Finite Group Databasebeta

← #28400025

Subgroups — #28400025

Order 14464.

496 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×#16813642C211yesmaximal, characteristic, complemented
2#20299144C211yesmaximal, characteristic, complemented
3#41×Dic113C211yesmaximal, characteristic, complemented
4#20298822C211yesmaximal, characteristic, complemented
5#20298818C211yesmaximal, characteristic, complemented
6#20298815C211yesmaximal, characteristic, complemented
7#20298811C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298801C211yesmaximal, characteristic, complemented
10#20298796C211yesmaximal, characteristic, complemented
11#20298791C211yesmaximal, characteristic, complemented
12C2×#16813551C211yesmaximal, characteristic, complemented
13#20298595C211yesmaximal, characteristic, complemented
14#20298594C211yesmaximal, characteristic, complemented
15C2×#135×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17#16813642—24no—
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813618C2211yescharacteristic
25#16813611C2211yescharacteristic
26#16813609C2211yescharacteristic
27#16813594—21no—
28#16813594—21no—
29Q8×Dic113C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31D4×Dic113—21no—
32D4×Dic113—21no—
33D4×Dic113C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35C4×C22⋊D113—21no—
36C4×C22⋊D113—21no—
37#16813581—21no—
38#16813581C2211yescharacteristic
39C2×C4×Dic113—21no—
40C2×C4×Dic113C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813543C2211yescharacteristic
52#16813543C2211yescharacteristic
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#14268647—22no—
62#14268647—22no—
63C2×Dic226C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C22×Dic113—21no—
70C22×Dic113D411yescharacteristic
71C22×Dic113D411yescharacteristic
72C2×C4×D113—21no—
73#14268637—22no—
74#14268635—22no—
75#14268634—22no—
76#14268632—22no—
77C2×#11744751—22no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113D411yescharacteristic
97C4×Dic113D411yescharacteristic
98C4×Dic113C2311yescharacteristic
99C4×Dic113C2311yescharacteristic
100#41×C113—22no—
101#41×C113—22no—
102#41×C113—22no—
103#41×C113D414yescomplemented
104C2×Q8×C113C2311yescharacteristic
105C2×Q8×C113C2311yescharacteristic
106C2×D4×C113—21no—
107C2×D4×C113—21no—
108C2×D4×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113—21no—
111C22×C4×C113—21no—
112C22×C4×C113C2311yescharacteristic
113Q16×C113—22no—
114SD16×C113—22no—
115SD16×C113—22no—
116D8×C113—22no—
117C2×C8×C113—22no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C23×C113—21no—
121C23×C113—21no—
122C23×C113C2×D411yescharacteristic
123C22×D113—21no—
124Q8×C113—21no—
125Q8×C113—21no—
126Q8×C113—21no—
127Q8×C113C2×D412yes—
128D4×C113—24no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—42no—
133D4×C113C2×D412yes—
134C2×C4×C113—21no—
135C2×C4×C113—24no—
136C2×C4×C113—21no—
137C2×C4×C113—42no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D412yes—
140C2×C4×C113#4112yes—
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—42no—
143C22⋊D113—42no—
144C22⋊D113—42no—
145C2×Dic113—22no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—41no—
150C2×Dic113—42no—
151C2×Dic113—42no—
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154C2×Dic113C2×D411yescharacteristic
155C2×Dic113C2×D411yescharacteristic
156D452—21no—
157D452—21no—
158C4×D113—42no—
159Dic226—21no—
160Dic226—21no—
161C8×C113—21no—
162C8×C113—21no—
163#11744751—21no—
164#11744751—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—22no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113#12112yes—
174C22×C113C22×D411yescharacteristic
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—41no—
178C4×C113—22no—
179C4×C113—41no—
180C4×C113#12112yes—
181C4×C113C22×D411yescharacteristic
182C4×C113C2×#4111yescharacteristic
183Dic113—21no—
184Dic113—21no—
185Dic113—21no—
186Dic113—41no—
187Dic113—41no—
188Dic113—41no—
189Dic113#13512yescomplemented
190C2×C113—22no—
191C2×C113—42no—
192C2×C113—81no—
193C2×C113C2×#12111yescharacteristic
194C2×C113C2×#13511yescharacteristic
195C2×C113#57511yescharacteristic
196D113—81no—
197#3035—1131nomaximal, Sylow
198C113#303511yescharacteristic, complemented, Sylow
199C2×#135—1131no—
