Finite Group Databasebeta

← #46813673

Subgroups — #46813673

Order 34432.

532 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575435C211yesmaximal, characteristic
2#31770505C211yesmaximal, characteristic
3#31770501C211yesmaximal, characteristic, complemented
4#31770499C211yesmaximal, characteristic, complemented
5#31770495C211yesmaximal, characteristic, complemented
6#31770494C211yesmaximal, characteristic, complemented
7#31770490C211yesmaximal, characteristic, complemented
8#31770489C211yesmaximal, characteristic, complemented
9#31770482C211yesmaximal, characteristic
10#31770477C211yesmaximal, characteristic, complemented
11#31770464C211yesmaximal, characteristic, complemented
12#31770456C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic269C211yesmaximal, characteristic, complemented
14C4×#16864379C211yesmaximal, characteristic, complemented
15#388×C269C211yesmaximal, characteristic, complemented
16C22×C22⋊D269C2211yescharacteristic
17C23×Dic269C2211yescharacteristic
18C22×C4×D269C2211yescharacteristic
19#22575435C418yescomplemented
20C2×C4⋊Dic269C2211yescharacteristic
21C2×#16864381C2211yescharacteristic
22C2×#16864381C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×C22⋊Dic269C2211yescharacteristic
27C2×C22⋊Dic269C2211yescharacteristic
28C2×#16864379C2211yescharacteristic
29C2×#16864379C2211yescharacteristic
30C2×#16864379C2211yescharacteristic
31C2×#16864379C2211yescharacteristic
32C2×#16864379C2211yescharacteristic
33C2×C4×Dic269C2211yescharacteristic
34C2×C4×Dic269C2211yescharacteristic
35C2×C4×Dic269C2211yescharacteristic
36C2×C4×Dic269C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45C2×C4⋊C4×C269C2211yescharacteristic
46C2×C22⋊C4×C269C2211yescharacteristic
47C2×C22⋊C4×C269C2211yescharacteristic
48C2×C22⋊C4×C269C2211yescharacteristic
49C2×C42×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C23×D269C2311yescharacteristic
53C2×C22⋊D269—41no—
54C2×C22⋊D269—41no—
55C2×C22⋊D269C2×C414yes—
56C22×Dic269—22no—
57C22×Dic269—41no—
58C22×Dic269—41no—
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C22×Dic269C2311yescharacteristic
64C22×Dic269C2311yescharacteristic
65C22×Dic269C2311yescharacteristic
66C2×C4×D269—41no—
67C2×C4×D269—41no—
68C2×C4×D269C2×C414yescomplemented
69C4⋊Dic269C2×C414yescomplemented
70#16864381—22no—
71#16864381—41no—
72#16864381—41no—
73#16864381—41no—
74#16864381C2×C414yescomplemented
75C22⋊Dic269—22no—
76C22⋊Dic269C2×C414yes—
77#16864379—22no—
78#16864379—22no—
79#16864379—41no—
80#16864379—41no—
81#16864379C2×C414yescomplemented
82C4×Dic269—22no—
83C4×Dic269—41no—
84C4×Dic269—41no—
85C4×Dic269—41no—
86C24×C269C2311yescharacteristic
87C22×C4×C269C2311yescharacteristic
88C22×C4×C269C2311yescharacteristic
89C22×C4×C269C2311yescharacteristic
90C22×C4×C269C2311yescharacteristic
91C22×C4×C269C2311yescharacteristic
92C22×C4×C269C2311yescharacteristic
93C4⋊C4×C269—41no—
94C22⋊C4×C269—41no—
95C22⋊C4×C269—41no—
96C22⋊C4×C269C2×C414yes—
97C42×C269—41no—
98C22×D269—21no—
99C22×D269—21no—
100C22×D269—21no—
101C22×D269—21no—
102C22×D269—21no—
103C22×D269—21no—
104C22×D269C22×C412yes—
105C22⋊D269—44no—
106C2×Dic269—21no—
107C2×Dic269—21no—
108C2×Dic269—21no—
109C2×Dic269—21no—
110C2×Dic269—21no—
111C2×Dic269—21no—
112C2×Dic269—21no—
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—44no—
123C2×Dic269C22×C412yes—
124C2×Dic269C22×C412yes—
125C2×Dic269C22×C412yes—
126C2×Dic269#4112yes—
127C2×Dic269#4112yes—
128C4×D269—44no—
129C23×C269—21no—
130C23×C269—21no—
131C23×C269—21no—
132C23×C269—21no—
133C23×C269—21no—
134C23×C269—21no—
135C23×C269C22×C412yes—
136C23×C269C2411yescharacteristic
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—
155C22×C269—22no—
156C22×C269—22no—
157C22×C269—22no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269C23×C411yescharacteristic
163C22×C269C2×#4111yescharacteristic
164C22×C269C2×#4111yescharacteristic
165C22×C269H(5,𝔽2)11yescharacteristic
166C22×C269H(5,𝔽2)11yescharacteristic
167C22×C269H(5,𝔽2)11yescharacteristic
168C22×C2692−1+411yescharacteristic
169C2×D269—22no—
170C2×D269—22no—
171C2×D269—22no—
172C2×D269—41no—
173C2×D269—41no—
174C2×D269—41no—
175C2×D269—41no—
176C4×C269—22no—
177C4×C269—22no—
178C4×C269—41no—
179C4×C269—41no—
180C4×C269—41no—
181C4×C269—41no—
182Dic269—22no—
183Dic269—22no—
184Dic269—22no—
185Dic269—22no—
186Dic269—22no—
187Dic269—41no—
