Finite Group Databasebeta

← #14856984

Subgroups — #14856984

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#13074582C211yesmaximal, characteristic, complemented
2#13071253C211yesmaximal, characteristic
3#13070115C211yesmaximal, characteristic, complemented
4#13070009C211yesmaximal, characteristic, complemented
5#13070002C211yesmaximal, characteristic
6#13069929C211yesmaximal, characteristic
7#13069349C211yesmaximal, characteristic, complemented
8#13069316C211yesmaximal, characteristic
9#13069309C211yesmaximal, characteristic, complemented
10#13069259C211yesmaximal, characteristic, complemented
11#13069203C211yesmaximal, characteristic, complemented
12#13068952C211yesmaximal, characteristic
13#13068865C211yesmaximal, characteristic
14#13068474C211yesmaximal, characteristic, complemented
15C11×#1968C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#390C2211yescharacteristic
24#10622843C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622598C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622558—21no—
40#10622557—21no—
41#10622556—21no—
42#10622555—21no—
43#10622545C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C11⋊#401—21no—
48#10622273—21no—
49#10622272—21no—
50#10622271—21no—
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75D4×Dic11—22no—
76D4×Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C11×#106—22no—
92C11×#103—22no—
93C11×#102—22no—
94C4×C8×C11—41no—
95C11×#95—21no—
96C11×#95—21no—
97#66899—22no—
98#66899—41no—
99#66896—22no—
100#66896—41no—
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
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66882—22no—
116#66882—41no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119#66867—41no—
120#29441—111nomaximal, Sylow
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—81no—
146C22×Dic11—81no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C11×SD16—44no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11#4112yes—
157C2×C8×C11#4112yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C22⋊C4—81no—
163C11×C22⋊C4—81no—
164C42×C11—21no—
165C42×C11—21no—
166C22⋊Dic11—24no—
167C22⋊Dic11—81no—
168C22⋊Dic11—81no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—81no—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—81no—
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#2645—111no—
194#2319—111no—
195#2088—111no—
196#2068—111no—
197#2067—111no—
198#2055—111no—
199#1968D1111yescharacteristic
200#1942—111no—
201#1936—111no—
202#1935—111no—
203#1928—111no—
204#1920—111no—
205#1877—111no—
206#1862—111no—
207#1768—111no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C22×D411yescharacteristic
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—41no—
223D4×C11—41no—
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—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
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—84no—
270C8×C11—22no—
271C8×C11—22no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C22×SD16C2×D1111yescharacteristic
275C2×C4×D4—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106C2×D1111yescharacteristic
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103C2×D1111yescharacteristic
284C2×#102—111no—
285C2×#102—111no—
286C2×#102C2×D1111yescharacteristic
287C2×#97—111no—
288C2×C4×C8C2×D1111yescharacteristic
289#401—221no—
290#400—221no—
291#400—221no—
292#400—221no—
293#391—111no—
294#391—111no—
295#391C2×D1111yescharacteristic
296#390—111no—
297#390C2×D1111yescharacteristic
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#376—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#336—111no—
316#336—111no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11#52511yescharacteristic
325C22×C11#53211yescharacteristic
326C22×C11#53711yescharacteristic
327C22×C11#57611yescharacteristic
328C22×C11#57711yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57811yescharacteristic
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#55111yescharacteristic
337C4×C11#55211yescharacteristic
338C4×C11#55311yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—41no—
341Dic11—42no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4C22×D1111yescharacteristic
350C23×C4—221no—
351C2×SD16—22no—
352C2×SD16—22no—
353C2×SD16—41no—
354C22×C8—111no—
355C22×C8—111no—
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—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—221no—
379C2×C42C22×D1111yescharacteristic
380#107—222no—
381#107—441no—
382#106—22no—
383C4⋊C8—222no—
384C4⋊C8—222no—
385#103—22no—
386#103—222no—
387#103—441no—
388#102—22no—
389#102—222no—
390#102—441no—
391#97—441no—
392C4×C8—41no—
393#95—21no—
394#95—21no—
395#95—111no—
396#95—111no—
397#95—111no—
398#95—111no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11—82no—
410C2×C11#260111yescharacteristic
411C2×C11#311811yescharacteristic
412C2×C11#312011yescharacteristic
413C2×C11#317411yescharacteristic
414C2×C11#317511yescharacteristic
415C2×C11#325711yescharacteristic
416C2×C11#325811yescharacteristic
417C24—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4#433912yes—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—221no—
438C22×C4—224no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—881no—
443C22×C4—881no—
444C22×C4D4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447SD16—44no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8#434112yes—
459C2×C8#434112yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—112no—
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—81no—
478C22⋊C4—81no—
479C22⋊C4—224no—
480C22⋊C4—881no—
481C22⋊C4—881no—
482C42—21no—
483C42—21no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—881no—
489C11#2944111yescharacteristic, complemented, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C2×D4×D1111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
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—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—222no—
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×#434111yescharacteristic
548C2×C4C2×#434111yescharacteristic
549C2×C4#6703711yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—22no—
553C8—22no—
554C8—441no—
555C8—441no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1062307811yescharacteristic
564C22#1062312811yescharacteristic
565C22#1062324711yescharacteristic
566C22#1062329311yescharacteristic
567C22#1062329311yescharacteristic
568C22#1062330011yescharacteristic
569C22#1062330211yescharacteristic
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—441no—
576C4—442no—
577C4—441no—
578C4—441no—
579C4—441no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062302611yescharacteristic
584C4#1062307211yescharacteristic
585C4#1062313211yescharacteristic
586C4#1062320211yescharacteristic
587C2—82no—
588C2#1307421011yescharacteristic
589C2#1307880611yescharacteristic
590C2#1307882611yescharacteristic
591C2#1307924111yescharacteristic
592C2#1307925211yescharacteristic
593C2#1308003011yescharacteristic
594C2#1308003511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1968C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1968D11
hypocenterC11#29441
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
1. #13074582C2semidirect
3. #13070115C2semidirect
4. #13070009C2semidirect
7. #13069349C2semidirect
9. #13069309C2semidirect
10. #13069259C2semidirect
11. #13069203C2semidirect
14. #13068474C2semidirect
489. C11#29441semidirect

Maximal subgroups

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

subgroupindex
#130745822
#130712532
#130701152
#130700092
#130700022
#130699292
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