Finite Group Databasebeta

← #28400264

Subgroups — #28400264

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813654C211yesmaximal, characteristic, complemented
2C2×#16813628C211yesmaximal, characteristic, complemented
3#20299178C211yesmaximal, characteristic
4#20299171C211yesmaximal, characteristic, complemented
5#20298854C211yesmaximal, characteristic, complemented
6#20298853C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298845C211yesmaximal, characteristic, complemented
9#20298838C211yesmaximal, characteristic, complemented
10#20298830C211yesmaximal, characteristic, complemented
11#20298827C211yesmaximal, characteristic, complemented
12#20298639C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#467×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813654—24no—
20C2×#14268637C2211yescharacteristic
21C2×#14268636C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23#16813628—24no—
24C2×#14268631C2211yescharacteristic
25C2×#14268630C2211yescharacteristic
26C2×#14268630C2211yescharacteristic
27C2×C8×D113C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813621—21no—
30#16813608—21no—
31#16813607—21no—
32#16813604—21no—
33#16813602C2211yescharacteristic
34#16813601C2211yescharacteristic
35#16813600—21no—
36#16813598C2211yescharacteristic
37#16813598C2211yescharacteristic
38#16813597—21no—
39#16813597C2211yescharacteristic
40#16813596C2211yescharacteristic
41#16813595—21no—
42#16813595—21no—
43#16813580C2211yescharacteristic
44C4⋊C4×D113C2211yescharacteristic
45#16813555C2211yescharacteristic
46#16813554C2211yescharacteristic
47#16813553C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813546C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813544C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic
57C22⋊Q8×C113C2211yescharacteristic
58#107×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#103×C113C2211yescharacteristic
61#14268648—22no—
62#14268648—22no—
63#14268647—22no—
64#14268647—22no—
65C2×Dic226—21no—
66C2×Dic226D411yescharacteristic
67C2×Dic226C2311yescharacteristic
68Q8×D113—22no—
69Q8×D113—22no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452D411yescharacteristic
73C2×D452C2311yescharacteristic
74C2×C22⋊D113—21no—
75C2×C22⋊D113D411yescharacteristic
76C2×C22⋊D113D411yescharacteristic
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81C2×C4×D113C2311yescharacteristic
82#14268637—22no—
83#14268636—22no—
84#14268634—22no—
85#14268631—22no—
86#14268630—22no—
87#14268630D414yescomplemented
88C2×#11744751C2311yescharacteristic
89C2×#11744751C2311yescharacteristic
90C8×D113—22no—
91C8×D113—22no—
92C4⋊Dic113—21no—
93C4⋊Dic113C2311yescharacteristic
94C4⋊Dic113C2311yescharacteristic
95#14268626—21no—
96#14268626—21no—
97#14268626—21no—
98#14268626—21no—
99C22⋊Dic113—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106C4×Dic113—21no—
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C22×C4×C113C2311yescharacteristic
110Q16×C113—22no—
111C2×C8×C113—22no—
112C2×C8×C113C2311yescharacteristic
113C2×C8×C113C2311yescharacteristic
114C4⋊C4×C113—21no—
115C4⋊C4×C113—21no—
116C4⋊C4×C113C2311yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C23×C113C2×D411yescharacteristic
121C22×D113—21no—
122C22×D113C2×D411yescharacteristic
123C22×D113C2×D411yescharacteristic
124Q8×C113—21no—
125Q8×C113—21no—
126Q8×C113—21no—
127Q8×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×C113C2×D411yescharacteristic
135C2×C4×C113C2411yescharacteristic
136C22⋊D113—22no—
137C22⋊D113—22no—
138C22⋊D113—81no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144D452—22no—
145D452—21no—
146D452—21no—
147D452—42no—
148D452—81no—
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—42no—
152C4×D113—42no—
153C4×D113—81no—
154C4×D113C2×D412yes—
155C4×D113#4112yes—
156Dic226—22no—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160C8×C113—21no—
161C8×C113C2×D412yes—
162#11744751—21no—
163#11744751C2×D412yes—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113C22×D411yescharacteristic
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113#12112yes—
177C4×C113—21no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113C22×D411yescharacteristic
183C4×C113C2×#4111yescharacteristic
184Dic113—21no—
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188Dic113#12112yes—
189C2×C113—41no—
