Finite Group Databasebeta

← #14926169

Subgroups — #14926169

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13074191C212yesmaximal, complemented
4#13074189C212yesmaximal, complemented
5#13073984C211yesmaximal, characteristic, complemented
6#13073980C211yesmaximal, characteristic, complemented
7#13073527C211yesmaximal, characteristic, complemented
8#13073523C211yesmaximal, characteristic, complemented
9#13072922C211yesmaximal, characteristic, complemented
10#13072920C211yesmaximal, characteristic, complemented
11#13072901C212yesmaximal, complemented
12#13071979C211yesmaximal, characteristic, complemented
13#13071977C211yesmaximal, characteristic, complemented
14#13071949C212yesmaximal
15#13071910C212yesmaximal, complemented
16#13071903C212yesmaximal, complemented
17C4×#66950C211yesmaximal, characteristic, complemented
18C4×#66977C211yesmaximal, characteristic, complemented
19C4×#66999C211yesmaximal, characteristic, complemented
20C4×#66947C212yesmaximal, complemented
21C4×#66936C212yesmaximal, complemented
22#13071012C211yesmaximal, characteristic, complemented
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C4×Q8×D11—28no—
38C2×#66950C2211yescharacteristic
39C2×#66947C2212yes—
40C2×C4⋊C4×D11C2212yes—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66940C2212yes—
43C2×#66940C2211yescharacteristic
44C2×#66936C2212yes—
45C4×#4339—28no—
46C2×C4×D44C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×#66925C2211yescharacteristic
50C2×C42×D11C2212yes—
51C2×C42×D11C2211yescharacteristic
52C2×C42×D11C2211yescharacteristic
53C2×C4×Dic22C2212yes—
54C2×C4×Dic22C2211yescharacteristic
55C2×C4×Dic22C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57C11×#391C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#387C2212yes—
60C11×#385C2212yes—
61C11×#380C2211yescharacteristic
62C4×C11×C4⋊C4C2212yes—
63C4×C11×C4⋊C4C2211yescharacteristic
64C4×C11×C22⋊C4C2212yes—
65#10622843C2211yescharacteristic
66#10622825C2211yescharacteristic
67#10622823C2212yes—
68C4×C22⋊Dic11C2212yes—
69#10622603C2212yes—
70#10622602C2212yes—
71#10622602C2212yes—
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622598C2211yescharacteristic
77#10622597C2212yes—
78#10622597C2212yes—
79#10622594C2212yes—
80#10622592C2212yes—
81#10622592C2212yes—
82#10622591C2212yes—
83#10622590C2211yescharacteristic
84#10622590C2211yescharacteristic
85#10622587C2211yescharacteristic
86#10622586C2211yescharacteristic
87#10622574C2212yes—
88#10622572C2212yes—
89#10622569C2212yes—
90#10622565C2212yes—
91#10622564C2212yes—
92#10622560C2212yes—
93#10622558C2212yes—
94C4×(C2×D11)⋊C4C2212yes—
95C4×(C2×D11)⋊C4C2212yes—
96C4×(C2×D11)⋊C4C2212yes—
97C4×C4⋊Dic11C2212yes—
98C4×C4⋊Dic11C2211yescharacteristic
99#10622546C2212yes—
100#10622545C2212yes—
101C4×Dic11⋊C4C2212yes—
102C4×Dic11⋊C4C2212yes—
103#10622542C2211yescharacteristic
104#10622541C2211yescharacteristic
105#10622288C2212yes—
106#10622286C2212yes—
107#10622282C2212yes—
108#10622281C2212yes—
109#10622281C2212yes—
110#10622278C2212yes—
111#10622277C2212yes—
112#10622277C2212yes—
113#10622277C2212yes—
114#10622273C2212yes—
115#10622271C2212yes—
116#10622270C2212yes—
117#10622270C2212yes—
118#10622269C2212yes—
119#10622269C2212yes—
120#10622268C2212yes—
121#10622267C2212yes—
122#10622266C2212yes—
