Finite Group Databasebeta

← #28402134

Subgroups — #28402134

Order 14464.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813655C211yesmaximal, characteristic, complemented
2C2×#16813644C211yesmaximal, characteristic, complemented
3#20299257C211yesmaximal, characteristic, complemented
4#20299253C211yesmaximal, characteristic, complemented
5#20298992C211yesmaximal, characteristic, complemented
6#20298844C211yesmaximal, characteristic, complemented
7#20298839C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298809C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298762C211yesmaximal, characteristic, complemented
12#20298756C211yesmaximal, characteristic, complemented
13#20298745C211yesmaximal, characteristic, complemented
14#20298700C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268647C2211yescharacteristic
19C22×Dic226C2211yescharacteristic
20#16813655—24no—
21#16813644—24no—
22C2×Dic452C2211yescharacteristic
23C2×Dic452C2211yescharacteristic
24C2×Dic452C2211yescharacteristic
25C2×Dic452C2211yescharacteristic
26C2×#14268636C2211yescharacteristic
27C2×#14268636C2211yescharacteristic
28C2×#14268636C2211yescharacteristic
29C2×#14268636C2211yescharacteristic
30C2×D904C2211yescharacteristic
31#16813622C2211yescharacteristic
32#16813610C2211yescharacteristic
33#16813608—21no—
34#16813604—21no—
35#16813604—21no—
36#16813601C2211yescharacteristic
37#16813601C2211yescharacteristic
38#16813601C2211yescharacteristic
39#16813600—21no—
40#16813596C2211yescharacteristic
41#16813594—21no—
42#16813593—21no—
43C4×Dic226C2211yescharacteristic
44C4×D452C2211yescharacteristic
45#16813582—21no—
46C4⋊C4×D113—21no—
47#16813556C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813547C2211yescharacteristic
51#16813547C2211yescharacteristic
52#16813544C2211yescharacteristic
53#16813544C2211yescharacteristic
54C2×M16×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic
56C4×D4×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C22⋊C8×C113C2211yescharacteristic
60#97×C113C2211yescharacteristic
61#14268647—22no—
62#14268647—22no—
63#14268647—22no—
64#14268647—41no—
65#14268647—41no—
66#14268647—41no—
67C2×Dic226—22no—
68C2×Dic226—21no—
69C2×Dic226—41no—
70C2×Dic226C2311yescharacteristic
71C2×Dic226C2311yescharacteristic
72C2×Dic226C2311yescharacteristic
73C2×Dic226C2311yescharacteristic
74C2×D452C2311yescharacteristic
75C2×D452C2311yescharacteristic
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79C2×C22⋊D113—21no—
80C22×Dic113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113—21no—
84C2×C4×D113—21no—
85Dic452—22no—
86Dic452—22no—
87Dic452—22no—
88Dic452—41no—
89#14268636—22no—
90#14268636—22no—
91#14268636—41no—
92#14268636D414yescomplemented
93D904—22no—
94C4⋊Dic113—21no—
95C4⋊Dic113—21no—
96C4⋊Dic113C2311yescharacteristic
97C4⋊Dic113C2311yescharacteristic
98#14268626—21no—
99#14268626—21no—
100#14268626—21no—
101#14268626—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104C22⋊Dic113—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109C4×Dic113—21no—
110C2×D4×C113D411yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C22×C4×C113C2311yescharacteristic
113M16×C113—22no—
114C2×C8×C113—22no—
115C2×C8×C113C2311yescharacteristic
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113C2311yescharacteristic
123C23×C113C2×D411yescharacteristic
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127D4×C113—41no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—42no—
148D452—21no—
149D452—21no—
150D452—21no—
151D452C2×D412yes—
152C4×D113—42no—
153C4×D113—42no—
154C4×D113—42no—
155C4×D113—42no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—21no—
161Dic226—21no—
162Dic226—21no—
163Dic226—42no—
164Dic226C2×D412yes—
165C8×C113—21no—
166C8×C113—21no—
167C8×C113—21no—
168C8×C113C2×D412yes—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113C22×D411yescharacteristic
176C2×D113—22no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C4×C113—21no—
183C4×C113—21no—
184C4×C113—21no—
185C4×C113—21no—
186C4×C113C22×D411yescharacteristic
187C4×C113H(5,𝔽2)11yescharacteristic
188Dic113—22no—
189Dic113—41no—
190Dic113—41no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—41no—
196C2×C113D4211yescharacteristic
197C2×C113#57511yescharacteristic
198C2×C113#57811yescharacteristic
199D113—42no—
