Finite Group Databasebeta

← #14769579

Subgroups — #14769579

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic, complemented
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13071456C211yesmaximal, characteristic
5#13069500C211yesmaximal, characteristic, complemented
6#13069473C211yesmaximal, characteristic, complemented
7#13068971C211yesmaximal, characteristic, complemented
8#13068971C211yesmaximal, characteristic, complemented
9#13068960C211yesmaximal, characteristic, complemented
10#13068960C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic
13#13068551C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C2×#66995—24no—
23C2×#66995—24no—
24C2×#66995C418yescomplemented
25C22×#4325C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C11×#391—21no—
31C11×#391—21no—
32C11×#391C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#380—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C22⋊C4—21no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622643—24no—
45C4×#4326—24no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52#10622570—21no—
53#10622570—21no—
54#10622552C2211yescharacteristic
55#10622552C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C2×C4×C11⋊C8C2211yescharacteristic
58#10622280—21no—
59#10622279—21no—
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622162C2211yescharacteristic
63#10622162C2211yescharacteristic
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×C414yes—
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×Dic22C2311yescharacteristic
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—41no—
88C4×Q8×C11—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×#4326—22no—
102C2×#4326—22no—
103C2×#4326C2×C414yes—
104C2×#4326C2×C414yes—
105C2×#4326D414yes—
106C2×#4326D414yes—
107#66995—232no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325—22no—
111C2×#4325—22no—
112C2×#4325C2×C414yes—
113C2×#4325C2×C414yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—21no—
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318C2×C414yes—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C4×Dic22—22no—
132C4×Dic22—22no—
133C4×Dic22—41no—
134C4×Dic22—41no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95D411yescharacteristic
141C11×#95D411yescharacteristic
142#66899—22no—
143#66899—22no—
144#66899—41no—
145#66899—41no—
146C11⋊#95—21no—
147C22⋊(C11⋊C8)—22no—
148#66874—22no—
149#66874—22no—
150#66873—41no—
151#66873—41no—
152#66872—22no—
153#66871—22no—
154#66867—22no—
155C4×C11⋊C8—22no—
156#22445—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×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11#4112yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11—42no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203#4339—28no—
204#4339—44no—
205#4339—44no—
206#4339—44no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44C22×C412yes—
213C2×C4×D11—24no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22C22×C412yes—
220C2×Dic22C2×D412yes—
221C2×Dic22C2×D412yes—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—41no—
230C11×C22⋊C4—42no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—42no—
236C42×C11—42no—
237C22⋊Dic11—81no—
238#4326—28no—
239#4326C22⋊C4116yescomplemented
240#4325—28no—
241#4325—28no—
242(C2×D11)⋊C4—42no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—81no—
245(C2×D11)⋊C4—81no—
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×#441—111no—
269C2×C4×Q16—111no—
270#2341—111no—
271Q8×C22⋊C4D1111yescharacteristic, complemented
272#1973—111no—
273#1968—111no—
274#1880—111no—
275#1880—111no—
276#1878—111no—
277#1878—111no—
278#1809—111no—
279#1788—111no—
280#1787—111no—
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—41no—
292C22×D11—41no—
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—21no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
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—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—48no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11C4×D412yes—
337C2×C4×C11#13712yescomplemented
338C2×C4×C11C23×C411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C22⋊D11—48no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354D44—22no—
355D44—22no—
356D44—41no—
357D44—41no—
358C4×D11—48no—
359Dic22—22no—
360Dic22—22no—
361Dic22—22no—
362Dic22C2×C22⋊C414yes—
363C11⋊C8—22no—
364C11⋊C8—41no—
365C11⋊C8—41no—
366C11⋊C8C2×C22⋊C414yes—
367C22×#41—111no—
368C23×Q8C2×D1111yescharacteristic
369C2×#137—118no—
370C2×#137—224no—
371C2×#137—224no—
372C22×Q16—111no—
373C22×Q16—111no—
374C22×SD16—111no—
375C22×SD16—111no—
376C22×M16—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×Q8C2×D1111yescharacteristic
380C2×C4×Q8C2×D1111yescharacteristic
381#441—224no—
382C4×Q16—224no—
383C2×#107—111no—
384C2×#106—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×C22⋊C8—111no—
394C2×#97—111no—
395C2×C4×C8—111no—
396#391—21no—
397#391—21no—
398#391C2×D1111yescharacteristic
399#391C2×D1111yescharacteristic
400#390—111no—
401#390—111no—
402#390—221no—
403#390—221no—
404#380—21no—
405#380—111no—
406#380—221no—
407#380C2×D1111yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4—221no—
410C4×C22⋊C4C2×D1111yescharacteristic
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11C2×C4×D411yescharacteristic
423C22×C11D4211yescharacteristic
424C22×C11D4211yescharacteristic
425C22×C11C2×#13711yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57711yescharacteristic
428C22×C11#57811yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—22no—
439C4×C11—42no—
440C4×C11—41no—
441C4×C11—41no—
442C4×C11—41no—
443C4×C11—81no—
444C4×C11—81no—
445C4×C11C22×C22⋊C411yescharacteristic
