Finite Group Databasebeta

← #28393244

Subgroups — #28393244

Order 14464.

632 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×#16813604C211yesmaximal, characteristic
2C2×#16813582C211yesmaximal, characteristic
3C2×C4⋊C4×D113C211yesmaximal, characteristic, complemented
4#20298496C211yesmaximal, characteristic, complemented
5#20298493C211yesmaximal, characteristic, complemented
6#20298492C211yesmaximal, characteristic, complemented
7#20298485C211yesmaximal, characteristic, complemented
8#20298481C211yesmaximal, characteristic, complemented
9#20298474C211yesmaximal, characteristic
10#20298473C211yesmaximal, characteristic, complemented
11#20298472C211yesmaximal, characteristic, complemented
12#20298470C211yesmaximal, characteristic, complemented
13#20298460C211yesmaximal, characteristic, complemented
14C4×#14268624C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C23×Dic113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813604C418yescomplemented
22#16813582—24no—
23C2×C4⋊Dic113C2211yescharacteristic
24C2×C4⋊Dic113C2211yescharacteristic
25C2×C4⋊Dic113C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×#14268626C2211yescharacteristic
29C2×#14268626C2211yescharacteristic
30C2×#14268626C2211yescharacteristic
31C4⋊C4×D113—24no—
32C2×C22⋊Dic113C2211yescharacteristic
33C2×C22⋊Dic113C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×#14268624C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47C2×C4⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C22⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C42×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53#95×C113C2211yescharacteristic
54C23×D113C2311yescharacteristic
55C2×C22⋊D113—22no—
56C2×C22⋊D113—22no—
57C2×C22⋊D113C2×C414yes—
58C22×Dic113—22no—
59C22×Dic113—41no—
60C22×Dic113—41no—
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C2×C4×D113—22no—
69C2×C4×D113—22no—
70C2×C4×D113—22no—
71C2×C4×D113—41no—
72C2×C4×D113—41no—
73C2×C4×D113—41no—
74C2×C4×D113—41no—
75C2×C4×D113C2×C414yescomplemented
76C2×C4×D113D414yes—
77C4⋊Dic113—22no—
78C4⋊Dic113—41no—
79C4⋊Dic113C2×C414yescomplemented
80#14268626—22no—
81#14268626—22no—
82#14268626—22no—
83#14268626—41no—
84#14268626C2×C414yescomplemented
85C22⋊Dic113—41no—
86C22⋊Dic113C2×C414yescomplemented
87#14268624—22no—
88#14268624—22no—
89#14268624C2×C414yescomplemented
90C4×Dic113—22no—
91C4×Dic113—41no—
92C24×C113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C22×C4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C4⋊C4×C113—22no—
100C22⋊C4×C113—22no—
101C22⋊C4×C113—41no—
102C22⋊C4×C113C2×C414yescomplemented
103C42×C113—41no—
104C23×C113—21no—
105C23×C113—21no—
106C23×C113—21no—
107C23×C113—21no—
108C23×C113—21no—
109C23×C113—21no—
110C23×C113C22×C412yes—
111C23×C113C2411yescharacteristic
112C22×D113—21no—
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—21no—
116C22×D113C22×C412yes—
117C22×D113C2×D412yes—
118C22×D113#4112yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113C22×C412yes—
135C2×C4×C113C22×C412yes—
136C2×C4×C113C2×D412yes—
137C22⋊D113—28no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—44no—
156C2×Dic113C22×C412yes—
157C2×Dic113C22×C412yes—
158C2×Dic113C22×C412yes—
159C2×Dic113C2×D412yes—
160C4×D113—28no—
161C4×D113—44no—
162C4×D113—44no—
163C22×C113—22no—
164C22×C113—22no—
165C22×C113—22no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113C23×C411yescharacteristic
171C22×C113C22×D411yescharacteristic
172C22×C113C2×#4111yescharacteristic
173C22×C113H(5,𝔽2)11yescharacteristic
174C22×C113H(5,𝔽2)11yescharacteristic
175C22×C1132−1+411yescharacteristic
176C22×C1132−1+411yescharacteristic
177C2×D113—22no—
178C2×D113—22no—
179C2×D113—22no—
180C2×D113—22no—
181C2×D113—22no—
182C2×D113—22no—
183C2×D113C4×D414yes—
184C4×C113—22no—
185C4×C113—22no—
186C4×C113—22no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113—41no—
190Dic113—22no—
191Dic113—22no—
192Dic113—22no—
193Dic113—22no—
194Dic113—41no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—42no—
198C2×C113C2×C4×D411yescharacteristic
199C2×C113#52011yescharacteristic
200C2×C113#52011yescharacteristic
201C2×C113#53411yescharacteristic
202C2×C113#53611yescharacteristic
203C2×C113#53911yescharacteristic
204C2×C113#53911yescharacteristic
205D113—24no—
206#2322—1131nomaximal, Sylow
207C113#232211yescharacteristic, complemented, Sylow
208C2×#123—1131no—
209C2×C4×D4—1131no—
210C22×C4⋊C4—1131no—
211#389—1131no—
212#389—1131no—