123#10622265C2212yes—
124#10622264C2212yes—
125C22×Q8×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C2×Q8×D11—24no—
132C2×Q8×D11—24no—
133C2×Q8×D11—24no—
134C2×#4339—24no—
135C2×#4339—24no—
136C2×#4339—24no—
137C22×D44C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×Dic22C2311yescharacteristic
147C22×Dic22C2312yes—
148C22×Dic22C2311yescharacteristic
149C11×C22⋊Q8—24no—
150C4×Q8×C11—24no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C42×C11—24no—
160C2×C42×C11C2312yes—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170#66999—24no—
171Q8×Dic11—24no—
172C4×C22⋊D11—24no—
173C4×C22⋊D11—24no—
174C4×C22⋊D11—24no—
175C4×C22⋊D11—24no—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186#66979—24no—
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2312yes—
192C2×C4⋊Dic11C2312yes—
193C2×C4⋊Dic11C2311yescharacteristic
194C2×C4⋊Dic11C2311yescharacteristic
195#66977—24no—
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217#66950—24no—
218#66947—28no—
219C4⋊C4×D11—24no—
220C4⋊C4×D11—28no—
221#66940—24no—
222#66940—28no—
223#66936—28no—
224C4×D44—24no—
225C4×D44—24no—
226#66925—24no—
227#66925—24no—
228C42×D11—28no—
229C42×D11—24no—
230C42×D11D418yes—
231C4×Dic22—24no—
232C4×Dic22—24no—
233C4×Dic22—24no—
234C4×Dic22—28no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259#34971—111nomaximal, Sylow
260C24×C11C2411yescharacteristic
261C23×D11C2411yescharacteristic
262C23×D11C2411yescharacteristic
263C2×Q8×C11—22no—
264C2×Q8×C11—22no—
265C2×Q8×C11#4114yescomplemented
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2412yes—
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C2×C22⋊D11—22no—
286C2×C22⋊D11—22no—
287C2×C22⋊D11—22no—
288C2×C22⋊D11—22no—
289C2×C22⋊D11—22no—
290C2×C22⋊D11#4114yes—
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2412yes—
301Q8×D11—232no—
302#4339—232no—
303C2×D44—22no—
304C2×D44—22no—
305C2×D44#4114yes—
306C2×C4×D11—22no—
307C2×C4×D11—24no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—22no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11C2×D414yes—
328C2×C4×D11C2×D414yes—
329C2×C4×D11C2×D414yes—
330C2×Dic22—22no—
331C2×Dic22—24no—
332C2×Dic22—22no—
333C2×Dic22—24no—
334C2×Dic22—22no—
335C2×Dic22—22no—
336C2×Dic22—24no—
337C2×Dic22—22no—
338C2×Dic22#4114yescomplemented
339C11×C4⋊C4—24no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—24no—
342C11×C4⋊C4—22no—
343C11×C4⋊C4—22no—
344C11×C4⋊C4—24no—
345C11×C22⋊C4—24no—
346C11×C22⋊C4—24no—
347C42×C11—24no—
348C42×C11—22no—
349C42×C11—22no—
350C42×C11—22no—
351C42×C11—24no—
352C42×C11C2×D414yes—
353C22⋊Dic11—22no—
354C22⋊Dic11—22no—
355C22⋊Dic11—24no—
356C22⋊Dic11—24no—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367C4⋊Dic11—22no—
368C4⋊Dic11—22no—
369C4⋊Dic11—24no—
370C4⋊Dic11—24no—
371C4⋊Dic11—24no—
372C4⋊Dic11—22no—
373C4⋊Dic11—22no—
374C4⋊Dic11—22no—
375Dic11⋊C4—22no—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378Dic11⋊C4—22no—
379Dic11⋊C4—24no—
380Dic11⋊C4—24no—
381Dic11⋊C4—24no—
382Dic11⋊C4—24no—
383Dic11⋊C4—24no—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386C4×Dic11—24no—
387C4×Dic11—24no—
388C4×Dic11—24no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—22no—
392C4×Dic11—24no—
393C4×Dic11C2×D414yes—
394C4×Dic11C2×D414yes—
395C4×Dic11C2×D414yes—
