Finite Group Databasebeta

← #28393333

Subgroups — #28393333

Order 14464.

596 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813594C211yesmaximal, characteristic
2#20298498C211yesmaximal, characteristic, complemented
3#20298488C211yesmaximal, characteristic, complemented
4#20298486C211yesmaximal, characteristic, complemented
5#20298482C211yesmaximal, characteristic, complemented
6#20298479C211yesmaximal, characteristic, complemented
7#20298478C211yesmaximal, characteristic, complemented
8#20298475C211yesmaximal, characteristic, complemented
9#20298474C211yesmaximal, characteristic, complemented
10#20298474C211yesmaximal, characteristic, complemented
11#20298459C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic113C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic113C211yesmaximal, characteristic, complemented
14C4×#14268624C211yesmaximal, characteristic, complemented
15#390×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C23×Dic113C2211yescharacteristic
19C23×Dic113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813594C418yescomplemented
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×C22⋊Dic113C2211yescharacteristic
25C2×C22⋊Dic113C2211yescharacteristic
26C2×C22⋊Dic113C2211yescharacteristic
27C2×C22⋊Dic113C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×C4×Dic113C2211yescharacteristic
33C2×C4×Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35#16813529C2211yescharacteristic
36#16813529C2211yescharacteristic
37#16813529C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45C22×D4×C113C2211yescharacteristic
46C2×C4⋊C4×C113C2211yescharacteristic
47C2×C22⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C22⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C42×C113C2211yescharacteristic
52C23×D113C2311yescharacteristic
53C2×C22⋊D113—41no—
54C2×C22⋊D113—41no—
55C2×C22⋊D113—41no—
56C2×C22⋊D113—41no—
57C2×C22⋊D113C2×C414yes—
58C2×C22⋊D113C2×C414yescomplemented
59C22×Dic113—22no—
60C22×Dic113—41no—
61C22×Dic113—41no—
62C22×Dic113—41no—
63C22×Dic113—41no—
64C22×Dic113C2×C414yescomplemented
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C22×Dic113C2311yescharacteristic
69C22×Dic113C2311yescharacteristic
70C22×Dic113C2311yescharacteristic
71C22×Dic113C2311yescharacteristic
72C2×C4×D113—22no—
73C2×C4×D113—41no—
74C2×C4×D113—41no—
75#14268626—41no—
76#14268626C2×C414yescomplemented
77C22⋊Dic113—22no—
78C22⋊Dic113—41no—
79C22⋊Dic113—41no—
80C22⋊Dic113C2×C414yescomplemented
81#14268624—22no—
82#14268624—41no—
83#14268624—41no—
84#14268624C2×C414yescomplemented
85C4×Dic113—41no—
86C4×Dic113—41no—
87C4×Dic113—41no—
88C24×C113C2311yescharacteristic
89C24×C113C2311yescharacteristic
90C2×D4×C113—41no—
91C2×D4×C113—41no—
92C2×D4×C113C2×C414yescomplemented
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C22×C4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C4⋊C4×C113—41no—
99C22⋊C4×C113—22no—
100C22⋊C4×C113—22no—
101C22⋊C4×C113—41no—
102C22⋊C4×C113—41no—
103C42×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×C113—21no—
115C23×C113—21no—
116C23×C113C22×C412yes—
117C23×C113C22×C412yes—
118C23×C113C2411yescharacteristic
119C22×D113—21no—
120C22×D113—21no—
121C22×D113—21no—
122C22×D113—21no—
123C22×D113—21no—
124C22×D113—21no—
125C22×D113C22×C412yes—
126D4×C113—44no—
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×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113C22×C412yes—
141C2×C4×C113#4112yes—
142C22⋊D113—44no—
143C22⋊D113—44no—
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—21no—
156C2×Dic113—21no—
157C2×Dic113—21no—
158C2×Dic113—21no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—44no—
162C2×Dic113—44no—
163C2×Dic113C22×C412yes—
164C2×Dic113C22×C412yes—
165C2×Dic113C22×C412yes—
166C2×Dic113#4112yes—
167C4×D113—44no—
168C22×C113—22no—
169C22×C113—22no—
170C22×C113—22no—
171C22×C113—22no—
172C22×C113—22no—
173C22×C113—22no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113C23×C411yescharacteristic
183C22×C113C2×#4111yescharacteristic
184C22×C113C2×#4111yescharacteristic
185C22×C113H(5,𝔽2)11yescharacteristic
186C22×C113H(5,𝔽2)11yescharacteristic
187C22×C113H(5,𝔽2)11yescharacteristic
188C22×C113H(5,𝔽2)11yescharacteristic
189C2×D113—22no—
190C2×D113—22no—
191C2×D113—22no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—41no—
195C2×D113—41no—
196C4×C113—22no—
197C4×C113—22no—
198C4×C113—41no—
199C4×C113—41no—
200C4×C113—41no—
201Dic113—22no—
202Dic113—22no—
203Dic113—22no—
204Dic113—22no—
205Dic113—41no—
206Dic113—41no—
207Dic113—41no—
208C2×C113—42no—
209C2×C113—42no—
210C2×C113C4×#4111yescharacteristic
211C2×C113#51811yescharacteristic
212C2×C113#51811yescharacteristic
213C2×C113#53811yescharacteristic
214C2×C113#53811yescharacteristic
215C2×C113#54011yescharacteristic
