Finite Group Databasebeta

← #14801000

Subgroups — #14801000

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622840C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622838C211yesmaximal, characteristic, complemented
5#13072034C211yesmaximal, characteristic
6#13070011C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069617C211yesmaximal, characteristic, complemented
10#13069473C211yesmaximal, characteristic, complemented
11#13069295C211yesmaximal, characteristic, complemented
12#13069052C211yesmaximal, characteristic, complemented
13#13069050C211yesmaximal, characteristic, complemented
14#13068813C211yesmaximal, characteristic, complemented
15C11×#2409C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#395—21no—
28C11×#393—21no—
29C11×#391C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#386—21no—
32C11×#385—21no—
33C11×#380C2211yescharacteristic
34#10622840—24no—
35#10622838—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42#10622836—21no—
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622662—24no—
47#10622625—24no—
48#10622603—21no—
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622572—21no—
54#10622570—21no—
55#10622552C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11D411yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×D44C2311yescharacteristic
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—41no—
82C11×C22⋊Q8—41no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×#4325—22no—
99C2×#4325—22no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—41no—
103C2×#4325—41no—
104#66983—22no—
105#66983—22no—
106#66983—22no—
107#66983—41no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112#66979—22no—
113#66979—41no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11—21no—
119C2×#4318—22no—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C2×#4318—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134#66899—22no—
135#66899—22no—
136#66899—22no—
137#66899—22no—
138#66899—22no—
139#66899D414yescomplemented
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)D414yescomplemented
144#66873—22no—
145#66873—41no—
146#66872—41no—
147#66871—22no—
148C4⋊(C11⋊C8)—22no—
149C4×C11⋊C8—22no—
150#25138—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D411yescharacteristic
153C23×D11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—28no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
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×C11—42no—
166C2×Q8×C11—42no—
167C2×Q8×C11—44no—
168C2×Q8×C11—44no—
169C2×Q8×C11—44no—
170C2×Q8×C11—42no—
171C2×Q8×C11C2×D412yes—
172C2×Q8×C11#4112yes—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11—41no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11#4112yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—81no—
204C2×C22⋊D11—81no—
205C2×C22⋊D11—81no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C42×C11—21no—
228C42×C11—21no—
229C22⋊Dic11—42no—
230C22⋊Dic11—81no—
231#4325—44no—
232#4325—44no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—81no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11C2×D412yes—
243Dic11⋊C4—81no—
244C4×Dic11—42no—
245#4318—44no—
246#4318—44no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8C2×D412yes—
257C2×C11⋊C8C2×D412yes—
258C2×C11⋊C8C2×D412yes—
259C2×#468—111no—
260C2×#448—111no—
261C2×#436—111no—
262C2×#419—111no—
263#2414—111no—
264#2409D1111yescharacteristic, complemented
265#2068—111no—
266#2055—111no—
267#2035—111no—
268#2000—111no—
269#1968—111no—
270#1933—111no—
271#1895—111no—
272#1894—111no—
273#1854—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11#12112yes—
288C23×C11C22×D411yescharacteristic
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—48no—
301Q8×C11—41no—
302Q8×C11—41no—
303Q8×C11—41no—
304Q8×C11—41no—
305D4×C11—44no—
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—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—48no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
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—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11#12112yes—
338C2×C4×C11#13712yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C22⋊D11—84no—
346C22⋊D11—84no—
347C2×Dic11—22no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356D44—41no—
357D44—41no—
358D44—41no—
359D44—41no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C11⋊C8—41no—
364C23×Q8C2×D1111yescharacteristic
365C22×SD16—111no—
366C22×SD16—111no—
367C22×M16—111no—
368C22×M16—111no—
369C2×C22⋊Q8C2×D1111yescharacteristic
370C2×C22⋊Q8C2×D1111yescharacteristic
371C2×#121—111no—
372C2×#121—111no—
373C2×C4×D4C2×D1111yescharacteristic
374C2×#117—111no—
375#468—224no—
376#448—224no—
377#436—224no—
378C2×#107—111no—
379C2×#106—111no—
380C2×C4⋊C8—111no—
381#419—224no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C4×C8—111no—
393#395—21no—
394#394—221no—
395#393—21no—
396#392—221no—
397#391C2×D1111yescharacteristic
398#391C2×D1111yescharacteristic
399#390—111no—
400#390—221no—
401#389—111no—
402#388—221no—
403#386—21no—
404#385—21no—
405#380—111no—
406#380C2×D1111yescharacteristic
407#340—111no—
408#340—111no—
409#340—111no—
410#340—111no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11C2×#12111yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11#54611yescharacteristic
428C22×C11C2×#13711yescharacteristic
429C22×C11#57511yescharacteristic
430C22×C11#57711yescharacteristic
431C22×C11#57711yescharacteristic