396C2×C4×#41—111no—
397C22×C4×Q8—111no—
398#2599—112no—
399#2599—112no—
400#2581—111no—
401#2581—111no—
402#2536—111no—
403#2536—111no—
404#2486—111no—
405#2486—111no—
406#2484—112no—
407#2409—111no—
408#2409—111no—
409#2406—112no—
410#2399—112no—
411#2398—112no—
412C4×C22⋊Q8—111no—
413C4×C22⋊Q8—111no—
414C4×C22⋊Q8—111no—
415C4×C22⋊Q8D1111yescharacteristic, complemented
416C4×#123—112no—
417C4×#123—112no—
418#2283—111no—
419C23×C11—21no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11C2×#4112yes—
426C23×C11C2511yescharacteristic
427C22×D11—21no—
428C22×D11—21no—
429C22×D11—21no—
430C22×D11—21no—
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—21no—
435C22×D11—21no—
436C22×D11—21no—
437C22×D11C22×D412yes—
438C22×D11C2×#4112yes—
439C22×D11C2×#4112yes—
440C22×D11C2×#4112yes—
441Q8×C11—28no—
442C2×C4×C11—28no—
443C2×C4×C11—22no—
444C2×C4×C11—21no—
445C2×C4×C11—22no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—44no—
465C2×C4×C11—44no—
466C2×C4×C11C22×D412yes—
467C2×C4×C11C22×D412yes—
468C2×C4×C11C22×D412yes—
469C2×C4×C11C2×#4114yes—
470C2×C4×C11C2×#4112yes—
471C2×C4×C11C2×#4112yes—
472C2×C4×C11C2×#4112yes—
473C2×C4×C112−1+412yes—
474C2×C4×C112−1+412yes—
475C22⋊D11—28no—
476C22⋊D11—28no—
477C2×Dic11—22no—
478C2×Dic11—21no—
479C2×Dic11—21no—
480C2×Dic11—22no—
481C2×Dic11—21no—
482C2×Dic11—21no—
483C2×Dic11—21no—
484C2×Dic11—21no—
485C2×Dic11—21no—
486C2×Dic11—21no—
487C2×Dic11—22no—
488C2×Dic11—21no—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—21no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11C22×D412yes—
503C2×Dic11C22×D412yes—
504C2×Dic11C22×D412yes—
505C2×Dic11C2×#4112yes—
506C2×Dic11C2×#4114yes—
507D44—28no—
508C4×D11—28no—
509C4×D11—216no—
510C4×D11—28no—
511C4×D11—28no—
512C4×D11—28no—
513C4×D11—48no—
514C4×D11—44no—
515C4×D11—44no—
516Dic22—28no—
517Dic22—216no—
518Dic22—28no—
519C22×#41—111no—
520C23×Q8—111no—
521C2×#123—112no—
522C2×#123—112no—
523C2×C22⋊Q8—111no—
524C2×C22⋊Q8—111no—
525C2×C22⋊Q8—111no—
526C2×C22⋊Q8C2×D1111yescharacteristic
527C4×#41—228no—
528C2×C4×Q8—111no—
529C2×C4×Q8—111no—
530C2×C4×Q8—112no—
531C2×C4×Q8—111no—
532C2×C4×Q8—112no—
533C2×C4×Q8—111no—
534C2×C4×Q8—111no—
535C2×C4×Q8—228no—
536C2×C4×Q8C2×D1111yescharacteristic
537C2×C4×D4—111no—
538C2×C4×D4—111no—
539C2×C4×D4—111no—
540C2×C4×D4—111no—
541C2×C4×D4—111no—
542C2×C4×D4—111no—
543C2×#117—111no—
544C2×#117—111no—
545C2×#117—111no—
546C22×C4⋊C4—112no—
547C22×C4⋊C4—111no—
548C22×C42—111no—
549C22×C42—112no—
550C22×C42—111no—
551C22×C42C2×D1111yescharacteristic
552#400—112no—
553#400—112no—
554#398—112no—
555#398—112no—
556#398—112no—
557#398—112no—
558#397—112no—
559#397—112no—
560#395—112no—
561#395—112no—
562#395—112no—
563#395—112no—
564#394—112no—
565#394—112no—
566#393—112no—
567#393—112no—
568#391—111no—
569#391—111no—
570#391—111no—
571#391C2×D1111yescharacteristic
572#389—111no—
573#389—111no—
574#389—111no—
575#389C2×D1111yescharacteristic
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#387—112no—
581#387—112no—
582#387—112no—
583#387—112no—
584#387—112no—
585#387—112no—
586#387—112no—
587#387C2×D1112yes—
588#386—112no—
589#386—112no—
590#385—112no—
591#385—112no—
592#385—112no—
593#385—112no—
594#385—112no—
595#385C2×D1112yes—
596#383—112no—
597#382—111no—
