Finite Group Databasebeta

← #14800840

Subgroups — #14800840

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622747C211yesmaximal, characteristic, complemented
2C2×#10622344C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4#13072067C211yesmaximal, characteristic, complemented
5#13071972C211yesmaximal, characteristic
6#13070003C211yesmaximal, characteristic, complemented
7#13069934C211yesmaximal, characteristic, complemented
8#13069799C211yesmaximal, characteristic, complemented
9#13069621C211yesmaximal, characteristic, complemented
10#13069497C211yesmaximal, characteristic, complemented
11#13069313C211yesmaximal, characteristic, complemented
12#13069054C211yesmaximal, characteristic, complemented
13#13069039C211yesmaximal, characteristic, complemented
14#13068806C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic, complemented
18C23×C8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66990—21no—
21C2×#66983C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic, complemented
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C11×#435—24no—
29C2×C11×C4⋊C8C2211yescharacteristic, complemented
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic, complemented
32C2×C11×#97C2211yescharacteristic, complemented
33#10622833—21no—
34#10622825C2211yescharacteristic
35#10622825C2211yescharacteristic, complemented
36#10622747—24no—
37C2×#66885—24no—
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66882C2211yescharacteristic, complemented
45C2×#66882C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47C2×#66880C2211yescharacteristic, complemented
48#10622604—21no—
49#10622597—21no—
50#10622573—21no—
51#10622568—21no—
52#10622561—21no—
53#10622555—21no—
54#10622552C2211yescharacteristic
55#10622552C2211yescharacteristic
56#10622542C2211yescharacteristic, complemented
57#10622541C2211yescharacteristic, complemented
58#10622344—24no—
59#10622189C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—21no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2311yescharacteristic
78C22×D44C2311yescharacteristic
79C22×Dic22C2311yescharacteristic
80C2×C11×M16—22no—
81C2×C11×M16—22no—
82C2×C11×M16—41no—
83C22×C8×C11—22no—
84C22×C8×C11—22no—
85C22×C8×C11—41no—
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100#66990—44no—
101#66983—22no—
102#66983—22no—
103#66983—41no—
104#66983—41no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—41no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—22no—
120#66977—22no—
121#66977—22no—
122#66977—41no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×#4314—22no—
127C2×#4314—22no—
128C2×#4314—22no—
129C2×#4314—22no—
130C2×#4314—41no—
131C2×#4314—41no—
132C11×C4⋊C8—22no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8D414yescomplemented
135C11×#97—22no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141#66885—22no—
142#66885—22no—
143#66885—22no—
144#66885—22no—
145#66885—22no—
146#66885D414yescomplemented
147#66882—22no—
148#66882—41no—
149#66880—22no—
150#66880—41no—
151#25128—111nomaximal, Sylow
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—42no—
157C23×D11—42no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—81no—
162C23×D11—81no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11#4112yes—
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—42no—
184C2×C22⋊D11—42no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—81no—
188C2×C22⋊D11—81no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—81no—
198C2×D44—28no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—42no—
210C2×D44—42no—
211C2×D44—44no—
212C2×D44—44no—
213C2×D44—44no—
214C2×D44—42no—
215C2×D44C2×D412yes—
216C2×D44#4112yes—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C11×M16—44no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—44no—
234C2×C8×C11C2×D412yes—
235C2×C8×C11C2×D412yes—
236C2×C8×C11C2×D412yes—
237C11×C4⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—22no—
240C42×C11—21no—
241C42×C11—21no—
242C22⋊Dic11—42no—
243C22⋊Dic11—42no—
244C22⋊Dic11—42no—
245C22⋊Dic11—81no—
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4—42no—
248(C2×D11)⋊C4—42no—
249(C2×D11)⋊C4—42no—
250(C2×D11)⋊C4—81no—
251(C2×D11)⋊C4—81no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—42no—
262C4⋊Dic11C2×D412yes—
263Dic11⋊C4—42no—
264Dic11⋊C4—42no—
265Dic11⋊C4—81no—
266#4314—44no—
267#4314—44no—
268C2×#468—111no—
269C2×#450—111no—
270C2×#435D1111yescharacteristic, complemented
271C22×#102—111no—
272#2417—111no—
273#2408—111no—
274#2067—111no—
275#2055—111no—
276#2033—111no—
277#2000—111no—
278#1973—111no—
