Finite Group Databasebeta

← #14811820

Subgroups — #14811820

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072329C211yesmaximal, characteristic
2#13070179C211yesmaximal, characteristic, complemented
3#13070118C211yesmaximal, characteristic, complemented
4#13070107C211yesmaximal, characteristic, complemented
5#13069954C211yesmaximal, characteristic, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069201C211yesmaximal, characteristic, complemented
9#13069194C211yesmaximal, characteristic, complemented
10#13068813C211yesmaximal, characteristic
11#13068801C211yesmaximal, characteristic
12#13068702C211yesmaximal, characteristic
13#13068647C211yesmaximal, characteristic
14#13068335C211yesmaximal, characteristic
15C11×#2345C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#387—21no—
23C11×#387—21no—
24C11×#380—21no—
25C11×#380C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66872C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36#10622562—21no—
37#10622561—21no—
38#10622548C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622267—21no—
44#10622260—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
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4Q814yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66979—22no—
80#66979—41no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—41no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66923—22no—
100#66923—41no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C22⋊(C11⋊C8)—22no—
112#66872—22no—
113#66872—22no—
114#66871—41no—
115#66871—41no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—41no—
118#26018—111nomaximal, Sylow
119C24×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
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—81no—
130C22×C4×C11—81no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×Q812yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—81no—
151C11×C4⋊C4—81no—
152C11×C4⋊C4C2×Q812yes—
153C11×C4⋊C4C2×Q812yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—42no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—81no—
162C42×C11—81no—
163C22⋊Dic11—42no—
164C22⋊Dic11—81no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—42no—
173C4⋊Dic11—81no—
174C4⋊Dic11#4112yes—
175Dic11⋊C4—42no—
176Dic11⋊C4—42no—
177Dic11⋊C4—42no—
178Dic11⋊C4—81no—
179C4×Dic11—42no—
180#4318—44no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
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#4112yes—
193#2441—111no—
194#2345D1111yescharacteristic
195#2100—111no—
196#2088—111no—
197#2086—111no—
198#2059—111no—
199#1989—111no—
200#1947—111no—
201#1920—111no—
202#1919—111no—
203#1854—111no—
204#1851—111no—
205#1823—111no—
206#1809—111no—
207#1736—111no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11C22⋊Q812yes—
215C23×C11C22×D411yescharacteristic
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—84no—
246C2×C4×C11C22⋊Q812yes—
247C2×C4×C11#13712yes—
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C11⋊C8—22no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C22×M16—111no—
271C2×#125—111no—
272C2×#117—111no—
273C22×C4⋊C4C2×D1111yescharacteristic
274C2×#107—111no—
275C2×#107—111no—
276C2×#106—111no—
277C2×#106—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C22⋊C8—111no—
281#399—221no—
282#396—221no—
283#389—111no—
284#389—111no—
285#389—221no—
286#389C2×D1111yescharacteristic
287#389C2×D1111yescharacteristic
288#387—21no—
289#387—21no—
290#387—221no—
291#384—111no—
292#380—21no—
293#380—111no—
294#380C2×D1111yescharacteristic
295C4×C4⋊C4C2×D1111yescharacteristic
296C4×C4⋊C4C2×D1111yescharacteristic
297C4×C22⋊C4—21no—
298C4×C22⋊C4C2×D1111yescharacteristic
299#340—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#336—111no—
312#336—111no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11C2×C22⋊Q811yescharacteristic
321C22×C11#54611yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#53311yescharacteristic
337C4×C11#54411yescharacteristic
338C4×C11#55111yescharacteristic
339C4×C11#55211yescharacteristic
340Dic11—42no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C23×C4—21no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—222no—
347C2×M16—222no—
348C2×M16—441no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353#125—222no—
354#125—441no—
355#117—222no—
356#117—441no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4Dic2214yes—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4C22⋊D1111yescharacteristic
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386#107—441no—
387#107—441no—
388#106—222no—
389#106—222no—
390C4⋊C8—222no—
391C4⋊C8—441no—
392C22⋊C8—222no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403C2×C11—42no—
404C2×C11#243811yescharacteristic
405C2×C11#307811yescharacteristic
406C2×C11#308111yescharacteristic
407C2×C11#330911yescharacteristic
408C2×C11#333111yescharacteristic
409C2×C11#334611yescharacteristic
410C2×C11#335111yescharacteristic
411C24C2×C22⋊D1111yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4C2×Dic2212yes—
428C22×C4#433912yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—444no—
436C2×C8—112no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—112no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—881no—
470C4⋊C4—881no—
471C4⋊C4C2×Dic2212yes—
472C4⋊C4C2×Dic2212yes—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—42no—
476C22⋊C4—442no—
477C22⋊C4—881no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—81no—
484C42—442no—
485C11#2601811yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23#6697712yes—
493C23C22×C22⋊D1111yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—222no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4#6697712yes—
537C2×C4#6699512yes—
538C2×C4C22×Dic2211yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C2×C4#6704211yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—222no—
545C8—441no—
546C8—441no—
547C8—441no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×#6697711yescharacteristic
556C22C2×#6699511yescharacteristic
557C22#1062335311yescharacteristic
558C22#1062335511yescharacteristic
559C22#1062336011yescharacteristic
560C22#1062336611yescharacteristic
561C22#1062336711yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—442no—
572C4—881no—
573C4—881no—
574C4—881no—
575C4#1062304811yescharacteristic
576C4#1062305011yescharacteristic
577C4#1062305811yescharacteristic
578C4#1062306211yescharacteristic
579C2—42no—
580C2#1307228611yescharacteristic
581C2#1307842111yescharacteristic
582C2#1307844711yescharacteristic
583C2#1308061611yescharacteristic
584C2#1308092611yescharacteristic
585C2#1308109511yescharacteristic
586C2#1308117011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2345C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2345D11
hypocenterC11#26018
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #13070179C2semidirect
3. #13070118C2semidirect
4. #13070107C2semidirect
5. #13069954C2semidirect
6. #13069573C2semidirect
7. #13069374C2semidirect
8. #13069201C2semidirect
9. #13069194C2semidirect
485. C11#26018semidirect

Maximal subgroups

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

subgroupindex
#130723292
#130701792
#130701182
#130701072
#130699542
#130695732
#130693742
#130692012
#130691942
#130688132
#130688012
#130687022
#130686472
#130683352
C11×#23452
#2601811