598#382—111no—
599#381—112no—
600#381—112no—
601#381—112no—
602#380—111no—
603#380—111no—
604#380—111no—
605#380—111no—
606#380—111no—
607#380C2×D1111yescharacteristic
608C4×C4⋊C4—112no—
609C4×C4⋊C4—112no—
610C4×C4⋊C4—112no—
611C4×C4⋊C4—111no—
612C4×C4⋊C4C2×D1112yes—
613C4×C4⋊C4C2×D1111yescharacteristic
614C4×C22⋊C4—112no—
615C4×C22⋊C4—112no—
616C4×C22⋊C4—112no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4C2×D1112yes—
619#376—112no—
620C22×C11—22no—
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—41no—
624C22×C11—41no—
625C22×C11—41no—
626C22×C11—41no—
627C22×C11C23×D411yescharacteristic
628C22×C11C22×#4111yescharacteristic
629C22×C11C22×#4111yescharacteristic
630C22×C11C22×#4111yescharacteristic
631C22×C11C22×#4111yescharacteristic
632C22×C11C2×2−1+411yescharacteristic
633C22×C11C2×2−1+411yescharacteristic
634C2×D11—22no—
635C2×D11—22no—
636C2×D11—22no—
637C2×D11—22no—
638C2×D11—22no—
639C2×D11—22no—
640C2×D11—22no—
641C2×D11—22no—
642C2×D11—22no—
643C2×D11—41no—
644C2×D11—41no—
645C2×D11—41no—
646C2×D11—41no—
647C2×D11#52514yes—
648C4×C11—22no—
649C4×C11—22no—
650C4×C11—24no—
651C4×C11—41no—
652C4×C11—42no—
653C4×C11—41no—
654C4×C11—42no—
655C4×C11—42no—
656C4×C11#52514yes—
657C4×C11#53614yes—
658Dic11—22no—
659Dic11—24no—
660Dic11—22no—
661Dic11—22no—
662Dic11—22no—
663Dic11—41no—
664Dic11—42no—
665Dic11—41no—
666Dic11—42no—
667Dic11—42no—
668C2×#41—224no—
669C2×#41—224no—
670C2×#41—224no—
671C22×Q8—111no—
672C22×Q8—112no—
673C22×Q8—111no—
674C22×Q8—224no—
675C22×Q8—224no—
676C22×Q8—224no—
677C22×Q8C22×D1111yescharacteristic
678C22×D4—111no—
679C22×D4—111no—
680C22×D4—111no—
681C23×C4—111no—
682C23×C4—111no—
683C23×C4—111no—
684C23×C4—112no—
685C23×C4—112no—
686C23×C4—111no—
687C23×C4—111no—
688C23×C4—111no—
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C23×C4C22×D1111yescharacteristic
692#123—228no—
693#123—228no—
694C22⋊Q8—24no—
695C22⋊Q8—224no—
696C22⋊Q8—224no—
697C22⋊Q8—224no—
698C4×Q8—24no—
699C4×Q8—228no—
700C4×Q8—224no—
701C4×Q8—224no—
702C4×Q8—228no—
703C4×Q8—224no—
704C4×Q8—224no—
705C4×Q8—224no—
706C4×D4—224no—
707C4×D4—224no—
708C4×D4—224no—
709C4×D4—224no—
710C4×D4—224no—
711C4×D4—224no—
712#117—224no—
713#117—224no—
714#117—224no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—112no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—112no—
720C2×C4⋊C4—111no—
721C2×C4⋊C4—111no—
722C2×C4⋊C4—111no—
723C2×C4⋊C4—111no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—111no—
726C2×C4⋊C4—111no—
727C2×C4⋊C4—111no—
728C2×C4⋊C4—112no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4—224no—
735C2×C4⋊C4—228no—
736C2×C4⋊C4C22×D1111yescharacteristic
737C2×C4⋊C4C22×D1112yes—
738C2×C4⋊C4C22×D1111yescharacteristic
739C2×C4⋊C4C22×D1111yescharacteristic
740C2×C4⋊C4C22×D1112yes—
741C2×C4⋊C4C22×D1112yes—
742C2×C22⋊C4—111no—
743C2×C22⋊C4—111no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—112no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4C22×D1112yes—
757C2×C22⋊C4C22×D1112yes—
758C2×C42—24no—
759C2×C42—111no—
760C2×C42—111no—
761C2×C42—111no—
762C2×C42—118no—
763C2×C42—111no—
764C2×C42—111no—
765C2×C42—112no—
766C2×C42—112no—
767C2×C42—111no—
768C2×C42—112no—
769C2×C42—112no—
770C2×C42—228no—
771C2×C42—224no—
772C2×C42C22×D1111yescharacteristic
