Finite Group Databasebeta

← #14769564

Subgroups — #14769564

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic, complemented
4C22⋊C4×Dic22C211yesmaximal, characteristic, complemented
5#13069486C211yesmaximal, characteristic, complemented
6#13069476C211yesmaximal, characteristic, complemented
7#13068960C211yesmaximal, characteristic, complemented
8#13068960C211yesmaximal, characteristic, complemented
9#13068950C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic
13#13068550C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#2339C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#67004—24no—
21C2×#67004—24no—
22C2×#67004C418yescomplemented
23C22×#4326C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4324C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C11×#386—21no—
33C11×#386—21no—
34C11×#381—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C22⋊C4C2211yescharacteristic
37C2×C11×#95—21no—
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622631—24no—
45C4×#4324—24no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52#10622555—21no—
53C22⋊C4×Dic11—21no—
54#10622542C2211yescharacteristic
55#10622542C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C2×C4×C11⋊C8C2211yescharacteristic
58#10622259—21no—
59#10622259—21no—
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622162C2211yescharacteristic
63#10622162C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yes—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—21no—
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—21no—
81C22×Dic22—22no—
82C22×Dic22—41no—
83C22×Dic22—41no—
84C22×Dic22C2×C414yescomplemented
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—41no—
90C4×D4×C11—41no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101#67004—232no—
102C2×#4326—22no—
103C2×#4326—22no—
104C2×#4326—22no—
105C2×#4326—22no—
106C2×#4326C2×C414yescomplemented
107C2×#4326C2×C414yescomplemented
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324C2×C414yes—
111C2×#4324C2×C414yes—
112C2×#4324D414yes—
113C2×#4324D414yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11—21no—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318C2×C414yescomplemented
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C4×Dic22—22no—
128C4×Dic22—22no—
129C4×Dic22—41no—
130C4×Dic22—41no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#66899—41no—
139#66899—41no—
140#66896—22no—
141#66896—22no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C22⋊(C11⋊C8)—22no—
148#66874—22no—
149#66874—22no—
150#66874—41no—
151#66874—41no—
152#66872—22no—
153#66871—22no—
154#66867—22no—
155C4×C11⋊C8—22no—
156#22444—111nomaximal, Sylow
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C11×#41—28no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11C22×C412yes—
169C2×D4×C11—24no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11C22×C412yes—
176C2×D4×C11C2×D412yes—
177C2×D4×C11C2×D412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—24no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—81no—
193C22×C4×C11—81no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—24no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C2×Dic22—28no—
210C2×Dic22—24no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—44no—
220C2×Dic22—44no—
221C2×Dic22—44no—
222C2×Dic22—42no—
223C2×Dic22—42no—
224C2×Dic22C22×C412yes—
225C2×Dic22C22×C412yes—
226C2×Dic22C2×D412yes—
227C2×Dic22C2×D412yes—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—41no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—81no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—21no—
241C22⋊Dic11—42no—
242#4326—28no—
243#4326—28no—
244#4324—28no—
245#4324C22⋊C4116yescomplemented
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250Dic11⋊C4—42no—
251Dic11⋊C4—42no—
252C4×Dic11—42no—
253C4×Dic11—42no—
254#4318—28no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8C22×C412yes—
264C2×C11⋊C8C22×C412yes—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C22×#137—111no—
