Finite Group Databasebeta

← #46819958

Subgroups — #46819958

Order 34432.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771151C211yesmaximal, characteristic
2#31770681C211yesmaximal, characteristic, complemented
3#31770680C211yesmaximal, characteristic, complemented
4#31770679C211yesmaximal, characteristic, complemented
5#31770676C211yesmaximal, characteristic, complemented
6#31770674C211yesmaximal, characteristic, complemented
7#31770673C211yesmaximal, characteristic, complemented
8C8×C22⋊D269C211yesmaximal, characteristic, complemented
9#31770668C211yesmaximal, characteristic, complemented
10#31770659C211yesmaximal, characteristic, complemented
11#31770655C211yesmaximal, characteristic, complemented
12#31770572C211yesmaximal, characteristic, complemented
13#31770570C211yesmaximal, characteristic, complemented
14#31770570C211yesmaximal, characteristic, complemented
15#408×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864386C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C2×#16864385C2211yescharacteristic
20C22×#14524130C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic
22C2×C8×D269C2211yescharacteristic
23#22575451C411yescharacteristic
24#22575449C411yescharacteristic
25#22575442C411yescharacteristic
26#22575440C411yescharacteristic
27#22575425C411yescharacteristic
28#22575425C411yescharacteristic
29#22575425C411yescharacteristic
30#22575425C411yescharacteristic
31C4×C22⋊D269C2211yescharacteristic
32C4×C22⋊D269C2211yescharacteristic
33C4×C22⋊D269C2211yescharacteristic
34C4×C22⋊D269C2211yescharacteristic
35C2×C4×Dic269C2211yescharacteristic
36#22575382C2211yescharacteristic
37#22575382C2211yescharacteristic
38#22575382C2211yescharacteristic
39#22575382C2211yescharacteristic
40C22⋊#14524130C2211yescharacteristic
41C22⋊#14524130C2211yescharacteristic
42C22⋊#14524130C2211yescharacteristic
43C22⋊#14524130C2211yescharacteristic
44#22575365C2211yescharacteristic
45#22575365C2211yescharacteristic
46#22575365C2211yescharacteristic
47#22575365C2211yescharacteristic
48#22575363C2211yescharacteristic
49#22575363C2211yescharacteristic
50C8×Dic269C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×#41×C269C2211yescharacteristic
53C2×M16×C269C2211yescharacteristic
54C22×C8×C269C2211yescharacteristic
55C22⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57C22⋊C8×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59#16864402—41no—
60#16864402—41no—
61C2×Dic538C2×C411yescharacteristic
62C2×D1076C2×C411yescharacteristic
63C2×C22⋊D269C2×C411yescharacteristic
64C2×C22⋊D269C2×C411yescharacteristic
65C2×C22⋊D269C2×C411yescharacteristic
66C2×C22⋊D269C2×C411yescharacteristic
67C2×C22⋊D269C2×C411yescharacteristic
68C2×C22⋊D269C2×C411yescharacteristic
69C22×Dic269C2×C411yescharacteristic
70C22×Dic269C2×C411yescharacteristic
71C2×C4×D269C2311yescharacteristic
72C2×C4×D269C2311yescharacteristic
73#16864386—41no—
74#16864385—41no—
75#16864385—41no—
76C2×#14524130—41no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C2×#14524130C2311yescharacteristic
81C8×D269—41no—
82C8×D269—41no—
83#16864381C2×C411yescharacteristic
84#16864381C2×C411yescharacteristic
85#16864381C2×C411yescharacteristic
86#16864381C2×C411yescharacteristic
87C22⋊Dic269C2×C411yescharacteristic
88C22⋊Dic269C2×C411yescharacteristic
89C22⋊Dic269C2×C411yescharacteristic
90C22⋊Dic269C2×C411yescharacteristic
91#16864379C2×C411yescharacteristic
92#16864379C2×C411yescharacteristic
93#16864379C2×C411yescharacteristic
94#16864379C2×C411yescharacteristic
