Finite Group Databasebeta

← #14911476

Subgroups — #14911476

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081625C211yesmaximal, characteristic
2#13081504C211yesmaximal, characteristic, complemented
3#13070849C211yesmaximal, characteristic, complemented
4#13070838C211yesmaximal, characteristic
5#13070775C211yesmaximal, characteristic, complemented
6#13070770C211yesmaximal, characteristic, complemented
7#13070756C211yesmaximal, characteristic, complemented
8#13070681C211yesmaximal, characteristic, complemented
9#13070675C211yesmaximal, characteristic, complemented
10#13070655C211yesmaximal, characteristic
11C16×Dic22C211yesmaximal, characteristic, complemented
12#13070472C211yesmaximal, characteristic, complemented
13#13070471C211yesmaximal, characteristic, complemented
14C4×#66864C211yesmaximal, characteristic, complemented
15C11×#2242C211yesmaximal, characteristic, complemented
16#10623216—21no—
17#10623212—21no—
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20#10622804C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23#10622778—21no—
24#10622776—21no—
25#10622764C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28#10622676—21no—
29#10622670—21no—
30C2×#66864C2211yescharacteristic
31#10622491C2211yescharacteristic
32#10622487C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622470—21no—
36#10622467—21no—
37C4×Dic44C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#358C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C4×C11×C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C11×#124—21no—
64#67000—21no—
65Q8×Dic11—21no—
66C2×#4325—21no—
67#66993—21no—
68D4×Dic11—21no—
69C2×#4323—21no—
70C2×Dic44C2311yescharacteristic
71C2×D88C2311yescharacteristic
72#66943—21no—
73#66942—41no—
74#66942—41no—
75#66941—21no—
76#66941—41no—
77#66940—21no—
78#66940—21no—
79#66940—41no—
80#66939—41no—
81#66938—41no—
82#66936—41no—
83(C22⋊D11)⋊C4—41no—
84C4×D44—21no—
85C4×Dic22—21no—
86C4×Dic22D411yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#106—21no—
92C4×C8×C11C2311yescharacteristic
93#66899—21no—
94#66896—21no—
95#66893—22no—
96#66891—22no—
97#66885—21no—
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66880—21no—
101Dic11⋊C8D411yescharacteristic
102Dic11⋊C8D411yescharacteristic
103C8×Dic11C2311yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66874—21no—
108#66874—21no—
109#66872—21no—
110#66871—21no—
111C4⋊(C11⋊C8)D411yescharacteristic
112#66864—22no—
113#33932—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C22×Dic11—41no—
119C2×D44—21no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×Dic22D811yescharacteristic
124C11×Q16—21no—
125C11×Q16—21no—
126C11×SD16—81no—
127C11×D8—21no—
128C11×D8—21no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139#4325—81no—
140#4323—81no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148C4⋊Dic11D811yescharacteristic
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4D811yescharacteristic
155Dic11⋊C4D811yescharacteristic
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164Dic44—21no—
165Dic44#4112yes—
166D88—21no—
167D88—21no—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396—111no—
173#3383—111no—
174#2242—111no—
175#2242D1111yescharacteristic, complemented
176#2240—111no—
177#2228—111no—
178#2228—111no—
179#2225—111no—
180#2211—111no—
181#2211—111no—
182#2207—111no—
183Q8×C16—111no—
184C4×Q32—111no—
185C4×SD32—111no—
186C4×SD32—111no—
187C23×C11—41no—
188C22×D11—41no—
189Q8×C11—41no—
190Q8×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—82no—
200C22⋊D11—161no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—161no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209D44—41no—
210D44—41no—
211C4×D11—161no—
212Dic22—22no—
213Dic22—22no—
214Dic22—41no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#559—221no—
222#557—221no—
223C2×Q32—111no—
224C2×SD32—111no—
225C2×SD32—111no—
226#500—111no—
227#499—111no—
228#499C2×D1111yescharacteristic
229#495—111no—
230#495C2×D1111yescharacteristic
231#493—111no—
232#479—221no—
233#479—221no—
234#475—221no—
235#463—221no—
236#463—221no—
