Finite Group Databasebeta

← #46813887

Subgroups — #46813887

Order 34432.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575431C211yesmaximal, characteristic
2C2×#22575418C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D269C211yesmaximal, characteristic
4#31770509C211yesmaximal, characteristic, complemented
5#31770502C211yesmaximal, characteristic, complemented
6#31770500C211yesmaximal, characteristic, complemented
7#31770491C211yesmaximal, characteristic, complemented
8#31770486C211yesmaximal, characteristic, complemented
9#31770476C211yesmaximal, characteristic
10#31770476C211yesmaximal, characteristic
11C4×#16864381C211yesmaximal, characteristic, complemented
12C4×#16864379C211yesmaximal, characteristic
13#31770452C211yesmaximal, characteristic
14#31770452C211yesmaximal, characteristic
15#389×C269C211yesmaximal, characteristic, complemented
16C22×Dic538C2211yescharacteristic
17C22×C4×D269C2211yescharacteristic
18C22×C4×D269C2211yescharacteristic
19C22×C4×D269C2211yescharacteristic
20#22575431C418yescomplemented
21#22575418—24no—
22C2×C4⋊Dic269C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×#16864381C2211yescharacteristic
28C2×#16864381C2211yescharacteristic
29C4⋊C4×D269—24no—
30C2×#16864379C2211yescharacteristic
31C2×#16864379C2211yescharacteristic
32C2×#16864379C2211yescharacteristic
33C2×#16864379C2211yescharacteristic
34C2×C4×Dic269C2211yescharacteristic
35C2×C4×Dic269C2211yescharacteristic
36C2×C4×Dic269C2211yescharacteristic
37C2×C4×Dic269C2211yescharacteristic
38C2×C4×Dic269C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45#22575360C2211yescharacteristic
46#22575360C2211yescharacteristic
47C2×C4⋊C4×C269C2211yescharacteristic
48C2×C4⋊C4×C269C2211yescharacteristic
49C2×C4⋊C4×C269C2211yescharacteristic
50C2×C4⋊C4×C269C2211yescharacteristic
51C2×C42×C269C2211yescharacteristic
52#95×C269C2211yescharacteristic
53#95×C269C2211yescharacteristic
54C23×D269C2311yescharacteristic
55C2×Dic538—22no—
56C2×Dic538—22no—
57C2×Dic538C2×C414yescomplemented
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C22×Dic269C2311yescharacteristic
64C22×Dic269C2311yescharacteristic
65C2×C4×D269—22no—
66C2×C4×D269—22no—
67C2×C4×D269—22no—
68C2×C4×D269—22no—
69C2×C4×D269—22no—
70C2×C4×D269—22no—
71C2×C4×D269—41no—
72C2×C4×D269—41no—
73C2×C4×D269C2×C414yes—
74C4⋊Dic269—22no—
75#16864381—22no—
76#16864381—22no—
77#16864381—41no—
78#16864381C2×C414yescomplemented
79#16864381C2×C414yescomplemented
80#16864381D414yes—
81#16864379—22no—
82#16864379C2×C414yes—
83#16864379C2×C414yes—
84#16864379Q814yescomplemented
85C4×Dic269—22no—
86C4×Dic269—22no—
87C4×Dic269—22no—
88C4×Dic269—22no—
89C4×Dic269—41no—
90C22×C4×C269C2311yescharacteristic
91C22×C4×C269C2311yescharacteristic
92C22×C4×C269C2311yescharacteristic
93C22×C4×C269C2311yescharacteristic
94C22×C4×C269C2311yescharacteristic
95C22×C4×C269C2311yescharacteristic
96C22×C4×C269C2311yescharacteristic
97C4⋊C4×C269—22no—
98C4⋊C4×C269—22no—
99C4⋊C4×C269—41no—
100C4⋊C4×C269C2×C414yescomplemented
