Finite Group Databasebeta

← #14911253

Subgroups — #14911253

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13070899C211yesmaximal, characteristic, complemented
3#13070804C211yesmaximal, characteristic, complemented
4#13070801C211yesmaximal, characteristic, complemented
5#13070799C211yesmaximal, characteristic, complemented
6#13070796C211yesmaximal, characteristic, complemented
7#13070773C211yesmaximal, characteristic, complemented
8#13070760C211yesmaximal, characteristic, complemented
9#13070717C211yesmaximal, characteristic, complemented
10#13070700C211yesmaximal, characteristic, complemented
11#13070490C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070402C211yesmaximal, characteristic, complemented
14C2×#10622128C211yesmaximal, characteristic, complemented
15C11×#3334C211yesmaximal, characteristic, complemented
16C11×#547—21no—
17#10623096—21no—
18C11×#500C2211yescharacteristic
19C11×#480—21no—
20C11×#480—21no—
21C11×#474—21no—
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622728C2211yescharacteristic
31#10622719C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622460—21no—
36#10622350—21no—
37#10622348—21no—
38C4×D88C2211yescharacteristic
39#10622296C2211yescharacteristic
40#10622200C2211yescharacteristic
41#10622200C2211yescharacteristic
42#10622200C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622129C2211yescharacteristic
46#10622129C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×#41—41no—
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C4⋊Q8—21no—
64C11×#123—41no—
65C11×#123—41no—
66C11×C22⋊Q8—41no—
67C11×#121—21no—
68C11×#121—21no—
69C4×D4×C11—21no—
70C4×D4×C11D411yescharacteristic
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73#66992—41no—
74#66983—21no—
75#66983—21no—
76#66979—21no—
77C2×C4⋊Dic11—21no—
78C2×D88C2311yescharacteristic
79#66951—41no—
80#66936—41no—
81(C22⋊D11)⋊C4—41no—
82C4×D44—21no—
83#66923—21no—
84C11×#107—21no—
85C11×#107—21no—
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#102—21no—
92C11×#102—21no—
93C11×#102—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66890—22no—
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66882—21no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66881—21no—
107#66876—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33912—111nomaximal, Sylow
114C11×#41—84no—
115C2×Q8×C11—41no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11D811yescharacteristic
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128C2×D44—21no—
129C2×C4×D11—41no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4D811yescharacteristic
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4D811yescharacteristic
151C11×C22⋊C4D811yescharacteristic
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164D88—21no—
165D88—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16—21no—
169C11⋊C16#4112yescomplemented
170#3339—111no—
171#3334D1111yescharacteristic, complemented
172#2255—111no—
173#2234—111no—
174#2233—111no—
175#2233—111no—
176#2232—111no—
177#2228—111no—
178#2226—111no—
179#2218—111no—
180#2215—111no—
181#2177—111no—
182#2168—111no—
183#2159—111no—
184C2×#367—111no—
185C23×C11—41no—
186C23×C11C2×D811yescharacteristic
187C23×C11C2×D811yescharacteristic
188C22×D11—41no—
189Q8×C11—82no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—82no—
194D4×C11—82no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—82no—
203C2×C4×C11—82no—
204C2×C4×C11—82no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C22⋊D11—82no—
211C22⋊D11—161no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—161no—
216D44—41no—
217D44—41no—
218C4×D11—161no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11C2×#4111yescharacteristic
223C8×C112−1+411yescharacteristic
224#553—221no—
225#547—21no—
226C2×D16—111no—
227C2×M32—111no—
228C22×C16—111no—
229#500C2×D1111yescharacteristic
230#499—111no—
231#482—221no—
232#481—221no—
233#480—21no—
234#480—21no—
235#478—221no—
236#474—21no—
237#466—111no—
238#466—111no—
239#466C2×D1111yescharacteristic
240#466C2×D1111yescharacteristic
241C4×D8—111no—
242C4×D8C2×D1111yescharacteristic
243C8×D4C2×D1111yescharacteristic
244#427—111no—
245C2×#107—111no—
