Finite Group Databasebeta

← #14769561

Subgroups — #14769561

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×#66995C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic, complemented
3C2×#10622401C211yesmaximal, characteristic, complemented
4Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13071444C211yesmaximal, characteristic
6#13069484C211yesmaximal, characteristic, complemented
7#13069474C211yesmaximal, characteristic, complemented
8#13068955C211yesmaximal, characteristic, complemented
9#13068955C211yesmaximal, characteristic, complemented
10#13068947C211yesmaximal, characteristic, complemented
11#13068947C211yesmaximal, characteristic, complemented
12#13068647C211yesmaximal, characteristic, complemented
13#13068557C211yesmaximal, characteristic
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C2×#66995—24no—
23C2×#66995—24no—
24C2×#66995C418yescomplemented
25C22×#4325C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#380C2211yescharacteristic
36#10622843—21no—
37#10622843—21no—
38#10622843C2211yescharacteristic
39#10622843C2211yescharacteristic
40#10622825—21no—
41#10622825C2211yescharacteristic
42C4×C22⋊Dic11—21no—
43C4×C22⋊Dic11C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622587C2211yescharacteristic
51#10622587C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622569—21no—
55#10622569—21no—
56#10622430—24no—
57#10622401—24no—
58#10622277—21no—
59D11×#95—21no—
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C2×#4339—22no—
77C2×#4339—22no—
78C2×#4339—22no—
79C2×#4339—41no—
80C2×#4339—41no—
81C2×#4339C2×C414yes—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11D411yescharacteristic
94C2×C22⋊Dic11D411yescharacteristic
95Q8×Dic11—22no—
96Q8×Dic11—22no—
97Q8×Dic11—41no—
98Q8×Dic11—41no—
99C2×#4326—22no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326—22no—
103C2×#4326C2×C414yescomplemented
104C2×#4326C2×C414yescomplemented
105#66995—232no—
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325C2×C414yes—
109C2×#4325C2×C414yes—
110C2×#4325D414yes—
111C2×#4325D414yes—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4×Dic11—21no—
119C2×C4×Dic11—21no—
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318C2×C414yescomplemented
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66946—22no—
128#66946—22no—
129#66946—41no—
130#66946—41no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#103—41no—
134C11×#103—41no—
135C11×C22⋊C8—22no—
136C11×#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95D411yescharacteristic
147C11⋊#95D411yescharacteristic
148#66885—22no—
149#66885—22no—
150#66880—41no—
151#66880—41no—
152#66879—22no—
153C8×Dic11—22no—
154#66872—22no—
155#66871—22no—
156#22444—111nomaximal, Sylow
157C24×C11C2×D411yescharacteristic
158C23×D11—21no—
159C2×Q8×C11—24no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—28no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—42no—
170C2×Q8×C11—42no—
171C2×Q8×C11—44no—
172C2×Q8×C11—44no—
173C2×Q8×C11—44no—
174C2×Q8×C11C22×C412yes—
175C2×Q8×C11C22×C412yes—
176C2×Q8×C11C2×D412yes—
177C2×Q8×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—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11#4112yes—
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—24no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203#4339—28no—
204#4339—44no—
205#4339—44no—
206#4339—44no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44C22×C412yes—
211C2×D44C2×D412yes—
212C2×D44C2×D412yes—
213C2×C4×D11—24no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—42no—
220C2×C4×D11—81no—
221C2×C4×D11—81no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22C22×C412yes—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C22⋊C4—81no—
239C22⋊Dic11—22no—
240C22⋊Dic11—41no—
241C22⋊Dic11—42no—
242#4326—28no—
243#4326—28no—
244#4325—28no—
245#4325C22⋊C4116yescomplemented
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4—42no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—42no—
