Finite Group Databasebeta

← #14801506

Subgroups — #14801506

Order 2816.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622629C211yesmaximal, characteristic, complemented
2C2×#10622831C211yesmaximal, characteristic, complemented
3C2×#10622830C211yesmaximal, characteristic
4C2×#10622627C211yesmaximal, characteristic, complemented
5#13072193C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069812C211yesmaximal, characteristic, complemented
8#13069798C211yesmaximal, characteristic, complemented
9#13069692C211yesmaximal, characteristic, complemented
10#13069496C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic, complemented
12#13068967C211yesmaximal, characteristic, complemented
13#13068950C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C2×#66928C2211yescharacteristic, complemented
27C2×C4×D44C2211yescharacteristic, complemented
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#386—21no—
31C11×#386—21no—
32C11×#380C2211yescharacteristic
33C11×#379—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622831—24no—
36#10622830—24no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622629—24no—
44#10622627—24no—
45C2×#66874C2211yescharacteristic, complemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66873C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic, complemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622572—21no—
52#10622569—21no—
53#10622542C2211yescharacteristic, complemented
54#10622541C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×#66867C2211yescharacteristic, complemented
57#10622288—21no—
58#10622280—21no—
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63C25×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—21no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×Dic22C2311yescharacteristic
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—44no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324—22no—
102C2×#4324—22no—
103C2×#4324—22no—
104C2×#4324—41no—
105C2×#4323—22no—
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323—22no—
109C2×#4323—41no—
110C2×#4323D414yes—
111#66983—22no—
112#66983—41no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—22no—
120#66977—41no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66928—22no—
128#66928—41no—
129C4×D44—22no—
130C4×D44—41no—
131C11×#95—21no—
132C11×#95D411yescharacteristic
133C11×#95D411yescharacteristic
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896D414yescomplemented
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143#66874—22no—
144#66874—41no—
145#66873—22no—
146#66873—22no—
147#66872—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151#25172—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11—24no—
154C24×C11—21no—
155C24×C11—42no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11—81no—
160C24×C11—81no—
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—44no—
175C2×D4×C11—44no—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11C2×D412yes—
179C2×D4×C11C2×D412yes—
180C2×D4×C11#4112yes—
181C2×D4×C11#4112yes—
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×C11—42no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—81no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44C2×D412yes—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—81no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—41no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—81no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C22⋊Dic11—42no—
241#4324—44no—
242#4324—44no—
243#4323—28no—
244#4323—44no—
245(C2×D11)⋊C4—42no—
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4—42no—
248(C2×D11)⋊C4—42no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11C2×D412yes—
253Dic11⋊C4—42no—
254Dic11⋊C4—81no—
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⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C2×#463—111no—
268C2×#450—111no—
269C2×#447—111no—
270C2×#442—111no—
271#2427—111no—
272D4×C22⋊C4D1111yescharacteristic, complemented
273#2065—111no—
274#2035—111no—
275#2033—111no—
276#2012—111no—
277#1973—111no—
278#1924—111no—
279#1879—111no—
280#1877—111no—
281#1862—111no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—22no—
292C23×C11—48no—
293C23×C11—48no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—84no—
305C23×C11—84no—
306C23×C11—84no—
307C23×C11—84no—
308C23×C11—84no—
309C23×C11AGL(1,ℤ/8)12yes—
310C23×C11C22×D411yescharacteristic
311C22×D11—22no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11#12114yes—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—84no—
353C2×C4×C11—84no—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—84no—
361C2×Dic11—22no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370D44—22no—
371D44—22no—
372D44—41no—
373D44—41no—
374C4×D11—84no—
375Dic22—41no—
376Dic22—41no—
377Dic22—41no—
378Dic22—41no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C23×D4C2×D1111yescharacteristic
384C22×SD16—111no—
385C22×SD16—111no—
386C22×D8—111no—
387C22×D8—111no—
388C2×#124—111no—
389C2×C22⋊Q8—111no—
390C2×#121—111no—
391C2×C4×D4—111no—
392C2×C4×D4C2×D1111yescharacteristic
393C2×C4×D4C2×D1111yescharacteristic
394C22×C22⋊C4—21no—
395#463—224no—
396#450—224no—
397#447—224no—
398#442—224no—
399C2×#107—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×C22⋊C8—111no—
411C2×C22⋊C8—111no—
412C2×#97—111no—
413#397—221no—
414#394—221no—
415#391—111no—
416#390C2×D1111yescharacteristic
417#390C2×D1111yescharacteristic
418#389—111no—
419#386—21no—
420#386—21no—
421#386—221no—
422#380—221no—
423#380C2×D1111yescharacteristic
424#379—21no—
425C4×C22⋊C4C2×D1111yescharacteristic
426#340—111no—
427#340—111no—
428#336—111no—
429#336—111no—
430C22×C11—22no—
431C22×C11—24no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—42no—
435C22×C11—41no—
436C22×C11—42no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—42no—
442C22×C11—41no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—816no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11#52511yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11D4211yescharacteristic