213#388—1131no—
214#388D11311yescharacteristic, complemented
215#387—1131no—
216#387—1131no—
217#386—1131no—
218#385—1131no—
219#385—1131no—
220#385—1131no—
221#381—1131no—
222C4×C22⋊C4—1131no—
223C22×D4—1131no—
224C23×C4—1131no—
225C23×C4—1131no—
226C23×C4—1131no—
227C23×C4—1131no—
228#123—1138no—
229C4×D4—2264no—
230C2×C4⋊C4—1131no—
231C2×C4⋊C4—1131no—
232C2×C4⋊C4—1131no—
233C2×C4⋊C4—1131no—
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—1131no—
236C2×C4⋊C4—1131no—
237C2×C4⋊C4—1131no—
238C2×C4⋊C4—2264no—
239C2×C4⋊C4C2×D11311yescharacteristic
240C2×C22⋊C4—1131no—
241C2×C22⋊C4—1131no—
242C2×C22⋊C4—1131no—
243C2×C22⋊C4—1131no—
244C2×C22⋊C4—1131no—
245C2×C22⋊C4C2×D11311yescharacteristic
246C2×C22⋊C4C2×D11311yescharacteristic
247C2×C22⋊C4C2×D11311yescharacteristic
248C2×C42—1131no—
249C2×C42—1131no—
250C2×C42C2×D11311yescharacteristic
251#95—1131no—
252#95—1131no—
253#95—1131no—
254#95—1131no—
255#95—1131no—
256#95—1131no—
257#95—1131no—
258#95—1131no—
259#95C2×D11311yescharacteristic
260#95C2×D11311yescharacteristic
261C24—1131no—
262C24C22×D11311yescharacteristic
263C2×D4—1134no—
264C2×D4—2262no—
265C2×D4—2262no—
266C22×C4—1131no—
267C22×C4—1131no—
268C22×C4—1131no—
269C22×C4—1131no—
270C22×C4—1134no—
271C22×C4—1134no—
272C22×C4—1131no—
273C22×C4—1131no—
274C22×C4—1131no—
275C22×C4—4521no—
276C22×C4—4521no—
277C22×C4—4521no—
278C22×C4—4521no—
279C22×C4—4521no—
280C22×C4—4521no—
281C22×C4—2262no—
282C22×C4—2262no—
283C22×C4—2262no—
284C22×C4—2262no—
285C22×C4C22×D11311yescharacteristic
286C22×C4C22×D11311yescharacteristic
287C22×C4C22×D11311yescharacteristic
288C22×C4C22×D11311yescharacteristic
289C22×C4C22×D11311yescharacteristic
290C22×C4C22×D11311yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—1134no—
293C4⋊C4—1134no—
294C4⋊C4—4521no—
295C4⋊C4—4521no—
296C4⋊C4—2262no—
297C4⋊C4—2262no—
298C4⋊C4—2262no—
299C4⋊C4—2262no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—1134no—
303C22⋊C4—1134no—
304C22⋊C4—4521no—
305C22⋊C4—2262no—
306C22⋊C4—2262no—
307C22⋊C4C4×D11314yescomplemented
308C42—41no—
309C42—4521no—
310C42—2262no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—1132no—
318C23—1132no—
319C23—1132no—
320C23—2261no—
321C23—2261no—
322C23—2261no—
323C23—2261no—
324C23C2×C4×D11312yes—
325C23C23×D11311yescharacteristic
326D4—2268no—
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—21no—
341C2×C4—21no—
342C2×C4—1132no—
343C2×C4—1132no—
344C2×C4—1132no—
345C2×C4—1132no—
346C2×C4—4524no—
347C2×C4—4524no—
348C2×C4—4524no—
349C2×C4—2268no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4—2261no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4C2×C4×D11312yes—
368C2×C4C2×C4×D11312yes—
369C2×C4D4×D11312yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—1134no—
378C22—2262no—
379C22—2262no—
380C22—2262no—
381C22—2262no—
382C22—2262no—
383C22—2262no—
384C22C22×C4×D11311yescharacteristic
385C22C2×D4×D11311yescharacteristic
386C22#41×D11311yescharacteristic
387C22#1681366711yescharacteristic
388C22#1681366811yescharacteristic
389C22#1681366911yescharacteristic
390C22#1681366911yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—4521no—
398C4—4521no—
399C4—4521no—
400C4—2262no—
401C4—2262no—
402C4—2262no—
403C4—2262no—
404C2—42no—
405C2—2264no—
406C2C4×D4×D11311yescharacteristic
407C2#2029907711yescharacteristic
408C2#2029907811yescharacteristic
409C2#2029915611yescharacteristic
410C2#2029916811yescharacteristic
411C2#2029918911yescharacteristic
412C2#2029919111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC22×C22⋊D113C22
hypercenter#388D113
hypocenterC113#2322
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D113C2semidirect
4. #20298496C2semidirect
5. #20298493C2semidirect
6. #20298492C2semidirect
7. #20298485C2semidirect
8. #20298481C2semidirect
10. #20298473C2semidirect
11. #20298472C2semidirect
12. #20298470C2semidirect
13. #20298460C2semidirect
14. C4×#14268624C2semidirect
15. #388×C113C2semidirect
21. #16813604C4semidirect
75. C2×C4×D113C2×C4semidirect
79. C4⋊Dic113C2×C4semidirect
84. #14268626C2×C4semidirect
86. C22⋊Dic113C2×C4semidirect
89. #14268624C2×C4semidirect
102. C22⋊C4×C113C2×C4semidirect
207. C113#2322semidirect
214. #388D113semidirect
307. C22⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136042
C2×#168135822
C2×C4⋊C4×D1132
#202984962
#202984932
#202984922
#202984852
#202984812
#202984742
#202984732
#202984722
#202984702
#202984602
C4×#142686242
#388×C1132
#2322113