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C2×D11—81no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—41no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—41no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11#52511yescharacteristic
448C4×C11#53811yescharacteristic
449C4×C11D4211yescharacteristic
450C4×C11#54611yescharacteristic
451Dic11—42no—
452Dic11—81no—
453Dic11—81no—
454C22×Q8—21no—
455C22×Q8—22no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8—41no—
460C22×Q8—41no—
461C22×Q8C22×D1111yescharacteristic
462C22×Q8C22×D1111yescharacteristic
463C22×D4—111no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4C22⋊D1111yescharacteristic
467C23×C4—21no—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C2×SD16—222no—
471C2×SD16—222no—
472C2×SD16—222no—
473C2×SD16—222no—
474C2×SD16—441no—
475C2×SD16—441no—
476C2×M16—222no—
477C2×M16—222no—
478C2×M16—222no—
479C2×M16—222no—
480C2×M16—441no—
481C2×M16—441no—
482C22×C8—111no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—111no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—41no—
489C22⋊Q8—41no—
490#121—222no—
491#121—222no—
492#121—222no—
493#121—441no—
494C4×D4—22no—
495C4×D4—22no—
496#117—222no—
497#117—441no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22⋊D1111yescharacteristic
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
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⋊C4—221no—
516C2×C22⋊C4C22⋊D1111yescharacteristic
517C2×C22⋊C4C22⋊D1111yescharacteristic
518C2×C42—221no—
519C2×C42C22×D1111yescharacteristic
520#107—222no—
521#106—441no—
522C4⋊C8—222no—
523#103—114no—
524#103—222no—
525#103—222no—
526#103—222no—
527#103—222no—
528#103—222no—
529#102—222no—
530#102—441no—
531C22⋊C8—114no—
532C22⋊C8—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—
541C2×C11—42no—
542C2×C11—81no—
543C2×C11#242411yescharacteristic
544C2×C11#305611yescharacteristic
545C2×C11#305711yescharacteristic
546C2×C11#327511yescharacteristic
547C2×C11#327811yescharacteristic
548C2×C11#332611yescharacteristic
549C2×C11#332911yescharacteristic
550D11—161no—
551C24—221no—
552C24C2×C22⋊D1111yescharacteristic
553C24C2×C22⋊D1111yescharacteristic
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—28no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8D4×D1112yes—
572C2×Q8#434112yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—41no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—442no—
583C2×D4—442no—
584C2×D4—442no—
585C2×D4—881no—
586C2×D4—881no—
587C2×D4—881no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4D4×D1112yes—
609C22×C4#434112yes—
610C22×C4C2×C22⋊D1111yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C23×D1111yescharacteristic
615SD16—444no—
616SD16—444no—
617M16—444no—
618M16—444no—
619C2×C8—112no—
620C2×C8—112no—
621C2×C8—112no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—112no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—881no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—442no—
653C22⋊C4—442no—
654C22⋊C4—881no—
655C22⋊C4—881no—
656C42—21no—
657C42—21no—
658C42—442no—
659C11#2513811yescharacteristic, complemented, Sylow
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23#6699212yes—
681C23C22×C22⋊D1111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691D4—44no—
692D4—441no—
693D4—441no—
694D4—441no—
695D4—441no—
696D4—884no—
697D4—884no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
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—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—222no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4#6699212yes—
739C2×C4#6699512yes—
740C2×C4C2×D4×D1111yescharacteristic
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4C2×#434111yescharacteristic
743C2×C4C2×#434111yescharacteristic
744C2×C4#6703711yescharacteristic
745C2×C4#6703711yescharacteristic
746C8—222no—
747C8—222no—
748C8—222no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—881no—
765C22—881no—
766C22—881no—
767C22—881no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22D4×C22⋊D1111yescharacteristic
772C22C2×#6699211yescharacteristic
773C22#1062333711yescharacteristic
774C22C2×#6699511yescharacteristic
775C22#1062335311yescharacteristic
776C22#1062336811yescharacteristic
777C22#1062336811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—442no—
787C4—881no—
788C4—881no—
789C4#1062311711yescharacteristic
790C4#1062312111yescharacteristic
791C4#1062312211yescharacteristic
792C4#1062312411yescharacteristic
793C2—42no—
794C2—81no—
795C2—1761no—
796C2#1307215611yescharacteristic
797C2#1307824211yescharacteristic
798C2#1307825711yescharacteristic
799C2#1308024811yescharacteristic
800C2#1308027811yescharacteristic
801C2#1308086911yescharacteristic
802C2#1308091011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2409C2
socleC23×C11C22×D4
prime radical#13072034C2
hypercenter#2409D11
hypocenterC11#25138
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622840C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622838C2semidirect
6. #13070011C2semidirect
7. #13069931C2semidirect
8. #13069809C2semidirect
9. #13069617C2semidirect
10. #13069473C2semidirect
11. #13069295C2semidirect
12. #13069052C2semidirect
13. #13069050C2semidirect
14. #13068813C2semidirect
15. C11×#2409C2semidirect
139. #66899D4semidirect
143. C22⋊(C11⋊C8)D4semidirect
264. #2409D11semidirect
659. C11#25138semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106228402
C2×#106226252
C2×#106228382
#130720342
#130700112
#130699312
#130698092
#130696172
#130694732
#130692952
#130690522
#130690502
#130688132
C11×#24092
#2513811