Finite Group Databasebeta

← #28401420

Subgroups — #28401420

Order 14464.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299162C211yesmaximal, characteristic, complemented
2#20298936C211yesmaximal, characteristic, complemented
3#20298919C211yesmaximal, characteristic, complemented
4#20298916C211yesmaximal, characteristic, complemented
5#20298911C211yesmaximal, characteristic, complemented
6#20298849C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298832C211yesmaximal, characteristic, complemented
9#20298829C211yesmaximal, characteristic, complemented
10#20298748C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298731C211yesmaximal, characteristic, complemented
14#20298565C211yesmaximal, characteristic, complemented
15#537×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268631C2211yescharacteristic, complemented
22C22×#11744751C2211yescharacteristic, complemented
23#16813618—21no—
24#16813611—21no—
25#16813596C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813590—21no—
30#16813590—21no—
31#16813581C2211yescharacteristic
32#16813555C2211yescharacteristic, complemented
33#16813555C2211yescharacteristic, complemented
34#16813553C2211yescharacteristic, complemented
35#16813553C2211yescharacteristic, complemented
36#16813546C2211yescharacteristic, complemented
37#16813546C2211yescharacteristic, complemented
38#16813543C2211yescharacteristic, complemented
39#16813543C2211yescharacteristic, complemented
40#16813542C2211yescharacteristic
41#16813542C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic, complemented
47C22⋊#11744751C2211yescharacteristic, complemented
48C2×#41×C113C2211yescharacteristic
49C2×#41×C113C2211yescharacteristic, complemented
50C22⋊Q8×C113—21no—
51C22⋊Q8×C113C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic, complemented
53#121×C113—21no—
54#121×C113—21no—
55#121×C113—21no—
56#121×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic, complemented
58C2×C4⋊C4×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×D452—21no—
61C2×D452—41no—
62C2×D452—41no—
63C2×D452C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69#14268634—41no—
70#14268634—41no—
71#14268632—41no—
72#14268632—41no—
73#14268631—41no—
74C2×#11744751—41no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C22⋊Dic113—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86C4×Dic113—21no—
87#41×C113—41no—
88#41×C113—41no—
89#41×C113—41no—
90#41×C113—41no—
91C2×Q8×C113D411yescharacteristic
92C2×Q8×C113C2311yescharacteristic
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113D411yescharacteristic
97C2×D4×C113D411yescharacteristic
98C2×D4×C113D411yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113—21no—
101C22×C4×C113—21no—
102C22×C4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C23×C113C2×D411yescharacteristic
117C23×C113C2×D411yescharacteristic
118C22×D113—21no—
119C22×D113—21no—
120C22×D113—42no—
121C22×D113—81no—
122C22×D113—81no—
123Q8×C113—21no—
124Q8×C113—21no—
125Q8×C113—41no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—41no—
129D4×C113—41no—
130D4×C113—41no—
131D4×C113—42no—
132D4×C113—81no—
133D4×C113—81no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—42no—
144C2×C4×C113—81no—
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2411yescharacteristic
149C22⋊D113—81no—
150C22⋊D113—81no—
151C22⋊D113—81no—
152C22⋊D113—81no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155D452—21no—
156D452—21no—
157D452—21no—
158D452—21no—
159D452—42no—
160#11744751—21no—
161#11744751—21no—
162#11744751—21no—
163#11744751—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113C22×D411yescharacteristic
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C4×C113—21no—
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113—41no—
190C4×C113H(5,𝔽2)11yescharacteristic
191C4×C113H(5,𝔽2)11yescharacteristic
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—41no—
196C2×C113—41no—
197C2×C113—81no—
198C2×C113#53411yescharacteristic
199C2×C113#57611yescharacteristic
200C2×C113#57711yescharacteristic
201D113—81no—
202D113—81no—
203#3198—1131nomaximal, Sylow
204C113#319811yescharacteristic, complemented, Sylow
205#537D11311yescharacteristic, complemented
206#535—1131no—
207#485—1131no—
208#482—1131no—
209#481—1131no—
210#480—1131no—
