Finite Group Databasebeta

← #14813262

Subgroups — #14813262

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073857C211yesmaximal, characteristic, complemented
2#13071521C211yesmaximal, characteristic
3#13070188C211yesmaximal, characteristic, complemented
4#13070185C211yesmaximal, characteristic, complemented
5#13070118C211yesmaximal, characteristic, complemented
6#13070105C211yesmaximal, characteristic, complemented
7#13069381C211yesmaximal, characteristic, complemented
8#13069338C211yesmaximal, characteristic, complemented
9#13068875C211yesmaximal, characteristic
10#13068748C211yesmaximal, characteristic, complemented
11#13068626C211yesmaximal, characteristic
12#13068624C211yesmaximal, characteristic
13#13068614C211yesmaximal, characteristic
14#13068443C211yesmaximal, characteristic
15C11×#1862C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25#10622823—21no—
26C2×C11⋊#95—21no—
27C2×#66879C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30#10622595—21no—
31#10622590C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66872C2211yescharacteristic
39#10622559—21no—
40#10622555—21no—
41#10622549C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622271—21no—
46#10622263—21no—
47C11×#340C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75D4×Dic11—22no—
76D4×Dic11—22no—
77D4×Dic11—41no—
78D4×Dic11Q814yes—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C11×#107—41no—
96C11×#102—22no—
97C11×#102—22no—
98C11×#95—21no—
99#66896—22no—
100#66896—22no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113#66879—22no—
114Dic11⋊C8—22no—
115Dic11⋊C8—41no—
116#66872—41no—
117C4⋊(C11⋊C8)—41no—
118#26125—111nomaximal, Sylow
119C24×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11C2×Q812yes—
124C2×D4×C11#4112yes—
125C2×D4×C11#4112yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—81no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11—81no—
143C22×Dic11—81no—
144C22×Dic11—81no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—81no—
162C11×C22⋊C4—42no—
163C42×C11—21no—
164C42×C11—21no—
165C22⋊Dic11—24no—
166C22⋊Dic11—42no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11C2×Q812yes—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—42no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—42no—
185C4×Dic11C2×Q812yes—
186C4×Dic11#4112yes—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193#2571—111no—
194#2349—111no—
195#2101—111no—
196#2101—111no—
197#2088—111no—
198#2086—111no—
199#1949—111no—
200#1940—111no—
201#1864—111no—
202#1862D1111yescharacteristic
203#1836—111no—
204#1804—111no—
205#1804—111no—
206#1802—111no—
207#1762—111no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C22×D411yescharacteristic
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11#12514yes—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—84no—
236C2×C4×C11C22×Q811yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
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—84no—
265C2×Dic11—84no—
266C2×Dic11C22⋊Q812yes—
267C2×Dic11C22⋊Q812yes—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C2×C4×D4C2×D1111yescharacteristic
275C2×#107C2×D1111yescharacteristic
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102C2×D1111yescharacteristic
283C2×#102C2×D1111yescharacteristic
284C2×#97—111no—
285#400—221no—
286#400—221no—
287#389—111no—
288#389—111no—
289#389—111no—
290#389—221no—
291#389C2×D1111yescharacteristic
292#385—221no—
293#385—221no—
294#384—111no—
295#382—111no—
296#382—111no—
297#382—111no—
298#382—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C2×#95—221no—
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#340—111no—
312#340C2×D1111yescharacteristic
313#336—111no—
314#336C2×D1111yescharacteristic
315C22×C11—24no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11C2×C22⋊Q811yescharacteristic
323C22×C11#54611yescharacteristic
324C22×C11#54811yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57611yescharacteristic
328C22×C11#57711yescharacteristic
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11C2×#12511yescharacteristic
335C4×C11#54411yescharacteristic
336C4×C11#55211yescharacteristic
337C4×C11#55311yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—42no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C22×D4C22×D1111yescharacteristic
347C23×C4—21no—
348C23×C4—221no—
349C23×C4—221no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C4×D4—22no—
355C4×D4—41no—
356C4×D4—114no—
357C4×D4—222no—
358C4×D4—222no—
359C4×D4—441no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382#107—41no—
383#106—441no—
384C4⋊C8—222no—
385C4⋊C8—441no—
386C4⋊C8—441no—
387#102—22no—
388#102—22no—
389#102—222no—
390#102—222no—
391#97—222no—
392#95—21no—
393#95—111no—
394#95—111no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405C2×C11—44no—
406C2×C11#244211yescharacteristic
407C2×C11#308011yescharacteristic
408C2×C11#308111yescharacteristic
409C2×C11#331111yescharacteristic
410C2×C11#331911yescharacteristic
411C2×C11#337011yescharacteristic
412C2×C11#337611yescharacteristic
413C24—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4#433912yes—
418C2×D4#434112yes—
419C2×D4Q8×D1112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—81no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4—881no—
438C22×C4—881no—
439C22×C4—881no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—112no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C4⋊C4—442no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4—881no—
477C22⋊C4—42no—
478C22⋊C4—224no—
479C22⋊C4—442no—
480C42—21no—
481C42—21no—
482C42—112no—
483C42—112no—
484C42—221no—
485C42—221no—
486C42—442no—
487C11#2612511yescharacteristic, complemented, Sylow
488C23—22no—
489C23—22no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C2×D4×D1111yescharacteristic
496D4—22no—
497D4—22no—
498D4—22no—
499D4#6694214yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—84no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—884no—
541C2×C4—884no—
542C2×C4C2×#433911yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4#6703711yescharacteristic
545C2×C4C2×Q8×D1111yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—41no—
549C8—41no—
550C8—441no—
551C8—441no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22#1062308311yescharacteristic
560C22#1062312211yescharacteristic
561C22D11×C22⋊Q811yescharacteristic
562C22#1062328811yescharacteristic
563C22#1062329911yescharacteristic
564C22#1062330411yescharacteristic
565C22#1062330911yescharacteristic
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—222no—
572C4—222no—
573C4—441no—
574C4—442no—
575C4—441no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4C2×#6694211yescharacteristic
580C4#1062307111yescharacteristic
581C4#1062315411yescharacteristic
582C4#1062318111yescharacteristic
583C2—44no—
584C2#1307233911yescharacteristic
585C2#1307843311yescharacteristic
586C2#1307844011yescharacteristic
587C2#1308065611yescharacteristic
588C2#1308076511yescharacteristic
589C2#1308136511yescharacteristic
590C2#1308144811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1862D11
hypocenterC11#26125
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. #13073857C2semidirect
3. #13070188C2semidirect
4. #13070185C2semidirect
5. #13070118C2semidirect
6. #13070105C2semidirect
7. #13069381C2semidirect
8. #13069338C2semidirect
10. #13068748C2semidirect
487. C11#26125semidirect

Maximal subgroups

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

subgroupindex
#130738572
#130715212
#130701882
#130701852
#130701182
#130701052
#130693812
#130693382
#130688752
#130687482
#130686262
#130686242
#130686142
#130684432
C11×#18622
#2612511