200D113—81no—
201#3269—1131nomaximal, Sylow
202C113#326911yescharacteristic, complemented, Sylow
203C2×#137—1131no—
204C2×#135—1131no—
205#548—1131no—
206#547—1131no—
207#497—1131no—
208#468—1131no—
209#467—1131no—
210#463—1131no—
211#462—1131no—
212#452—1131no—
213#452—1131no—
214#451—1131no—
215#449—1131no—
216#440—1131no—
217#435D11311yescharacteristic, complemented
218C2×#41—1131no—
219C2×#41—1131no—
220C2×#41—1131no—
221C22×Q8—1131no—
222#137—2264no—
223#135—2264no—
224C2×Q16—1131no—
225C2×Q16—1131no—
226C2×Q16—1131no—
227C2×Q16—1131no—
228C2×SD16—1131no—
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×D8—1131no—
233C2×M16C2×D11311yescharacteristic
234C22×C8C2×D11311yescharacteristic
235C4⋊Q8—1131no—
236#124—1131no—
237#124—2261no—
238#123—2261no—
239#123—2261no—
240C22⋊Q8—1131no—
241C22⋊Q8—1131no—
242C22⋊Q8—1131no—
243C22⋊Q8—2261no—
244#121—1131no—
245#121—2261no—
246#121—2261no—
247C4×Q8—1131no—
248C4×D4—1131no—
249C4×D4—2261no—
250C4×D4C2×D11311yescharacteristic
251C2×C4⋊C4—2261no—
252#107—1131no—
253C4⋊C8C2×D11311yescharacteristic
254#103—1131no—
255#103—1131no—
256#103—1131no—
257#103—1131no—
258#102—1131no—
259#102—1131no—
260C22⋊C8C2×D11311yescharacteristic
261C22⋊C8C2×D11311yescharacteristic
262#97C2×D11311yescharacteristic
263#41—4521no—
264#41—4521no—
265#41—4521no—
266#41—2262no—
267#41—2262no—
268#41—2262no—
269C2×Q8—1131no—
270C2×Q8—1131no—
271C2×Q8—1131no—
272C2×Q8—1131no—
273C2×Q8—4521no—
274C2×Q8—2262no—
275C2×Q8—2261no—
276C2×D4—1131no—
277C2×D4—1131no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4D45211yescharacteristic
283C22×C4—2261no—
284C22×C4—2261no—
285C22×C4—2261no—
286C22×C4—2261no—
287C22×C4—2261no—
288C22×C4C22×D11311yescharacteristic
289C22×C4C22×D11311yescharacteristic
290Q16—4521no—
291Q16—2262no—
292Q16—2262no—
293Q16—2262no—
294SD16—1134no—
295SD16—4521no—
296SD16—2262no—
297SD16—2262no—
298D8—2262no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D11311yescharacteristic
302C2×C8C22×D11311yescharacteristic
303C2×C8C22×D11311yescharacteristic
304C2×C8C22×D11311yescharacteristic
305C4⋊C4—1131no—
306C4⋊C4—1131no—
307C4⋊C4—2261no—
308C4⋊C4—2261no—
309C4⋊C4—2261no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4—2261no—
313C4⋊C4D45211yescharacteristic
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4D45211yescharacteristic
322C22⋊C4D45211yescharacteristic
323C42—2261no—
324C42C22×D11311yescharacteristic
325C23—2261no—
326C23—2261no—
327C23C2×D45211yescharacteristic
328C23C2×D45211yescharacteristic
329Q8—1132no—
330Q8—4522no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8—2261no—
335Q8—2261no—
336Q8—2261no—
337Q8—2261no—
338D4—41no—
339D4—1132no—
340D4—4522no—
341D4—4522no—
342D4—4522no—
343D4—4522no—
344D4—2261no—
345D4—2261no—
346D4—2261no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—4522no—
352C2×C4—4522no—
353C2×C4—4522no—
354C2×C4—4522no—
355C2×C4—4522no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4C2×D45211yescharacteristic
363C2×C4C2×D45211yescharacteristic
364C2×C4C2×D45211yescharacteristic
365C2×C4C2×D45211yescharacteristic
366C2×C4C23×D11311yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D11312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—2262no—
383C22C22×D45211yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—4521no—
389C4—4521no—
390C4—4521no—
391C4—4521no—
392C4—4521no—
393C4—2262no—
394C4C2×D4×D11311yescharacteristic
395C4#1681366811yescharacteristic
396C2—41no—
397C2—41no—
398C2—9041no—
399C2—4522no—
400C2D4×D45211yescharacteristic
401C2#2029939811yescharacteristic
402C2#2029941511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3269
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C2×#16813644C2semidirect
3. #20299257C2semidirect
4. #20299253C2semidirect
5. #20298992C2semidirect
6. #20298844C2semidirect
7. #20298839C2semidirect
8. #20298814C2semidirect
9. #20298809C2semidirect
10. #20298762C2semidirect
11. #20298762C2semidirect
12. #20298756C2semidirect
13. #20298745C2semidirect
14. #20298700C2semidirect
15. #435×C113C2semidirect
92. #14268636D4semidirect
202. C113#3269semidirect
217. #435D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C2×#168136442
#202992572
#202992532
#202989922
#202988442
#202988392
#202988142
#202988092
#202987622
#202987562
#202987452
#202987002
#435×C1132
#3269113