268C2×#440—111no—
269C2×C4×SD16—111no—
270Q8×C22⋊C4—111no—
271#2339D1111yescharacteristic
272#1971—111no—
273#1969—111no—
274#1878—111no—
275#1878—111no—
276#1877—111no—
277#1877—111no—
278#1809—111no—
279#1788—111no—
280#1787—111no—
281#1753—111no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11C4×D412yes—
296C23×C11C22×D411yescharacteristic
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—41no—
300Q8×C11—41no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—48no—
305D4×C11C2×C22⋊C414yes—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—48no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—84no—
334C2×C4×C11—84no—
335C2×C4×C11C4×D412yes—
336C2×C4×C11#13712yescomplemented
337C2×C4×C11C23×C411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—48no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22—22no—
360Dic22—22no—
361Dic22—48no—
362Dic22—41no—
363Dic22—41no—
364Dic22C2×C22⋊C414yes—
365C11⋊C8—22no—
366C11⋊C8—41no—
367C11⋊C8—41no—
368C11⋊C8C2×C22⋊C414yes—
369C22×#41C2×D1111yescharacteristic
370C23×Q8—111no—
371C2×#137—118no—
372C2×#137—224no—
373C2×#137—224no—
374C22×Q16—111no—
375C22×Q16—111no—
376C22×SD16—111no—
377C22×SD16—111no—
378C22×M16—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381C2×C4×D4C2×D1111yescharacteristic
382C2×C4×D4C2×D1111yescharacteristic
383#440—224no—
384C4×SD16—224no—
385C2×#107—111no—
386C2×#106—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#103—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×C22⋊C8—111no—
396C2×#97—111no—
397C2×C4×C8—111no—
398#391—111no—
399#391—111no—
400#391—221no—
401#391—221no—
402#391C2×D1111yescharacteristic
403#391C2×D1111yescharacteristic
404#386—21no—
405#386—21no—
406#381—21no—
407#380—111no—
408#380—221no—
409#380C2×D1111yescharacteristic
410C4×C22⋊C4—221no—
411C4×C22⋊C4C2×D1111yescharacteristic
412C2×#95—21no—
413#340—111no—
414#340—111no—
415#336—111no—
416#336—111no—
417C22×C11—22no—
418C22×C11—24no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—42no—
431C22×C11C2×C4×D411yescharacteristic
432C22×C11D4211yescharacteristic
433C22×C11D4211yescharacteristic
434C22×C11C2×#13711yescharacteristic
435C22×C11#57511yescharacteristic
436C22×C11#57711yescharacteristic
437C22×C11#57811yescharacteristic
438C4×C11—22no—
439C4×C11—22no—
440C4×C11—42no—
441C4×C11—41no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—81no—
445C4×C11—81no—
446C4×C11C22×C22⋊C411yescharacteristic
447C4×C11#51811yescharacteristic
448C4×C11#54611yescharacteristic
449C4×C11#54611yescharacteristic
450Dic11—24no—
451Dic11—42no—
452Dic11—81no—
453Dic11—81no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—41no—
458C2×#41—41no—
459C2×#41C4×D1114yes—
460C22×Q8—114no—
461C22×Q8—111no—
462C22×Q8—111no—
463C22×Q8—222no—
464C22×Q8—222no—
465C22×Q8—222no—
466C22×Q8—221no—
467C22×Q8—441no—
468C22×Q8—441no—
469C22×Q8C22×D1111yescharacteristic
470C22×D4—21no—
471C22×D4C22×D1111yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—221no—
476C23×C4C22×D1111yescharacteristic
477#137—2232no—
478C2×Q16—114no—
479C2×Q16—114no—
480C2×Q16—222no—
481C2×Q16—222no—
482C2×Q16—222no—
483C2×Q16—222no—
484C2×SD16—114no—
485C2×SD16—114no—
486C2×SD16—114no—
487C2×SD16—114no—
488C2×SD16—222no—
489C2×SD16—222no—
490C2×M16—114no—
491C2×M16—222no—
492C2×M16—222no—
493C22×C8—111no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8—111no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—441no—
500C4×Q8—441no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4C22⋊D1111yescharacteristic
516C2×C22⋊C4C22⋊D1111yescharacteristic
517C2×C42—221no—
518C2×C42—221no—
519C2×C42C22×D1111yescharacteristic
520C2×C42C22×D1111yescharacteristic
521#107—222no—
522#106—222no—
523#103—222no—
524#103—222no—
525#103—441no—
526#103—441no—
527#103—441no—
528#103—441no—
529#102—222no—
530#102—222no—
531C22⋊C8—222no—
532#97—222no—
533C4×C8—222no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544#95C22⋊D1111yescharacteristic
545#95C22⋊D1111yescharacteristic