253C4⋊Dic11—42no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11—21no—
257C4×Dic11—21no—
258C4×Dic11—42no—
259C4×Dic11—42no—
260#4318—28no—
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#2339—111no—
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#1787D1111yescharacteristic, complemented
281#1753—111no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11C4×D412yes—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—48no—
303Q8×C11—41no—
304Q8×C11—41no—
305Q8×C11C2×C22⋊C414yes—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—48no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11C4×D412yes—
326C2×C4×C11C23×C411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C22⋊D11—48no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—22no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11#13712yescomplemented
354D44—22no—
355D44—22no—
356D44—22no—
357D44C2×C22⋊C414yes—
358C4×D11—48no—
359C4×D11—84no—
360C4×D11—84no—
361Dic22—22no—
362Dic22—22no—
363Dic22—41no—
364Dic22—41no—
365C8×C11—41no—
366C8×C11—41no—
367C11⋊C8—22no—
368C11⋊C8C2×C22⋊C414yes—
369C22×#41—111no—
370C23×Q8C2×D1111yescharacteristic
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×D4—111no—
382C2×C4×D4—111no—
383#440—224no—
384C4×SD16—224no—
385C2×#107—111no—
386C2×#106—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103C2×D1111yescharacteristic
390C2×#103C2×D1111yescharacteristic
391C2×#103C2×D1111yescharacteristic
392C2×#103C2×D1111yescharacteristic
393C2×#102—111no—
394C2×#102—111no—
395C2×C22⋊C8C2×D1111yescharacteristic
396C2×#97—111no—
397C2×C4×C8—111no—
398#391—111no—
399#391—111no—
400#391—111no—
401#391—111no—
402#391—221no—
403#391—221no—
404#386—221no—
405#386—221no—
406#381—221no—
407#380—111no—
408#380—221no—
409#380C2×D1111yescharacteristic
410C4×C22⋊C4—111no—
411C4×C22⋊C4—221no—
412C2×#95—221no—
413#340—111no—
414#340—111no—
415#336—111no—
416#336—111no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11C2×C4×D411yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11C2×#13711yescharacteristic
428C22×C11#57511yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57811yescharacteristic
431C2×D11—24no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C4×C11—22no—
439C4×C11—24no—
440C4×C11—42no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11C22×C22⋊C411yescharacteristic
444C4×C11#51811yescharacteristic
445C4×C11#54611yescharacteristic
446C4×C11#54611yescharacteristic
447Dic11—22no—
448Dic11—42no—
449Dic11—41no—
450Dic11—41no—
451Dic11—41no—
452Dic11—81no—
453Dic11—81no—
454C2×#41—114no—
455C2×#41—222no—
456C2×#41—222no—
457C2×#41—222no—
458C2×#41—441no—
459C2×#41—441no—
460C22×Q8—21no—
461C22×Q8—22no—
462C22×Q8—22no—
463C22×Q8—22no—
464C22×Q8—41no—
465C22×Q8—41no—
466C22×Q8—111no—
467C22×Q8C4×D1114yescomplemented
468C22×Q8C22×D1111yescharacteristic
469C22×Q8C22×D1111yescharacteristic
470C22×D4—111no—
471C22×D4—221no—
472C23×C4—21no—
473C23×C4—221no—
474C23×C4—221no—
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×C8C22×D1111yescharacteristic
496C22×C8C22×D1111yescharacteristic
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—441no—
500C4×Q8—441no—
501C4×D4—222no—
502C4×D4—222no—
503C4×D4—441no—
504C4×D4—441no—
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—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—111no—
518C2×C42—111no—
519C2×C42—221no—
520C2×C42—221no—
521#107—222no—
522#106—222no—
523#103—22no—
524#103—22no—
525#103—41no—
526#103—41no—
527#103—441no—
528#103—441no—
529#102—222no—
530#102—222no—
531C22⋊C8—22no—
532#97—222no—
533C4×C8—222no—
534#95—21no—
535#95—111no—
536#95—111no—
537#95—221no—
538#95—221no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544#95—221no—
545#95—221no—
546C2×C11—42no—
547C2×C11D4×C22⋊C411yescharacteristic
548C2×C11C4×#13711yescharacteristic
549C2×C11#294711yescharacteristic
550C2×C11#326611yescharacteristic
551C2×C11#326911yescharacteristic
552C2×C11#327511yescharacteristic
553C2×C11#327611yescharacteristic
