Finite Group Databasebeta

← #46813883

Subgroups — #46813883

Order 34432.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575434C211yesmaximal, characteristic
2C2×D4×Dic269C211yesmaximal, characteristic
3C2×#22575409C211yesmaximal, characteristic, complemented
4#31770502C211yesmaximal, characteristic, complemented
5#31770499C211yesmaximal, characteristic, complemented
6#31770493C211yesmaximal, characteristic, complemented
7#31770492C211yesmaximal, characteristic, complemented
8#31770487C211yesmaximal, characteristic, complemented
9#31770477C211yesmaximal, characteristic, complemented
10#31770477C211yesmaximal, characteristic, complemented
11#31770456C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic269C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic269C211yesmaximal, characteristic, complemented
14C2×#22575360C211yesmaximal, characteristic, complemented
15#386×C269C211yesmaximal, characteristic
16C23×Dic269C2211yescharacteristic
17C23×Dic269C2211yescharacteristic
18C23×Dic269C2211yescharacteristic
19#22575434C418yescomplemented
20D4×Dic269—24no—
21#22575409—24no—
22C2×C4⋊Dic269C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×#16864381C2211yescharacteristic
28C2×#16864381C2211yescharacteristic
29C2×C22⋊Dic269C2211yescharacteristic
30C2×C22⋊Dic269C2211yescharacteristic
31C2×C22⋊Dic269C2211yescharacteristic
32C2×C22⋊Dic269C2211yescharacteristic
33C2×C22⋊Dic269C2211yescharacteristic
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
47C22×D4×C269C2211yescharacteristic
48C23×C4×C269C2211yescharacteristic
49C2×C22⋊C4×C269C2211yescharacteristic
50C2×C22⋊C4×C269C2211yescharacteristic
51C2×C22⋊C4×C269C2211yescharacteristic
52#95×C269C2211yescharacteristic
53#95×C269C2211yescharacteristic
54C22×Dic269—22no—
55C22×Dic269—22no—
56C22×Dic269—22no—
57C22×Dic269—22no—
58C22×Dic269—22no—
59C22×Dic269—22no—
60C22×Dic269—41no—
61C22×Dic269—41no—
62C22×Dic269C2×C414yescomplemented
63C22×Dic269C2311yescharacteristic
64C22×Dic269C2311yescharacteristic
65C22×Dic269C2311yescharacteristic
66C22×Dic269C2311yescharacteristic
67C22×Dic269C2311yescharacteristic
68C22×Dic269C2311yescharacteristic
69C22×Dic269C2311yescharacteristic
70C22×Dic269C2311yescharacteristic
71C4⋊Dic269—22no—
72#16864381—22no—
73#16864381—22no—
74#16864381—22no—
75#16864381—41no—
76#16864381C2×C414yescomplemented
77#16864381C2×C414yescomplemented
78C22⋊Dic269—22no—
79C22⋊Dic269C2×C414yescomplemented
80C22⋊Dic269C2×C414yescomplemented
81C22⋊Dic269C2×C414yescomplemented
82C22⋊Dic269D414yes—
83C4×Dic269—22no—
84C4×Dic269—22no—
85C4×Dic269—22no—
86C4×Dic269—22no—
87C4×Dic269—41no—
88C24×C269C2311yescharacteristic
89C24×C269C2311yescharacteristic
90C2×D4×C269—22no—
91C2×D4×C269—22no—
92C2×D4×C269C2×C414yes—
93C22×C4×C269—22no—
94C22×C4×C269—22no—
95C22×C4×C269—41no—
96C22×C4×C269C2311yescharacteristic
97C22×C4×C269C2311yescharacteristic
98C22×C4×C269C2311yescharacteristic
99C22×C4×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101C22⋊C4×C269—22no—
102C22⋊C4×C269—22no—
103C22⋊C4×C269—41no—
104C2×Dic269—28no—
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×Dic269—21no—
122C2×Dic269—44no—
123C2×Dic269—44no—
124C2×Dic269C22×C412yes—
