Finite Group Databasebeta

← #28399830

Subgroups — #28399830

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×#16813653C211yesmaximal, characteristic, complemented
3C2×#16813598C211yesmaximal, characteristic, complemented
4#20298759C212yesmaximal, complemented
5#20298757C212yesmaximal, complemented
6#20298752C212yesmaximal, complemented
7#20298747C212yesmaximal, complemented
8#20298600C211yesmaximal, characteristic, complemented
9#20298599C211yesmaximal, characteristic, complemented
10#20298561C211yesmaximal, characteristic, complemented
11C2×#137×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×#14268647—21no—
14C2×#14268647C2211yescharacteristic
15C2×#14268646—21no—
16C2×#14268646C2211yescharacteristic
17#41×D113—24no—
18#41×D113—24no—
19C2×Q8×D113C2211yescharacteristic
20C2×D4×D113—21no—
21C2×D4×D113C2211yescharacteristic
22C22×C4×D113—21no—
23C22×C4×D113C2211yescharacteristic
24#16813653—24no—
25C2×#14268637C2212yescomplemented
26C2×#14268634C2212yescomplemented
27C2×#14268631C2211yescharacteristic, complemented
28#16813598—21no—
29#16813598—21no—
30#16813598C2212yes—
31#16813598C2212yescomplemented
32C2×C4⋊Dic113C2211yescharacteristic, complemented
33C2×#14268626—21no—
34C2×#14268624—21no—
35#16813547C2212yescomplemented
36#16813546C2212yescomplemented
37#16813544C2212yescomplemented
38#16813543C2212yescomplemented
39#16813534C2212yes—
40#16813534C2212yescomplemented
41C2×#41×C113C2211yescharacteristic
42C22×Q8×C113C2211yescharacteristic, complemented
43#137×C113—24no—
44C2×Q16×C113C2212yescomplemented
45C2×SD16×C113C2212yescomplemented
46C2×M16×C113C2211yescharacteristic, complemented
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×Dic226C2311yescharacteristic
59Q8×D113—22no—
60Q8×D113—22no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66D4×D113—28no—
67D4×D113—22no—
68D4×D113—22no—
69C22×Dic113—21no—
70C22×Dic113—21no—
71C22×Dic113D411yescharacteristic
72C2×C4×D113—28no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—22no—
76C2×C4×D113—22no—
77C2×C4×D113—21no—
78C2×C4×D113D411yescharacteristic
79C2×C4×D113D411yescharacteristic
80C2×C4×D113C2311yescharacteristic
81C2×C4×D113C2311yescharacteristic
82#14268637—24no—
83#14268634—24no—
84#14268631—22no—
85C2×#11744751C2312yes—
86C4⋊Dic113—21no—
87C4⋊Dic113C2312yes—
88#14268626—22no—
89#14268626—22no—
90#14268624—22no—
91#14268624—22no—
92#41×C113—22no—
93#41×C113D414yes—
94C2×Q8×C113—21no—
95C2×Q8×C113—22no—
96C2×Q8×C113—22no—
97C2×Q8×C113C2312yes—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113—21no—
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104Q16×C113—24no—
105SD16×C113—24no—
106M16×C113—22no—
107C2×C8×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×C113—22no—
121Q8×C113—22no—
122Q8×C113—42no—
123Q8×C113C2×D412yes—
124D4×C113—24no—
125D4×C113—21no—
126D4×C113C2×D412yes—
127C2×C4×C113—21no—
128C2×C4×C113—24no—
129C2×C4×C113—22no—
130C2×C4×C113—42no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D412yes—
133C2×C4×C113C2×D412yes—
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—24no—
136C22⋊D113—24no—
137C22⋊D113—24no—
138C2×Dic113—24no—
139C2×Dic113—22no—
140C2×Dic113—21no—
141C2×Dic113—22no—
142C2×Dic113—42no—
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145D452—24no—
146D452—21no—
147D452C2×D412yes—
148C4×D113—24no—
149C4×D113—24no—