546C2×C11—42no—
547C2×C11—44no—
548C2×C11D4×C22⋊C411yescharacteristic
549C2×C11C4×#13711yescharacteristic
550C2×C11#294711yescharacteristic
551C2×C11#326611yescharacteristic
552C2×C11#326911yescharacteristic
553C2×C11#327511yescharacteristic
554C2×C11#327611yescharacteristic
555C24—21no—
556C24C2×C22⋊D1111yescharacteristic
557#41—28no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—112no—
567C2×Q8—112no—
568C2×Q8—112no—
569C2×Q8—112no—
570C2×Q8—228no—
571C2×Q8—224no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8—442no—
581C2×Q8—442no—
582C2×Q8—444no—
583C2×Q8—444no—
584C2×Q8—444no—
585C2×Q8C2×C4×D1112yes—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4C2×C4×D1112yes—
593C2×D4D4×D1112yes—
594C2×D4D4×D1112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—221no—
612C22×C4—224no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4C2×C4×D1112yes—
619C22×C4#433912yes—
620C22×C4C2×C22⋊D1111yescharacteristic
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626Q16—228no—
627Q16—228no—
628SD16—1116no—
629SD16—228no—
630M16—228no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—112no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—442no—
652C4⋊C4—442no—
653C22⋊C4—22no—
654C22⋊C4—41no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—442no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—442no—
664C42—442no—
665C11#2244411yescharacteristic, complemented, Sylow
666C23—22no—
667C23—22no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C4×C22⋊D1112yes—
680C23C22×C22⋊D1111yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—114no—
686Q8—222no—
687Q8—222no—
688Q8—222no—
689Q8—222no—
690Q8—222no—
691Q8—448no—
692Q8—441no—
693Q8—441no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—48no—
698D4C22⋊C4×D1114yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—48no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—448no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4C4×C22⋊D1112yes—
742C2×C4#6700412yescomplemented
743C2×C4C22×C4×D1111yescharacteristic
744C2×C4C2×#433911yescharacteristic
745C2×C4C2×D4×D1111yescharacteristic
746C2×C4C2×D4×D1111yescharacteristic
747C2×C4#6703711yescharacteristic
748C2×C4#6703711yescharacteristic
749C8—114no—
750C8—222no—
751C8—441no—
752C8—441no—
753C22—22no—
754C22—24no—
755C22—22no—
756C22—22no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22C2×C4×C22⋊D1111yescharacteristic
768C22D4×C22⋊D1111yescharacteristic
769C22D4×C22⋊D1111yescharacteristic
770C22#1062335311yescharacteristic
771C22C2×#6700411yescharacteristic
772C22#1062336711yescharacteristic
773C22#1062336911yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—224no—
783C4—442no—
784C4—881no—
785C4—881no—
786C4C2×C22⋊C4×D1111yescharacteristic
787C4#1062301711yescharacteristic
788C4#1062302111yescharacteristic
789C4#1062302111yescharacteristic
790C2—42no—
791C2—44no—
792C2C22⋊C4×C22⋊D1111yescharacteristic
793C2C4×#6700411yescharacteristic
794C2#1307745511yescharacteristic
795C2#1308012211yescharacteristic
796C2#1308016711yescharacteristic
797C2#1308024311yescharacteristic
798C2#1308025811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2339C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2339D11
hypocenterC11#22444
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
3. C2×C4×#4324C2semidirect
4. C22⋊C4×Dic22C2semidirect
5. #13069486C2semidirect
6. #13069476C2semidirect
7. #13068960C2semidirect
8. #13068960C2semidirect
9. #13068950C2semidirect
10. #13068950C2semidirect
11. #13068647C2semidirect
13. #13068550C2semidirect
14. #13068400C2semidirect
22. C2×#67004C4semidirect
84. C22×Dic22C2×C4semidirect
106. C2×#4326C2×C4semidirect
107. C2×#4326C2×C4semidirect
122. C2×#4318C2×C4semidirect
245. #4324C22⋊C4semidirect
336. C2×C4×C11#137semidirect
665. C11#22444semidirect
742. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106226312
C2×C4×#43242
C22⋊C4×Dic222
#130694862
#130694762
#130689602
#130689502
#130686472
#130685562
#130685502
#130684002
C11×#23392
#2244411