Finite Group Databasebeta

← #14811370

Subgroups — #14811370

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072318C211yesmaximal, characteristic
2#13070174C211yesmaximal, characteristic, complemented
3#13070107C211yesmaximal, characteristic, complemented
4#13070107C211yesmaximal, characteristic, complemented
5#13069944C211yesmaximal, characteristic, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069187C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13068803C211yesmaximal, characteristic
11#13068796C211yesmaximal, characteristic
12#13068702C211yesmaximal, characteristic
13#13068643C211yesmaximal, characteristic
14C2×#10622167C211yesmaximal, characteristic
15C11×#2344C211yesmaximal, characteristic
16C2×C11×#117—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×#66931—21no—
21C2×#66922C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#387—21no—
25C11×#387—21no—
26C11×#381—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622563—21no—
38#10622548C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622274—21no—
44#10622269—21no—
45#10622167C2211yescharacteristic
46#10622167C2211yescharacteristic
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22—21no—
63C11×#117—44no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4Q814yescomplemented
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—41no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8—22no—
95C22×C11⋊C8—41no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66931—44no—
101#66922—22no—
102#66922—41no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C22⋊(C11⋊C8)—22no—
114#66871—22no—
115#66871—22no—
116#66871—41no—
117#66871—41no—
118C4⋊(C11⋊C8)—22no—
119C4⋊(C11⋊C8)—41no—
120#25988—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—24no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×Q812yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—81no—
148C2×Dic22—42no—
149C2×Dic22—42no—
150C2×Dic22—81no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×Q812yes—
161C11×C4⋊C4C2×Q812yes—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4D814yes—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—42no—
170C42×C11—42no—
171C22⋊Dic11—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—42no—
180C4⋊Dic11—42no—
181C4⋊Dic11—42no—
182C4⋊Dic11—81no—
183C4⋊Dic11#4112yes—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—44no—
198C2×C11⋊C8#4112yes—
199#2440—111no—
200#2344D1111yescharacteristic
201#2099—111no—
202#2086—111no—
203#2086—111no—
204#2057—111no—
205#1988—111no—
206#1947—111no—
207#1918—111no—
208#1918—111no—
209#1852—111no—
210#1850—111no—
211#1823—111no—
212#1808—111no—
213C2×#340—111no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C22⋊Q812yes—
219C23×C11C2×D812yes—
220C23×C11#13712yes—
221C23×C11C22×D411yescharacteristic
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—48no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C22⋊Q812yes—
252C2×C4×C11C2×D812yes—
253C2×C4×C11C2×D812yes—
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—22no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—84no—
273Dic22—84no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C23×C8—111no—
279C2×C4⋊Q8—111no—
280C2×C22⋊Q8—221no—
281C2×#117—21no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C2×#107—111no—
285C2×#107—111no—
286C2×#107—111no—
287C2×#107—111no—
288C2×C4⋊C8—111no—
289C2×C4⋊C8—111no—
290C2×C22⋊C8—111no—
291#398—221no—
292#395—221no—
293#389—111no—
294#389—111no—
295#389C2×D1111yescharacteristic
296#389C2×D1111yescharacteristic
297#387—21no—
298#387—21no—
299#385—221no—
300#384—111no—
301#381—21no—
302#380—111no—
303#380C2×D1111yescharacteristic
304C4×C4⋊C4C2×D1111yescharacteristic
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C22⋊C4C2×D1111yescharacteristic
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#336—111no—
320#336—111no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11#47414yes—
328C22×C11C2×C22⋊Q811yescharacteristic
329C22×C11#54611yescharacteristic
330C22×C11#54711yescharacteristic
331C22×C11C22×D811yescharacteristic
332C22×C11C2×#13711yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57811yescharacteristic
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#53311yescharacteristic
345C4×C11#54411yescharacteristic
346C4×C11#55111yescharacteristic
347C4×C11#55211yescharacteristic
348Dic11—42no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8—221no—
353C23×C4—21no—
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—222no—
361C22×C8—222no—
362C22×C8—441no—
363C4⋊Q8—222no—
364C4⋊Q8—441no—
365C22⋊Q8—444no—
366#117—44no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—441no—
383C2×C4⋊C4Dic2214yescomplemented
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4C22⋊D1111yescharacteristic
391C2×C22⋊C4C22⋊D1111yescharacteristic
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396#107—222no—
397#107—222no—
398#107—441no—
399#107—441no—
400C4⋊C8—222no—
401C4⋊C8—441no—
402C22⋊C8—222no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95C22⋊D1111yescharacteristic
412#95C22⋊D1111yescharacteristic
413C2×C11—24no—
414C2×C11#243811yescharacteristic
415C2×C11C2×#47411yescharacteristic
416C2×C11#308211yescharacteristic
417C2×C11#329411yescharacteristic
418C2×C11#331211yescharacteristic
419C2×C11#333411yescharacteristic
420C2×C11#334411yescharacteristic
421C24C2×C22⋊D1111yescharacteristic
422C2×Q8—442no—
423C2×Q8—442no—
424C2×Q8—881no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—881no—
443C22×C4C2×Dic2212yes—
444C22×C4#433912yes—
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C2×C8—112no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—444no—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—112no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4C2×Dic2212yes—
488C4⋊C4C2×Dic2212yes—
489C22⋊C4—22no—
490C22⋊C4—42no—
491C22⋊C4—442no—
492C22⋊C4#432314yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—42no—
499C11#2598811yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#6697712yes—
505C23C2×#432312yes—
506C23#6700412yes—
507C23C22×C22⋊D1111yescharacteristic
508Q8—884no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—48no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—222no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—884no—
551C2×C4#6697712yes—
552C2×C4C2×#432312yes—
553C2×C4C2×#432312yes—
554C2×C4C22×Dic2211yescharacteristic
555C2×C4C2×#433911yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#6704211yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—222no—
561C8—441no—
562C8—441no—
563C8—441no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1062262014yes—
571C22C2×#6697711yescharacteristic
572C22C22×#432311yescharacteristic
573C22C2×#6700411yescharacteristic
574C22#1062335511yescharacteristic
575C22#1062336011yescharacteristic
576C22#1062336811yescharacteristic
577C22#1062336911yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—442no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062304811yescharacteristic
592C4#1062305011yescharacteristic
593C4#1062305811yescharacteristic
594C4#1062306211yescharacteristic
595C2—24no—
596C2#1307228611yescharacteristic
597C2C2×#1062262011yescharacteristic
598C2#1307845811yescharacteristic
599C2#1308042311yescharacteristic
600C2#1308066111yescharacteristic
601C2#1308095911yescharacteristic
602C2#1308107111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2344C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2344D11
hypocenterC11#25988
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #13070174C2semidirect
3. #13070107C2semidirect
4. #13070107C2semidirect
5. #13069944C2semidirect
6. #13069568C2semidirect
7. #13069374C2semidirect
8. #13069187C2semidirect
9. #13069187C2semidirect
68. C2×C11×C4⋊C4Q8semidirect
383. C2×C4⋊C4Dic22semidirect
499. C11#25988semidirect

Maximal subgroups

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

subgroupindex
#130723182
#130701742
#130701072
#130699442
#130695682
#130693742
#130691872
#130688032
#130687962
#130687022
#130686432
C2×#106221672
C11×#23442
#2598811