190C2×C113C2×#12111yescharacteristic
191C2×C113#57711yescharacteristic
192C2×C113#57811yescharacteristic
193D113—22no—
194D113—41no—
195D113—81no—
196#3063—1131nomaximal, Sylow
197C113#306311yescharacteristic, complemented, Sylow
198C2×#137—1131no—
199C2×#131—1131no—
200#537—1131no—
201#536—1131no—
202#470—1131no—
203#470—1131no—
204#468—1131no—
205#468—1131no—
206#467—1131no—
207#467D11311yescharacteristic, complemented
208#465—1131no—
209#465—1131no—
210#428—1131no—
211#416—1131no—
212C2×#103—1131no—
213C2×#41—1131no—
214C2×#41—1131no—
215C22×Q8—1131no—
216#137—2264no—
217C2×Q16—1131no—
218C2×Q16C2×D11311yescharacteristic
219C2×SD16—1131no—
220C2×SD16—1131no—
221#131—2264no—
222C2×M16—1131no—
223C2×M16—1131no—
224C2×M16—1131no—
225C22×C8—1131no—
226C22×C8—1131no—
227C22×C8C2×D11311yescharacteristic
228C4⋊Q8—2261no—
229#124—2261no—
230#123—2261no—
231#123—2261no—
232C22⋊Q8—1131no—
233C22⋊Q8—1131no—
234C22⋊Q8—1131no—
235C22⋊Q8—1131no—
236C22⋊Q8—2261no—
237C22⋊Q8C2×D11311yescharacteristic
238C22⋊Q8C2×D11311yescharacteristic
239#121—1131no—
240#121—1131no—
241#121—2261no—
242#121—2261no—
243#121—2261no—
244#117—1131no—
245C2×C4⋊C4—1131no—
246#107—1131no—
247#107C2×D11311yescharacteristic
248#106—1131no—
249#106—1131no—
250#103—1131no—
251#103—1131no—
252#103—1131no—
253#103—1131no—
254#103C2×D11311yescharacteristic
255#103C2×D11311yescharacteristic
256#102—1131no—
257#102—1131no—
258#41—2262no—
259#41—2262no—
260#41—2262no—
261#41—2262no—
262C2×Q8—1131no—
263C2×Q8—1131no—
264C2×Q8—2261no—
265C2×Q8—2262no—
266C2×Q8—2262no—
267C2×Q8C22×D11311yescharacteristic
268C2×Q8C22×D11311yescharacteristic
269C2×D4—1131no—
270C2×D4—1131no—
271C2×D4—1131no—
272C2×D4—1131no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2261no—
276C22×C4—1131no—
277C22×C4—1131no—
278C22×C4—2261no—
279C22×C4—2261no—
280C22×C4—2261no—
281C22×C4C22×D11311yescharacteristic
282Q16—22no—
283Q16—2262no—
284SD16—2262no—
285SD16—2262no—
286M16—1134no—
287M16—2262no—
288M16—2262no—
289C2×C8—22no—
290C2×C8—1131no—
291C2×C8—1131no—
292C2×C8—2262no—
293C2×C8—2262no—
294C2×C8C22×D11311yescharacteristic
295C2×C8C22×D11311yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—1131no—
299C4⋊C4—1131no—
300C4⋊C4—2261no—
301C4⋊C4—2261no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4C22×D11311yescharacteristic
306C4⋊C4C22×D11311yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C42—2261no—
317C23—1131no—
318C23—1131no—
319C23—2261no—
320C23D4×D11311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—4522no—
326Q8—2262no—
327Q8—2261no—
328Q8—2261no—
329D4—9041no—
330D4—9041no—
331D4—4522no—
332D4—2262no—
333D4—2262no—
334D4—2262no—
335D4—2261no—
336D4—2261no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—1131no—
344C2×C4—1132no—
345C2×C4—1132no—
346C2×C4—1131no—
347C2×C4—9041no—
348C2×C4—4522no—
349C2×C4—4522no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4D4×D11311yescharacteristic
356C2×C4C23×D11311yescharacteristic
357C8—21no—
358C8—1132no—
359C8—2261no—
360C8D4×D11312yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—1132no—
365C22—4521no—
366C22—4521no—
367C22—4521no—
368C22—2261no—
369C22—2261no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22C2×D4×D11311yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—1132no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4C2×D4×D11311yescharacteristic
385C4#41×D11311yescharacteristic
386C2—41no—
387C2—9041no—
388C2—4521no—
389C2—2262no—
390C2#121×D11311yescharacteristic
391C2#2029940511yescharacteristic
392C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#467×C113C2
socleC22×C113C22×D4
prime radical#20299178C2
hypercenter#467D113
hypocenterC113#3063
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×#16813628C2semidirect
4. #20299171C2semidirect
5. #20298854C2semidirect
6. #20298853C2semidirect
7. #20298846C2semidirect
8. #20298845C2semidirect
9. #20298838C2semidirect
10. #20298830C2semidirect
11. #20298827C2semidirect
12. #20298639C2semidirect
13. #20298593C2semidirect
14. #103×D113C2semidirect
15. #467×C113C2semidirect
87. #14268630D4semidirect
197. C113#3063semidirect
207. #467D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×#168136282
#202991782
#202991712
#202988542
#202988532
#202988462
#202988452
#202988382
#202988302
#202988272
#202986392
#202985932
#103×D1132
#467×C1132
#3063113