Finite Group Databasebeta

← #46822886

Subgroups — #46822886

Order 34432.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771307C211yesmaximal, characteristic, complemented
2#31771273C211yesmaximal, characteristic, complemented
3#31770968C211yesmaximal, characteristic, complemented
4#31770931C211yesmaximal, characteristic, complemented
5#31770916C211yesmaximal, characteristic, complemented
6#31770915C211yesmaximal, characteristic, complemented
7#31770840C211yesmaximal, characteristic, complemented
8#31770798C211yesmaximal, characteristic, complemented
9#31770748C211yesmaximal, characteristic, complemented
10#31770747C211yesmaximal, characteristic, complemented
11#31770702C211yesmaximal, characteristic, complemented
12#31770674C211yesmaximal, characteristic, complemented
13#31770607C211yesmaximal, characteristic, complemented
14#31770598C211yesmaximal, characteristic, complemented
15#469×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864401C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575449—21no—
22#22575449C2211yescharacteristic
23#22575446—21no—
24#22575444C2211yescharacteristic
25#22575437—21no—
26#22575428C2211yescharacteristic
27#22575426—21no—
28#22575425—21no—
29#22575425—21no—
30#22575424C2211yescharacteristic
31#22575418C2211yescharacteristic
32D4×Dic269—21no—
33D4×Dic269C2211yescharacteristic
34C4×C22⋊D269C2211yescharacteristic
35#22575413—21no—
36#22575411C2211yescharacteristic
37C2×C4⋊Dic269C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575373C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575363C2211yescharacteristic
52C2×D8×C269C2211yescharacteristic
53C2×M16×C269C2211yescharacteristic
54#121×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—41no—
61#16864401—22no—
62#16864401—41no—
63C2×Dic538C2311yescharacteristic
64C2×D1076—21no—
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C2×C22⋊D269D411yescharacteristic
72C22×Dic269—21no—
73C22×Dic269—21no—
74C22×Dic269—21no—
75C2×C4×D269—21no—
76C2×C4×D269C2311yescharacteristic
77#16864390—22no—
78#16864387—41no—
79C2×#14524130C2311yescharacteristic
80C2×#14524130C2311yescharacteristic
81C8×D269—41no—
82C4⋊Dic269—21no—
83C4⋊Dic269—21no—
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86#16864381—21no—
87#16864381—21no—
88#16864381D411yescharacteristic
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269D411yescharacteristic
92#16864379—21no—
93#16864379—21no—
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269C2311yescharacteristic
98C2×D4×C269—21no—
99C2×D4×C269—21no—
100C2×D4×C269C2311yescharacteristic
101C2×D4×C269C2311yescharacteristic
102C22×C4×C269C2311yescharacteristic
103D8×C269—41no—
104M16×C269—41no—
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C22⋊C4×C269—21no—
111C22×D269—21no—
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538#4112yes—
115D1076—21no—
116D1076—21no—
117D1076—81no—
118C22⋊D269—41no—
119C22⋊D269—42no—
120C22⋊D269—42no—
121C22⋊D269—42no—
122C22⋊D269—81no—
123C22⋊D269—81no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—42no—
128C2×Dic269—81no—
129C2×Dic269—81no—
130C2×Dic269C2×D411yescharacteristic
131C2×Dic269C2×D411yescharacteristic
132C2×Dic269C2×D411yescharacteristic
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—42no—
136#14524130—21no—
137#14524130—21no—
138C23×C269—21no—
139C23×C269—21no—
140C23×C269C2×D411yescharacteristic
141D4×C269—21no—
142D4×C269—21no—
143D4×C269—21no—
144D4×C269—21no—
145D4×C269—42no—
146D4×C269—81no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269—41no—
164C22×C269C22×D411yescharacteristic
165C2×D269—21no—
166C2×D269—21no—
167C2×D269—21no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C4×C269—21no—
172C4×C269—41no—
173C4×C269—41no—
174C4×C269C2×#4111yescharacteristic
175C4×C269H(5,𝔽2)11yescharacteristic
176Dic269—21no—
177Dic269—22no—
178Dic269—21no—
179Dic269—21no—
180Dic269—41no—
181Dic269—41no—
182C2×C269—41no—
183C2×C269—81no—
184C2×C269—81no—
185C2×C269#54611yescharacteristic
186C2×C269#57511yescharacteristic
187C2×C269#57611yescharacteristic
188D269—41no—
189D269—81no—
190C269#330911yescharacteristic, complemented, Sylow