554D11—44no—
555C24—221no—
556C24D4×D1111yescharacteristic
557#41—228no—
558#41—444no—
559#41—444no—
560#41—444no—
561C2×Q8—24no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—28no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—112no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8C2×C4×D1112yes—
583C2×Q8C2×C4×D1112yes—
584C2×Q8D4×D1112yes—
585C2×Q8D4×D1112yes—
586C2×D4—112no—
587C2×D4—112no—
588C2×D4—112no—
589C2×D4—224no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—442no—
594C2×D4—442no—
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—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—221no—
611C22×C4—224no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—881no—
621C22×C4—881no—
622C22×C4C2×C4×D1112yes—
623C22×C4D4×D1111yescharacteristic
624C22×C4#434112yes—
625C22×C4C23×D1111yescharacteristic
626Q16—228no—
627Q16—228no—
628SD16—1116no—
629SD16—228no—
630M16—228no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—112no—
638C2×C8—112no—
639C2×C8—112no—
640C2×C8—112no—
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—81no—
654C22⋊C4—222no—
655C22⋊C4—442no—
656C22⋊C4—442no—
657C22⋊C4—441no—
658C22⋊C4—442no—
659C42—221no—
660C42—221no—
661C42—221no—
662C42—221no—
663C42—442no—
664C42—442no—
665C11#2244411yescharacteristic, complemented, Sylow
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23(C22⋊D11)⋊C412yes—
680C23C2×D4×D1111yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—222no—
690Q8—222no—
691Q8—441no—
692Q8—441no—
693Q8C22⋊C4×D1114yes—
694D4—114no—
695D4—222no—
696D4—222no—
697D4—222no—
698D4—448no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—48no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—112no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—222no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—448no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—884no—
741C2×C4—884no—
742C2×C4(C22⋊D11)⋊C412yes—
743C2×C4C22×C4×D1111yescharacteristic
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4C2×D4×D1111yescharacteristic
746C2×C4C2×#434111yescharacteristic
747C2×C4#6703711yescharacteristic
748C2×C4#6703711yescharacteristic
749C8—41no—
750C8—41no—
751C8—114no—
752C8—222no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—224no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22C2×(C22⋊D11)⋊C411yescharacteristic
768C22#1062312111yescharacteristic
769C22#1062312111yescharacteristic
770C22#1062329311yescharacteristic
771C22#1062329711yescharacteristic
772C22D11×#13711yescharacteristic
773C22#1062330811yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—81no—
778C4—81no—
779C4—222no—
780C4—442no—
781C4—441no—
782C4—441no—
783C4—441no—
784C4—881no—
785C4—881no—
786C4C2×C22⋊C4×D1111yescharacteristic
787C4#1062301711yescharacteristic
788C4#1062312211yescharacteristic
789C4#1062312211yescharacteristic
790C2—42no—
791C2—444no—
792C2#1307143211yescharacteristic
793C2#1307743111yescharacteristic
794C2#1307745311yescharacteristic
795C2#1308012911yescharacteristic
796C2#1308017411yescharacteristic
797C2#1308025011yescharacteristic
798C2#1308025511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22444
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
3. C2×#10622401C2semidirect
4. Q8×C22⋊Dic11C2semidirect
6. #13069484C2semidirect
7. #13069474C2semidirect
8. #13068955C2semidirect
9. #13068955C2semidirect
10. #13068947C2semidirect
11. #13068947C2semidirect
12. #13068647C2semidirect
14. #13068402C2semidirect
15. C11×#1787C2semidirect
24. C2×#66995C4semidirect
70. C22×Q8×C11C2×C4semidirect
103. C2×#4326C2×C4semidirect
104. C2×#4326C2×C4semidirect
124. C2×#4318C2×C4semidirect
245. #4325C22⋊C4semidirect
280. #1787D11semidirect
353. C2×Dic11#137semidirect
467. C22×Q8C4×D11semidirect
665. C11#22444semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106224302
C2×#106224012
Q8×C22⋊Dic112
#130714442
#130694842
#130694742
#130689552
#130689472
#130686472
#130685572
#130684022
C11×#17872
#2244411