Finite Group Databasebeta

← #28393501

Subgroups — #28393501

Order 14464.

660 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×D4×Dic113C211yesmaximal, characteristic
2C2×#16813578C211yesmaximal, characteristic, complemented
3C22×#14268626C211yesmaximal, characteristic, complemented
4#20298492C211yesmaximal, characteristic, complemented
5#20298486C211yesmaximal, characteristic, complemented
6#20298483C211yesmaximal, characteristic, complemented
7#20298481C211yesmaximal, characteristic, complemented
8#20298478C211yesmaximal, characteristic
9#20298462C211yesmaximal, characteristic, complemented
10#20298456C211yesmaximal, characteristic, complemented
11#20298456C211yesmaximal, characteristic, complemented
12#20298449C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic113C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic113C211yesmaximal, characteristic, complemented
15#386×C113C211yesmaximal, characteristic
16C23×Dic113C2211yescharacteristic
17C23×Dic113C2211yescharacteristic
18C23×Dic113C2211yescharacteristic
19D4×Dic113C418yescomplemented
20#16813578—24no—
21C2×C4⋊Dic113C2211yescharacteristic
22C2×#14268626—24no—
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×#14268626C2211yescharacteristic
29C2×C22⋊Dic113C2211yescharacteristic
30C2×C22⋊Dic113C2211yescharacteristic
31C2×C22⋊Dic113C2211yescharacteristic
32C2×C22⋊Dic113C2211yescharacteristic
33C2×C22⋊Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35C2×C4×Dic113C2211yescharacteristic
36C2×C4×Dic113C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47C22×D4×C113C2211yescharacteristic
48C23×C4×C113C2211yescharacteristic
49C2×C22⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C22⋊C4×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53#95×C113C2211yescharacteristic
54C22×Dic113—22no—
55C22×Dic113—22no—
56C22×Dic113—22no—
57C22×Dic113—22no—
58C22×Dic113—22no—
59C22×Dic113—22no—
60C22×Dic113—41no—
61C22×Dic113C2×C414yes—
62C22×Dic113C2×C414yescomplemented
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C22×Dic113C2311yescharacteristic
69C22×Dic113C2311yescharacteristic
70C22×Dic113C2311yescharacteristic
71C4⋊Dic113C2×C414yescomplemented
72#14268626—22no—
73#14268626—22no—
74#14268626—22no—
75#14268626—22no—
76#14268626—22no—
77#14268626D414yescomplemented
78C22⋊Dic113—22no—
79C22⋊Dic113—22no—
80C22⋊Dic113—41no—
81C22⋊Dic113C2×C414yes—
82C22⋊Dic113C2×C414yescomplemented
83C4×Dic113—22no—
84C4×Dic113—22no—
85C4×Dic113—41no—
86C4×Dic113—41no—
87C4×Dic113C2×C414yescomplemented
88C24×C113C2311yescharacteristic
89C24×C113C2311yescharacteristic
90C2×D4×C113—22no—
91C2×D4×C113—22no—
92C2×D4×C113C2×C414yes—
93C22×C4×C113—22no—
94C22×C4×C113—22no—
95C22×C4×C113—41no—
96C22×C4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C22⋊C4×C113—22no—
102C22⋊C4×C113—22no—
103C22⋊C4×C113—41no—
104C23×C113—21no—
105C23×C113—21no—
106C23×C113—21no—
107C23×C113—21no—
108C23×C113—21no—
109C23×C113—21no—
110C23×C113—21no—
111C23×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113C22×C412yes—
115C23×C113C22×C412yes—
116C23×C113#4112yes—
117C23×C113#4112yes—
118C23×C113C2411yescharacteristic
119D4×C113—28no—
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—44no—
134C2×C4×C113C22×C412yes—
135C2×C4×C113C2×D412yes—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—28no—
145C2×Dic113—28no—
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×Dic113C22×C412yes—
160C2×Dic113C2×D412yes—
161C2×Dic113C2×D412yes—
162C2×Dic113#4112yes—
163C22×C113—22no—
164C22×C113—22no—
165C22×C113—22no—
166C22×C113—22no—
167C22×C113—22no—
168C22×C113—22no—
169C22×C113—22no—
170C22×C113—22no—
171C22×C113—22no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113#11714yescomplemented
177C22×C113C23×C411yescharacteristic
178C22×C113C22×D411yescharacteristic
179C22×C113C2×#4111yescharacteristic
180C22×C113C2×#4111yescharacteristic
181C22×C113C2×#4111yescharacteristic
182C22×C113H(5,𝔽2)11yescharacteristic
183C22×C1132−1+411yescharacteristic
184C4×C113—22no—
185C4×C113—22no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113—41no—
189Dic113—22no—
190Dic113—22no—
191Dic113—22no—
192Dic113—22no—
193Dic113—41no—
194Dic113—41no—
195Dic113—41no—
196Dic113C4×D414yes—
197C2×C113—24no—
198C2×C113—42no—
199C2×C113C2×#11711yescharacteristic
200C2×C113C2×C4×D411yescharacteristic
