Finite Group Databasebeta

← #14856987

Subgroups — #14856987

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#13070117C211yesmaximal, characteristic, complemented
3#13070008C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic
5#13069933C211yesmaximal, characteristic
6#13069469C211yesmaximal, characteristic
7#13069346C211yesmaximal, characteristic, complemented
8#13069316C211yesmaximal, characteristic
9#13069305C211yesmaximal, characteristic, complemented
10#13069257C211yesmaximal, characteristic, complemented
11#13069201C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic
13#13068863C211yesmaximal, characteristic
14#13068473C211yesmaximal, characteristic, complemented
15C11×#2319C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C11×#390C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#388—21no—
23C11×#388—21no—
24C11×#381—21no—
25C11×#380—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#376C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66874C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622542C2211yescharacteristic
38#10622542C2211yescharacteristic
39#10622542C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47C11⋊#401—21no—
48#10622271—21no—
49#10622271—21no—
50#10622271—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×Dic22C2311yescharacteristic
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×#4324—22no—
79C2×#4324—22no—
80C2×#4324—41no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97C11×#95D411yescharacteristic
98#66896—22no—
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—
110#66874—22no—
111#66874—22no—
112#66874—41no—
113#66872—22no—
114#66871—22no—
115#66871—41no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118#66867—41no—
119C4×C11⋊C8—41no—
120#29441—111nomaximal, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—81no—
133C22×C4×C11—81no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4#4112yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—81no—
161C11×C22⋊C4—81no—
162C11×C22⋊C4—81no—
163C11×C22⋊C4—81no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—81no—
171#4324—44no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
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#4112yes—
192C2×C11⋊C8#4112yes—
193#2645—111no—
194#2319D1111yescharacteristic
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#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
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
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×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
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—41no—
246C2×C4×C11—41no—
247C2×C4×C11—84no—
248C2×C4×C11C2×#4111yescharacteristic
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—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—41no—
265C2×Dic11—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—41no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C22×SD16—111no—
275C2×C4×D4C2×D1111yescharacteristic
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#102—111no—
287C2×#97—111no—
288C2×C4×C8—111no—
289#401—221no—
290#400—221no—
291#400—221no—
292#400—221no—
293#391—111no—
294#391—111no—
295#391—111no—
296#390C2×D1111yescharacteristic
297#390C2×D1111yescharacteristic
298#389—111no—
299#389—111no—
300#389—111no—
301#389C2×D1111yescharacteristic
302#389C2×D1111yescharacteristic
303#388—21no—
304#388—21no—
305#381—21no—
306#380—21no—
307C4×C4⋊C4C2×D1111yescharacteristic
308#376C2×D1111yescharacteristic
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—42no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11#55111yescharacteristic
341C4×C11#55211yescharacteristic
342C4×C11#55311yescharacteristic
343C4×C11#55611yescharacteristic
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8—111no—
349C22×D4C22×D1111yescharacteristic
350C23×C4—21no—
351C2×SD16—222no—
352C2×SD16—222no—
353C2×SD16—441no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C4×D4—22no—
359C4×D4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380#107—222no—
381#107—441no—
382#106—222no—
383C4⋊C8—222no—
384C4⋊C8—222no—
385#103—222no—
386#103—222no—
387#103—441no—
388#102—222no—
389#102—222no—
390#102—441no—
391#97—441no—
392C4×C8—441no—
393#95—21no—
394#95—21no—
395#95—21no—
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#95C22⋊D1111yescharacteristic
406#95C22⋊D1111yescharacteristic
407#95C22⋊D1111yescharacteristic
408#95C22⋊D1111yescharacteristic
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—221no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4#433912yes—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447SD16—444no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4#433912yes—
477C22⋊C4—24no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C22⋊C4—81no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—81no—
489C11#2944111yescharacteristic, complemented, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C22×C22⋊D1111yescharacteristic
498Q8—441no—
499Q8—441no—
500Q8—441no—
501Q8—441no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
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—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
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—441no—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#6704211yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—222no—
553C8—222no—
554C8—441no—
555C8—441no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1062332211yescharacteristic
564C22#1062336311yescharacteristic
565C22#1062336411yescharacteristic
566C22#1062336611yescharacteristic
567C22#1062336711yescharacteristic
568C22#1062336711yescharacteristic
569C22#1062336911yescharacteristic
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—881no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062305811yescharacteristic
584C4#1062306111yescharacteristic
585C4#1062306211yescharacteristic
586C4#1062306411yescharacteristic
587C2—82no—
588C2#1307421311yescharacteristic
589C2#1307880011yescharacteristic
590C2#1307883011yescharacteristic
591C2#1307923811yescharacteristic
592C2#1307924911yescharacteristic
593C2#1308002111yescharacteristic
594C2#1308004211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2319C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2319D11
hypocenterC11#29441
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
1. #13074581C2semidirect
2. #13070117C2semidirect
3. #13070008C2semidirect
7. #13069346C2semidirect
9. #13069305C2semidirect
10. #13069257C2semidirect
11. #13069201C2semidirect
14. #13068473C2semidirect
489. C11#29441semidirect

Maximal subgroups

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

subgroupindex
#130745812
#130701172
#130700082
#130700042
#130699332
#130694692
#130693462
#130693162
#130693052
#130692572
#130692012
#130689502
#130688632
#130684732
C11×#23192
#2944111