Finite Group Databasebeta

← #28393168

Subgroups — #28393168

Order 14464.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D113C211yesmaximal, characteristic
2#20298492C211yesmaximal, characteristic, complemented
3#20298491C211yesmaximal, characteristic, complemented
4#20298490C211yesmaximal, characteristic, complemented
5#20298489C211yesmaximal, characteristic, complemented
6#20298488C211yesmaximal, characteristic, complemented
7#20298487C211yesmaximal, characteristic, complemented
8#20298486C211yesmaximal, characteristic, complemented
9#20298457C211yesmaximal, characteristic, complemented
10#20298455C211yesmaximal, characteristic, complemented
11#20298453C211yesmaximal, characteristic
12#20298453C211yesmaximal, characteristic
13C4×#14268624C211yesmaximal, characteristic, complemented
14#20298445C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic, complemented
16C24×D113C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×C4⋊Dic113C2211yescharacteristic, complemented
20C2×#14268626C2211yescharacteristic, complemented
21C2×#14268626C2211yescharacteristic, complemented
22C2×C22⋊Dic113C2211yescharacteristic
23C2×C22⋊Dic113C2211yescharacteristic
24C2×C22⋊Dic113C2211yescharacteristic
25C2×#14268624C2211yescharacteristic
26C2×#14268624C2211yescharacteristic
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C22⋊C4×D113C418yescomplemented
36C2×C4×Dic113C2211yescharacteristic, complemented
37C2×C4×Dic113C2211yescharacteristic, complemented
38C2×C4×Dic113C2211yescharacteristic, complemented
39#16813529C2211yescharacteristic, complemented
40#16813529C2211yescharacteristic, complemented
41#16813529C2211yescharacteristic, complemented
42#16813529C2211yescharacteristic, complemented
43#16813529C2211yescharacteristic, complemented
44#16813529C2211yescharacteristic, complemented
45C2×C4⋊C4×C113C2211yescharacteristic, complemented
46C2×C22⋊C4×C113C2211yescharacteristic
47C2×C22⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic, complemented
50#95×C113C2211yescharacteristic, complemented
51#95×C113C2211yescharacteristic, complemented
52C23×D113—22no—
53C23×D113—22no—
54C23×D113—41no—
55C23×D113—41no—
56C23×D113—41no—
57C23×D113—41no—
58C23×D113C2×C414yes—
59C23×D113C2311yescharacteristic
60C23×D113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C2×C4×D113—41no—
68C2×C4×D113—41no—
69C2×C4×D113—41no—
70C2×C4×D113—41no—
71C2×C4×D113C2×C414yes—
72C2×C4×D113C2×C414yes—
73C4⋊Dic113—41no—
74#14268626—41no—
75#14268626—41no—
76C22⋊Dic113—41no—
77C22⋊Dic113—41no—
78C22⋊Dic113C2×C414yes—
79#14268624—22no—
80#14268624—22no—
81#14268624—22no—
82#14268624—22no—
83#14268624—41no—
84#14268624—41no—
85#14268624—41no—
86#14268624—41no—
87#14268624C2×C414yes—
88#14268624C2×C414yes—
89C4×Dic113—41no—
90C4×Dic113—41no—
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—41no—
100C22⋊C4×C113—41no—
101C22⋊C4×C113—41no—
102C22⋊C4×C113C2×C414yes—
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×D113—21no—
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—21no—
120C22×D113—21no—
121C22×D113—21no—
122C22×D113—28no—
123C22×D113—44no—
124C22×D113—44no—
125C22×D113—44no—
126C22×D113—44no—
127C22×D113—44no—
128C22×D113—44no—
129C22×D113C22×C412yes—
130C22×D113C22×C412yes—
131C22×D113#4112yes—
132C22×D113#4112yes—
