Finite Group Databasebeta

← #46813824

Subgroups — #46813824

Order 34432.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575415C211yesmaximal, characteristic
2#31770497C211yesmaximal, characteristic, complemented
3#31770495C211yesmaximal, characteristic, complemented
4#31770491C211yesmaximal, characteristic, complemented
5#31770483C211yesmaximal, characteristic
6#31770483C211yesmaximal, characteristic
7#31770472C211yesmaximal, characteristic, complemented
8#31770467C211yesmaximal, characteristic, complemented
9#31770462C211yesmaximal, characteristic, complemented
10C4×#16864379C211yesmaximal, characteristic, complemented
11C4×#16864379C211yesmaximal, characteristic, complemented
12#31770452C211yesmaximal, characteristic, complemented
13#31770450C211yesmaximal, characteristic, complemented
14#95×D269C211yesmaximal, characteristic, complemented
15#387×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic
17C22×C4×D269C2211yescharacteristic
18C22×C4×D269C2211yescharacteristic
19C22×C4×D269C2211yescharacteristic
20C22×C4×D269C2211yescharacteristic
21#22575415C418yescomplemented
22C2×C4⋊Dic269C2211yescharacteristic
23C2×#16864379C2211yescharacteristic
24C2×#16864379C2211yescharacteristic
25C2×#16864379C2211yescharacteristic
26C2×#16864379C2211yescharacteristic
27C2×#16864379C2211yescharacteristic
28C2×#16864379C2211yescharacteristic
29C2×#16864379C2211yescharacteristic
30C2×#16864379C2211yescharacteristic
31C2×C4×Dic269C2211yescharacteristic
32C2×C4×Dic269C2211yescharacteristic
33C2×C4×Dic269C2211yescharacteristic
34C2×C4×Dic269C2211yescharacteristic
35#22575360C2211yescharacteristic
36#22575360C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45C2×C4⋊C4×C269C2211yescharacteristic
46C2×C4⋊C4×C269C2211yescharacteristic
47C2×C42×C269C2211yescharacteristic
48#95×C269C2211yescharacteristic
49#95×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C23×D269C2311yescharacteristic
53C23×D269C2311yescharacteristic
54C2×D1076—22no—
55C2×D1076—22no—
56C2×D1076C2×C414yes—
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C2×C4×D269—22no—
64C2×C4×D269—22no—
65C2×C4×D269—22no—
66C2×C4×D269—22no—
67C2×C4×D269—41no—
68C2×C4×D269—41no—
69C2×C4×D269—41no—
70C2×C4×D269—41no—
71C2×C4×D269—41no—
72C2×C4×D269—41no—
73C2×C4×D269C2×C414yes—
74C2×C4×D269C2×C414yescomplemented
75C4⋊Dic269—41no—
76#16864379—22no—
77#16864379—22no—
78#16864379—22no—
79#16864379—22no—
80#16864379—41no—
81#16864379—41no—
82#16864379C2×C414yes—
83#16864379C2×C414yescomplemented
84C4×Dic269—22no—
85C4×Dic269—22no—
86C4×Dic269—41no—
87C4×Dic269C2×C414yescomplemented
88C22×C4×C269C2311yescharacteristic
89C22×C4×C269C2311yescharacteristic
90C22×C4×C269C2311yescharacteristic
91C22×C4×C269C2311yescharacteristic
92C22×C4×C269C2311yescharacteristic
93C22×C4×C269C2311yescharacteristic
94C22×C4×C269C2311yescharacteristic
95C4⋊C4×C269—41no—
96C4⋊C4×C269C2×C414yescomplemented
97C42×C269—41no—
98C22×D269—21no—
99C22×D269—21no—
100C22×D269—21no—
101C22×D269—21no—
102C22×D269—21no—
103C22×D269—21no—
104C22×D269—21no—
105C22×D269—21no—
106C22×D269—21no—
107C22×D269—21no—