773C2×C42C22×D1111yescharacteristic
774C2×C42C22×D1111yescharacteristic
775C2×C42C22×D1112yes—
776C2×C42C22×D1112yes—
777C2×C42C22×D1111yescharacteristic
778#95—112no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95—112no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95—112no—
791#95—112no—
792#95—112no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—112no—
797#95C22×D1112yes—
798#95C22×D1112yes—
799#95C22×D1112yes—
800#95C22×D1112yes—
801#95C22×D1112yes—
802C2×C11—42no—
803C2×C11C2×#52511yescharacteristic
804C2×C11C2×#52511yescharacteristic
805C2×C11C2×#53611yescharacteristic
806C2×C11#348211yescharacteristic
807C2×C11#348211yescharacteristic
808C2×C11#348211yescharacteristic
809C2×C11#348211yescharacteristic
810D11—24no—
811D11—42no—
812C24—111no—
813C24—111no—
814C24C23×D1111yescharacteristic
815#41—2232no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—114no—
819C2×Q8—224no—
820C2×Q8—222no—
821C2×Q8—224no—
822C2×Q8—222no—
823C2×Q8—2232no—
824C2×Q8—224no—
825C2×Q8—222no—
826C2×Q8—222no—
827C2×Q8—222no—
828C2×Q8#433914yescomplemented
829C2×D4—114no—
830C2×D4—114no—
831C2×D4—222no—
832C2×D4—222no—
833C2×D4—222no—
834C2×D4—222no—
835C2×D4—222no—
836C2×D4—222no—
837C2×D4—222no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—111no—
848C22×C4—111no—
849C22×C4—112no—
850C22×C4—111no—
851C22×C4—111no—
852C22×C4—114no—
853C22×C4—114no—
854C22×C4—114no—
855C22×C4—111no—
856C22×C4—112no—
857C22×C4—112no—
858C22×C4—111no—
859C22×C4—112no—
860C22×C4—224no—
861C22×C4—222no—
862C22×C4—224no—
863C22×C4—222no—
864C22×C4—222no—
865C22×C4—222no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—224no—
869C22×C4—224no—
870C22×C4—222no—
871C22×C4—222no—
872C22×C4—222no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—222no—
876C22×C4—222no—
877C22×C4—222no—
878C22×C4—222no—
879C22×C4—222no—
880C22×C4—222no—
881C22×C4C23×D1112yes—
882C22×C4C23×D1111yescharacteristic
883C22×C4C23×D1112yes—
884C22×C4C23×D1112yes—
885C22×C4C23×D1111yescharacteristic
886C22×C4C23×D1112yes—
887C22×C4C23×D1111yescharacteristic
888C22×C4C23×D1111yescharacteristic
889C22×C4C23×D1111yescharacteristic
890C22×C4C23×D1111yescharacteristic
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—224no—
898C4⋊C4—224no—
899C4⋊C4—224no—
900C4⋊C4—222no—
901C4⋊C4—222no—
902C4⋊C4—222no—
903C4⋊C4—222no—
904C4⋊C4—222no—
905C4⋊C4—222no—
906C4⋊C4—224no—
907C4⋊C4—224no—
908C4⋊C4—224no—
909C4⋊C4—224no—
910C4⋊C4—224no—
911C4⋊C4—222no—
912C4⋊C4—224no—
913C4⋊C4—222no—
914C4⋊C4—222no—
915C4⋊C4—224no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—222no—
919C22⋊C4—222no—
920C22⋊C4—224no—
921C22⋊C4—222no—
922C22⋊C4—222no—
923C22⋊C4—224no—
924C22⋊C4—224no—
925C22⋊C4—224no—
926C22⋊C4—224no—
927C22⋊C4—222no—
928C22⋊C4—222no—
929C22⋊C4—224no—
930C22⋊C4—224no—
931C22⋊C4—224no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—24no—
936C42—24no—
937C42—114no—
938C42—114no—
939C42—114no—
940C42—224no—
941C42—224no—
942C42—222no—
943C42—222no—
944C42—222no—
945C42—224no—
946C42—224no—
947C42D4×D1114yes—
948C11#3497111yescharacteristic, complemented, Sylow
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—112no—
956C23—112no—
957C23—112no—
958C23—112no—
959C23—221no—
960C23—221no—
961C23—221no—
962C23—221no—
963C23—221no—
964C23—221no—
965C23—221no—