150C4×D113—22no—
151C4×D113—24no—
152C4×D113—22no—
153C4×D113—21no—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—21no—
157Dic226—24no—
158Dic226—21no—
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×#137D11311yescharacteristic, complemented
202C2×C22⋊Q8—1131no—
203#452—1132no—
204#452—1132no—
205#451—1132no—
206#450—1132no—
207#417—1131no—
208#417—1131no—
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×Q8C2×D11311yescharacteristic, complemented
220C22×D4—1131no—
221C22×D4—2261no—
222C23×C4—1131no—
223C23×C4—2261no—
224#137—24no—
225#137—2264no—
226C2×Q16—1132no—
227C2×Q16C2×D11312yescomplemented
228C2×SD16—1132no—
229C2×SD16C2×D11312yescomplemented
230C2×M16—1131no—
231C2×M16C2×D11311yescharacteristic, complemented
232C22⋊Q8—1132no—
233C22⋊Q8—1132no—
234C22⋊Q8—2261no—
235C22⋊Q8—2261no—
236C2×C4⋊C4—1131no—
237C2×C4⋊C4—2261no—
238C2×C22⋊C4—2261no—
239#103—1132no—
240#103—1132no—
241#102—1132no—
242#102—1132no—
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#41C22⋊D11314yes—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—1131no—
261C2×Q8—2261no—
262C2×Q8—2262no—
263C2×Q8—2262no—
264C2×Q8C22×D11312yes—
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—24no—
293Q16—2264no—
294SD16—24no—
295SD16—2264no—
296M16—22no—
297M16—2262no—
298C2×C8—1132no—
299C2×C8C22×D11312yes—
300C4⋊C4—1132no—
301C4⋊C4—2262no—
302C4⋊C4—2262no—
303C4⋊C4—2261no—
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—22no—
319Q8—22no—
320Q8—42no—
321Q8—1132no—
322Q8—2264no—
323Q8—2261no—
324Q8C2×C22⋊D11312yes—
325D4—24no—
326D4—21no—
327D4—1132no—
328D4—2264no—
329D4—2264no—
330D4—2264no—
331D4—2264no—
332D4—2261no—
333D4C2×C22⋊D11312yes—
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×C22⋊D11312yes—
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#1681359012yes—
377C22C2×D4×D11311yescharacteristic
378C4—22no—
379C4—42no—
380C4—4522no—
381C4—2261no—
382C4—2261no—
383C4—2262no—
384C4#1681359012yes—
385C4C2×D4×D11311yescharacteristic
386C4C22×C22⋊D11311yescharacteristic
387C2—22no—
388C2—42no—
389C2—4522no—
390C2—4521no—
391C2—2262no—
392C2C2×#1681359011yescharacteristic
393C2#137×D11311yescharacteristic
394C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×D113C2
hypercenterC2×#137D113
hypocenterC113#3007
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#16813653C2semidirect
3. C2×#16813598C2semidirect
4. #20298759C2semidirect
5. #20298757C2semidirect
6. #20298752C2semidirect
7. #20298747C2semidirect
8. #20298600C2semidirect
9. #20298599C2semidirect
10. #20298561C2semidirect
11. C2×#137×C113C2semidirect
25. C2×#14268637C22semidirect
26. C2×#14268634C22semidirect
27. C2×#14268631C22semidirect
31. #16813598C22semidirect
32. C2×C4⋊Dic113C22semidirect
35. #16813547C22semidirect
36. #16813546C22semidirect
37. #16813544C22semidirect
38. #16813543C22semidirect
40. #16813534C22semidirect
42. C22×Q8×C113C22semidirect
44. C2×Q16×C113C22semidirect
45. C2×SD16×C113C22semidirect
46. C2×M16×C113C22semidirect
179. C2×D113#137semidirect
198. C113#3007semidirect
201. C2×#137D113semidirect
219. C22×Q8C2×D113semidirect
227. C2×Q16C2×D113semidirect
229. C2×SD16C2×D113semidirect
231. C2×M16C2×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×#168136532
C2×#168135982
#202987592
#202987572
#202987522
#202987472
#202986002
#202985992
#202985612
C2×#137×C1132
#3007113