101C42×C269—41no—
102C22×D269—21no—
103C22×D269—21no—
104C22×D269—21no—
105C22×D269—21no—
106C22×D269C22×C412yes—
107C22×D269C2×Q812yes—
108C22×D269#4112yes—
109Dic538—28no—
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×Dic269—21no—
124C2×Dic269C22×C412yes—
125C2×Dic269C22×C412yes—
126C2×Dic269C22×C412yes—
127C2×Dic269C2×D412yes—
128C2×Dic269C2×D412yes—
129C2×Dic269C2×Q812yes—
130C2×Dic269#4112yes—
131C4×D269—28no—
132C4×D269—44no—
133C4×D269—44no—
134C23×C269C2411yescharacteristic
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×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269C22×C412yes—
152C2×C4×C269C22×C412yes—
153C2×C4×C269C22×C412yes—
154C2×C4×C269C2×D412yes—
155C2×C4×C269C2×Q812yes—
156C22×C269C23×C411yescharacteristic
157C22×C269C22×D411yescharacteristic
158C22×C269C22×Q811yescharacteristic
159C22×C269C2×#4111yescharacteristic
160C22×C269C2×#4111yescharacteristic
161C22×C269H(5,𝔽2)11yescharacteristic
162C22×C2692−1+411yescharacteristic
163C2×D269—22no—
164C2×D269—22no—
165C2×D269—22no—
166C2×D269—22no—
167C2×D269—22no—
168C2×D269—22no—
169C2×D269C4×Q814yescomplemented
170C4×C269—22no—
171C4×C269—22no—
172C4×C269—22no—
173C4×C269—22no—
174C4×C269—22no—
175C4×C269—41no—
176C4×C269—41no—
177Dic269—22no—
178Dic269—22no—
179Dic269—22no—
180Dic269—22no—
181Dic269—41no—
182Dic269—41no—
183Dic269C4×D414yes—
184C2×C269C2×C4×D411yescharacteristic
185C2×C269C2×C4×Q811yescharacteristic
186C2×C269#52011yescharacteristic
187C2×C269#54611yescharacteristic
188C2×C269D4×Q811yescharacteristic
189C2×C269#55211yescharacteristic
190C2×C269#55411yescharacteristic
191D269—24no—
192C269#236011yescharacteristic, complemented, Sylow
193#2360—2691nomaximal, Sylow
194C2×C22⋊Q8—2691no—
195C2×C4×Q8—2691no—
196C22×C4⋊C4—2691no—
197#391—2691no—
198#389—2691no—
199#389—2691no—
200#389D26911yescharacteristic, complemented
201#387—2691no—
202#387—2691no—
203#385—2691no—
204#385—2691no—
205C4×C4⋊C4—2691no—
206C4×C22⋊C4—2691no—
207C4×C22⋊C4—2691no—
208C4×C22⋊C4—2691no—
209C22×Q8—2691no—
210C23×C4—2691no—
211C23×C4—2691no—
212C23×C4—2691no—
213C22⋊Q8—2698no—
214C4×Q8—5384no—
215C2×C4⋊C4—2691no—
216C2×C4⋊C4—2691no—
217C2×C4⋊C4—2691no—
218C2×C4⋊C4—2691no—
219C2×C4⋊C4—2691no—
220C2×C4⋊C4—2691no—
221C2×C4⋊C4—2691no—
222C2×C4⋊C4—5384no—
223C2×C4⋊C4C2×D26911yescharacteristic
224C2×C4⋊C4C2×D26911yescharacteristic
225C2×C4⋊C4C2×D26911yescharacteristic
226C2×C4⋊C4C2×D26911yescharacteristic
227C2×C22⋊C4—2691no—
228C2×C22⋊C4—2691no—
229C2×C22⋊C4—2691no—
230C2×C22⋊C4—2691no—
231C2×C42—2691no—
232C2×C42—2691no—
233C2×C42—2691no—
234C2×C42—2691no—
235C2×C42—2691no—
236C2×C42C2×D26911yescharacteristic
237#95—2691no—
238#95—2691no—
239#95—2691no—
240#95—2691no—
241#95—2691no—
242#95—2691no—
243#95—2691no—
244#95—2691no—
245#95C2×D26911yescharacteristic
246#95C2×D26911yescharacteristic
247C24—2691no—
248C2×Q8—2694no—
249C2×Q8—5382no—
250C2×Q8—5382no—
251C22×C4—2691no—
252C22×C4—2691no—
253C22×C4—2691no—
254C22×C4—2691no—
255C22×C4—2691no—
256C22×C4—2694no—
