Finite Group Databasebeta

← #28399835

Subgroups — #28399835

Order 14464.

754 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D113C211yesmaximal, characteristic
2C2×#16813655C211yesmaximal, characteristic, complemented
3C2×#16813652C211yesmaximal, characteristic, complemented
4C2×#16813602C211yesmaximal, characteristic, complemented
5#20298763C212yesmaximal, complemented
6#20298761C212yesmaximal, complemented
7#20298755C212yesmaximal, complemented
8#20298750C212yesmaximal, complemented
9#20298597C211yesmaximal, characteristic, complemented
10#20298561C211yesmaximal, characteristic, complemented
11#417×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×#14268647—21no—
14C2×#14268647C2211yescharacteristic
15C2×#14268646—21no—
16C2×#14268646C2211yescharacteristic
17#41×D113—24no—
18#41×D113—24no—
19C22×Dic226C2211yescharacteristic, complemented
20C2×Q8×D113C2211yescharacteristic
21C2×D4×D113—21no—
22C2×D4×D113C2211yescharacteristic
23C22×C4×D113—21no—
24C22×C4×D113C2211yescharacteristic
25#16813655—24no—
26#16813652—24no—
27C2×Dic452C2212yescomplemented
28C2×#14268637C2212yescomplemented
29C2×#14268636C2212yescomplemented
30C2×#14268635C2212yescomplemented
31C2×#14268631C2211yescharacteristic, complemented
32#16813602—21no—
33#16813602—21no—
34#16813602C2212yes—
35#16813602C2212yescomplemented
36C2×C4⋊Dic113—21no—
37C2×#14268624—21no—
38#16813545C2212yescomplemented
39#16813542C2212yescomplemented
40#16813534C2212yes—
41#16813534C2212yescomplemented
42C2×#41×C113C2211yescharacteristic
43C2×M16×C113C2211yescharacteristic, complemented
44C2×C4⋊C4×C113C2211yescharacteristic, complemented
45#103×C113C2212yescomplemented
46#102×C113C2212yescomplemented
47C23×D113—21no—
48C23×D113D411yescharacteristic
49#14268648—22no—
50#14268648—22no—
51#14268647—28no—
52#14268647—22no—
53#14268647D414yes—
54#14268646—28no—
55#14268646—22no—
56#14268646—22no—
57C2×Dic226—21no—
58C2×Dic226—22no—
59C2×Dic226—22no—
60C2×Dic226—21no—
61C2×Dic226C2312yes—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—22no—
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70D4×D113—28no—
71D4×D113—22no—
72D4×D113—22no—
73C22×Dic113—21no—
74C22×Dic113—21no—
75C22×Dic113D411yescharacteristic
76C2×C4×D113—28no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—22no—
80C2×C4×D113—22no—
81C2×C4×D113—21no—
82C2×C4×D113D411yescharacteristic
83C2×C4×D113D411yescharacteristic
84C2×C4×D113C2311yescharacteristic
85C2×C4×D113C2311yescharacteristic
86Dic452—24no—
87#14268637—24no—
88#14268636—24no—
89#14268635—24no—
90#14268631—22no—
91C2×#11744751C2312yes—
92C4⋊Dic113—22no—
93C4⋊Dic113—22no—
94#14268624—22no—
95#14268624—22no—
96#41×C113—22no—
97#41×C113D414yes—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113—21no—
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104M16×C113—22no—
105C2×C8×C113C2312yes—
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2312yes—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—24no—
111C22×D113—22no—
112C22×D113—21no—
113C22×D113—22no—
114C22×D113—41no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113C2×D411yescharacteristic
118C22×D113C2×D411yescharacteristic
119Q8×C113—21no—