279#1936—111no—
280#1895—111no—
281#1892—111no—
282#1852—111no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11#12112yes—
295C23×C11AGL(1,ℤ/8)12yes—
296C23×C11#13712yes—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—48no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—84no—
314C22×D11—84no—
315C22×D11—84no—
316C22×D11—84no—
317C22×D11—84no—
318C22×D11—84no—
319D4×C11—44no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—21no—
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—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11#12112yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C22⋊D11—84no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—84no—
367D44—22no—
368D44—22no—
369D44—22no—
370D44—22no—
371D44—48no—
372D44—41no—
373D44—41no—
374D44—41no—
375D44—41no—
376Dic22—41no—
377Dic22—41no—
378Dic22—41no—
379Dic22—41no—
380C8×C11—22no—
381C8×C11—22no—
382C8×C11—22no—
383C8×C11—41no—
384C23×D4—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16C2×D1111yescharacteristic, complemented
388C23×C8C2×D1111yescharacteristic
389C2×C22⋊Q8—111no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×#121—111no—
393C2×#120—221no—
394C2×C4×D4C2×D1111yescharacteristic
395C22×C4⋊C4—111no—
396#468—224no—
397#450—224no—
398#435—24no—
399C2×#107—111no—
400C2×#107—111no—
401C2×C4⋊C8C2×D1111yescharacteristic, complemented
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×#102—224no—
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×C22⋊C8C2×D1111yescharacteristic, complemented
413C2×#97C2×D1111yescharacteristic, complemented
414#398—221no—
415#396—221no—
416#394—221no—
417#392—221no—
418#391—111no—
419#390—111no—
420#390—111no—
421#389—111no—
422#386—221no—
423#380—111no—
424#380—111no—
425#380—221no—
426#379—221no—
427#340—111no—
428#340—111no—
429#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11#46814yescomplemented
445C22×C11C2×#12111yescharacteristic
446C22×C11D4211yescharacteristic
447C22×C11#54611yescharacteristic
448C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
449C22×C11C2×#13711yescharacteristic
450C22×C11#57611yescharacteristic
451C22×C11#57711yescharacteristic
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—816no—
459C2×D11—81no—
460C2×D11—81no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C2×D11—81no—
466C2×D11—81no—
467C4×C11—22no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11#52511yescharacteristic
472C4×C11#53811yescharacteristic
473C4×C11D4211yescharacteristic
474C4×C11#54611yescharacteristic
475Dic11—42no—
476Dic11—81no—
477Dic11—81no—
478Dic11—81no—
479Dic11—81no—
480Dic11—81no—
481C25—221no—
482C22×Q8—111no—
483C22×D4—111no—
484C22×D4—111no—
485C22×D4—222no—
486C22×D4—222no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—222no—
491C22×D4—222no—
492C22×D4—441no—
493C22×D4—441no—
494C22×D4D4411yescharacteristic
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×SD16—222no—
499C2×SD16—222no—
500C2×SD16—222no—
501C2×SD16—222no—
502C2×SD16—441no—
503C2×SD16—441no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C22×C8C22×D1111yescharacteristic
513C22×C8C22×D1111yescharacteristic
514C22⋊Q8—222no—
515C22⋊Q8—222no—
516C22⋊Q8—222no—
517C22⋊Q8—441no—
518#121—222no—
519#121—222no—
520#121—441no—
521#121—441no—
522#120—444no—
523C4×D4—22no—
524C4×D4—22no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—441no—
536C2×C4⋊C4D4411yescharacteristic
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4D4411yescharacteristic
548C2×C22⋊C4D4411yescharacteristic
549C2×C42C22×D1111yescharacteristic
550#107—222no—
551#107—441no—
552C4⋊C8—22no—
553#103—222no—
554#103—441no—
555#102—114no—
556#102—222no—
557#102—222no—
558#102—222no—
559#102—222no—
560#102—222no—
561C22⋊C8—22no—
562C22⋊C8C22⋊D1114yescomplemented
563#97—22no—
564#95—221no—
565#95—221no—
566#95—221no—
567#95—221no—
568#95—221no—
569C2×C11—24no—
570C2×C11—81no—
571C2×C11#242411yescharacteristic
572C2×C11C2×#46811yescharacteristic
573C2×C11#306211yescharacteristic
574C2×C11#326411yescharacteristic
575C2×C11#326611yescharacteristic
576C2×C11#331011yescharacteristic
577C2×C11#331411yescharacteristic
578D11—82no—
579D11—82no—
580C24—221no—
581C24—221no—
582C24—442no—
583C24—442no—
584C24—442no—
585C24—442no—
586C24—442no—
587C24—881no—
588C24—881no—
589C24C2×D4411yescharacteristic
590C24C2×D4411yescharacteristic
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—112no—
601C2×D4—112no—
602C2×D4—228no—
603C2×D4—221no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—444no—
614C2×D4—444no—
615C2×D4—442no—
616C2×D4—442no—