125C2×Dic269C22×C412yes—
126C2×Dic269C22×C412yes—
127C2×Dic269C22×C412yes—
128C2×Dic269C2×D412yes—
129C2×Dic269C2×D412yes—
130C2×Dic269#4112yes—
131C23×C269—21no—
132C23×C269—21no—
133C23×C269—21no—
134C23×C269—21no—
135C23×C269—21no—
136C23×C269—21no—
137C23×C269—21no—
138C23×C269—21no—
139C23×C269—21no—
140C23×C269—21no—
141C23×C269C22×C412yes—
142C23×C269C22×C412yes—
143C23×C269C2×D412yes—
144C23×C269#4112yes—
145C23×C269C2411yescharacteristic
146D4×C269—28no—
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×C269—21no—
154C2×C4×C269—21no—
155C2×C4×C269—21no—
156C2×C4×C269—21no—
157C2×C4×C269—21no—
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269—44no—
161C2×C4×C269C22×C412yes—
162C2×C4×C269#4112yes—
163C22×C269—22no—
164C22×C269—22no—
165C22×C269—22no—
166C22×C269—22no—
167C22×C269—22no—
168C22×C269—22no—
169C22×C269—22no—
170C22×C269—22no—
171C22×C269—22no—
172C22×C269—41no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269—41no—
176C22×C269C4×D414yes—
177C22×C269C23×C411yescharacteristic
178C22×C269C22×D411yescharacteristic
179C22×C269C2×#4111yescharacteristic
180C22×C269C2×#4111yescharacteristic
181C22×C269C2×#4111yescharacteristic
182C22×C269H(5,𝔽2)11yescharacteristic
183C22×C2692−1+411yescharacteristic
184C4×C269—22no—
185C4×C269—22no—
186C4×C269—41no—
187C4×C269—41no—
188C4×C269—41no—
189Dic269—22no—
190Dic269—22no—
191Dic269—22no—
192Dic269—22no—
193Dic269—22no—
194Dic269—22no—
195Dic269—22no—
196Dic269—41no—
197C2×C269—24no—
198C2×C269—42no—
199C2×C269C2×C4×D411yescharacteristic
200C2×C269C4×#4111yescharacteristic
201C2×C269#52011yescharacteristic
202C2×C269#54611yescharacteristic
203C2×C269#54711yescharacteristic
204C2×C269#55111yescharacteristic
205C2×C269#55211yescharacteristic
206C269#235911yescharacteristic, complemented, Sylow
207#2359—2691nomaximal, Sylow
208C2×#123—2691no—
209C2×C4×D4—2691no—
210C2×#117—2691no—
211#389—2691no—
212#388—2691no—
213#388—2691no—
214#387—2691no—
215#387—2691no—
216#386D26911yescharacteristic
217#385—2691no—
218#385—2691no—
219C4×C4⋊C4—2691no—
220C4×C22⋊C4—2691no—
221C4×C22⋊C4—2691no—
222C2×#95—2691no—
223C22×D4C2×D26911yescharacteristic
224C23×C4—2691no—
225C23×C4—2691no—
226C23×C4—2691no—
227C23×C4C2×D26911yescharacteristic
228#123—2698no—
229C4×D4—5384no—
230#117—5384no—
231C2×C4⋊C4—2691no—
232C2×C4⋊C4—2691no—
233C2×C4⋊C4—2691no—
234C2×C4⋊C4—2691no—
235C2×C4⋊C4—2691no—
236C2×C4⋊C4—2691no—
237C2×C4⋊C4—2691no—
238C2×C22⋊C4—2691no—
239C2×C22⋊C4—2691no—
240C2×C22⋊C4—2691no—
241C2×C22⋊C4—2691no—
242C2×C22⋊C4—2691no—
243C2×C22⋊C4C2×D26911yescharacteristic
244C2×C22⋊C4C2×D26911yescharacteristic
245C2×C22⋊C4C2×D26911yescharacteristic
246C2×C42—2691no—
247C2×C42—2691no—
248C2×C42—2691no—
249C2×C42—2691no—
250C2×C42—2691no—
251#95—2691no—
252#95—2691no—
253#95—2691no—
254#95—2691no—
255#95—2691no—
256#95—2691no—
257#95—2691no—
258#95—2691no—
259#95C2×D26911yescharacteristic
260#95C2×D26911yescharacteristic
261C24C22×D26911yescharacteristic
262C24C22×D26911yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C4×D26914yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—2694no—
270C22×C4—2691no—
271C22×C4—2691no—
272C22×C4—2691no—
273C22×C4—2691no—
274C22×C4—2691no—