455C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C11#57511yescharacteristic
457C22×C11#57611yescharacteristic
458C22×C11#57711yescharacteristic
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C2×D11—81no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11—81no—
472C4×C11—81no—
473C4×C11C2×#12111yescharacteristic
474C4×C11#53811yescharacteristic
475C4×C11#54611yescharacteristic
476C4×C11#54611yescharacteristic
477Dic11—42no—
478Dic11—81no—
479Dic11—81no—
480C25—21no—
481C22×Q8—111no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—41no—
488C22×D4—41no—
489C22×D4—111no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C2×SD16—222no—
498C2×SD16—222no—
499C2×SD16—222no—
500C2×SD16—222no—
501C2×SD16—222no—
502C2×SD16—441no—
503C2×D8—114no—
504C2×D8—222no—
505C2×D8—222no—
506C2×D8—222no—
507C2×D8—222no—
508C2×D8—441no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—111no—
512C22×C8—111no—
513#124—222no—
514#124—441no—
515C22⋊Q8—222no—
516C22⋊Q8—441no—
517#121—222no—
518#121—441no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—41no—
522C4×D4—41no—
523C4×D4—222no—
524C4×D4—441no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—44no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C22⋊C4C22⋊D1111yescharacteristic
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548#107—441no—
549#106—222no—
550C4⋊C8—222no—
551#103—222no—
552#103—441no—
553#102—114no—
554#102—222no—
555#102—222no—
556#102—222no—
557#102—222no—
558#102—222no—
559C22⋊C8—222no—
560C22⋊C8—222no—
561#97—222no—
562#95—21no—
563#95—221no—
564#95—221no—
565#95—221no—
566#95C22⋊D1111yescharacteristic
567#95C22⋊D1111yescharacteristic
568C2×C11—42no—
569C2×C11—44no—
570C2×C11—82no—
571C2×C11#242411yescharacteristic
572C2×C11#311411yescharacteristic
573C2×C11#311811yescharacteristic
574C2×C11#326411yescharacteristic
575C2×C11#326511yescharacteristic
576C2×C11#326711yescharacteristic
577C2×C11#327311yescharacteristic
578D11—82no—
579C24—21no—
580C24—24no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—81no—
587C24—81no—
588C24—221no—
589C24C2×C22⋊D1111yescharacteristic
590C2×Q8—221no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—112no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—221no—
617C2×D4—442no—
618C2×D4—442no—
619C2×D4—881no—
620C2×D4#433912yes—
621C2×D4#433912yes—
622C2×D4D4×D1112yes—
623C2×D4D4×D1112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—881no—
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C23×D1111yescharacteristic
650SD16—444no—
651SD16—444no—
652D8—228no—
653D8—444no—
654C2×C8—112no—
655C2×C8—112no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—112no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—442no—
675C4⋊C4—881no—
676C22⋊C4—22no—
677C22⋊C4—41no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C22⋊C4—442no—
689C22⋊C4—442no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C11#2517211yescharacteristic, complemented, Sylow
695C23—21no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—48no—
706C23—48no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—84no—
722C23—222no—
723C23—441no—
724C23—441no—
725C23—441no—
726C23—441no—
727C23—441no—
728C23—441no—
729C23#6698512yes—
730C23C22×C22⋊D1111yescharacteristic
731Q8—441no—
732Q8—441no—
733Q8—441no—
734Q8—441no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—41no—
742D4—41no—
743D4—222no—
744D4—222no—
745D4—441no—
746D4—441no—
747D4—884no—
748D4#6693714yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—222no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—884no—
786C2×C4C2×#433911yescharacteristic
787C2×C4C2×#433911yescharacteristic
788C2×C4C2×D4×D1111yescharacteristic
789C2×C4C2×D4×D1111yescharacteristic
790C2×C4#6703711yescharacteristic
791C2×C4#6703711yescharacteristic
792C8—222no—
793C8—222no—
794C8—441no—
795C8—441no—
796C22—24no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—816no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—881no—
822C22—881no—
823C22—881no—
824C22—881no—
825C22#1062332211yescharacteristic
826C22C2×#6698511yescharacteristic
827C22D4×C22⋊D1111yescharacteristic
828C22D4×C22⋊D1111yescharacteristic
829C22#1062335311yescharacteristic
830C22#1062336611yescharacteristic
831C22#1062336711yescharacteristic
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—442no—
840C4—881no—
841C4—881no—
842C4C2×#6693711yescharacteristic
843C4#1062302111yescharacteristic
844C4#1062302111yescharacteristic
845C4#1062302511yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—882no—
850C2#1307215211yescharacteristic
851C2#1307875411yescharacteristic
852C2#1307880011yescharacteristic
853C2#1308009211yescharacteristic
854C2#1308010711yescharacteristic
855C2#1308013711yescharacteristic
856C2#1308022311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterD4×C22⋊C4D11
hypocenterC11#25172
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622629C2semidirect
2. C2×#10622831C2semidirect
4. C2×#10622627C2semidirect
5. #13072193C2semidirect
6. #13069990C2semidirect
7. #13069812C2semidirect
8. #13069798C2semidirect
9. #13069692C2semidirect
10. #13069496C2semidirect
11. #13069231C2semidirect
12. #13068967C2semidirect
13. #13068950C2semidirect
14. #13068863C2semidirect
15. D4×C11×C22⋊C4C2semidirect
26. C2×#66928C22semidirect
27. C2×C4×D44C22semidirect
45. C2×#66874C22semidirect
46. C2×#66874C22semidirect
47. C2×#66873C22semidirect
48. C2×#66873C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
53. #10622542C22semidirect
54. #10622541C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×#66867C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
137. #66896D4semidirect
272. D4×C22⋊C4D11semidirect
694. C11#25172semidirect

Maximal subgroups

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

subgroupindex
C2×#106226292
C2×#106228312
C2×#106228302
C2×#106226272
#130721932
#130699902
#130698122
#130697982
#130696922
#130694962
#130692312
#130689672
#130689502
#130688632
D4×C11×C22⋊C42
#2517211