257C22×C4—2691no—
258C22×C4—2691no—
259C22×C4—5382no—
260C22×C4—5382no—
261C22×C4—5382no—
262C22×C4—5382no—
263C22×C4—5382no—
264C22×C4—5382no—
265C22×C4—10761no—
266C22×C4—10761no—
267C22×C4C22×D26911yescharacteristic
268C22×C4C22×D26911yescharacteristic
269C22×C4C22×D26911yescharacteristic
270C22×C4C22×D26911yescharacteristic
271C22×C4C22×D26911yescharacteristic
272C22×C4C22×D26911yescharacteristic
273C22×C4C22×D26911yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—2694no—
278C4⋊C4—2694no—
279C4⋊C4—2694no—
280C4⋊C4—5382no—
281C4⋊C4—5382no—
282C4⋊C4—5382no—
283C4⋊C4—10761no—
284C4⋊C4C4×D26914yescomplemented
285C22⋊C4—2694no—
286C22⋊C4—2694no—
287C22⋊C4—2694no—
288C22⋊C4—5382no—
289C42—41no—
290C42—5382no—
291C42—5382no—
292C42—5382no—
293C42—5382no—
294C42—10761no—
295C23—2692no—
296C23—2692no—
297C23—2692no—
298C23—5381no—
299C23—5381no—
300C23—5381no—
301C23—5381no—
302C23C23×D26911yescharacteristic
303Q8—5388no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2692no—
321C2×C4—2692no—
322C2×C4—2692no—
323C2×C4—2692no—
324C2×C4—2692no—
325C2×C4—2692no—
326C2×C4—2692no—
327C2×C4—5388no—
328C2×C4—5381no—
329C2×C4—5381no—
330C2×C4—5381no—
331C2×C4—5381no—
332C2×C4—5381no—
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—10764no—
343C2×C4—10764no—
344C2×C4C2×C4×D26912yes—
345C2×C4C2×C4×D26912yes—
346C2×C4C2×C4×D26912yes—
347C2×C4D4×D26912yes—
348C2×C4Q8×D26912yes—
349C22—2694no—
350C22—5382no—
351C22—5382no—
352C22—5382no—
353C22—5382no—
354C22—5382no—
355C22—5382no—
356C22C22×C4×D26911yescharacteristic
357C22C2×D4×D26911yescharacteristic
358C22C2×Q8×D26911yescharacteristic
359C22#41×D26911yescharacteristic
360C22#41×D26911yescharacteristic
361C22#2257549811yescharacteristic
362C22#2257550111yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—2694no—
371C4—5382no—
372C4—5382no—
373C4—5382no—
374C4—5382no—
375C4—10761no—
376C4—10761no—
377C2—5384no—
378C2C4×D4×D26911yescharacteristic
379C2C4×Q8×D26911yescharacteristic
380C2#3177108611yescharacteristic
381C2#3177124411yescharacteristic
382C2#3177127011yescharacteristic
383C2#3177128711yescharacteristic
384C2#3177130911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#389×C269C2
socle, cosocleC23×C269C24
prime radicalC23×D269C23
hypercenter#389D269
hypocenterC269#2360
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#22575418C2semidirect
4. #31770509C2semidirect
5. #31770502C2semidirect
6. #31770500C2semidirect
7. #31770491C2semidirect
8. #31770486C2semidirect
11. C4×#16864381C2semidirect
15. #389×C269C2semidirect
20. #22575431C4semidirect
57. C2×Dic538C2×C4semidirect
78. #16864381C2×C4semidirect
79. #16864381C2×C4semidirect
84. #16864379Q8semidirect
100. C4⋊C4×C269C2×C4semidirect
169. C2×D269C4×Q8semidirect
192. C269#2360semidirect
200. #389D269semidirect
284. C4⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754312
C2×#225754182
C2×C4⋊C4×D2692
#317705092
#317705022
#317705002
#317704912
#317704862
#317704762
C4×#168643812
C4×#168643792
#317704522
#389×C2692
#2360269