidirect
23. C4×C11×C4⋊Q8C2semidirect
215. #66925Q8semidirect
217. C42×D11Q8semidirect
381. C4×C4⋊Q8D11semidirect
465. C4×D11C4⋊Q8semidirect
593. C4×C11#533semidirect
851. C11#34938semidirect
969. C4#10623109semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130736502
#130736492
#130736442
#130736432
#130736362
#130736342
#130736262
#130736252
#130723212
#130723202
#130723162
#130723142
#130719102
#130719072
C4×#669222
C4×#669412
#130710962
#130710202
C4×#669252
C4×C4⋊C4×D112
C4×C11×C4⋊Q82
#3493811