Finite Group Databasebeta

← #28401426

Subgroups — #28401426

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#20299176C211yesmaximal, characteristic, complemented
2#20298939C211yesmaximal, characteristic, complemented
3#20298922C211yesmaximal, characteristic, complemented
4#20298914C211yesmaximal, characteristic, complemented
5#20298909C211yesmaximal, characteristic, complemented
6#20298849C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298832C211yesmaximal, characteristic, complemented
9#20298825C211yesmaximal, characteristic, complemented
10#20298749C211yesmaximal, characteristic, complemented
11#20298741C211yesmaximal, characteristic, complemented
12#20298741C211yesmaximal, characteristic, complemented
13#20298732C211yesmaximal, characteristic, complemented
14#20298565C211yesmaximal, characteristic, complemented
15#535×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic, complemented
17C2×#14268635C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268631C2211yescharacteristic, complemented
22C22×#11744751C2211yescharacteristic, complemented
23#16813601C2211yescharacteristic
24#16813601C2211yescharacteristic, complemented
25#16813598—21no—
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic, complemented
28#16813594—21no—
29#16813594—21no—
30#16813593—21no—
31C2×C4⋊Dic113C2211yescharacteristic, complemented
32#16813555C2211yescharacteristic, complemented
33#16813555C2211yescharacteristic, complemented
34#16813553C2211yescharacteristic, complemented
35#16813553C2211yescharacteristic, complemented
36#16813545C2211yescharacteristic, complemented
37#16813545C2211yescharacteristic, complemented
38#16813543C2211yescharacteristic
39#16813543C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic, complemented
43#16813542C2211yescharacteristic, complemented
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic, complemented
47C22⋊#11744751C2211yescharacteristic, complemented
48C2×#41×C113C2211yescharacteristic
49C22×D4×C113C2211yescharacteristic
50#127×C113—21no—
51#124×C113—21no—
52#121×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic
54#121×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#120×C113—21no—
57#120×C113—21no—
58#117×C113C2211yescharacteristic
59#14268647—41no—
60#14268647—41no—
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68#14268635—41no—
69#14268635—41no—
70#14268632—41no—
71#14268632—41no—
72#14268631—41no—
73C2×#11744751—41no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87C24×C113—21no—
88#41×C113—41no—
89#41×C113—41no—
90C2×Q8×C113D411yescharacteristic
91C2×D4×C113—21no—
92C2×D4×C113—21no—
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113—41no—
97C2×D4×C113—41no—
98C2×D4×C113D411yescharacteristic
99C2×D4×C113D411yescharacteristic
100C2×D4×C113D411yescharacteristic
101C2×D4×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105C22×C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—42no—
117C23×C113—81no—
118C23×C113—81no—
119C23×C113C2×D411yescharacteristic
120C23×C113C2×D411yescharacteristic
121C23×C113C2×D411yescharacteristic
122C22×D113—21no—
123Q8×C113—41no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—41no—
129D4×C113—41no—
130D4×C113—41no—
131D4×C113—42no—
132D4×C113—81no—
133D4×C113—81no—
134D4×C113—81no—
135D4×C113—81no—
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—21no—
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2411yescharacteristic
148C22⋊D113—42no—
149C22⋊D113—81no—
150C22⋊D113—81no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—81no—
155D452—21no—
156D452—21no—
157C4×D113—42no—
158Dic226—21no—
159Dic226—21no—
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×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—84no—
180C22×C113C22×D411yescharacteristic
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—41no—
184C4×C113—21no—
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113H(5,𝔽2)11yescharacteristic
190C4×C113H(5,𝔽2)11yescharacteristic
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—41no—
196C2×C113—41no—
197C2×C113—81no—
198C2×C113—81no—
199C2×C113#53411yescharacteristic
200C2×C113#57611yescharacteristic
201C2×C113#57711yescharacteristic
202D113—81no—
203#3198—1131nomaximal, Sylow
204C113#319811yescharacteristic, complemented, Sylow
205#537—1131no—
206#535D11311yescharacteristic, complemented
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×#41—1131no—
221C2×#41C2×D11311yescharacteristic
222C22×D4C2×D11311yescharacteristic
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×M16—1131no—
228C22×C8—1131no—
229#127—21no—
230#124—21no—
231C22⋊Q8—1131no—
232C22⋊Q8—1131no—
233C22⋊Q8—2261no—
234#121—1131no—
235#121—1131no—
236#121—2261no—
237#121—2261no—
238#121—2261no—
239#121C2×D11311yescharacteristic
240#121C2×D11311yescharacteristic
241#121C2×D11311yescharacteristic
242#121C2×D11311yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D11311yescharacteristic
246C2×C4⋊C4—1131no—
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—21no—
264#41—41no—
265#41—41no—
266#41—4521no—
267#41—4521no—
268C2×Q8—1131no—
269C2×Q8C22⋊D11311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—1131no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4C22⋊D11311yescharacteristic
282C2×D4C22⋊D11311yescharacteristic
283C2×D4C22⋊D11311yescharacteristic
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—2261no—
287C22×C4—2261no—
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—1131no—
302C4⋊C4—1131no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4C22×D11311yescharacteristic
307C4⋊C4C22×D11311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—2261no—
324C23C2×C22⋊D11311yescharacteristic
325C23C2×C22⋊D11311yescharacteristic
326C23C2×C22⋊D11311yescharacteristic
327Q8—41no—
328Q8—2261no—
329Q8—2261no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—9041no—
343D4—9041no—
344D4—4522no—
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—9041no—
356C2×C4—4522no—
357C2×C4—2261no—
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—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22C22×C22⋊D11311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—4521no—
394C4—4521no—
395C4—4521no—
396C4#1681366711yescharacteristic
397C4#1681366711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—9041no—
404C2#2029915711yescharacteristic
405C2#2029940111yescharacteristic
406C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3198
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20299176C2semidirect
2. #20298939C2semidirect
3. #20298922C2semidirect
4. #20298914C2semidirect
5. #20298909C2semidirect
6. #20298849C2semidirect
7. #20298842C2semidirect
8. #20298832C2semidirect
9. #20298825C2semidirect
10. #20298749C2semidirect
11. #20298741C2semidirect
12. #20298741C2semidirect
13. #20298732C2semidirect
14. #20298565C2semidirect
15. #535×C113C2semidirect
16. C2×#14268647C22semidirect
21. C2×#14268631C22semidirect
22. C22×#11744751C22semidirect
24. #16813601C22semidirect
27. #16813596C22semidirect
31. C2×C4⋊Dic113C22semidirect
32. #16813555C22semidirect
33. #16813555C22semidirect
34. #16813553C22semidirect
35. #16813553C22semidirect
36. #16813545C22semidirect
37. #16813545C22semidirect
42. #16813542C22semidirect
43. #16813542C22semidirect
46. C22⋊#11744751C22semidirect
47. C22⋊#11744751C22semidirect
204. C113#3198semidirect
206. #535D113semidirect

Maximal subgroups

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

subgroupindex
#202991762
#202989392
#202989222
#202989142
#202989092
#202988492
#202988422
#202988322
#202988252
#202987492
#202987412
#202987322
#202985652
#535×C1132
#3198113