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×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113C22×C412yes—
150C2×C4×C113C22×C412yes—
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—21no—
162C2×Dic113—21no—
163C2×Dic113—21no—
164C2×Dic113—21no—
165C2×Dic113—21no—
166C2×Dic113—21no—
167C2×Dic113C22×C412yes—
168C2×Dic113C22×C412yes—
169C4×D113—44no—
170C4×D113—44no—
171C22×C113—22no—
172C22×C113—22no—
173C22×C113—22no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113C23×C411yescharacteristic
179C22×C113C2×#4111yescharacteristic
180C22×C113C2×#4111yescharacteristic
181C22×C113H(5,𝔽2)11yescharacteristic
182C22×C113H(5,𝔽2)11yescharacteristic
183C22×C113H(5,𝔽2)11yescharacteristic
184C22×C113H(5,𝔽2)11yescharacteristic
185C2×D113—22no—
186C2×D113—22no—
187C2×D113—22no—
188C2×D113—22no—
189C2×D113—22no—
190C2×D113—22no—
191C2×D113—22no—
192C2×D113—22no—
193C2×D113—22no—
194C2×D113—416no—
195C2×D113—41no—
196C2×D113—41no—
197C2×D113—41no—
198C2×D113—41no—
199C2×D113#11714yes—
200C4×C113—22no—
201C4×C113—22no—
202C4×C113—41no—
203C4×C113—41no—
204C4×C113—41no—
205C4×C113—41no—
206Dic113—22no—
207Dic113—22no—
208Dic113—41no—
209Dic113—41no—
210Dic113—41no—
211Dic113—41no—
212C2×C113—42no—
213C2×C113C2×#11711yescharacteristic
214C2×C113#51811yescharacteristic
215C2×C113#51811yescharacteristic
216C2×C113#53811yescharacteristic
217C2×C113#53811yescharacteristic
218C2×C113#53811yescharacteristic
219C2×C113#53811yescharacteristic
220D113—24no—
221D113—42no—
222#2312—1131nomaximal, Sylow
223C113#231211yescharacteristic, complemented, Sylow
224C22×C22⋊C4—1131no—
225#388—1131no—
226#388—1131no—
227#388—1131no—
228#388—1131no—
229#388—1131no—
230#388—1131no—
231#388—1131no—
232#388D11311yescharacteristic, complemented
233#380—1131no—
234#380—1131no—
235#379—1131no—
236#379—1131no—
237C4×C22⋊C4—1131no—
238C4×C22⋊C4—1131no—
239C25—1131no—
240C23×C4—1131no—
241C23×C4—1131no—
242C2×C4⋊C4—1131no—
243C2×C4⋊C4—1131no—
244C2×C4⋊C4—1131no—
245C2×C4⋊C4C2×D11311yescharacteristic, complemented
246C2×C22⋊C4—1131no—
247C2×C22⋊C4—1131no—
248C2×C22⋊C4—1131no—
249C2×C22⋊C4—1138no—
250C2×C22⋊C4—1131no—
251C2×C22⋊C4—1131no—
252C2×C22⋊C4—1131no—
253C2×C22⋊C4—1131no—
254C2×C22⋊C4—1131no—
255C2×C22⋊C4—1131no—
256C2×C22⋊C4—1131no—
257C2×C22⋊C4—1131no—
258C2×C22⋊C4—1131no—
259C2×C22⋊C4—1131no—
260C2×C22⋊C4C2×D11311yescharacteristic
261C2×C22⋊C4C2×D11311yescharacteristic
262C2×C22⋊C4C2×D11311yescharacteristic
263C2×C42—1131no—
264C2×C42—1131no—
265C2×C42—1131no—
266C2×C42C2×D11311yescharacteristic, complemented
267#95—1131no—
268#95—1131no—
269#95—1131no—
270#95—1131no—
271#95—1131no—
272#95—1131no—
273#95C2×D11311yescharacteristic, complemented
274#95C2×D11311yescharacteristic, complemented
275C24—1131no—
276C24—1134no—
277C24—1131no—
278C24—4521no—
279C24—4521no—
280C24—4521no—
281C24—4521no—
282C24—2262no—
283C24—2262no—
284C24C22×D11311yescharacteristic
285C22×C4—1131no—
286C22×C4—1131no—
287C22×C4—1134no—
288C22×C4—1134no—
289C22×C4—1131no—
290C22×C4—1131no—
291C22×C4—1131no—
292C22×C4—1131no—
293C22×C4—4521no—
294C22×C4—4521no—
295C22×C4—4521no—
296C22×C4—4521no—
297C22×C4C22×D11311yescharacteristic
298C22×C4C22×D11311yescharacteristic
299C22×C4C22×D11311yescharacteristic
300C22×C4C22×D11311yescharacteristic
301C22×C4C22×D11311yescharacteristic
302C22×C4C22×D11311yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—4521no—