237#460—221no—
238C8×Q8—111no—
239C4×Q16—111no—
240C4×Q16—111no—
241C4×Q16—111no—
242C4×Q16—111no—
243C4×D8—111no—
244C4×D8—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358C2×D1111yescharacteristic
254#358C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357C2×D1111yescharacteristic
260#357C2×D1111yescharacteristic
261C4×C16—111no—
262C4×C16—111no—
263C4×C16C2×D1111yescharacteristic
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#54811yescharacteristic
277C4×C11#57711yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—21no—
281Dic11—42no—
282Dic11—81no—
283Dic11—81no—
284Dic11#50812yes—
285C2×Q16—111no—
286C2×Q16C22×D1111yescharacteristic
287C2×SD16—21no—
288C2×SD16—221no—
289C2×D8—111no—
290C2×D8—221no—
291C2×D8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293C4⋊Q8—441no—
294#127—221no—
295#125—21no—
296#125—221no—
297#125—441no—
298#125—441no—
299#124—21no—
300#124—221no—
301#124—441no—
302#123—441no—
303#123—441no—
304C4×Q8—111no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×Q8—221no—
309C4×Q8—441no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—441no—
313Q32—222no—
314SD32—222no—
315SD32—222no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16C22×D1111yescharacteristic
319C2×C16C22×D1111yescharacteristic
320#107—111no—
321#107—111no—
322#107—221no—
323#107C22×D1111yescharacteristic
324#107C22×D1111yescharacteristic
325#106—21no—
326#106—221no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—111no—
330#103—221no—
331#103—221no—
332#103—221no—
333#103—221no—
334#102—221no—
335#102—221no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8C22×D1111yescharacteristic
339C2×C11—161no—
340C2×C11#335811yescharacteristic
341C2×C11C2×#50811yescharacteristic
342C2×C11#341611yescharacteristic
343D11—161no—
344C2×Q8—21no—
345C2×Q8—111no—
346C2×Q8—221no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—221no—
350C2×D4—441no—
351C2×D4—441no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—21no—
356Q16—112no—
357Q16—221no—
358SD16—81no—
359SD16—881no—
360D8—21no—
361D8—21no—
362D8—221no—
363D8—221no—
364D8—881no—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8D4×D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—111no—
374C4⋊C4—111no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—111no—
392C42—111no—
393C42—441no—
394C42—441no—
395C42—441no—
396C42—441no—
397C42D4×D1111yescharacteristic
398C16—21no—
399C16—21no—
400C16—221no—
401C16—221no—
402C11#3393211yescharacteristic, complemented, Sylow
403C23—41no—
404C23—441no—
405Q8—41no—
406Q8—41no—
407Q8—222no—
408Q8—222no—
409Q8—441no—
410Q8—882no—
411D4—41no—
412D4—41no—
413D4—441no—
414D4—441no—
415D4—882no—
416D4—1761no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—111no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—1761no—
428C2×C4—1761no—
429C2×C4D8×D1111yescharacteristic
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—221no—
434C8—221no—
435C8#41×D1111yescharacteristic
436C8#6704311yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—112no—
450C4—221no—
451C4—221no—
452C4—221no—
453C4—442no—
454C4—881no—
455C4—881no—
456C4#1062320811yescharacteristic
457C4#1062329311yescharacteristic
458C2—161no—
459C2—1761no—
460C2#1308124811yescharacteristic
461C2D11×#50811yescharacteristic
462C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radical#10622764C22
hypercenter#2242D11
hypocenterC11#33932
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
2. #13081504C2semidirect
3. #13070849C2semidirect
5. #13070775C2semidirect
6. #13070770C2semidirect
7. #13070756C2semidirect
8. #13070681C2semidirect
9. #13070675C2semidirect
11. C16×Dic22C2semidirect
12. #13070472C2semidirect
13. #13070471C2semidirect
14. C4×#66864C2semidirect
15. C11×#2242C2semidirect
175. #2242D11semidirect
402. C11#33932semidirect

Maximal subgroups

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

subgroupindex
#130816252
#130815042
#130708492
#130708382
#130707752
#130707702
#130707562
#130706812
#130706752
#130706552
C16×Dic222
#130704722
#130704712
C4×#668642
C11×#22422
#3393211