Finite Group Databasebeta

← #14908494

Subgroups — #14908494

Order 2816.

534 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#13079153C211yesmaximal, characteristic, complemented
2#13077486C211yesmaximal, characteristic
3#13070779C211yesmaximal, characteristic, complemented
4#13070777C211yesmaximal, characteristic, complemented
5#13070775C211yesmaximal, characteristic, complemented
6#13070763C211yesmaximal, characteristic, complemented
7#13070761C211yesmaximal, characteristic, complemented
8#13070759C211yesmaximal, characteristic, complemented
9#13070757C211yesmaximal, characteristic, complemented
10#13070401C211yesmaximal, characteristic, complemented
11D11×#367C211yesmaximal, characteristic, complemented
12#13070373C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic
14#13070320C211yesmaximal, characteristic
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17#10623220—21no—
18#10623077—21no—
19C11×#499C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22#10622678—21no—
23#10622631—21no—
24C2×#66862C2211yescharacteristic
25C2×C16×D11C2211yescharacteristic
26#10622493C2211yescharacteristic
27D11×#107C2211yescharacteristic
28D11×#107C2211yescharacteristic
29#10622491C2211yescharacteristic
30#10622487C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622474—21no—
33#10622469—21no—
34#10622384—21no—
35#10622370—21no—
36C4×Dic44C2211yescharacteristic
37#10622302C2211yescharacteristic
38#10622295C2211yescharacteristic
39C11×#367C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622143C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4341—21no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63D4×Dic11—21no—
64C2×#4324—21no—
65C4×C22⋊D11—41no—
66C2×Dic11⋊C4—41no—
67#66965—22no—
68#66965Q814yescomplemented
69C2×Dic44C2311yescharacteristic
70C2×#4313D411yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66950—41no—
73#66949—41no—
74#66945—21no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77#66943—21no—
78#66942—41no—
79#66941—21no—
80#66941—41no—
81#66940—21no—
82(C22⋊D11)⋊C4—41no—
83#66930—41no—
84#66925D411yescharacteristic
85#66922—21no—
86C4×Dic22—21no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95#66896—21no—
96#66882—21no—
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66880—21no—
101#66879D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2311yescharacteristic
105#66874—21no—
106#66872—21no—
107#66872—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66867D411yescharacteristic
112#66862—22no—
113C16×D11—22no—
114#33634—111nomaximal, Sylow
115C2×D4×C11—21no—
116C22×C4×C11—41no—
117C2×C22⋊D11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120#4341—24no—
121#4341—42no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—21no—
126C2×Dic22—41no—
127C2×Dic22—41no—
128C11×D8—21no—
129C11×D8C2×Q812yes—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140#4324—24no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4D811yescharacteristic
143(C2×D11)⋊C4D811yescharacteristic
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4D811yescharacteristic
156Dic11⋊C4D811yescharacteristic
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163Dic44—21no—
164Dic44C2×Q812yes—
165#4313—22no—
166C8×D11C2×Q812yes—
167C8×D11#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3164—111no—
173#2951—111no—
174#2229—111no—
175#2229—111no—
176#2228—111no—
177#2228D1111yescharacteristic, complemented
178#2226—111no—
179#2226—111no—
180#2225—111no—
181#2225—111no—
182#2159—111no—
183C2×#367—111no—
184#2151—111no—
185#2139—111no—
186#2138—111no—
187C23×C11—41no—
188C22×D11C2×D811yescharacteristic
189D4×C11—22no—
190D4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—161no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—44no—
199C2×Dic11—41no—
200C2×Dic11—44no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—161no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C4×D11—161no—
209C4×D11—161no—
210C4×D11C22⋊Q812yes—
211C4×D11#13712yes—
212Dic22—22no—
213Dic22—41no—
214Dic22—161no—
215Dic22—161no—
216C8×C11—21no—
217C8×C11C22×Q811yescharacteristic
218C8×C11C2×#4111yescharacteristic
219C11⋊C8—21no—
220C11⋊C8C22⋊Q812yes—
221C2×#135—111no—
222#544—221no—
223#520—221no—
224C2×M32—111no—
225C22×C16—111no—
226#501—221no—
227#501—221no—
228#500—111no—
229#500—111no—
230#499—111no—
231#499C2×D1111yescharacteristic
232#440—221no—
233#440—221no—
234C4×Q16—111no—