446C4×C11#51811yescharacteristic
447C4×C11#54611yescharacteristic
448C4×C11#54611yescharacteristic
449Dic11—24no—
450Dic11—81no—
451Dic11—81no—
452C2×#41—114no—
453C2×#41—222no—
454C2×#41—222no—
455C2×#41—222no—
456C2×#41—441no—
457C2×#41—441no—
458C22×Q8—22no—
459C22×Q8—21no—
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—41no—
463C22×Q8—41no—
464C22×Q8—111no—
465C22×Q8C4×D1114yes—
466C22×Q8C22×D1111yescharacteristic
467C22×Q8C22×D1111yescharacteristic
468C22×D4—111no—
469C22×D4—221no—
470C23×C4—21no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473#137—2232no—
474C2×Q16—114no—
475C2×Q16—114no—
476C2×Q16—114no—
477C2×Q16—114no—
478C2×Q16—222no—
479C2×Q16—222no—
480C2×SD16—114no—
481C2×SD16—114no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×M16—114no—
487C2×M16—222no—
488C2×M16—222no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8—111no—
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8—41no—
496C4×Q8—41no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—441no—
500C4×Q8—441no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4C22⋊D1111yescharacteristic
516C2×C22⋊C4C22⋊D1111yescharacteristic
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—221no—
520C2×C42—221no—
521C2×C42C22×D1111yescharacteristic
522C2×C42C22×D1111yescharacteristic
523#107—222no—
524#106—222no—
525#103—222no—
526#103—222no—
527#103—222no—
528#103—222no—
529#103—441no—
530#103—441no—
531#102—441no—
532#102—441no—
533C22⋊C8—222no—
534#97—222no—
535C4×C8—222no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—221no—
542#95C22⋊D1111yescharacteristic
543#95C22⋊D1111yescharacteristic
544C2×C11—42no—
545C2×C11D4×C22⋊C411yescharacteristic
546C2×C11C4×#13711yescharacteristic
547C2×C11#294711yescharacteristic
548C2×C11#327011yescharacteristic
549C2×C11#327111yescharacteristic
550C2×C11#327711yescharacteristic
551C2×C11#327811yescharacteristic
552D11—82no—
553C24—221no—
554C24C2×C22⋊D1111yescharacteristic
555#41—228no—
556#41—444no—
557#41—444no—
558#41—444no—
559C2×Q8—24no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8—44no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—112no—
575C2×Q8—112no—
576C2×Q8—112no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8C2×C4×D1112yes—
581C2×Q8C2×C4×D1112yes—
582C2×Q8D4×D1112yes—
583C2×Q8D4×D1112yes—
584C2×D4—112no—
585C2×D4—224no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—442no—
592C2×D4—442no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—221no—
605C22×C4—224no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—442no—
609C22×C4—442no—
610C22×C4C2×C4×D1112yes—
611C22×C4#433912yes—
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618Q16—1116no—
619Q16—228no—
620SD16—228no—
621SD16—228no—
622M16—228no—
623C2×C8—112no—
624C2×C8—112no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—442no—
646C4⋊C4—442no—
647C22⋊C4—22no—
648C22⋊C4—41no—
649C22⋊C4—42no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C22⋊C4—881no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—42no—
660C42—42no—
661C42—442no—
662C42—442no—
663C11#2244511yescharacteristic, complemented, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—222no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23C4×C22⋊D1112yes—
678C23C22×C22⋊D1111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—48no—
685Q8—41no—
686Q8—41no—
687Q8—114no—
688Q8—222no—
689Q8—222no—
690Q8—222no—
691Q8C22⋊C4×D1114yes—
692D4—222no—
693D4—222no—
694D4—448no—
695D4—441no—
696D4—441no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
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—21no—
718C2×C4—48no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—448no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4C4×C22⋊D1112yes—
738C2×C4#6699512yescomplemented
739C2×C4C22×C4×D1111yescharacteristic
740C2×C4C2×#433911yescharacteristic
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4C2×D4×D1111yescharacteristic
743C2×C4#6703711yescharacteristic
744C2×C4#6703711yescharacteristic
745C8—114no—
746C8—222no—
747C8—441no—
748C8—441no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—881no—
760C22—881no—
761C22—881no—
762C22—881no—
763C22C2×C4×C22⋊D1111yescharacteristic
764C22D4×C22⋊D1111yescharacteristic
765C22D4×C22⋊D1111yescharacteristic
766C22C2×#6699511yescharacteristic
767C22#1062335311yescharacteristic
768C22#1062336811yescharacteristic
769C22#1062336911yescharacteristic
770C4—22no—
771C4—24no—
772C4—22no—
773C4—42no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—224no—
780C4—881no—
781C4—881no—
782C4C2×C22⋊C4×D1111yescharacteristic
783C4#1062301711yescharacteristic
784C4#1062302111yescharacteristic
785C4#1062302111yescharacteristic
786C2—42no—
787C2—882no—
788C2C22⋊C4×C22⋊D1111yescharacteristic
789C2C4×#6699511yescharacteristic
790C2#1307745911yescharacteristic
791C2#1308018711yescharacteristic
792C2#1308020211yescharacteristic
793C2#1308026911yescharacteristic
794C2#1308027811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11#22445
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622643C2semidirect
3. C2×C4×#4326C2semidirect
5. #13069500C2semidirect
6. #13069473C2semidirect
7. #13068971C2semidirect
8. #13068971C2semidirect
9. #13068960C2semidirect
10. #13068960C2semidirect
11. #13068647C2semidirect
13. #13068551C2semidirect
14. #13068400C2semidirect
15. Q8×C11×C22⋊C4C2semidirect
24. C2×#66995C4semidirect
239. #4326C22⋊C4semidirect
271. Q8×C22⋊C4D11semidirect
337. C2×C4×C11#137semidirect
663. C11#22445semidirect
738. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106226432
C2×C4×#43262
#130714562
#130695002
#130694732
#130689712
#130689602
#130686472
#130685542
#130685512
#130684002
Q8×C11×C22⋊C42
#2244511