95C4×Dic269C2×C411yescharacteristic
96C4×Dic269C2×C411yescharacteristic
97C4×Dic269C2311yescharacteristic
98C4×Dic269C2311yescharacteristic
99#41×C269—41no—
100#41×C269—41no—
101C2×Q8×C269C2×C411yescharacteristic
102C2×D4×C269C2×C411yescharacteristic
103C2×D4×C269C2×C411yescharacteristic
104C2×D4×C269C2×C411yescharacteristic
105C22×C4×C269C2311yescharacteristic
106C22×C4×C269C2311yescharacteristic
107C22×C4×C269C2311yescharacteristic
108M16×C269—41no—
109C2×C8×C269—41no—
110C2×C8×C269C2311yescharacteristic
111C2×C8×C269C2311yescharacteristic
112C2×C8×C269C2311yescharacteristic
113C2×C8×C269C2311yescharacteristic
114C22×D269C22×C411yescharacteristic
115C22×D269C22×C411yescharacteristic
116Dic538—41no—
117D1076—41no—
118C22⋊D269—22no—
119C22⋊D269—22no—
120C22⋊D269—41no—
121C22⋊D269—41no—
122C22⋊D269—41no—
123C22⋊D269—41no—
124C2×Dic269—22no—
125C2×Dic269—41no—
126C2×Dic269C22×C411yescharacteristic
127C2×Dic269C22×C411yescharacteristic
128C2×Dic269C22×C411yescharacteristic
129C2×Dic269C22×C411yescharacteristic
130C2×Dic269C22×C411yescharacteristic
131C2×Dic269C22×C411yescharacteristic
132C4×D269—21no—
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—21no—
136#14524130—21no—
137#14524130—21no—
138#14524130—21no—
139#14524130—21no—
140C23×C269C22×C411yescharacteristic
141C23×C269C22×C411yescharacteristic
142C23×C269C22×C411yescharacteristic
143Q8×C269—41no—
144D4×C269—41no—
145D4×C269—41no—
146D4×C269—41no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269—21no—
152C2×C4×C269—21no—
153C2×C4×C269C22×C411yescharacteristic
154C2×C4×C269C22×C411yescharacteristic
155C2×C4×C269C22×C411yescharacteristic
156C2×C4×C269C2411yescharacteristic
157C8×C269—21no—
158C8×C269—21no—
159C8×C269—21no—
160C8×C269—21no—
161C22×C269—21no—
162C22×C269—21no—
163C22×C269—21no—
164C22×C269—21no—
165C22×C269—21no—
166C22×C269—21no—
167C22×C269—21no—
168C22×C269—21no—
169C22×C269—21no—
170C22×C269C23×C411yescharacteristic
171C2×D269—21no—
172C2×D269—21no—
173C2×D269—21no—
174C2×D269—21no—
175C2×D269—21no—
176C2×D269—21no—
177C4×C269—21no—
178C4×C269—21no—
179C4×C269—21no—
180C4×C269H(5,𝔽2)11yescharacteristic
181C4×C269H(5,𝔽2)11yescharacteristic
182Dic269—21no—
183Dic269—21no—
184Dic269—21no—
185Dic269—21no—
186Dic269—21no—
187Dic269#13112yes—
188C2×C269—41no—
189C2×C269—41no—
190C2×C269—41no—
191C2×C269#51811yescharacteristic
192C2×C269C2×#13111yescharacteristic
193C2×C269#56811yescharacteristic
194D269—41no—
195D269—41no—
196C269#298111yescharacteristic, complemented, Sylow
197#2981—2691nomaximal, Sylow
198#532—2691no—
199#436—2691no—
200#436—2691no—
201#435—2691no—
202#435—2691no—
203#435—2691no—
204#435—2691no—
205C8×D4—2691no—
206C8×D4—2691no—
207#432—2691no—
208#431—2691no—
209#408—2691no—
210#408—2691no—
211#408—2691no—
212#408D26911yescharacteristic, complemented
213C2×#41—2691no—
214C2×#41C2×D26911yescharacteristic
215C2×M16—2691no—
216C2×M16—2691no—
217C2×M16—2691no—
218C2×M16C2×D26911yescharacteristic
219C22×C8—2691no—
220C22×C8—2691no—
221C22×C8—2691no—
222C22×C8C2×D26911yescharacteristic
223C4⋊Q8—2691no—
224#127—2691no—
225#124—2691no—
226#124—2691no—
227#121—2691no—
228#121—2691no—
229#121—2691no—
230#121—2691no—
231C4×D4—2691no—
232C4×D4—2691no—
233C4×D4—2691no—
234C4×D4—2691no—
235C2×C42—2691no—
236C4⋊C8—2691no—
237C4⋊C8—2691no—
238C4⋊C8—2691no—
239C4⋊C8—2691no—
240C22⋊C8—2691no—
241C22⋊C8—2691no—
242C22⋊C8—2691no—
243C22⋊C8—2691no—
244C22⋊C8—2691no—
245C22⋊C8—2691no—
246C22⋊C8—2691no—
247C22⋊C8—2691no—
248C22⋊C8C2×D26911yescharacteristic