246C2×#107C2×D1111yescharacteristic
247C2×#107C2×D1111yescharacteristic
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367—111no—
253#367—111no—
254#366—111no—
255#366—111no—
256#366—111no—
257C4⋊C16—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264C22⋊C16—111no—
265C22⋊C16—111no—
266#346—111no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11#50912yes—
276C22×C11C22×D811yescharacteristic
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11#54711yescharacteristic
288C4×C11#57811yescharacteristic
289Dic11—81no—
290Dic11—81no—
291Dic11—81no—
292C2×#41—41no—
293C2×D8—111no—
294C2×D8C22×D1111yescharacteristic
295C22×C8C22×D1111yescharacteristic
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—21no—
298#126—441no—
299#125—221no—
300#123—41no—
301#123—41no—
302#123—441no—
303C22⋊Q8—41no—
304#121—21no—
305#121—21no—
306#121—221no—
307#121—221no—
308#121—441no—
309C4×D4—21no—
310C4×D4—221no—
311C4×D4—441no—
312C4×D4C22⋊D1111yescharacteristic
313#117—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—221no—
317D16—222no—
318M32—222no—
319C2×C16—111no—
320C2×C16—111no—
321C2×C16—111no—
322C2×C16—111no—
323C2×C16—222no—
324#107—21no—
325#107—21no—
326#107—21no—
327#107—111no—
328#107—111no—
329#107—111no—
330#107—221no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#107C22×D1111yescharacteristic
334#106—221no—
335#106—221no—
336C4⋊C8C22⋊D1111yescharacteristic
337#102—21no—
338#102—21no—
339#102—21no—
340#102—221no—
341#102—221no—
342#102—221no—
343C22⋊C8C22⋊D1111yescharacteristic
344C22⋊C8C22⋊D1111yescharacteristic
345C4×C8C22×D1111yescharacteristic
346C2×C11—22no—
347C2×C11—41no—
348C2×C11—161no—
349C2×C11#333411yescharacteristic
350C2×C11C2×#50911yescharacteristic
351C2×C11#341611yescharacteristic
352D11—161no—
353#41—84no—
354C2×Q8—41no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—221no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4#432311yescharacteristic
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369D8—21no—
370D8—21no—
371D8—221no—
372D8—221no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C2×C22⋊D1111yescharacteristic
378C2×C8C2×C22⋊D1111yescharacteristic
379C2×C8C2×C22⋊D1111yescharacteristic
380C2×C8C23×D1111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4#432311yescharacteristic
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4#432311yescharacteristic
402C22⋊C4#432311yescharacteristic
403C42—441no—
404C42C2×C22⋊D1111yescharacteristic
405C16—112no—
406C16—221no—
407C16—221no—
408C16—221no—
409C11#3391211yescharacteristic, complemented, Sylow
410C23—41no—
411C23—441no—
412C23C2×#432311yescharacteristic
413C23C2×#432311yescharacteristic
414Q8—82no—
415D4—22no—
416D4—41no—
417D4—41no—
418D4—82no—
419D4—82no—
420D4—441no—
421D4—441no—
422D4—882no—
423D4—1761no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—1761no—
438C2×C4—1761no—
439C2×C4C2×#432311yescharacteristic
440C2×C4C2×#432311yescharacteristic
441C2×C4C2×#432311yescharacteristic
442C2×C4C2×#432311yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8#41×D1111yescharacteristic
448C8#6704311yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22#1062276012yes—
461C22C22×#432311yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062335511yescharacteristic
473C4#1062336911yescharacteristic
474C2—22no—
475C2—41no—
476C2—161no—
477C2—1761no—
478C2#1308095911yescharacteristic
479C2C2×#1062276011yescharacteristic
480C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33912
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13070899C2semidirect
3. #13070804C2semidirect
4. #13070801C2semidirect
5. #13070799C2semidirect
6. #13070796C2semidirect
7. #13070773C2semidirect
8. #13070760C2semidirect
9. #13070717C2semidirect
10. #13070700C2semidirect
11. #13070490C2semidirect
12. #13070442C2semidirect
13. #13070402C2semidirect
14. C2×#10622128C2semidirect
15. C11×#3334C2semidirect
169. C11⋊C16#41semidirect
171. #3334D11semidirect
409. C11#33912semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708992
#130708042
#130708012
#130707992
#130707962
#130707732
#130707602
#130707172
#130707002
#130704902
#130704422
#130704022
C2×#106221282
C11×#33342
#3391211