305C4⋊C4—4521no—
306C4⋊C4—4521no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—1134no—
310C22⋊C4—1134no—
311C22⋊C4—1134no—
312C22⋊C4—4521no—
313C22⋊C4—4521no—
314C22⋊C4—4521no—
315C22⋊C4—4521no—
316C22⋊C4—4521no—
317C22⋊C4—4521no—
318C22⋊C4—2262no—
319C22⋊C4—2262no—
320C22⋊C4—2262no—
321C22⋊C4—2262no—
322C22⋊C4C4×D11314yes—
323C42—41no—
324C42—4521no—
325C42—4521no—
326C42—4521no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—1132no—
334C23—1132no—
335C23—1132no—
336C23—1132no—
337C23—4524no—
338C23—4524no—
339C23—4524no—
340C23—4524no—
341C23—4524no—
342C23—4524no—
343C23—2268no—
344C23—2261no—
345C23—2261no—
346C23—2261no—
347C23—2261no—
348C23—2261no—
349C23—2261no—
350C23—2261no—
351C23—2261no—
352C23—2261no—
353C23—2261no—
354C23C2×C4×D11312yes—
355C23C23×D11311yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—1132no—
373C2×C4—1132no—
374C2×C4—4524no—
375C2×C4—4524no—
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×C4—2261no—
386C2×C4—2261no—
387C2×C4—2261no—
388C2×C4—2261no—
389C2×C4—2261no—
390C2×C4—2261no—
391C2×C4—2261no—
392C2×C4C2×C4×D11312yes—
393C2×C4C2×C4×D11312yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—1134no—
402C22—45216no—
403C22—4521no—
404C22—4521no—
405C22—4521no—
406C22—4521no—
407C22—2262no—
408C22—2262no—
409C22—2262no—
410C22—2262no—
411C22—2262no—
412C22—2262no—
413C22—2262no—
414C22—2262no—
415C22—2262no—
416C22C22×C4×D11311yescharacteristic
417C22#41×D11311yescharacteristic
418C22#41×D11311yescharacteristic
419C22#1681366711yescharacteristic
420C22#1681366711yescharacteristic
421C22#1681366811yescharacteristic
422C22#1681366811yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—4521no—
430C4—4521no—
431C4—4521no—
432C4—4521no—
433C4—2262no—
434C4—2262no—
435C2—42no—
436C2—4522no—
437C2—2264no—
438C2#117×D11311yescharacteristic
439C2#2029907011yescharacteristic
440C2#2029907011yescharacteristic
441C2#2029918011yescharacteristic
442C2#2029918211yescharacteristic
443C2#2029918411yescharacteristic
444C2#2029918711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC24×D113C22
hypercenter#388D113
hypocenterC113#2312
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20298492C2semidirect
3. #20298491C2semidirect
4. #20298490C2semidirect
5. #20298489C2semidirect
6. #20298488C2semidirect
7. #20298487C2semidirect
8. #20298486C2semidirect
9. #20298457C2semidirect
10. #20298455C2semidirect
13. C4×#14268624C2semidirect
14. #20298445C2semidirect
15. #388×C113C2semidirect
19. C2×C4⋊Dic113C22semidirect
20. C2×#14268626C22semidirect
21. C2×#14268626C22semidirect
35. C22⋊C4×D113C4semidirect
36. C2×C4×Dic113C22semidirect
37. C2×C4×Dic113C22semidirect
38. C2×C4×Dic113C22semidirect
39. #16813529C22semidirect
40. #16813529C22semidirect
41. #16813529C22semidirect
42. #16813529C22semidirect
43. #16813529C22semidirect
44. #16813529C22semidirect
45. C2×C4⋊C4×C113C22semidirect
49. C2×C42×C113C22semidirect
50. #95×C113C22semidirect
51. #95×C113C22semidirect
223. C113#2312semidirect
232. #388D113semidirect
245. C2×C4⋊C4C2×D113semidirect
266. C2×C42C2×D113semidirect
273. #95C2×D113semidirect
274. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D1132
#202984922
#202984912
#202984902
#202984892
#202984882
#202984872
#202984862
#202984572
#202984552
#202984532
C4×#142686242
#202984452
#388×C1132
#2312113