108C22×D269C22×C412yes—
109C22×D269C22×C412yes—
110C22×D269#4112yes—
111C22×D269#4112yes—
112D1076—28no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269C22×C412yes—
129C2×Dic269C22×C412yes—
130C2×Dic269#4112yes—
131C4×D269—44no—
132C4×D269—44no—
133C4×D269—44no—
134C4×D269—44no—
135C23×C269C2411yescharacteristic
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
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×C412yes—
154C2×C4×C269C22×C412yes—
155C2×C4×C269C22×C412yes—
156C2×C4×C269#4112yes—
157C22×C269C23×C411yescharacteristic
158C22×C269C2×#4111yescharacteristic
159C22×C269C2×#4111yescharacteristic
160C22×C269C2×#4111yescharacteristic
161C22×C269C2×#4111yescharacteristic
162C22×C269H(5,𝔽2)11yescharacteristic
163C22×C269H(5,𝔽2)11yescharacteristic
164C2×D269—22no—
165C2×D269—22no—
166C2×D269—22no—
167C2×D269—22no—
168C2×D269—22no—
169C2×D269—22no—
170C2×D269—22no—
171C2×D269—22no—
172C2×D269—22no—
173C2×D269—41no—
174C2×D269—41no—
175C2×D269—41no—
176C2×D269—41no—
177C2×D269#11714yes—
178C4×C269—22no—
179C4×C269—22no—
180C4×C269—22no—
181C4×C269—22no—
182C4×C269—41no—
183C4×C269—41no—
184C4×C269—41no—
185Dic269—22no—
186Dic269—22no—
187Dic269—22no—
188Dic269—41no—
189Dic269—41no—
190Dic269—41no—
191C2×C269C2×#11711yescharacteristic
192C2×C269C4×#4111yescharacteristic
193C2×C269#51811yescharacteristic
194C2×C269#55111yescharacteristic
195C2×C269#55111yescharacteristic
196C2×C269#55311yescharacteristic
197C2×C269#55311yescharacteristic
198D269—24no—
199D269—42no—
200C269#235311yescharacteristic, complemented, Sylow
201#2353—2691nomaximal, Sylow
202C2×C4×D4—2691no—
203#388—2691no—
204#388—2691no—
205#387—2691no—
206#387D26911yescharacteristic, complemented
207#386—2691no—
208#386—2691no—
209#383—2691no—
210#381—2691no—
211#380—2691no—
212C4×C22⋊C4—2691no—
213C4×C22⋊C4—2691no—
214C4×C22⋊C4—2691no—
215#376—2691no—
216C2×#95—2691no—
217C22×D4—2691no—
218C23×C4—2691no—
219C23×C4—2691no—
220C23×C4—2691no—
221C23×C4—2691no—
222C4×D4—2698no—
223C2×C4⋊C4—2691no—
224C2×C4⋊C4C2×D26911yescharacteristic
225C2×C4⋊C4C2×D26911yescharacteristic
226C2×C22⋊C4—2691no—
227C2×C22⋊C4—2691no—
228C2×C22⋊C4—2691no—
229C2×C22⋊C4—2691no—
230C2×C22⋊C4—2691no—
231C2×C22⋊C4—2691no—
232C2×C22⋊C4—2691no—
233C2×C22⋊C4—2691no—
234C2×C42—2691no—
235C2×C42—2691no—
236C2×C42—2691no—
237C2×C42—2691no—
238C2×C42C2×D26911yescharacteristic
239#95—2691no—
240#95—2691no—
241#95—2691no—
242#95—2691no—
243#95—2691no—
244#95—2691no—
245#95—2691no—
246#95—2691no—
247#95—2691no—
248#95—2691no—
249#95C2×D26911yescharacteristic
250#95C2×D26911yescharacteristic
251#95C2×D26911yescharacteristic
252#95C2×D26911yescharacteristic
253C24—2691no—
254C24—2691no—
255C2×D4—2694no—
256C2×D4—5382no—
257C2×D4—5382no—
258C22×C4—2691no—
259C22×C4—2691no—
260C22×C4—2691no—
261C22×C4—2694no—
262C22×C4—2694no—
263C22×C4—2691no—
264C22×C4—2691no—
265C22×C4—2691no—
266C22×C4—5382no—
267C22×C4—5382no—
268C22×C4—5382no—
269C22×C4—5382no—
270C22×C4—10761no—
271C22×C4—10761no—
272C22×C4—10761no—
273C22×C4—10761no—
274C22×C4—10761no—
275C22×C4—10761no—
276C22×C4C22×D26911yescharacteristic