201C2×C113#52011yescharacteristic
202C2×C113#54611yescharacteristic
203C2×C113#54811yescharacteristic
204C2×C113#55211yescharacteristic
205C2×C113#55311yescharacteristic
206#2352—1131nomaximal, Sylow
207C113#235211yescharacteristic, complemented, Sylow
208C2×C4×D4—1131no—
209C2×#117—1131no—
210C22×C4⋊C4—1131no—
211#388—1131no—
212#388—1131no—
213#387—1131no—
214#387—1131no—
215#386—1131no—
216#386D11311yescharacteristic
217#382—1131no—
218#380—1131no—
219#380—1131no—
220C4×C4⋊C4—1131no—
221C4×C22⋊C4—1131no—
222C4×C22⋊C4—1131no—
223C22×D4C2×D11311yescharacteristic
224C23×C4—1131no—
225C23×C4—1131no—
226C23×C4—1131no—
227C23×C4C2×D11311yescharacteristic
228C4×D4—1138no—
229#117—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—2264no—
238C2×C22⋊C4—1131no—
239C2×C22⋊C4—1131no—
240C2×C22⋊C4—1131no—
241C2×C22⋊C4—1131no—
242C2×C22⋊C4—1131no—
243C2×C22⋊C4C2×D11311yescharacteristic
244C2×C22⋊C4C2×D11311yescharacteristic
245C2×C22⋊C4C2×D11311yescharacteristic
246C2×C42—1131no—
247C2×C42—1131no—
248C2×C42—1131no—
249C2×C42—1131no—
250C2×C42—1131no—
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
261C24C22×D11311yescharacteristic
262C24C22×D11311yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C4×D11314yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—1131no—
270C22×C4—1134no—
271C22×C4—1134no—
272C22×C4—1131no—
273C22×C4—1131no—
274C22×C4—1131no—
275C22×C4—1131no—
276C22×C4—1131no—
277C22×C4—1131no—
278C22×C4—1131no—
279C22×C4—4521no—
280C22×C4—2262no—
281C22×C4—2262no—
282C22×C4—2262no—
283C22×C4—2262no—
284C22×C4—2262no—
285C22×C4—2262no—
286C22×C4C22×D11311yescharacteristic
287C22×C4C22×D11311yescharacteristic
288C22×C4C22×D11311yescharacteristic
289C22×C4C22×D11311yescharacteristic
290C22×C4C22×D11311yescharacteristic
291C4⋊C4—1134no—
292C4⋊C4—1134no—
293C4⋊C4—2262no—
294C4⋊C4—2262no—
295C4⋊C4—2262no—
296C4⋊C4—2262no—
297C4⋊C4—2262no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—1134no—
302C22⋊C4—1134no—
303C22⋊C4—4521no—
304C22⋊C4—2262no—
305C22⋊C4—2262no—
306C42—1134no—
307C42—4521no—
308C42—4521no—
309C42—2262no—
310C42—2262no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4×D11312yes—
322C23C2×C4×D11312yes—
323C23#1426864612yes—
324C23#1426864612yes—
325C23C23×D11311yescharacteristic
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—1132no—
342C2×C4—1132no—
343C2×C4—1132no—
344C2×C4—1132no—
345C2×C4—1132no—
346C2×C4—1132no—
347C2×C4—1132no—
348C2×C4—4524no—
349C2×C4—2268no—
350C2×C4—2268no—
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×C4—2261no—
368C2×C4C2×C4×D11312yes—
369C2×C4D4×D11312yes—
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#1681357814yescomplemented
384C22C22×C4×D11311yescharacteristic
385C22C2×D4×D11311yescharacteristic
386C22#41×D11311yescharacteristic
387C22C2×#1426864611yescharacteristic
388C22C2×#1426864611yescharacteristic
389C22#1681366711yescharacteristic
390C22#1681366911yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—1134no—
397C4—4521no—
398C4—4521no—
399C4—4521no—
400C4—2262no—
401C4—2262no—
402C4—2262no—
403C4—2262no—
404C2—24no—
405C2—42no—
406C2C2×#1681357811yescharacteristic
407C2C4×D4×D11311yescharacteristic
408C2#2029907711yescharacteristic
409C2#2029923511yescharacteristic
410C2#2029925411yescharacteristic
411C2#2029928511yescharacteristic
412C2#2029929111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#386×C113C2
socle, cosocleC23×C113C24
prime radicalC22×D4×C113C22
hypercenter#386D113
hypocenterC113#2352
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#16813578C2semidirect
3. C22×#14268626C2semidirect
4. #20298492C2semidirect
5. #20298486C2semidirect
6. #20298483C2semidirect
7. #20298481C2semidirect
9. #20298462C2semidirect
10. #20298456C2semidirect
11. #20298456C2semidirect
12. #20298449C2semidirect
13. C22⋊C4×Dic113C2semidirect
14. C4×C22⋊Dic113C2semidirect
19. D4×Dic113C4semidirect
62. C22×Dic113C2×C4semidirect
71. C4⋊Dic113C2×C4semidirect
77. #14268626D4semidirect
82. C22⋊Dic113C2×C4semidirect
87. C4×Dic113C2×C4semidirect
176. C22×C113#117semidirect
207. C113#2352semidirect
383. C22#16813578semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1132
C2×#168135782
C22×#142686262
#202984922
#202984862
#202984832
#202984812
#202984782
#202984622
#202984562
#202984492
C22⋊C4×Dic1132
C4×C22⋊Dic1132
#386×C1132
#2352113