Finite Group Databasebeta

← #46813670

Subgroups — #46813670

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#31770502C211yesmaximal, characteristic, complemented
4#31770499C211yesmaximal, characteristic, complemented
5#31770498C211yesmaximal, characteristic, complemented
6#31770495C211yesmaximal, characteristic, complemented
7#31770494C211yesmaximal, characteristic, complemented
8#31770490C211yesmaximal, characteristic, complemented
9#31770486C211yesmaximal, characteristic, complemented
10#31770484C211yesmaximal, characteristic
11#31770462C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic269C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic269C211yesmaximal, characteristic, complemented
14#31770452C211yesmaximal, characteristic, complemented
15#385×C269C211yesmaximal, characteristic, complemented
16C22×C22⋊D269C2211yescharacteristic
17C22×C4×D269C2211yescharacteristic
18#22575435C418yescomplemented
19C2×C4⋊Dic269C2211yescharacteristic
20C2×C4⋊Dic269C2211yescharacteristic
21C2×#16864381C2211yescharacteristic
22C2×#16864381C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×C22⋊Dic269C2211yescharacteristic
25C2×C22⋊Dic269C2211yescharacteristic
26C2×C22⋊Dic269C2211yescharacteristic
27C2×#16864379C2211yescharacteristic
28C2×#16864379C2211yescharacteristic
29C2×#16864379C2211yescharacteristic
30C2×#16864379C2211yescharacteristic
31C2×#16864379C2211yescharacteristic
32C2×C4×Dic269C2211yescharacteristic
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
45C23×C4×C269C2211yescharacteristic
46C2×C4⋊C4×C269C2211yescharacteristic
47C2×C4⋊C4×C269C2211yescharacteristic
48C2×C22⋊C4×C269C2211yescharacteristic
49C2×C22⋊C4×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C23×D269C2311yescharacteristic
53C2×C22⋊D269—41no—
54C2×C22⋊D269—41no—
55C2×C22⋊D269C2×C414yes—
56C22×Dic269C2311yescharacteristic
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C2×C4×D269—41no—
64C2×C4×D269—41no—
65C2×C4×D269C2×C414yescomplemented
66C4⋊Dic269—41no—
67C4⋊Dic269C2×C414yescomplemented
68#16864381—41no—
69#16864381—41no—
70#16864381C2×C414yescomplemented
71C22⋊Dic269—22no—
72C22⋊Dic269—41no—
73C22⋊Dic269C2×C414yes—
74#16864379—22no—
75#16864379—22no—
76#16864379—41no—
77#16864379—41no—
78#16864379C2×C414yescomplemented
79C4×Dic269—22no—
80C4×Dic269—41no—
81C4×Dic269—41no—
82C4×Dic269—41no—
83C4×Dic269—41no—
84C24×C269C2311yescharacteristic
85C22×C4×C269—22no—
86C22×C4×C269—41no—
87C22×C4×C269—41no—
88C22×C4×C269C2311yescharacteristic
89C22×C4×C269C2311yescharacteristic
90C22×C4×C269C2311yescharacteristic
91C22×C4×C269C2311yescharacteristic
92C22×C4×C269C2311yescharacteristic
93C22×C4×C269C2311yescharacteristic
94C4⋊C4×C269—22no—
95C4⋊C4×C269—41no—
96C22⋊C4×C269—41no—
97C22⋊C4×C269C2×C414yes—
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—21no—
123C2×Dic269C22×C412yes—
124C2×Dic269C22×C412yes—
125C2×Dic269C22×C412yes—
126C2×Dic269#4112yes—
127C4×D269—44no—
128C23×C269—21no—
129C23×C269—21no—
130C23×C269—21no—
131C23×C269—21no—
132C23×C269—21no—
133C23×C269—21no—
134C23×C269C22×C412yes—
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—44no—
152C2×C4×C269C22×C412yes—
153C2×C4×C269C22×C412yes—
154C2×C4×C269#4112yes—
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—22no—
