Finite Group Databasebeta

← #28402298

Subgroups — #28402298

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813643C211yesmaximal, characteristic, complemented
2#20299267C211yesmaximal, characteristic, complemented
3#20299247C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298827C211yesmaximal, characteristic, complemented
6#20298824C211yesmaximal, characteristic, complemented
7#20298806C211yesmaximal, characteristic, complemented
8#20298791C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298759C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298740C211yesmaximal, characteristic, complemented
13SD16×Dic113C211yesmaximal, characteristic, complemented
14C8×C22⋊D113C211yesmaximal, characteristic, complemented
15C2×#135×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18#16813643—24no—
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23C2×#14268632C2211yescharacteristic
24C2×C8×D113C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813618—21no—
27#16813618C2211yescharacteristic
28#16813605—21no—
29#16813603—21no—
30#16813601C2211yescharacteristic
31#16813598C2211yescharacteristic
32#16813596—21no—
33#16813596C2211yescharacteristic
34#16813594—21no—
35#16813593—21no—
36#16813593C2211yescharacteristic
37Q8×Dic113C2211yescharacteristic
38D4×Dic113C2211yescharacteristic
39C4×C22⋊D113—21no—
40C4×C22⋊D113C2211yescharacteristic
41C2×#14268626—21no—
42#16813554C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50C22⋊#11744751C2211yescharacteristic
51#16813534C2211yescharacteristic
52C8×Dic113C2211yescharacteristic
53C2×#41×C113C2211yescharacteristic
54C2×#41×C113C2211yescharacteristic
55#135×C113—24no—
56C2×Q16×C113C2211yescharacteristic
57C2×SD16×C113C2211yescharacteristic
58C2×SD16×C113C2211yescharacteristic
59C2×D8×C113C2211yescharacteristic
60C22×C8×C113C2211yescharacteristic
61#14268648—22no—
62#14268648—41no—
63#14268646—22no—
64#14268646—41no—
65C2×Dic226C2311yescharacteristic
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113D411yescharacteristic
74C22×Dic113—21no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78#14268637—22no—
79#14268636—22no—
80#14268635—41no—
81#14268634—41no—
82#14268632—22no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C8×D113—22no—
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93#14268626D411yescharacteristic
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113D411yescharacteristic
98#14268624—21no—
99#14268624—21no—
100#14268624D411yescharacteristic
101C4×Dic113—21no—
102C4×Dic113C2311yescharacteristic
103#41×C113—22no—
104#41×C113—22no—
105#41×C113—41no—
106#41×C113—41no—
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113—21no—
110C2×D4×C113—21no—
111C2×D4×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117SD16×C113—22no—
118SD16×C113D414yescomplemented
119D8×C113—22no—
120C2×C8×C113—22no—
121C2×C8×C113C2311yescharacteristic
122C2×C8×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113C2×D411yescharacteristic
128Q8×C113—21no—
129Q8×C113—21no—
130Q8×C113—21no—
131Q8×C113C2×D412yes—
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—42no—
136D4×C113—42no—
137D4×C113C2×D412yes—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—42no—
143C2×C4×C113—42no—
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2411yescharacteristic
146C22⋊D113—22no—
147C22⋊D113—42no—
148C22⋊D113—42no—
149C22⋊D113—81no—
150C22⋊D113—81no—
151C22⋊D113—81no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—42no—
156C2×Dic113—42no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159C2×Dic113C2×D411yescharacteristic
160D452—21no—
161D452—21no—
162D452—42no—
163C4×D113—21no—
164C4×D113—21no—
165C4×D113—42no—
166Dic226—21no—
167Dic226—21no—
168C8×C113—21no—
169C8×C113C2×D412yes—
170#11744751—21no—
171#11744751—21no—
172C22×C113—22no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113C22×D411yescharacteristic
182C2×D113—21no—
183C2×D113—21no—
184C2×D113—21no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C4×C113—22no—
189C4×C113—21no—
190C4×C113—41no—
191C4×C113C22×D411yescharacteristic
192C4×C113H(5,𝔽2)11yescharacteristic
193Dic113—21no—
194Dic113—21no—
195Dic113—41no—
196Dic113—41no—
197Dic113—41no—
198Dic113#13512yescomplemented
199C2×C113—41no—
200C2×C113—42no—
201C2×C113—81no—
202C2×C113D4211yescharacteristic
203C2×C113C2×#13511yescharacteristic
204C2×C113#57711yescharacteristic
205D113—41no—
206D113—81no—
207#3284—1131nomaximal, Sylow