277C22×C4C22×D26911yescharacteristic
278C22×C4C22×D26911yescharacteristic
279C22×C4C22×D26911yescharacteristic
280C22×C4C22×D26911yescharacteristic
281C22×C4C22×D26911yescharacteristic
282C22×C4C22×D26911yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—10761no—
285C4⋊C4C4×D26914yescomplemented
286C22⋊C4—2694no—
287C22⋊C4—2694no—
288C22⋊C4—5382no—
289C22⋊C4—5382no—
290C22⋊C4—5382no—
291C22⋊C4—5382no—
292C22⋊C4—10761no—
293C22⋊C4—10761no—
294C42—41no—
295C42—2694no—
296C42—5382no—
297C42—5382no—
298C42—10761no—
299C23—2692no—
300C23—2692no—
301C23—2692no—
302C23—2692no—
303C23—5381no—
304C23—5381no—
305C23—5381no—
306C23—5381no—
307C23—5381no—
308C23—5381no—
309C23—5381no—
310C23—5381no—
311C23—5381no—
312C23—5381no—
313C23C23×D26911yescharacteristic
314D4—5388no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2692no—
333C2×C4—2692no—
334C2×C4—2692no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—5381no—
338C2×C4—5381no—
339C2×C4—5381no—
340C2×C4—5381no—
341C2×C4—5381no—
342C2×C4—5381no—
343C2×C4—5381no—
344C2×C4—5381no—
345C2×C4—5381no—
346C2×C4—5381no—
347C2×C4—5381no—
348C2×C4—5381no—
349C2×C4—5381no—
350C2×C4—10764no—
351C2×C4—10764no—
352C2×C4—10764no—
353C2×C4—10764no—
354C2×C4C2×C4×D26912yes—
355C2×C4C2×C4×D26912yes—
356C2×C4C2×C4×D26912yes—
357C2×C4#1686440312yes—
358C22—2694no—
359C22—5382no—
360C22—5382no—
361C22—5382no—
362C22—5382no—
363C22—5382no—
364C22—5382no—
365C22—5382no—
366C22—5382no—
367C22—5382no—
368C22—10761no—
369C22—10761no—
370C22—10761no—
371C22—10761no—
372C22C22×C4×D26911yescharacteristic
373C22#41×D26911yescharacteristic
374C22#41×D26911yescharacteristic
375C22#41×D26911yescharacteristic
376C22C2×#1686440311yescharacteristic
377C22#2257549811yescharacteristic
378C22#2257549911yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—5382no—
387C4—5382no—
388C4—5382no—
389C4—10761no—
390C4—10761no—
391C4—10761no—
392C2—5384no—
393C2—10762no—
394C2#117×D26911yescharacteristic
395C2C4×#1686440311yescharacteristic
396C2#3177107711yescharacteristic
397C2#3177128011yescharacteristic
398C2#3177128211yescharacteristic
399C2#3177130011yescharacteristic
400C2#3177130811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#387×C269C2
socle, cosocleC23×C269C24
prime radicalC22×D1076C22
hypercenter#387D269
hypocenterC269#2353
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31770497C2semidirect
3. #31770495C2semidirect
4. #31770491C2semidirect
7. #31770472C2semidirect
8. #31770467C2semidirect
9. #31770462C2semidirect
10. C4×#16864379C2semidirect
11. C4×#16864379C2semidirect
12. #31770452C2semidirect
13. #31770450C2semidirect
14. #95×D269C2semidirect
15. #387×C269C2semidirect
21. #22575415C4semidirect
74. C2×C4×D269C2×C4semidirect
83. #16864379C2×C4semidirect
87. C4×Dic269C2×C4semidirect
96. C4⋊C4×C269C2×C4semidirect
200. C269#2353semidirect
206. #387D269semidirect
285. C4⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754152
#317704972
#317704952
#317704912
#317704832
#317704722
#317704672
#317704622
C4×#168643792
#317704522
#317704502
#95×D2692
#387×C2692
#2353269