275C22×C4—2691no—
276C22×C4—2691no—
277C22×C4—2691no—
278C22×C4—5382no—
279C22×C4—5382no—
280C22×C4—5382no—
281C22×C4—5382no—
282C22×C4—5382no—
283C22×C4—5382no—
284C22×C4—10761no—
285C22×C4—10761no—
286C22×C4C22×D26911yescharacteristic
287C22×C4C22×D26911yescharacteristic
288C22×C4C22×D26911yescharacteristic
289C22×C4C22×D26911yescharacteristic
290C22×C4C22×D26911yescharacteristic
291C4⋊C4—2694no—
292C4⋊C4—2694no—
293C4⋊C4—5382no—
294C4⋊C4—5382no—
295C4⋊C4—5382no—
296C4⋊C4—5382no—
297C4⋊C4—10761no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—2694no—
302C22⋊C4—2694no—
303C22⋊C4—2694no—
304C22⋊C4—2694no—
305C22⋊C4—5382no—
306C42—5382no—
307C42—5382no—
308C42—5382no—
309C42—5382no—
310C42—10761no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4×D26912yes—
322C23C2×C4×D26912yes—
323C23D4×D26912yes—
324C23#1686440112yes—
325C23C23×D26911yescharacteristic
326D4—28no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—2692no—
342C2×C4—2692no—
343C2×C4—2692no—
344C2×C4—2692no—
345C2×C4—2692no—
346C2×C4—2692no—
347C2×C4—2692no—
348C2×C4—5388no—
349C2×C4—5381no—
350C2×C4—5381no—
351C2×C4—5381no—
352C2×C4—5381no—
353C2×C4—5381no—
354C2×C4—5381no—
355C2×C4—5381no—
356C2×C4—5381no—
357C2×C4—5381no—
358C2×C4—5381no—
359C2×C4—5381no—
360C2×C4—5381no—
361C2×C4—5381no—
362C2×C4—5381no—
363C2×C4—5381no—
364C2×C4—5381no—
365C2×C4—5381no—
366C2×C4—10764no—
367C2×C4—10764no—
368C2×C4C2×C4×D26912yes—
369C2×C4#1686440112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22#2257541314yes—
384C22C22×C4×D26911yescharacteristic
385C22C2×D4×D26911yescharacteristic
386C22#41×D26911yescharacteristic
387C22C2×#1686440111yescharacteristic
388C22C2×#1686440111yescharacteristic
389C22#2257549811yescharacteristic
390C22#2257550011yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—5382no—
397C4—5382no—
398C4—5382no—
399C4—5382no—
400C4—5382no—
401C4—5382no—
402C4—5382no—
403C4—10761no—
404C2—24no—
405C2—42no—
406C2C2×#2257541311yescharacteristic
407C2C4×#1686440111yescharacteristic
408C2#3177108411yescharacteristic
409C2#3177124411yescharacteristic
410C2#3177125511yescharacteristic
411C2#3177128611yescharacteristic
412C2#3177129211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#386×C269C2
socle, cosocleC23×C269C24
prime radicalC22×D4×C269C22
hypercenter#386D269
hypocenterC269#2359
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. C2×#22575409C2semidirect
4. #31770502C2semidirect
5. #31770499C2semidirect
6. #31770493C2semidirect
7. #31770492C2semidirect
8. #31770487C2semidirect
9. #31770477C2semidirect
10. #31770477C2semidirect
11. #31770456C2semidirect
12. C22⋊C4×Dic269C2semidirect
13. C4×C22⋊Dic269C2semidirect
14. C2×#22575360C2semidirect
19. #22575434C4semidirect
62. C22×Dic269C2×C4semidirect
76. #16864381C2×C4semidirect
77. #16864381C2×C4semidirect
79. C22⋊Dic269C2×C4semidirect
80. C22⋊Dic269C2×C4semidirect
81. C22⋊Dic269C2×C4semidirect
206. C269#2359semidirect

Maximal subgroups

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

subgroupindex
C2×#225754342
C2×D4×Dic2692
C2×#225754092
#317705022
#317704992
#317704932
#317704922
#317704872
#317704772
#317704562
C22⋊C4×Dic2692
C4×C22⋊Dic2692
C2×#225753602
#386×C2692
#2359269