200C2×#135D11311yescharacteristic, complemented
201#532—1131no—
202C4×#41—1131no—
203#464—1131no—
204#464—1131no—
205#463—1131no—
206#463—1131no—
207#462—1131no—
208#461—1131no—
209#460—1131no—
210#459—1131no—
211C2×C4⋊C8—1131no—
212#416—1131no—
213#416—1131no—
214C2×#41—1131no—
215C2×#41C2×D11311yescharacteristic
216C2×#41C2×D11311yescharacteristic
217#135—24no—
218#135—2264no—
219C2×Q16—1131no—
220C2×Q16C2×D11311yescharacteristic
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16C2×D11311yescharacteristic
224C2×SD16C2×D11311yescharacteristic
225C2×D8—1131no—
226C2×D8C2×D11311yescharacteristic
227C22×C8—1131no—
228C22×C8C2×D11311yescharacteristic
229C4⋊Q8—1131no—
230#127—1131no—
231#124—1131no—
232#124—1131no—
233#121—2261no—
234#121—2261no—
235C4×Q8—1131no—
236C4×Q8—1131no—
237C4×D4—1131no—
238C4×D4—1131no—
239C4×D4—2261no—
240C4×D4—2261no—
241C4×D4—2261no—
242C4×D4—2261no—
243#117—1131no—
244#117—2261no—
245C2×C42—1131no—
246C2×C42—2261no—
247C4⋊C8—1131no—
248C4⋊C8—1131no—
249C4⋊C8—1131no—
250C4⋊C8—1131no—
251#103—1131no—
252#103—1131no—
253#103—1131no—
254#103—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102—1131no—
259#41—22no—
260#41—22no—
261#41—22no—
262#41—2262no—
263#41—2262no—
264#41C22⋊D11314yescomplemented
265C2×Q8—1131no—
266C2×Q8C22×D11311yescharacteristic
267C2×Q8C22×D11311yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—1131no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4C22×D11311yescharacteristic
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1131no—
279C22×C4—1131no—
280C22×C4—2261no—
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4C22×D11311yescharacteristic
284Q16—22no—
285Q16—2262no—
286SD16—22no—
287SD16—22no—
288SD16—2262no—
289SD16—2262no—
290D8—22no—
291D8—2262no—
292C2×C8—22no—
293C2×C8—1131no—
294C2×C8—1131no—
295C2×C8—2262no—
296C2×C8C22×D11311yescharacteristic
297C2×C8C22×D11311yescharacteristic
298C4⋊C4—1131no—
299C4⋊C4—1131no—
300C4⋊C4—2261no—
301C4⋊C4—2261no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C42—1131no—
312C42—1131no—
313C42—1131no—
314C42—1131no—
315C42—2261no—
316C42—2261no—
317C42—2261no—
318C23—21no—
319C23—21no—
320C23—2261no—
321C23D4×D11311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—2261no—
326Q8—2261no—
327Q8C2×C22⋊D11312yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—4522no—
334D4—4522no—
335D4—4522no—
336D4—2261no—
337D4—2261no—
338D4C2×C22⋊D11312yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—1131no—
344C2×C4—1131no—
345C2×C4—1131no—
346C2×C4—1131no—
347C2×C4—4522no—
348C2×C4—4522no—
349C2×C4—4522no—
350C2×C4—4521no—
351C2×C4—2262no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4D4×D11311yescharacteristic
356C2×C4C2×C22⋊D11312yes—
357C2×C4#1426864612yes—
358C2×C4C23×D11311yescharacteristic
359C8—21no—
360C8—21no—
361C8—2261no—
362C8—2261no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—4521no—
372C22—4521no—
373C22—4521no—
374C22#1681359412yes—
375C22C2×D4×D11311yescharacteristic
376C4—22no—
377C4—41no—
378C4—1132no—
379C4—4521no—
380C4—4521no—
381C4—4521no—
382C4—2261no—
383C4—2261no—
384C4—2261no—
385C4#1681359412yes—
386C4C22×C22⋊D11311yescharacteristic
387C4C2×#1426864611yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—9041no—
392C2C2×#1681359411yescharacteristic
393C2#135×D11311yescharacteristic
394C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#135×C113C2
socleC22×C113C22×D4
hypercenterC2×#135D113
hypocenterC113#3035
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#16813642C2semidirect
2. #20299144C2semidirect
3. #41×Dic113C2semidirect
4. #20298822C2semidirect
5. #20298818C2semidirect
6. #20298815C2semidirect
7. #20298811C2semidirect
8. #20298806C2semidirect
9. #20298801C2semidirect
10. #20298796C2semidirect
11. #20298791C2semidirect
12. C2×#16813551C2semidirect
13. #20298595C2semidirect
14. #20298594C2semidirect
15. C2×#135×C113C2semidirect
103. #41×C113D4semidirect
189. Dic113#135semidirect
198. C113#3035semidirect
200. C2×#135D113semidirect
264. #41C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136422
#202991442
#41×Dic1132
#202988222
#202988182
#202988152
#202988112
#202988062
#202988012
#202987962
#202987912
C2×#168135512
#202985952
#202985942
C2×#135×C1132
#3035113