191#3309—2691nomaximal, Sylow
192#553—2691no—
193#550—2691no—
194#490—2691no—
195#482—2691no—
196#480—2691no—
197#479—2691no—
198#469D26911yescharacteristic, complemented
199#466—2691no—
200#459—2691no—
201#449—2691no—
202#449—2691no—
203#440—2691no—
204#435—2691no—
205#417—2691no—
206#416—2691no—
207C2×#41—2691no—
208C2×#41—2691no—
209C2×SD16—2691no—
210C2×D8—2691no—
211C2×D8C2×D26911yescharacteristic
212C2×M16C2×D26911yescharacteristic
213C22×C8—2691no—
214#127—2691no—
215#127—5381no—
216#126—5381no—
217#125—2691no—
218#123—5381no—
219#121—2691no—
220#121—2691no—
221#121—5381no—
222#121—5381no—
223#121—5381no—
224#121C2×D26911yescharacteristic
225#121C2×D26911yescharacteristic
226C4×Q8—2691no—
227C4×D4—2691no—
228C4×D4—2691no—
229C4×D4—5381no—
230C4×D4—5381no—
231#117—2691no—
232C2×C4⋊C4—2691no—
233#107—2691no—
234#107—2691no—
235#106C2×D26911yescharacteristic
236C4⋊C8—2691no—
237#103—2691no—
238#103—2691no—
239#103—2691no—
240#102—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102C2×D26911yescharacteristic
246#102C2×D26911yescharacteristic
247C22⋊C8—2691no—
248C22⋊C8—2691no—
249#97—2691no—
250#41—5382no—
251#41—5382no—
252#41—10761no—
253#41—10761no—
254C2×Q8—2691no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2691no—
258C2×D4—2691no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5381no—
263C2×D4—5381no—
264C2×D4—5381no—
265C2×D4C22×D26911yescharacteristic
266C2×D4C22×D26911yescharacteristic
267C22×C4—2691no—
268C22×C4—5381no—
269C22×C4—5381no—
270C22×C4—5381no—
271C22×C4—5381no—
272C22×C4C22×D26911yescharacteristic
273SD16—5382no—
274D8—41no—
275D8—10761no—
276M16—41no—
277C2×C8—2691no—
278C2×C8—2691no—
279C2×C8—10761no—
280C2×C8C22×D26911yescharacteristic
281C2×C8C22×D26911yescharacteristic
282C4⋊C4—2691no—
283C4⋊C4—2691no—
284C4⋊C4—2691no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4—5381no—
289C4⋊C4C22×D26911yescharacteristic
290C4⋊C4C22×D26911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—2691no—
294C22⋊C4—2691no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C42—2691no—
300C42—5381no—
301C42—5381no—
302C23—21no—
303C23—21no—
304C23—2691no—
305C23—5381no—
306C23D4×D26911yescharacteristic
307Q8—2692no—
308Q8—5381no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—5381no—
316D4—5381no—
317D4—10761no—
318D4—10762no—
319D4—10762no—
320D4—10762no—
321D4—21521no—
322D4—21521no—
323D4—21521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2691no—
329C2×C4—2691no—
330C2×C4—2691no—
331C2×C4—5381no—
332C2×C4—5381no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—10762no—
337C2×C4—10762no—
338C2×C4—21521no—
339C2×C4—21521no—
340C2×C4D4×D26911yescharacteristic
341C2×C4C23×D26911yescharacteristic
342C8—21no—
343C8—21no—
344C8—5381no—
345C8—5381no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—5381no—
356C22—5381no—
357C22—5381no—
358C22—10761no—
359C22—10761no—
360C22—10761no—
361C22C2×D4×D26911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—5381no—
366C4—5381no—
367C4—5381no—
368C4—5382no—
369C4—10761no—
370C4—10761no—
371C4#41×D26911yescharacteristic
372C4#2257549811yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—10761no—
377C2—21521no—
378C2#3177124411yescharacteristic
379C2#3177140111yescharacteristic
380C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#469×C269C2
socleC22×C269C22×D4
hypercenter#469D269
hypocenterC269#3309
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #31771307C2semidirect
2. #31771273C2semidirect
3. #31770968C2semidirect
4. #31770931C2semidirect
5. #31770916C2semidirect
6. #31770915C2semidirect
7. #31770840C2semidirect
8. #31770798C2semidirect
9. #31770748C2semidirect
10. #31770747C2semidirect
11. #31770702C2semidirect
12. #31770674C2semidirect
13. #31770607C2semidirect
14. #31770598C2semidirect
15. #469×C269C2semidirect
190. C269#3309semidirect
198. #469D269semidirect

Maximal subgroups

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

subgroupindex
#317713072
#317712732
#317709682
#317709312
#317709162
#317709152
#317708402
#317707982
#317707482
#317707472
#317707022
#317706742
#317706072
#317705982
#469×C2692
#3309269