Finite Group Databasebeta

← #46813614

Subgroups — #46813614

Order 34432.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575433C211yesmaximal, characteristic
2#31770509C211yesmaximal, characteristic, complemented
3#31770509C211yesmaximal, characteristic, complemented
4#31770503C211yesmaximal, characteristic, complemented
5#31770501C211yesmaximal, characteristic, complemented
6#31770491C211yesmaximal, characteristic, complemented
7#31770490C211yesmaximal, characteristic, complemented
8#31770488C211yesmaximal, characteristic, complemented
9#31770479C211yesmaximal, characteristic
10#31770476C211yesmaximal, characteristic
11#31770464C211yesmaximal, characteristic
12C4×#16864379C211yesmaximal, characteristic
13#31770452C211yesmaximal, characteristic
14#95×D269C211yesmaximal, characteristic
15#387×C269C211yesmaximal, characteristic, complemented
16C22×Dic538C2211yescharacteristic
17C22×C4×D269C2211yescharacteristic
18C22×C4×D269C2211yescharacteristic
19C22×C4×D269C2211yescharacteristic
20#22575433C418yescomplemented
21C2×C4⋊Dic269C2211yescharacteristic
22C2×C4⋊Dic269C2211yescharacteristic
23C2×C4⋊Dic269C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×#16864381C2211yescharacteristic
28C2×#16864379C2211yescharacteristic
29C2×#16864379C2211yescharacteristic
30C2×#16864379C2211yescharacteristic
31C2×#16864379C2211yescharacteristic
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
53C2×Dic538—41no—
54C2×Dic538—41no—
55C2×Dic538C2×C414yescomplemented
56C22×Dic269C2311yescharacteristic
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C2×C4×D269—22no—
64C2×C4×D269—41no—
65C2×C4×D269—41no—
66C2×C4×D269—41no—
67C2×C4×D269—41no—
68C2×C4×D269—41no—
69C2×C4×D269—41no—
70C2×C4×D269C2×C414yes—
71C2×C4×D269Q814yescomplemented
72C4⋊Dic269—41no—
73C4⋊Dic269C2×C414yescomplemented
74C4⋊Dic269C2×C414yescomplemented
75#16864381—41no—
76#16864381—41no—
77#16864381—41no—
78#16864381—41no—
79#16864379—22no—
80#16864379—22no—
81#16864379C2×C414yes—
82#16864379C2×C414yes—
83C4×Dic269—41no—
84C4×Dic269—41no—
85C4×Dic269—41no—
86C22×C4×C269C2311yescharacteristic
87C22×C4×C269C2311yescharacteristic
88C22×C4×C269C2311yescharacteristic
89C22×C4×C269C2311yescharacteristic
90C22×C4×C269C2311yescharacteristic
91C22×C4×C269C2311yescharacteristic
92C22×C4×C269C2311yescharacteristic
93C4⋊C4×C269—41no—
94C4⋊C4×C269C2×C414yescomplemented
95C42×C269—41no—
96C22×D269—21no—
97C22×D269—21no—
98C22×D269—21no—
99C22×D269—21no—
100C22×D269C22×C412yes—
101C22×D269C2×Q812yes—
102C22×D269#4112yes—
103Dic538—44no—
104C2×Dic269—21no—
105C2×Dic269—21no—
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×Dic269C22×C412yes—
122C2×Dic269C22×C412yes—
123C2×Dic269C22×C412yes—
124C2×Dic269C2×Q812yes—
125C4×D269—44no—
126C4×D269—44no—
127C4×D269—44no—
128C23×C269C2411yescharacteristic
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
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×C269C22×C412yes—
147C2×C4×C269C22×C412yes—
148C2×C4×C269C22×C412yes—
149C2×C4×C269C2×Q812yes—
150C22×C269C23×C411yescharacteristic
151C22×C269C22×Q811yescharacteristic
152C22×C269C2×#4111yescharacteristic
153C22×C269H(5,𝔽2)11yescharacteristic
154C22×C269H(5,𝔽2)11yescharacteristic
155C22×C269H(5,𝔽2)11yescharacteristic
156C22×C2692−1+411yescharacteristic
157C2×D269—22no—
158C2×D269—22no—
159C2×D269—22no—
160C2×D269—22no—
161C2×D269—22no—
162C2×D269—22no—
163C2×D269C4×Q814yes—
164C4×C269—22no—
165C4×C269—22no—
166C4×C269—22no—
167C4×C269—22no—
168C4×C269—41no—
169C4×C269—41no—
170C4×C269—41no—
171Dic269—22no—
172Dic269—22no—
173Dic269—22no—
174Dic269—22no—
175Dic269—41no—
176Dic269—41no—
177Dic269—41no—
178C2×C269C2×C4×Q811yescharacteristic
179C2×C269#51811yescharacteristic
180C2×C269#52011yescharacteristic
181C2×C269#53811yescharacteristic
182C2×C269#53911yescharacteristic
183C2×C269#54311yescharacteristic
184C2×C269#54411yescharacteristic
185D269—24no—
186C269#232911yescharacteristic, complemented, Sylow
187#2329—2691nomaximal, Sylow
188C2×C22⋊Q8—2691no—
189#391—2691no—