120Q8×C113C2×D412yes—
121D4×C113—24no—
122D4×C113—21no—
123D4×C113C2×D412yes—
124C2×C4×C113—21no—
125C2×C4×C113—24no—
126C2×C4×C113—22no—
127C2×C4×C113—42no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D412yes—
130C2×C4×C113C2×D412yes—
131C2×C4×C113C2411yescharacteristic
132C22⋊D113—24no—
133C22⋊D113—24no—
134C22⋊D113—24no—
135C2×Dic113—24no—
136C2×Dic113—22no—
137C2×Dic113—21no—
138C2×Dic113—22no—
139C2×Dic113—42no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—24no—
143D452—21no—
144D452C2×D412yes—
145C4×D113—24no—
146C4×D113—24no—
147C4×D113—22no—
148C4×D113—24no—
149C4×D113—22no—
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—21no—
153C4×D113—21no—
154Dic226—24no—
155Dic226—21no—
156Dic226—22no—
157Dic226—22no—
158Dic226—42no—
159Dic226C2×D412yes—
160C8×C113—22no—
161#11744751—22no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—22no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113#12012yes—
168C22×C113C22×D411yescharacteristic
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—22no—
173C2×D113—21no—
174C2×D113—21no—
175C2×D113—44no—
176C2×D113—48no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113#13712yescomplemented
180C4×C113—22no—
181C4×C113—42no—
182C4×C113#12012yes—
183C4×C113C22×D411yescharacteristic
184C4×C113C22×D411yescharacteristic
185Dic113—21no—
186Dic113—22no—
187Dic113—21no—
188Dic113—42no—
189C2×C113—22no—
190C2×C113—42no—
191C2×C113C2×#12011yescharacteristic
192C2×C113C2×#13711yescharacteristic
193C2×C113#57511yescharacteristic
194D113—22no—
195D113—41no—
196D113—42no—
197#3007—1131nomaximal, Sylow
198C113#300711yescharacteristic, complemented, Sylow
199C22×#41—1131no—
200C2×#137—1131no—
201C2×#137—1131no—
202C2×C22⋊Q8—1131no—
203#452—1132no—
204#452—1132no—
205#451—1132no—
206#450—1132no—
207#417—1131no—
208#417D11311yescharacteristic, complemented
209#407—1131no—
210C2×#41—1131no—
211C2×#41—1131no—
212C2×#41—1131no—
213C2×#41—2261no—
214C2×#41—2261no—
215C2×#41—2264no—
216C2×#41—2264no—
217C2×#41C2×D11311yescharacteristic
218C22×Q8—1131no—
219C22×Q8—1131no—
220C22×D4—1131no—
221C22×D4—2261no—
222C23×C4—1131no—
223C23×C4—2261no—
224#137—2264no—
225#137—2264no—
226C2×Q16—1132no—
227C2×Q16—1132no—
228C2×SD16—1132no—
229C2×SD16—1132no—
230C2×M16—1131no—
231C2×M16C2×D11311yescharacteristic, complemented
232C22⋊Q8—1132no—
233C22⋊Q8—1132no—
234C22⋊Q8—2261no—
235C22⋊Q8—2261no—
236C2×C4⋊C4—2261no—
237C2×C4⋊C4C2×D11311yescharacteristic, complemented
238C2×C22⋊C4—2261no—
239#103—1132no—
240#103C2×D11312yescomplemented
241#102—1132no—
242#102C2×D11312yescomplemented
243C22⋊C8—1132no—
244C22⋊C8—1132no—
245C24—1131no—
246C24—2261no—
247#41—22no—
248#41—1134no—
249#41—2268no—
250#41—2262no—
251#41—2268no—
252#41—2262no—
253#41—2262no—
254#41—2262no—
255#41—2262no—
256#41D45214yes—
257C2×Q8—1131no—
258C2×Q8—1132no—
259C2×Q8—2261no—
260C2×Q8—2262no—
261C2×Q8—2262no—
262C2×Q8—2262no—
263C2×Q8—2262no—
264C2×Q8—2261no—
265C2×Q8C22×D11311yescharacteristic
266C2×D4—21no—
267C2×D4—1131no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2262no—
271C2×D4—2268no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2262no—
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1131no—