188Dic269—41no—
189C2×C269—42no—
190C2×C269C4×#4111yescharacteristic
191C2×C269#51811yescharacteristic
192C2×C269#52011yescharacteristic
193C2×C269#53811yescharacteristic
194C2×C269#53911yescharacteristic
195C2×C269#54011yescharacteristic
196C2×C269#54211yescharacteristic
197D269—42no—
198C269#233511yescharacteristic, complemented, Sylow
199#2335—2691nomaximal, Sylow
200C2×#123—2691no—
201#390—2691no—
202#389—2691no—
203#388—2691no—
204#388—2691no—
205#388—2691no—
206#388D26911yescharacteristic, complemented
207#387—2691no—
208#387—2691no—
209#386—2691no—
210#385—2691no—
211#380—2691no—
212C4×C4⋊C4—2691no—
213C4×C22⋊C4—2691no—
214C4×C22⋊C4—2691no—
215C22×D4—2691no—
216C23×C4—2691no—
217C23×C4—2691no—
218#123—2698no—
219C2×C4⋊C4—2691no—
220C2×C4⋊C4—2691no—
221C2×C4⋊C4—2691no—
222C2×C4⋊C4—2691no—
223C2×C4⋊C4—2691no—
224C2×C4⋊C4—2691no—
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⋊C4C2×D26911yescharacteristic
234C2×C22⋊C4C2×D26911yescharacteristic
235C2×C22⋊C4C2×D26911yescharacteristic
236C2×C42—2691no—
237C2×C42—2691no—
238C2×C42—2691no—
239C2×C42—2691no—
240C2×C42C2×D26911yescharacteristic
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
251C24—2691no—
252C24C22×D26911yescharacteristic
253C2×D4—2694no—
254C2×D4—10761no—
255C2×D4—10761no—
256C22×C4—2691no—
257C22×C4—2691no—
258C22×C4—2691no—
259C22×C4—2691no—
260C22×C4—2691no—
261C22×C4—2694no—
262C22×C4—2691no—
263C22×C4—2691no—
264C22×C4—5382no—
265C22×C4—10761no—
266C22×C4—10761no—
267C22×C4—10761no—
268C22×C4—10761no—
269C22×C4C22×D26911yescharacteristic
270C22×C4C22×D26911yescharacteristic
271C22×C4C22×D26911yescharacteristic
272C22×C4C22×D26911yescharacteristic
273C22×C4C22×D26911yescharacteristic
274C22×C4C22×D26911yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—2694no—
277C4⋊C4—2694no—
278C4⋊C4—5382no—
279C4⋊C4—10761no—
280C4⋊C4—10761no—
281C4⋊C4—10761no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—2694no—
285C22⋊C4—2694no—
286C22⋊C4—5382no—
287C22⋊C4—5382no—
288C22⋊C4—5382no—
289C22⋊C4—10761no—
290C22⋊C4—10761no—
291C22⋊C4C4×D26914yes—
292C42—41no—
293C42—5382no—
294C42—10761no—
295C42—10761no—
296C42—10761no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—2692no—
304C23—5381no—
305C23—5381no—
306C23—5381no—
307C23—5381no—
308C23—5381no—
309C23—5381no—
310C23C2×C4×D26912yes—
311C23C23×D26911yescharacteristic
312D4—10764no—
313C2×C4—21no—
314C2×C4—21no—
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—2692no—
330C2×C4—2692no—
331C2×C4—2692no—
332C2×C4—2692no—
333C2×C4—2692no—
334C2×C4—5381no—
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×C4C2×C4×D26912yes—
353C2×C4C2×C4×D26912yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—5382no—
362C22—5382no—
363C22—5382no—
364C22—10761no—
365C22—10761no—
366C22—10761no—
367C22—10761no—
368C22C22×C4×D26911yescharacteristic
369C22#41×D26911yescharacteristic
370C22#41×D26911yescharacteristic
371C22#2257549811yescharacteristic
372C22#2257549811yescharacteristic
373C22#2257549911yescharacteristic
374C22#2257550011yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—5382no—
382C4—5382no—
383C4—5382no—
384C4—5382no—
385C4—5382no—
386C4—10761no—
387C4—10761no—
388C2—42no—
389C2—10762no—
390C2#3177107311yescharacteristic
391C2#3177107711yescharacteristic
392C2#3177108411yescharacteristic
393C2#3177118911yescharacteristic
394C2#3177119611yescharacteristic
395C2#3177120511yescharacteristic
396C2#3177122311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#388×C269C2
socle, cosocleC23×C269C24
prime radicalC22×C22⋊D269C22
hypercenter#388D269
hypocenterC269#2335
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #31770501C2semidirect
4. #31770499C2semidirect
5. #31770495C2semidirect
6. #31770494C2semidirect
7. #31770490C2semidirect
8. #31770489C2semidirect
10. #31770477C2semidirect
11. #31770464C2semidirect
12. #31770456C2semidirect
13. C22⋊C4×Dic269C2semidirect
14. C4×#16864379C2semidirect
15. #388×C269C2semidirect
19. #22575435C4semidirect
68. C2×C4×D269C2×C4semidirect
69. C4⋊Dic269C2×C4semidirect
74. #16864381C2×C4semidirect
81. #16864379C2×C4semidirect
198. C269#2335semidirect
206. #388D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754352
#317705052
#317705012
#317704992
#317704952
#317704942
#317704902
#317704892
#317704822
#317704772
#317704642
#317704562
C22⋊C4×Dic2692
C4×#168643792
#388×C2692
#2335269