249C22⋊C8C2×D26911yescharacteristic
250C22⋊C8C2×D26911yescharacteristic
251C22⋊C8C2×D26911yescharacteristic
252#97—2691no—
253#97—2691no—
254C4×C8—2691no—
255C4×C8—2691no—
256#41—41no—
257#41—41no—
258#41—10761no—
259#41—10761no—
260C2×Q8—2691no—
261C2×Q8C4×D26911yescharacteristic
262C2×D4—2691no—
263C2×D4—2691no—
264C2×D4—2691no—
265C2×D4—2691no—
266C2×D4—2691no—
267C2×D4—2691no—
268C2×D4—2691no—
269C2×D4C4×D26911yescharacteristic
270C2×D4C4×D26911yescharacteristic
271C2×D4C4×D26911yescharacteristic
272C22×C4—2691no—
273C22×C4—2691no—
274C22×C4—2691no—
275C22×C4—2691no—
276C22×C4C22×D26911yescharacteristic
277C22×C4C22×D26911yescharacteristic
278C22×C4C22×D26911yescharacteristic
279M16—41no—
280M16—10761no—
281M16—10761no—
282M16—10761no—
283C2×C8—41no—
284C2×C8—2691no—
285C2×C8—2691no—
286C2×C8—2691no—
287C2×C8—2691no—
288C2×C8—10761no—
289C2×C8—10761no—
290C2×C8—10761no—
291C2×C8C22×D26911yescharacteristic
292C2×C8C22×D26911yescharacteristic
293C2×C8C22×D26911yescharacteristic
294C2×C8C22×D26911yescharacteristic
295C4⋊C4—2691no—
296C4⋊C4—2691no—
297C4⋊C4—2691no—
298C4⋊C4—2691no—
299C22⋊C4—2691no—
300C22⋊C4—2691no—
301C22⋊C4—2691no—
302C22⋊C4—2691no—
303C22⋊C4—2691no—
304C22⋊C4—2691no—
305C22⋊C4—2691no—
306C22⋊C4—2691no—
307C42—2691no—
308C42—2691no—
309C42—2691no—
310C42—2691no—
311C23—2691no—
312C23—2691no—
313C23C2×C4×D26911yescharacteristic
314C23C2×C4×D26911yescharacteristic
315C23C2×C4×D26911yescharacteristic
316Q8—41no—
317Q8—10761no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—5382no—
322D4—5382no—
323D4—10761no—
324D4—10761no—
325D4—10761no—
326D4—10761no—
327D4—10761no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2691no—
335C2×C4—2691no—
336C2×C4—2691no—
337C2×C4—2691no—
338C2×C4—2691no—
339C2×C4—2691no—
340C2×C4—5382no—
341C2×C4—5381no—
342C2×C4—5381no—
343C2×C4—5381no—
344C2×C4—5381no—
345C2×C4—10761no—
346C2×C4C2×C4×D26911yescharacteristic
347C2×C4C2×C4×D26911yescharacteristic
348C2×C4C2×C4×D26911yescharacteristic
349C2×C4C23×D26911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—5381no—
355C8—5381no—
356C8—5381no—
357C8—5381no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—5381no—
368C22—5381no—
369C22—5381no—
370C22—5381no—
371C22—5381no—
372C22—5381no—
373C22C22×C4×D26911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—2692no—
378C4—5381no—
379C4—5381no—
380C4—5381no—
381C4—5381no—
382C4—5381no—
383C4#2257549811yescharacteristic
384C4#2257549811yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—10761no—
389C2—10761no—
390C2#3177107811yescharacteristic
391C2#131×D26911yescharacteristic
392C2#3177137011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D269
commutator, socleC22×C269C23×C4
Fitting#408×C269C2
prime radical#31771151C2
cosocleC2×C4×C269C24
hypercenter#408D269
hypocenterC269#2981
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #31770681C2semidirect
3. #31770680C2semidirect
4. #31770679C2semidirect
5. #31770676C2semidirect
6. #31770674C2semidirect
7. #31770673C2semidirect
8. C8×C22⋊D269C2semidirect
9. #31770668C2semidirect
10. #31770659C2semidirect
11. #31770655C2semidirect
12. #31770572C2semidirect
13. #31770570C2semidirect
14. #31770570C2semidirect
15. #408×C269C2semidirect
196. C269#2981semidirect
212. #408D269semidirect

Maximal subgroups

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

subgroupindex
#317711512
#317706812
#317706802
#317706792
#317706762
#317706742
#317706732
C8×C22⋊D2692
#317706682
#317706592
#317706552
#317705722
#317705702
#408×C2692
#2981269