279C22×C4—1131no—
280C22×C4—1131no—
281C22×C4—1131no—
282C22×C4—1131no—
283C22×C4—2261no—
284C22×C4—2261no—
285C22×C4—2268no—
286C22×C4—2261no—
287C22×C4—2261no—
288C22×C4—2262no—
289C22×C4—2261no—
290C22×C4—2262no—
291C22×C4C22×D11311yescharacteristic
292Q16—2264no—
293Q16—2264no—
294SD16—2264no—
295SD16—2264no—
296M16—22no—
297M16—2262no—
298C2×C8—1132no—
299C2×C8C22×D11312yes—
300C4⋊C4—21no—
301C4⋊C4—2262no—
302C4⋊C4—2262no—
303C4⋊C4C22×D11312yes—
304C22⋊C4—2262no—
305C22⋊C4—2262no—
306C23—21no—
307C23—1131no—
308C23—1131no—
309C23—4521no—
310C23—4522no—
311C23—4522no—
312C23—2262no—
313C23—2264no—
314C23—2262no—
315C23—2261no—
316C23D4×D11311yescharacteristic
317Q8—21no—
318Q8—1132no—
319Q8—4522no—
320Q8—2264no—
321Q8—2262no—
322Q8—2262no—
323Q8—2261no—
324Q8C2×D45212yes—
325D4—24no—
326D4—21no—
327D4—1132no—
328D4—2264no—
329D4—2264no—
330D4—2264no—
331D4—2264no—
332D4—2261no—
333D4C2×D45212yes—
334C2×C4—21no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—1131no—
339C2×C4—1131no—
340C2×C4—4522no—
341C2×C4—2264no—
342C2×C4—2264no—
343C2×C4—2262no—
344C2×C4—2264no—
345C2×C4—2262no—
346C2×C4—2261no—
347C2×C4—2262no—
348C2×C4—2262no—
349C2×C4—2264no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4D4×D11311yescharacteristic
355C2×C4D4×D11312yes—
356C2×C4C2×D45212yes—
357C2×C4C23×D11311yescharacteristic
358C8—22no—
359C8—2262no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—41no—
364C22—41no—
365C22—1132no—
366C22—4524no—
367C22—4528no—
368C22—4521no—
369C22—4521no—
370C22—2262no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22—2261no—
375C22—2261no—
376C22#1681359212yes—
377C22C2×D4×D11311yescharacteristic
378C4—22no—
379C4—42no—
380C4—4522no—
381C4—2261no—
382C4—2261no—
383C4—2262no—
384C4#1681359212yes—
385C4C2×D4×D11311yescharacteristic
386C4C22×D45211yescharacteristic
387C2—22no—
388C2—42no—
389C2—4522no—
390C2—4521no—
391C2—2262no—
392C2C2×#1681359211yescharacteristic
393C2#137×D11311yescharacteristic
394C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×D113C2
hypercenter#417D113
hypocenterC113#3007
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#16813655C2semidirect
3. C2×#16813652C2semidirect
4. C2×#16813602C2semidirect
5. #20298763C2semidirect
6. #20298761C2semidirect
7. #20298755C2semidirect
8. #20298750C2semidirect
9. #20298597C2semidirect
10. #20298561C2semidirect
11. #417×C113C2semidirect
19. C22×Dic226C22semidirect
27. C2×Dic452C22semidirect
28. C2×#14268637C22semidirect
29. C2×#14268636C22semidirect
30. C2×#14268635C22semidirect
31. C2×#14268631C22semidirect
35. #16813602C22semidirect
38. #16813545C22semidirect
39. #16813542C22semidirect
41. #16813534C22semidirect
43. C2×M16×C113C22semidirect
44. C2×C4⋊C4×C113C22semidirect
45. #103×C113C22semidirect
46. #102×C113C22semidirect
179. C2×D113#137semidirect
198. C113#3007semidirect
208. #417D113semidirect
231. C2×M16C2×D113semidirect
237. C2×C4⋊C4C2×D113semidirect
240. #103C2×D113semidirect
242. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1132
C2×#168136552
C2×#168136522
C2×#168136022
#202987632
#202987612
#202987552
#202987502
#202985972
#202985612
#417×C1132
#3007113