208C113#328411yescharacteristic, complemented, Sylow
209C2×#135—1131no—
210C2×#135D11311yescharacteristic, complemented
211#550—1131no—
212#547—1131no—
213#492—1131no—
214#465—1131no—
215#465—1131no—
216#462—1131no—
217#459—1131no—
218#452—1131no—
219#452—1131no—
220#449—1131no—
221#449—1131no—
222C4×SD16—1131no—
223C8×D4—1131no—
224C2×#41—1131no—
225C2×#41—1131no—
226C2×#41C2×D11311yescharacteristic
227C2×#41C2×D11311yescharacteristic
228#135—24no—
229#135—2264no—
230C2×Q16—1131no—
231C2×Q16C2×D11311yescharacteristic
232C2×SD16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16C2×D11311yescharacteristic
236C2×SD16C2×D11311yescharacteristic
237C2×D8—1131no—
238C2×D8C2×D11311yescharacteristic
239C22×C8—1131no—
240C22×C8C2×D11311yescharacteristic
241C4⋊Q8—1131no—
242#127—1131no—
243#127—2261no—
244#123—2261no—
245#123—2261no—
246C22⋊Q8—1131no—
247C22⋊Q8—1131no—
248#121—1131no—
249#121—1131no—
250#121—2261no—
251#121—2261no—
252#121—2261no—
253C4×Q8—1131no—
254C4×D4—1131no—
255C4×D4—1131no—
256C4×D4—2261no—
257C2×C4⋊C4—2261no—
258#106—1131no—
259C4⋊C8—1131no—
260#103—1131no—
261#103—1131no—
262#103—1131no—
263#102—1131no—
264#102—1131no—
265#102—1131no—
266C22⋊C8—1131no—
267C22⋊C8—1131no—
268C4×C8—1131no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—4521no—
274#41—4521no—
275#41—2262no—
276#41—2262no—
277C2×Q8—1131no—
278C2×Q8C22×D11311yescharacteristic
279C2×Q8C22×D11311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—1131no—
283C2×D4—1131no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2261no—
290C2×D4C22×D11311yescharacteristic
291C2×D4C22×D11311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—1131no—
295C22×C4—2261no—
296C22×C4—2261no—
297C22×C4—2261no—
298C22×C4C22×D11311yescharacteristic
299Q16—22no—
300Q16—2262no—
301SD16—22no—
302SD16—4521no—
303SD16—4521no—
304SD16—2262no—
305SD16C22⋊D11314yescomplemented
306D8—22no—
307D8—2262no—
308C2×C8—22no—
309C2×C8—1131no—
310C2×C8—1131no—
311C2×C8—2262no—
312C2×C8C22×D11311yescharacteristic
313C2×C8C22×D11311yescharacteristic
314C4⋊C4—1131no—
315C4⋊C4—1131no—
316C4⋊C4—1131no—
317C4⋊C4—2261no—
318C4⋊C4—2261no—
319C4⋊C4—2261no—
320C4⋊C4—2261no—
321C4⋊C4—2261no—
322C22⋊C4—1131no—
323C22⋊C4—1131no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C42—1131no—
330C42—2261no—
331C23—21no—
332C23—21no—
333C23—1131no—
334C23—2261no—
335C23D4×D11311yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—2261no—
340Q8—2261no—
341Q8C2×C22⋊D11312yes—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—42no—
347D4—9041no—
348D4—9041no—
349D4—9041no—
350D4—4522no—
351D4—4522no—
352D4—4522no—
353D4—2262no—
354D4—2261no—
355D4—2261no—
356D4C2×C22⋊D11312yes—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—1131no—
364C2×C4—1131no—
365C2×C4—1131no—
366C2×C4—4522no—
367C2×C4—4522no—
368C2×C4—4522no—
369C2×C4—2261no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4D4×D11311yescharacteristic
375C2×C4C23×D11311yescharacteristic
376C8—21no—
377C8—2261no—
378C8—2261no—
379C8C2×C22⋊D11312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—4521no—
390C22—4521no—
391C22—4521no—
392C22—2261no—
393C22—2261no—
394C22—2261no—
395C22C2×D4×D11311yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—1132no—
400C4—4521no—
401C4—4521no—
402C4—4521no—
403C4—2261no—
404C4—2261no—
405C4C22×C22⋊D11311yescharacteristic
406C4#1681366711yescharacteristic
407C2—41no—
408C2—42no—
409C2—81no—
410C2—9041no—
411C2—4521no—
412C2D4×C22⋊D11311yescharacteristic
413C2#135×D11311yescharacteristic
414C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#135×C113C2
socleC22×C113C22×D4
hypercenterC2×#135D113
hypocenterC113#3284
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#16813643C2semidirect
2. #20299267C2semidirect
3. #20299247C2semidirect
4. #20298969C2semidirect
5. #20298827C2semidirect
6. #20298824C2semidirect
7. #20298806C2semidirect
8. #20298791C2semidirect
9. #20298760C2semidirect
10. #20298759C2semidirect
11. #20298743C2semidirect
12. #20298740C2semidirect
13. SD16×Dic113C2semidirect
14. C8×C22⋊D113C2semidirect
15. C2×#135×C113C2semidirect
118. SD16×C113D4semidirect
198. Dic113#135semidirect
208. C113#3284semidirect
210. C2×#135D113semidirect
305. SD16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136432
#202992672
#202992472
#202989692
#202988272
#202988242
#202988062
#202987912
#202987602
#202987592
#202987432
#202987402
SD16×Dic1132
C8×C22⋊D1132
C2×#135×C1132
#3284113