Finite Group Databasebeta

← #14856981

Subgroups — #14856981

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074581C211yesmaximal, characteristic, complemented
2#13071260C211yesmaximal, characteristic
3#13070114C211yesmaximal, characteristic, complemented
4#13070010C211yesmaximal, characteristic, complemented
5#13070003C211yesmaximal, characteristic
6#13069934C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic
8#13069349C211yesmaximal, characteristic, complemented
9#13069313C211yesmaximal, characteristic
10#13069306C211yesmaximal, characteristic, complemented
11#13069258C211yesmaximal, characteristic, complemented
12#13069202C211yesmaximal, characteristic, complemented
13#13068949C211yesmaximal, characteristic
14#13068866C211yesmaximal, characteristic
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#376C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32#10622552C2211yescharacteristic
33#10622552C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622542C2211yescharacteristic
36#10622542C2211yescharacteristic
37#10622542C2211yescharacteristic
38#10622541C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622282—21no—
44#10622282—21no—
45#10622280—21no—
46#10622277—21no—
47C11⋊#401—21no—
48#10622271—21no—
49#10622271—21no—
50#10622271—21no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×#4314—22no—
87C2×#4314—22no—
88C2×#4314—41no—
89C4×D44—22no—
90C4×D44—22no—
91C11×C4⋊C8—22no—
92C11×C4⋊C8—22no—
93C11×#97—41no—
94C4×C8×C11—41no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97C11×#95D411yescharacteristic
98C11×#95D411yescharacteristic
99C11⋊#95—21no—
100C11⋊#95—21no—
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—
111#66885—22no—
112#66885—22no—
113#66885—41no—
114#66882—22no—
115#66882—41no—
116#66881—22no—
117#66880—22no—
118#66880—22no—
119#66880—41no—
120#29441—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44#4112yes—
142C2×C4×D11—24no—
143C2×C4×D11—81no—
144C2×C4×D11—81no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11#4112yes—
162C2×C8×C11#4112yes—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—81no—
171(C2×D11)⋊C4—81no—
172(C2×D11)⋊C4—81no—
173(C2×D11)⋊C4—81no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11#4112yes—
186Dic11⋊C4—81no—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C4×Dic11—81no—
192#4314—44no—
193#2645—111no—
194#2319—111no—
195#2088—111no—
196#2068—111no—
197#2067—111no—
198#2055—111no—
199#1968—111no—
200#1942—111no—
201#1936—111no—
202#1935—111no—
203#1928—111no—
204#1920—111no—
205#1877—111no—
206#1862—111no—
207#1768D1111yescharacteristic, complemented
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
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—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×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265C4×D11—84no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—41no—
270C8×C11—22no—
271C8×C11—22no—
272C8×C11—41no—
273C8×C11—41no—
274C22×SD16—111no—
275C2×C4×D4—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#102—111no—
287C2×#97C2×D1111yescharacteristic
288C2×C4×C8C2×D1111yescharacteristic
289#401—221no—
290#400—221no—
291#400—221no—
292#400—221no—
293#391—111no—
294#391—111no—
295#391—111no—
296#390—111no—
297#390—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#389—111no—
303#388—221no—
304#388—221no—
305#381—221no—
306#380—221no—
307C4×C4⋊C4—111no—
308#376C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#336C2×D1111yescharacteristic
316#336C2×D1111yescharacteristic
317C22×C11#52511yescharacteristic
318C22×C11#53211yescharacteristic
319C22×C11#53711yescharacteristic
320C22×C11#57611yescharacteristic
321C22×C11#57711yescharacteristic
322C22×C11#57711yescharacteristic
323C22×C11#57811yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11#55111yescharacteristic
338C4×C11#55211yescharacteristic
339C4×C11#55311yescharacteristic
340C4×C11#55611yescharacteristic
341Dic11—42no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8—111no—
349C22×D4—111no—
350C23×C4—221no—
351C2×SD16—222no—
352C2×SD16—222no—
353C2×SD16—441no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358C4×D4—222no—
359C4×D4—222no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—221no—
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380#107—222no—
381#107—441no—
382#106—222no—
383C4⋊C8—22no—
384C4⋊C8—22no—
385#103—222no—
386#103—222no—
387#103—441no—
388#102—222no—
389#102—222no—
390#102—441no—
391#97—41no—
392C4×C8—41no—
393#95—221no—
394#95—221no—
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—
405#95D4411yescharacteristic
406#95D4411yescharacteristic
407#95D4411yescharacteristic
408#95D4411yescharacteristic
409C2×C11#260111yescharacteristic
410C2×C11#311811yescharacteristic
411C2×C11#312011yescharacteristic
412C2×C11#317411yescharacteristic
413C2×C11#317511yescharacteristic
414C2×C11#325711yescharacteristic
415C2×C11#325811yescharacteristic
416D11—82no—
417C24—221no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×D4—112no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—881no—
439C22×C4—881no—
440C22×C4C2×D4411yescharacteristic
441C22×C4C2×D4411yescharacteristic
442C22×C4C2×D4411yescharacteristic
443C22×C4C2×D4411yescharacteristic
444C22×C4C2×D4411yescharacteristic
445C22×C4C2×D4411yescharacteristic
446C22×C4C23×D1111yescharacteristic
447SD16—444no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8#433912yes—
459C2×C8#433912yes—
460C4⋊C4—112no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4—881no—
477C22⋊C4—224no—
478C22⋊C4—881no—
479C22⋊C4—881no—
480C22⋊C4—881no—
481C22⋊C4—881no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—881no—
489C11#2944111yescharacteristic, complemented, Sylow
490C23—222no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23C22×D4411yescharacteristic
498Q8—441no—
499Q8—441no—
500Q8—441no—
501Q8—441no—
502D4—222no—
503D4—222no—
504D4—441no—
505D4—441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—884no—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4#6703711yescharacteristic
549C2×C4#6704011yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22#1062300811yescharacteristic
564C22#1062304111yescharacteristic
565C22#1062305511yescharacteristic
566C22#1062328211yescharacteristic
567C22#1062328211yescharacteristic
568C22#1062328311yescharacteristic
569C22#1062328411yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—442no—
577C4—881no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062307111yescharacteristic
584C4#1062308711yescharacteristic
585C4#1062309911yescharacteristic
586C4#1062311211yescharacteristic
587C2—882no—
588C2#1307420711yescharacteristic
589C2#1307880211yescharacteristic
590C2#1307883211yescharacteristic
591C2#1307924411yescharacteristic
592C2#1307925511yescharacteristic
593C2#1308002911yescharacteristic
594C2#1308004411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1768C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1768D11
hypocenterC11#29441
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
1. #13074581C2semidirect
3. #13070114C2semidirect
4. #13070010C2semidirect
8. #13069349C2semidirect
10. #13069306C2semidirect
11. #13069258C2semidirect
12. #13069202C2semidirect
15. C11×#1768C2semidirect
207. #1768D11semidirect
489. C11#29441semidirect

Maximal subgroups

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

subgroupindex
#130745812
#130712602
#130701142
#130700102
#130700032
#130699342
#130694702
#130693492
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