966C23—221no—
967C23—221no—
968C23—221no—
969C23#41×D1112yes—
970C23C24×D1111yescharacteristic
971Q8—28no—
972Q8—2216no—
973Q8—228no—
974Q8—228no—
975D4—228no—
976D4—228no—
977D4—228no—
978C2×C4—28no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—112no—
1003C2×C4—112no—
1004C2×C4—112no—
1005C2×C4—114no—
1006C2×C4—112no—
1007C2×C4—228no—
1008C2×C4—2216no—
1009C2×C4—228no—
1010C2×C4—221no—
1011C2×C4—222no—
1012C2×C4—221no—
1013C2×C4—222no—
1014C2×C4—221no—
1015C2×C4—221no—
1016C2×C4—221no—
1017C2×C4—221no—
1018C2×C4—221no—
1019C2×C4—221no—
1020C2×C4—228no—
1021C2×C4—228no—
1022C2×C4—222no—
1023C2×C4—221no—
1024C2×C4—221no—
1025C2×C4—221no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—221no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—221no—
1036C2×C4—221no—
1037C2×C4—448no—
1038C2×C4—444no—
1039C2×C4—444no—
1040C2×C4C2×#433914yes—
1041C2×C4C2×#433912yes—
1042C2×C4C2×D4×D1112yes—
1043C2×C4C2×D4×D1112yes—
1044C2×C4C2×D4×D1112yes—
1045C2×C4#6704012yes—
1046C2×C4#41×D1112yes—
1047C2×C4#41×D1112yes—
1048C2×C4#6704312yes—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22—114no—
1057C22—222no—
1058C22—222no—
1059C22—222no—
1060C22—222no—
1061C22—222no—
1062C22—222no—
1063C22—222no—
1064C22—222no—
1065C22—222no—
1066C22—441no—
1067C22—441no—
1068C22—441no—
1069C22—441no—
1070C22C22×#433911yescharacteristic
1071C22C22×D4×D1111yescharacteristic
1072C22C2×#6704011yescharacteristic
1073C22C2×#41×D1111yescharacteristic
1074C22C2×#41×D1111yescharacteristic
1075C22C2×#41×D1111yescharacteristic
1076C22C2×#6704311yescharacteristic
1077C4—24no—
1078C4—22no—
1079C4—22no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—222no—
1086C4—224no—
1087C4—222no—
1088C4—222no—
1089C4—222no—
1090C4—441no—
1091C4—441no—
1092C4—442no—
1093C4—442no—
1094C4—442no—
1095C4#1062307814yes—
1096C4#1062315914yes—
1097C2—42no—
1098C2—224no—
1099C2—442no—
1100C2D11×#52511yescharacteristic
1101C2C2×#1062307811yescharacteristic
1102C2C2×#1062315911yescharacteristic
1103C2#1308222911yescharacteristic
1104C2#1308223311yescharacteristic
1105C2#1308223411yescharacteristic
1106C2#1308223811yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×C22⋊Q8C2
prime radicalC22×#4339C22
hypercenterC4×C22⋊Q8D11
hypocenterC11#34971
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13074191C2semidirect
4. #13074189C2semidirect
5. #13073984C2semidirect
6. #13073980C2semidirect
7. #13073527C2semidirect
8. #13073523C2semidirect
9. #13072922C2semidirect
10. #13072920C2semidirect
11. #13072901C2semidirect
12. #13071979C2semidirect
13. #13071977C2semidirect
15. #13071910C2semidirect
16. #13071903C2semidirect
17. C4×#66950C2semidirect
18. C4×#66977C2semidirect
19. C4×#66999C2semidirect
20. C4×#66947C2semidirect
21. C4×#66936C2semidirect
22. #13071012C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
265. C2×Q8×C11#41semidirect
338. C2×Dic22#41semidirect
415. C4×C22⋊Q8D11semidirect
828. C2×Q8#4339semidirect
948. C11#34971semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
C2×C4×Q8×D112
#130741912
#130741892
#130739842
#130739802
#130735272
#130735232
#130729222
#130729202
#130729012
#130719792
#130719772
#130719492
#130719102
#130719032
C4×#669502
C4×#669772
C4×#669992
C4×#669472
C4×#669362
#130710122
C4×C11×C22⋊Q82
#3497111