216C2×C113#54011yescharacteristic
217D113—42no—
218#2333—1131nomaximal, Sylow
219C113#233311yescharacteristic, complemented, Sylow
220C2×#121—1131no—
221#390—1131no—
222#390D11311yescharacteristic, complemented
223#388—1131no—
224#388—1131no—
225#387—1131no—
226#387—1131no—
227#386—1131no—
228#386—1131no—
229#386—1131no—
230#386—1131no—
231#381—1131no—
232C4×C22⋊C4—1131no—
233C4×C22⋊C4—1131no—
234C4×C22⋊C4—1131no—
235C22×D4—1131no—
236C22×D4—1131no—
237C22×D4C2×D11311yescharacteristic
238C23×C4—1131no—
239C23×C4—1131no—
240C23×C4—1131no—
241#121—1138no—
242C2×C4⋊C4—1131no—
243C2×C4⋊C4—1131no—
244C2×C4⋊C4C2×D11311yescharacteristic
245C2×C22⋊C4—1131no—
246C2×C22⋊C4—1131no—
247C2×C22⋊C4—1131no—
248C2×C22⋊C4—1131no—
249C2×C22⋊C4—1131no—
250C2×C22⋊C4—1131no—
251C2×C22⋊C4—1131no—
252C2×C22⋊C4—1131no—
253C2×C22⋊C4C2×D11311yescharacteristic
254C2×C22⋊C4C2×D11311yescharacteristic
255C2×C22⋊C4C2×D11311yescharacteristic
256C2×C22⋊C4C2×D11311yescharacteristic
257C2×C42—1131no—
258C2×C42—1131no—
259C2×C42—1131no—
260C2×C42C2×D11311yescharacteristic
261#95—1131no—
262#95—1131no—
263#95—1131no—
264#95—1131no—
265#95—1131no—
266#95—1131no—
267#95—1131no—
268#95—1131no—
269#95—1131no—
270#95—1131no—
271C24—1131no—
272C24C22×D11311yescharacteristic
273C24C22×D11311yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—1134no—
277C2×D4—1134no—
278C2×D4—4521no—
279C2×D4—4521no—
280C2×D4—4521no—
281C2×D4—4521no—
282C2×D4C4×D11314yescomplemented
283C22×C4—1134no—
284C22×C4—1131no—
285C22×C4—1131no—
286C22×C4—1131no—
287C22×C4—1131no—
288C22×C4—1131no—
289C22×C4—1131no—
290C22×C4—1131no—
291C22×C4—4521no—
292C22×C4—4521no—
293C22×C4—4521no—
294C22×C4—4521no—
295C22×C4—4521no—
296C22×C4—4521no—
297C22×C4—2262no—
298C22×C4—2262no—
299C22×C4C22×D11311yescharacteristic
300C22×C4C22×D11311yescharacteristic
301C22×C4C22×D11311yescharacteristic
302C22×C4C22×D11311yescharacteristic
303C22×C4C22×D11311yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—1134no—
306C4⋊C4—4521no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—1134no—
312C22⋊C4—1134no—
313C22⋊C4—4521no—
314C22⋊C4—4521no—
315C22⋊C4—4521no—
316C22⋊C4—4521no—
317C22⋊C4—2262no—
318C22⋊C4—2262no—
319C42—41no—
320C42—4521no—
321C42—4521no—
322C42—4521no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—1132no—
336C23—2261no—
337C23—2261no—
338C23—2261no—
339C23—2261no—
340C23—2261no—
341C23—2261no—
342C23C2×C4×D11312yes—
343C23C2×C4×D11312yes—
344C23C23×D11311yescharacteristic
345D4—44no—
346D4—4524no—
347D4—4524no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—1132no—
362C2×C4—1132no—
363C2×C4—1132no—
364C2×C4—1132no—
365C2×C4—4524no—
366C2×C4—4524no—
367C2×C4—4524no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4—2261no—
375C2×C4—2261no—
376C2×C4—2261no—
377C2×C4—2261no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4—2261no—
385C2×C4C2×C4×D11312yes—
386C2×C4#1426864612yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—4521no—
402C22—4521no—
403C22—4521no—
404C22—4521no—
405C22—2262no—
406C22—2262no—
407C22—2262no—
408C22C22×C4×D11311yescharacteristic
409C22#41×D11311yescharacteristic
410C22C2×#1426864611yescharacteristic
411C22#1681366711yescharacteristic
412C22#1681366711yescharacteristic
413C22#1681366711yescharacteristic
414C22#1681366811yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—4521no—
421C4—4521no—
422C4—4521no—
423C4—2262no—
424C4—2262no—
425C4—2262no—
426C4—2262no—
427C2—42no—
428C2—42no—
429C2—4522no—
430C2C4×#1426864611yescharacteristic
431C2#2029907011yescharacteristic
432C2#2029907111yescharacteristic
433C2#2029918211yescharacteristic
434C2#2029918511yescharacteristic
435C2#2029919811yescharacteristic
436C2#2029920211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#390×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813594C2
hypercenter#390D113
hypocenterC113#2333
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #20298498C2semidirect
3. #20298488C2semidirect
4. #20298486C2semidirect
5. #20298482C2semidirect
6. #20298479C2semidirect
7. #20298478C2semidirect
8. #20298475C2semidirect
9. #20298474C2semidirect
10. #20298474C2semidirect
11. #20298459C2semidirect
12. C22⋊C4×Dic113C2semidirect
13. C22⋊C4×Dic113C2semidirect
14. C4×#14268624C2semidirect
15. #390×C113C2semidirect
21. #16813594C4semidirect
58. C2×C22⋊D113C2×C4semidirect
64. C22×Dic113C2×C4semidirect
76. #14268626C2×C4semidirect
80. C22⋊Dic113C2×C4semidirect
84. #14268624C2×C4semidirect
92. C2×D4×C113C2×C4semidirect
219. C113#2333semidirect
222. #390D113semidirect
282. C2×D4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135942
#202984982
#202984882
#202984862
#202984822
#202984792
#202984782
#202984752
#202984742
#202984592
C22⋊C4×Dic1132
C4×#142686242
#390×C1132
#2333113