179C4×C269—41no—
180C4×C269—41no—
181C4×C269—41no—
182Dic269—22no—
183Dic269—22no—
184Dic269—22no—
185Dic269—22no—
186Dic269—41no—
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#388—2691no—
207#387—2691no—
208#387—2691no—
209#386—2691no—
210#385D26911yescharacteristic, complemented
211#380—2691no—
212C4×C4⋊C4—2691no—
213C4×C22⋊C4—2691no—
214C4×C22⋊C4—2691no—
215C22×D4—2691no—
216C23×C4—2691no—
217C23×C4C2×D26911yescharacteristic
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⋊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×C22⋊C4C2×D26911yescharacteristic
235C2×C22⋊C4C2×D26911yescharacteristic
236C2×C42—2691no—
237C2×C42—2691no—
238C2×C42—2691no—
239C2×C42—2691no—
240C2×C42—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
251C24—2691no—
252C24C22×D26911yescharacteristic
253C2×D4—2694no—
254C2×D4—10761no—
255C2×D4—10761no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—2691no—
260C22×C4—2691no—
261C22×C4—2691no—
262C22×C4—2691no—
263C22×C4—2694no—
264C22×C4—2691no—
265C22×C4—2691no—
266C22×C4—2691no—
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—22no—
276C4⋊C4—41no—
277C4⋊C4—2694no—
278C4⋊C4—2694no—
279C4⋊C4—10761no—
280C4⋊C4—10761no—
281C4⋊C4—10761no—
282C22⋊C4—41no—
283C22⋊C4—2694no—
284C22⋊C4—2694no—
285C22⋊C4—5382no—
286C22⋊C4—5382no—
287C22⋊C4—5382no—
288C22⋊C4—10761no—
289C22⋊C4—10761no—
290C22⋊C4—10761no—
291C22⋊C4C4×D26914yes—
292C42—5382no—
293C42—10761no—
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—44no—
329C2×C4—2692no—
330C2×C4—2692no—
331C2×C4—2692no—
332C2×C4—2692no—
333C2×C4—5381no—
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×C4C2×C4×D26912yes—
352C2×C4C2×C4×D26912yes—
353C2×C4#1686440112yes—
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
370C22C2×#1686440111yescharacteristic
371C22#2257549811yescharacteristic
372C22#2257549811yescharacteristic
373C22#2257549911yescharacteristic
374C22#2257550111yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—5382no—
382C4—5382no—
383C4—5382no—
384C4—5382no—
385C4—10761no—
386C4—10761no—
387C4—10761no—
388C2—42no—
389C2—10762no—
390C2C4×#1686440111yescharacteristic
391C2#3177107711yescharacteristic
392C2#3177108611yescharacteristic
393C2#3177119011yescharacteristic
394C2#3177120111yescharacteristic
395C2#3177120711yescharacteristic
396C2#3177122811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#385×C269C2
socle, cosocleC23×C269C24
prime radicalC22×C22⋊D269C22
hypercenter#385D269
hypocenterC269#2335
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #31770502C2semidirect
4. #31770499C2semidirect
5. #31770498C2semidirect
6. #31770495C2semidirect
7. #31770494C2semidirect
8. #31770490C2semidirect
9. #31770486C2semidirect
11. #31770462C2semidirect
12. C4⋊C4×Dic269C2semidirect
13. C4×C22⋊Dic269C2semidirect
14. #31770452C2semidirect
15. #385×C269C2semidirect
18. #22575435C4semidirect
65. C2×C4×D269C2×C4semidirect
67. C4⋊Dic269C2×C4semidirect
70. #16864381C2×C4semidirect
78. #16864379C2×C4semidirect
198. C269#2335semidirect
210. #385D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754352
#317705052
#317705022
#317704992
#317704982
#317704952
#317704942
#317704902
#317704862
#317704842
#317704622
C4⋊C4×Dic2692
C4×C22⋊Dic2692
#317704522
#385×C2692
#2335269