Finite Group Databasebeta

← #14769577

Subgroups — #14769577

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×#66971C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3#13071454C211yesmaximal, characteristic
4Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13069497C211yesmaximal, characteristic, complemented
6#13069468C211yesmaximal, characteristic, complemented
7#13068971C211yesmaximal, characteristic, complemented
8#13068969C211yesmaximal, characteristic, complemented
9#13068957C211yesmaximal, characteristic, complemented
10#13068955C211yesmaximal, characteristic, complemented
11#13068646C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic
13#13068549C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic, complemented
15C2×C11×#441C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×Q8×D11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66971—24no—
26C2×#66971—24no—
27C2×#66971C418yescomplemented
28C22×#4314C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C11×#441—24no—
31C2×C11×#106C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37Q16×Dic11—24no—
38C2×#66885C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622601—21no—
44#10622601C2211yescharacteristic
45#10622600—21no—
46#10622600—21no—
47#10622600C2211yescharacteristic
48#10622600C2211yescharacteristic
49#10622587—21no—
50#10622587C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53#10622552—21no—
54#10622552C2211yescharacteristic
55C4×(C2×D11)⋊C4—21no—
56C4×(C2×D11)⋊C4—21no—
57C4×(C2×D11)⋊C4C2211yescharacteristic
58#10622542—21no—
59#10622542C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C2×#4343—22no—
67C2×#4343—22no—
68C2×#4343—22no—
69C2×#4343—41no—
70C2×#4343—41no—
71C2×#4343C2×C414yes—
72C2×Q8×D11—22no—
73C2×Q8×D11—22no—
74C2×Q8×D11—22no—
75C2×Q8×D11—41no—
76C2×Q8×D11—41no—
77C2×Q8×D11C2×C414yes—
78C22×D44—21no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C22×Dic22—21no—
84C22×Dic22C2311yescharacteristic
85C2×C11×Q16C2×C414yes—
86C2×C11×Q16D414yes—
87C2×C11×Q16D414yes—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—41no—
93C4×Q8×C11—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101Q8×Dic11—22no—
102Q8×Dic11—22no—
103Q8×Dic11—41no—
104Q8×Dic11—41no—
105C2×#4326—22no—
106C2×#4326—22no—
107C2×#4326C2×C414yes—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325C2×C414yes—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4×Dic11—21no—
124C2×C4×Dic11—21no—
125C2×C4×Dic11C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66971—232no—
129C2×#4314—22no—
130C2×#4314—22no—
131C2×#4314C2×C414yes—
132C2×#4313—22no—
133C2×#4313—22no—
134C2×#4313C2×C414yes—
135C11×#106—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#97—22no—
139#66899—22no—
140#66899—22no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95D411yescharacteristic
148C11⋊#95D411yescharacteristic
149#66885—41no—
150(C2×D11)⋊C8—22no—
151#66882—22no—
152#66880—41no—
153C8×Dic11—22no—
154#66874—41no—
155#66873—41no—
156#22445—111nomaximal, Sylow
157C23×D11—21no—
158C23×D11C2×D411yescharacteristic
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11C22×C412yes—
166C2×Q8×C11C22×C412yes—
167C2×Q8×C11C2×D412yes—
168C2×Q8×C11C2×D412yes—
169C2×Q8×C11C2×D412yes—
170C2×Q8×C11C2×D412yes—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184#4343—28no—
185#4343—44no—
186#4343—44no—
187#4343—44no—
188Q8×D11—28no—
189Q8×D11—44no—
190Q8×D11—44no—
191Q8×D11—44no—
192C2×D44—24no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—42no—
199C2×D44—42no—
200C2×D44C22×C412yes—
201C2×C4×D11—24no—
202C2×C4×D11—24no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11C22×C412yes—
212C2×C4×D11#4112yes—
213C2×Dic22—24no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—42no—
220C2×Dic22—42no—
221C2×Dic22C22×C412yes—
222C11×Q16C22⋊C4116yescomplemented
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11C22×C412yes—
227C2×C8×C11C2×D412yes—
228C2×C8×C11C2×D412yes—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—42no—
234C11×C4⋊C4—42no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—42no—
238C42×C11—42no—
239#4326—28no—