211#469—1131no—
212#468—1131no—
213#466—1131no—
214#465—1131no—
215#450—1131no—
216#449—1131no—
217#449—1131no—
218#447—1131no—
219#408—1131no—
220C2×#41C2×D11311yescharacteristic
221C2×#41C2×D11311yescharacteristic, complemented
222C22×D4—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×M16—1131no—
228C22×C8—1131no—
229#127—2261no—
230#124—2261no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D11311yescharacteristic
233C22⋊Q8C2×D11311yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—1131no—
238#121—1131no—
239#121—1131no—
240#121—1131no—
241#121C2×D11311yescharacteristic
242#121C2×D11311yescharacteristic, complemented
243#120—2261no—
244#120—2261no—
245#117—1131no—
246C2×C4⋊C4C2×D11311yescharacteristic, complemented
247#107—1131no—
248#107—1131no—
249#106—1131no—
250#106—1131no—
251#103—1131no—
252#103—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102—1131no—
259C22⋊C8—1131no—
260C22⋊C8—1131no—
261C22⋊C8—1131no—
262C22⋊C8—1131no—
263C24—2261no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D11311yescharacteristic
269C2×Q8C22×D11311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—1131no—
274C2×D4—1131no—
275C2×D4—4521no—
276C2×D4—4521no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4C22⋊D11311yescharacteristic
283C2×D4C22⋊D11311yescharacteristic
284C2×D4C22⋊D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D11311yescharacteristic
289C22×C4C22×D11311yescharacteristic
290C22×C4C22×D11311yescharacteristic
291SD16—4521no—
292SD16—4521no—
293D8—4521no—
294D8—4521no—
295M16—4521no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8—1131no—
299C2×C8—1131no—
300C2×C8—4521no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—1131no—
305C4⋊C4—1131no—
306C4⋊C4C22×D11311yescharacteristic
307C4⋊C4C22×D11311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—2261no—
318C23—21no—
319C23—9041no—
320C23—9041no—
321C23—4522no—
322C23—2261no—
323C23—2261no—
324C23C2×C22⋊D11311yescharacteristic
325C23C2×C22⋊D11311yescharacteristic
326C23C2×C22⋊D11311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—9041no—
339D4—9041no—
340D4—9041no—
341D4—9041no—
342D4—4522no—
343D4—2261no—
344D4—2261no—
345D4—2261no—
346D4—2261no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4C2×C22⋊D11311yescharacteristic
361C2×C4C2×C22⋊D11311yescharacteristic
362C2×C4C2×C22⋊D11311yescharacteristic
363C2×C4C23×D11311yescharacteristic
364C8—2261no—
365C8—2261no—
366C8—2261no—
367C8—2261no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—9044no—
381C22—4521no—
382C22—4521no—
383C22—4521no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22C22×C22⋊D11311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—4521no—
395C4—4521no—
396C4#1681366711yescharacteristic
397C4#1681366711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—9041no—
403C2—9041no—
404C2#2029915711yescharacteristic
405C2#2029940111yescharacteristic
406C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#537×C113C2
socleC22×C113C22×D4
hypercenter#537D113
hypocenterC113#3198
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20299162C2semidirect
2. #20298936C2semidirect
3. #20298919C2semidirect
4. #20298916C2semidirect
5. #20298911C2semidirect
6. #20298849C2semidirect
7. #20298846C2semidirect
8. #20298832C2semidirect
9. #20298829C2semidirect
10. #20298748C2semidirect
11. #20298743C2semidirect
12. #20298743C2semidirect
13. #20298731C2semidirect
14. #20298565C2semidirect
15. #537×C113C2semidirect
21. C2×#14268631C22semidirect
22. C22×#11744751C22semidirect
32. #16813555C22semidirect
33. #16813555C22semidirect
34. #16813553C22semidirect
35. #16813553C22semidirect
36. #16813546C22semidirect
37. #16813546C22semidirect
38. #16813543C22semidirect
39. #16813543C22semidirect
46. C22⋊#11744751C22semidirect
47. C22⋊#11744751C22semidirect
49. C2×#41×C113C22semidirect
52. C22⋊Q8×C113C22semidirect
57. #121×C113C22semidirect
58. C2×C4⋊C4×C113C22semidirect
204. C113#3198semidirect
205. #537D113semidirect
221. C2×#41C2×D113semidirect
233. C22⋊Q8C2×D113semidirect
242. #121C2×D113semidirect
246. C2×C4⋊C4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202989362
#202989192
#202989162
#202989112
#202988492
#202988462
#202988322
#202988292
#202987482
#202987432
#202987312
#202985652
#537×C1132
#3198113