617C2×D4—444no—
618C2×D4—442no—
619C2×D4—442no—
620C2×D4—442no—
621C2×D4—442no—
622C2×D4—442no—
623C2×D4—881no—
624C2×D4—881no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—881no—
644C22×C4C2×D4411yescharacteristic
645C22×C4C2×D4411yescharacteristic
646C22×C4C2×D4411yescharacteristic
647C22×C4C2×D4411yescharacteristic
648C22×C4#433912yes—
649C22×C4C2×C22⋊D1112yes—
650C22×C4C23×D1111yescharacteristic
651SD16—444no—
652SD16—444no—
653M16—44no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—44no—
664C2×C8D4×D1112yes—
665C2×C8C2×C22⋊D1112yes—
666C2×C8C2×C22⋊D1112yes—
667C4⋊C4—22no—
668C4⋊C4—112no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—442no—
679C4⋊C4—442no—
680C4⋊C4—442no—
681C4⋊C4—881no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C22⋊C4—442no—
689C22⋊C4—442no—
690C22⋊C4—442no—
691C22⋊C4—881no—
692C22⋊C4—881no—
693C22⋊C4—881no—
694C42—21no—
695C42—21no—
696C11#2512811yescharacteristic, complemented, Sylow
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—222no—
709C23—222no—
710C23—448no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23—441no—
715C23—441no—
716C23—441no—
717C23—441no—
718C23—441no—
719C23—441no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—884no—
724C23—884no—
725C23—884no—
726C23—884no—
727C23—884no—
728C23—884no—
729C23#6696112yes—
730C23#6696212yes—
731C23#6698312yes—
732C23C22×D4411yescharacteristic
733Q8—441no—
734Q8—441no—
735Q8—441no—
736Q8—441no—
737D4—44no—
738D4—222no—
739D4—222no—
740D4—222no—
741D4—222no—
742D4—448no—
743D4—441no—
744D4—441no—
745D4—441no—
746D4—441no—
747D4—884no—
748D4—884no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
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—222no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
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—441no—
786C2×C4—884no—
787C2×C4#6698312yes—
788C2×C4C2×#433911yescharacteristic
789C2×C4C2×D4×D1111yescharacteristic
790C2×C4#6703711yescharacteristic
791C2×C4#41×D1111yescharacteristic
792C2×C4#6704211yescharacteristic
793C2×C4C22×C22⋊D1111yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—8816no—
818C22—881no—
819C22—881no—
820C22—881no—
821C22—881no—
822C22—881no—
823C22—881no—
824C22—881no—
825C22—881no—
826C22#1062274714yescomplemented
827C22D4×D4411yescharacteristic
828C22#1062308511yescharacteristic
829C22C2×#6696111yescharacteristic
830C22C2×#6696211yescharacteristic
831C22#1062328211yescharacteristic
832C22#1062328311yescharacteristic
833C22C2×#6698311yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—442no—
839C4—881no—
840C4—881no—
841C4—881no—
842C4—881no—
843C4—881no—
844C4#1062307811yescharacteristic
845C4#1062309111yescharacteristic
846C4D4×C22⋊D1111yescharacteristic
847C4#1062336011yescharacteristic
848C2—24no—
849C2—81no—
850C2—882no—
851C2—882no—
852C2#1307214611yescharacteristic
853C2C2×#1062274711yescharacteristic
854C2#1307829611yescharacteristic
855C2#1308010111yescharacteristic
856C2#1308013111yescharacteristic
857C2#1308063911yescharacteristic
858C2#1308069911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radical#13071972C2
hypercenterC2×#435D11
hypocenterC11#25128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10622747C2semidirect
2. C2×#10622344C2semidirect
3. C22×#66885C2semidirect
4. #13072067C2semidirect
6. #13070003C2semidirect
7. #13069934C2semidirect
8. #13069799C2semidirect
9. #13069621C2semidirect
10. #13069497C2semidirect
11. #13069313C2semidirect
12. #13069054C2semidirect
13. #13069039C2semidirect
14. #13068806C2semidirect
15. C2×C11×#435C2semidirect
17. C22×C11×M16C22semidirect
25. C2×#66977C22semidirect
29. C2×C11×C4⋊C8C22semidirect
31. C2×C11×C22⋊C8C22semidirect
32. C2×C11×#97C22semidirect
35. #10622825C22semidirect
44. C2×#66882C22semidirect
45. C2×#66882C22semidirect
46. C2×#66880C22semidirect
47. C2×#66880C22semidirect
56. #10622542C22semidirect
57. #10622541C22semidirect
59. #10622189C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622189C22semidirect
134. C11×C22⋊C8D4semidirect
146. #66885D4semidirect
270. C2×#435D11semidirect
387. C22×M16C2×D11semidirect
401. C2×C4⋊C8C2×D11semidirect
412. C2×C22⋊C8C2×D11semidirect
413. C2×#97C2×D11semidirect
444. C22×C11#468semidirect
562. C22⋊C8C22⋊D11semidirect
696. C11#25128semidirect
826. C22#10622747semidirect

Maximal subgroups

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

subgroupindex
C2×#106227472
C2×#106223442
C22×#668852
#130720672
#130719722
#130700032
#130699342
#130697992
#130696212
#130694972
#130693132
#130690542
#130690392
#130688062
C2×C11×#4352
#2512811