190#391—2691no—
191#389—2691no—
192#389—2691no—
193#387—2691no—
194#387—2691no—
195#387—2691no—
196#387D26911yescharacteristic, complemented
197#385—2691no—
198#385—2691no—
199#380—2691no—
200C4×C22⋊C4—2691no—
201C4×C22⋊C4—2691no—
202C2×#95—2691no—
203C22×Q8—2691no—
204C23×C4—2691no—
205C23×C4—2691no—
206C23×C4—2691no—
207C22⋊Q8—2698no—
208C2×C4⋊C4—2691no—
209C2×C4⋊C4—2691no—
210C2×C4⋊C4—2691no—
211C2×C4⋊C4—2691no—
212C2×C4⋊C4—2691no—
213C2×C4⋊C4—2691no—
214C2×C4⋊C4—2691no—
215C2×C4⋊C4C2×D26911yescharacteristic
216C2×C4⋊C4C2×D26911yescharacteristic
217C2×C22⋊C4—2691no—
218C2×C22⋊C4—2691no—
219C2×C22⋊C4—2691no—
220C2×C22⋊C4—2691no—
221C2×C42—2691no—
222C2×C42—2691no—
223C2×C42—2691no—
224C2×C42C2×D26911yescharacteristic
225#95—2691no—
226#95—2691no—
227#95—2691no—
228#95—2691no—
229#95—2691no—
230#95—2691no—
231#95—2691no—
232#95—2691no—
233#95—2691no—
234#95—2691no—
235#95C2×D26911yescharacteristic
236#95C2×D26911yescharacteristic
237#95C2×D26911yescharacteristic
238#95C2×D26911yescharacteristic
239C24—2691no—
240C2×Q8—2694no—
241C2×Q8—10761no—
242C2×Q8—10761no—
243C22×C4—2691no—
244C22×C4—2691no—
245C22×C4—2691no—
246C22×C4—2691no—
247C22×C4—2694no—
248C22×C4—2694no—
249C22×C4—2691no—
250C22×C4—2691no—
251C22×C4—2691no—
252C22×C4—5382no—
253C22×C4—10761no—
254C22×C4—10761no—
255C22×C4—10761no—
256C22×C4—10761no—
257C22×C4—10761no—
258C22×C4—10761no—
259C22×C4C22×D26911yescharacteristic
260C22×C4C22×D26911yescharacteristic
261C22×C4C22×D26911yescharacteristic
262C22×C4C22×D26911yescharacteristic
263C22×C4C22×D26911yescharacteristic
264C22×C4C22×D26911yescharacteristic
265C22×C4C22×D26911yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—2694no—
268C4⋊C4—2694no—
269C4⋊C4—10761no—
270C4⋊C4—10761no—
271C4⋊C4—10761no—
272C4⋊C4—10761no—
273C4⋊C4—10761no—
274C4⋊C4C4×D26914yescomplemented
275C22⋊C4—2694no—
276C22⋊C4—2694no—
277C22⋊C4—5382no—
278C22⋊C4—5382no—
279C42—41no—
280C42—10761no—
281C42—10761no—
282C42—10761no—
283C23—2692no—
284C23—2692no—
285C23—2692no—
286C23—5381no—
287C23—5381no—
288C23—5381no—
289C23—5381no—
290C23C23×D26911yescharacteristic
291Q8—10764no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2692no—
310C2×C4—2692no—
311C2×C4—2692no—
312C2×C4—2692no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—5381no—
330C2×C4—10764no—
331C2×C4—10764no—
332C2×C4—10764no—
333C2×C4C2×C4×D26912yes—
334C2×C4C2×C4×D26912yes—
335C2×C4C2×C4×D26912yes—
336C2×C4Q8×D26912yes—
337C22—2694no—
338C22—5382no—
339C22—5382no—
340C22—5382no—
341C22—5382no—
342C22—5382no—
343C22—5382no—
344C22C22×C4×D26911yescharacteristic
345C22C2×Q8×D26911yescharacteristic
346C22#41×D26911yescharacteristic
347C22#2257549811yescharacteristic
348C22#2257549911yescharacteristic
349C22#2257549911yescharacteristic
350C22#2257550011yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—5382no—
359C4—5382no—
360C4—5382no—
361C4—5382no—
362C4—10761no—
363C4—10761no—
364C4—10761no—
365C2—5384no—
366C2C4×Q8×D26911yescharacteristic
367C2#3177107911yescharacteristic
368C2#3177108411yescharacteristic
369C2#3177119111yescharacteristic
370C2#3177119611yescharacteristic
371C2#3177123011yescharacteristic
372C2#3177123511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#387×C269C2
socle, cosocleC23×C269C24
prime radicalC23×D269C23
hypercenter#387D269
hypocenterC269#2329
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31770509C2semidirect
3. #31770509C2semidirect
4. #31770503C2semidirect
5. #31770501C2semidirect
6. #31770491C2semidirect
7. #31770490C2semidirect
8. #31770488C2semidirect
15. #387×C269C2semidirect
20. #22575433C4semidirect
55. C2×Dic538C2×C4semidirect
71. C2×C4×D269Q8semidirect
73. C4⋊Dic269C2×C4semidirect
74. C4⋊Dic269C2×C4semidirect
94. C4⋊C4×C269C2×C4semidirect
186. C269#2329semidirect
196. #387D269semidirect
274. C4⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754332
#317705092
#317705032
#317705012
#317704912
#317704902
#317704882
#317704792
#317704762
#317704642
C4×#168643792
#317704522
#95×D2692
#387×C2692
#2329269