235C4×Q16—111no—
236C4×D8—111no—
237C4×D8C2×D1111yescharacteristic
238#428—221no—
239#427—111no—
240C2×#107—111no—
241C2×#107—111no—
242#417—221no—
243#405—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#367—111no—
248#367—111no—
249#367C2×D1111yescharacteristic
250#366—111no—
251#366C2×D1111yescharacteristic
252C4⋊C16—111no—
253C4⋊C16—111no—
254C4⋊C16—111no—
255C4⋊C16C2×D1111yescharacteristic
256#358—111no—
257#358—111no—
258#358—111no—
259#358—111no—
260#357—111no—
261#357—111no—
262#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—21no—
269C2×D11—21no—
270C2×D11#47412yes—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11C2×C22⋊Q811yescharacteristic
277C4×C11C2×#13711yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—42no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11#47412yes—
285C2×#41—221no—
286#135—114no—
287#135—222no—
288C2×Q16—111no—
289C2×SD16—221no—
290C2×D8C22×D1111yescharacteristic
291C2×M16—111no—
292C22×C8—111no—
293C4⋊Q8—221no—
294C4⋊Q8—221no—
295C4⋊Q8—441no—
296#125—21no—
297#125—221no—
298#125—441no—
299C22⋊Q8—441no—
300C22⋊Q8—441no—
301C4×Q8—221no—
302C4×Q8—221no—
303C4×D4—21no—
304C4×D4—221no—
305C4×D4—441no—
306C4×D4—441no—
307#117—111no—
308#117—221no—
309#117—441no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—441no—
313M32—222no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16—222no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319#107—111no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#107—221no—
325#107—221no—
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—21no—
330#106—221no—
331#106—221no—
332#103—221no—
333#103—221no—
334#102—21no—
335#102—221no—
336#97—111no—
337#97—111no—
338C4×C8—111no—
339C4×C8C22×D1111yescharacteristic
340C2×C11—82no—
341C2×C11C2×#47411yescharacteristic
342C2×C11#341611yescharacteristic
343C2×C11#341611yescharacteristic
344D11—22no—
345#41—224no—
346#41—442no—
347C2×Q8—221no—
348C2×Q8—441no—
349C2×Q8—441no—
350C2×D4—21no—
351C2×D4—441no—
352C22×C4—41no—
353C22×C4—111no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358Q16—112no—
359Q16—221no—
360SD16—224no—
361D8—21no—
362D8Q8×D1112yes—
363M16—222no—
364C2×C8—111no—
365C2×C8—112no—
366C2×C8—112no—
367C2×C8—111no—
368C2×C8D4×D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—111no—
376C4⋊C4—111no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—41no—
389C22⋊C4—111no—
390C22⋊C4—111no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C42—111no—
394C42—441no—
395C42—441no—
396C42—441no—
397C42D4×D1111yescharacteristic
398C16—21no—
399C16—21no—
400C16—221no—
401C16—221no—
402C11#3363411yescharacteristic, complemented, Sylow
403C23—41no—
404C23—111no—
405Q8—222no—
406Q8—441no—
407Q8—1761no—
408Q8—1761no—
409D4—22no—
410D4—41no—
411D4—444no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—111no—
416C2×C4—112no—
417C2×C4—112no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—161no—
421C2×C4—444no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—1761no—
427C2×C4—1761no—
428C2×C4—1761no—
429C2×C4D8×D1111yescharacteristic
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—112no—
434C8—221no—
435C8C2×Q8×D1111yescharacteristic
436C8#41×D1111yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—112no—
441C22—221no—
442C22—221no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—112no—
450C4—221no—
451C4—221no—
452C4—442no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4D11×C22⋊Q811yescharacteristic
457C4D11×#13711yescharacteristic
458C2—82no—
459C2—222no—
460C2D11×#47411yescharacteristic
461C2#1308175911yescharacteristic
462C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radicalC2×#66965C22
hypercenter#2228D11
hypocenterC11#33634
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13079153C2semidirect
3. #13070779C2semidirect
4. #13070777C2semidirect
5. #13070775C2semidirect
6. #13070763C2semidirect
7. #13070761C2semidirect
8. #13070759C2semidirect
9. #13070757C2semidirect
10. #13070401C2semidirect
11. D11×#367C2semidirect
12. #13070373C2semidirect
15. C11×#2228C2semidirect
68. #66965Q8semidirect
177. #2228D11semidirect
402. C11#33634semidirect

Maximal subgroups

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

subgroupindex
#130791532
#130774862
#130707792
#130707772
#130707752
#130707632
#130707612
#130707592
#130707572
#130704012
D11×#3672
#130703732
#130703252
#130703202
C11×#22282
#3363411