240#4325—28no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4—41no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—42no—
246(C2×D11)⋊C4—81no—
247(C2×D11)⋊C4—81no—
248(C2×D11)⋊C4—81no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—42no—
254C4⋊Dic11—42no—
255C4×Dic11—21no—
256C4×Dic11—21no—
257C4×Dic11—42no—
258C4×Dic11—42no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8C22×C412yes—
265#4314—28no—
266#4313—28no—
267C22×#137—111no—
268C2×#441D1111yescharacteristic, complemented
269C2×C4×Q16—111no—
270#2341—111no—
271Q8×C22⋊C4—111no—
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×C11C22×D411yescharacteristic
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—22no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11C4×D412yes—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11C2×C22⋊C414yes—
304Q8×C11C2×C22⋊C414yes—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—22no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11C4×D412yes—
346C2×Dic11#13712yescomplemented
347D44—22no—
348D44—22no—
349D44—48no—
350D44—41no—
351D44—41no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—22no—
355C4×D11—22no—
356C4×D11—48no—
357C4×D11—48no—
358Dic22—22no—
359Dic22—22no—
360Dic22—48no—
361Dic22—41no—
362Dic22—41no—
363C8×C11—41no—
364C8×C11C2×C22⋊C414yes—
365C11⋊C8—22no—
366C11⋊C8—41no—
367C22×#41—111no—
368C23×Q8—111no—
369C2×#137—118no—
370C2×#137—224no—
371C2×#137—224no—
372C22×Q16—111no—
373C22×Q16C2×D1111yescharacteristic
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—24no—
382C4×Q16—224no—
383C2×#107—111no—
384C2×#106C2×D1111yescharacteristic
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103C2×D1111yescharacteristic
390C2×#103C2×D1111yescharacteristic
391C2×#102—111no—
392C2×#102—111no—
393C2×C22⋊C8—111no—
394C2×#97C2×D1111yescharacteristic
395C2×C4×C8—111no—
396#391—111no—
397#391—111no—
398#391—221no—
399#391—221no—
400#390—111no—
401#390—111no—
402#390—221no—
403#390—221no—
404#380—111no—
405#380—111no—
406#380—221no—
407#380—221no—
408C4×C22⋊C4—111no—
409C4×C22⋊C4—221no—
410C4×C22⋊C4—221no—
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11C2×C4×D411yescharacteristic
416C22×C11D4211yescharacteristic
417C22×C11D4211yescharacteristic
418C22×C11C2×#13711yescharacteristic
419C22×C11#57511yescharacteristic
420C22×C11#57711yescharacteristic
421C22×C11#57811yescharacteristic
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—41no—
426C2×D11—41no—
427C2×D11—41no—
428C2×D11—41no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—24no—
437C4×C11—24no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—81no—
441C4×C11—81no—
442C4×C11C22×C22⋊C411yescharacteristic
443C4×C11#51811yescharacteristic
444C4×C11#54611yescharacteristic
445C4×C11#54611yescharacteristic
446Dic11—22no—
447Dic11—22no—
448Dic11—42no—
449Dic11—41no—
450Dic11—81no—
451Dic11—81no—
452C2×#41—114no—
453C2×#41—222no—
454C2×#41—222no—
455C2×#41—222no—
456C2×#41—441no—
457C2×#41—441no—
458C22×Q8—114no—
459C22×Q8—111no—
460C22×Q8—221no—
461C22×Q8—222no—
462C22×Q8—222no—
463C22×Q8—222no—
464C22×Q8—441no—
465C22×Q8—441no—
466C22×Q8C22×D1111yescharacteristic
467C22×Q8C22×D1111yescharacteristic
468C22×D4—111no—
469C22×D4—221no—
470C23×C4—111no—
471C23×C4—221no—
472C23×C4—221no—
473#137—2232no—
474C2×Q16—114no—
475C2×Q16—222no—
476C2×Q16—222no—
477C2×Q16C4×D1114yes—
478C2×Q16D4414yes—
479C2×Q16C22⋊D1114yes—
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×C8C22×D1111yescharacteristic
492C22×C8C22×D1111yescharacteristic
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—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—111no—
520C2×C42—221no—
521C2×C42—221no—
522C2×C42C22×D1111yescharacteristic
523#107—222no—
524#106—22no—
525#103—22no—
526#103—22no—
527#103—222no—
528#103—222no—
529#103—441no—
530#103—441no—
531#102—441no—
532#102—441no—
533C22⋊C8—222no—
534#97—22no—
535C4×C8—222no—
536#95—111no—
537#95—111no—
538#95—221no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544C2×C11D4×C22⋊C411yescharacteristic
545C2×C11C4×#13711yescharacteristic
546C2×C11#294711yescharacteristic
547C2×C11#327011yescharacteristic
548C2×C11#327111yescharacteristic
549C2×C11#327711yescharacteristic
550C2×C11#327811yescharacteristic
551D11—42no—
552D11—82no—
553C24—111no—
554C24—221no—
555#41—228no—
556#41—444no—
557#41—444no—
558#41—444no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—112no—
566C2×Q8—224no—
567C2×Q8—221no—
568C2×Q8—228no—
569C2×Q8—221no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—442no—
574C2×Q8—442no—
575C2×Q8—444no—
576C2×Q8—444no—
577C2×Q8—444no—
578C2×Q8C2×C4×D1112yes—
579C2×Q8C2×C4×D1112yes—
580C2×Q8C2×D4412yes—
581C2×Q8C2×D4412yes—
582C2×Q8C2×C22⋊D1112yes—
583C2×Q8C2×C22⋊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—111no—
598C22×C4—111no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—111no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—442no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4D4×D1111yescharacteristic
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618Q16—228no—
619Q16(C2×D11)⋊C4116yescomplemented
620SD16—228no—
621SD16—228no—
622M16—228no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—112no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8C2×C4×D1112yes—
633C2×C8C2×D4412yes—
634C2×C8C2×C22⋊D1112yes—
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—222no—
648C22⋊C4—441no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C22⋊C4—881no—
655C42—21no—
656C42—21no—
657C42—42no—
658C42—42no—
659C42—221no—
660C42—221no—
661C42—442no—
662C42—442no—
663C11#2244511yescharacteristic, complemented, Sylow
664C23—112no—
665C23—221no—
666C23—221no—
667C23—221no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—222no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23C2×D4×D1111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—222no—
686Q8—222no—
687Q8—448no—
688Q8—441no—
689Q8—441no—
690Q8C2×(C2×D11)⋊C414yes—
691Q8C2×(C2×D11)⋊C414yes—
692D4—222no—
693D4—222no—
694D4—448no—
695D4—441no—
696D4—441no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—222no—
728C2×C4—221no—
729C2×C4—448no—
730C2×C4—448no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4C22×C4×D1111yescharacteristic
740C2×C4C22×D4411yescharacteristic
741C2×C4#6703711yescharacteristic
742C2×C4#41×D1111yescharacteristic
743C2×C4#6704211yescharacteristic
744C2×C4C22×C22⋊D1111yescharacteristic
745C8—41no—
746C8—222no—
747C8—441no—
748C8C2×(C2×D11)⋊C414yes—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—441no—
753C22—441no—
754C22—441no—
755C22—441no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—881no—
760C22—881no—
761C22—881no—
762C22—881no—
763C22C4×D4×D1111yescharacteristic
764C22D4×D4411yescharacteristic
765C22D11×#13711yescharacteristic
766C22#1062330811yescharacteristic
767C22#1062330911yescharacteristic
768C22#1062331011yescharacteristic
769C22D4×C22⋊D1111yescharacteristic
770C4—24no—
771C4—24no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—222no—
777C4—222no—
778C4—442no—
779C4—441no—
780C4—881no—
781C4—881no—
782C4#1062307611yescharacteristic
783C4#1062308511yescharacteristic
784C4C22×(C2×D11)⋊C411yescharacteristic
785C4#1062336011yescharacteristic
786C2—442no—
787C2—882no—
788C2D4×(C2×D11)⋊C411yescharacteristic
789C2#1307743211yescharacteristic
790C2#1307745811yescharacteristic
791C2#1308018811yescharacteristic
792C2#1308020311yescharacteristic
793C2#1308026711yescharacteristic
794C2#1308027611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
cosocleC22×C4×C11C24
hypercenterC2×#441D11
hypocenterC11#22445
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
4. Q8×(C2×D11)⋊C4C2semidirect
5. #13069497C2semidirect
6. #13069468C2semidirect
7. #13068971C2semidirect
8. #13068969C2semidirect
9. #13068957C2semidirect
10. #13068955C2semidirect
11. #13068646C2semidirect
13. #13068549C2semidirect
14. #13068401C2semidirect
15. C2×C11×#441C2semidirect
27. C2×#66971C4semidirect
222. C11×Q16C22⋊C4semidirect
268. C2×#441D11semidirect
346. C2×Dic11#137semidirect
619. Q16(C2×D11)⋊C4semidirect
663. C11#22445semidirect

Maximal subgroups

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

subgroupindex
C22×#669712
C2×Q16×Dic112
#130714542
Q8×(C2×D11)⋊C42
#130694972
#130694682
#130689712
#130689692
#130689572
#130689552
#130686462
#130685552
#130685492
#130684012
C2×C11×#4412
#2244511