Finite Group Databasebeta

← #28400108

Subgroups — #28400108

Order 14464.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C2×#16813641C211yesmaximal, characteristic, complemented
3#20299161C211yesmaximal, characteristic, complemented
4#20299077C211yesmaximal, characteristic, complemented
5#20298821C211yesmaximal, characteristic, complemented
6#20298819C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298811C211yesmaximal, characteristic, complemented
9#20298797C211yesmaximal, characteristic, complemented
10#20298795C211yesmaximal, characteristic, complemented
11#20298791C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813646—24no—
20#16813641—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×#14268636C2211yescharacteristic
23C2×#14268635C2211yescharacteristic
24C2×#14268635C2211yescharacteristic, complemented
25C2×#14268635C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813618C2211yescharacteristic
30#16813610C2211yescharacteristic
31#16813609C2211yescharacteristic
32#16813594—21no—
33#16813594—21no—
34#16813590—21no—
35#16813590—21no—
36C4×Dic226C2211yescharacteristic, complemented
37#16813587C2211yescharacteristic, complemented
38D4×Dic113C2211yescharacteristic, complemented
39C4×C22⋊D113—21no—
40#16813582—21no—
41#16813579C2211yescharacteristic
42#16813578—21no—
43C2×#14268626—21no—
44C4⋊C4×D113C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic
51#16813543C2211yescharacteristic
52#16813543C2211yescharacteristic, complemented
53#16813542C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic, complemented
56#127×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268646—22no—
63#14268646—22no—
64#14268646—22no—
65#14268646D414yescomplemented
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74D4×D113—22no—
75D4×D113—22no—
76C22×Dic113—21no—
77C22×Dic113—21no—
78C22×Dic113—21no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81Dic452—22no—
82#14268636—22no—
83#14268635—22no—
84#14268635—22no—
85#14268635—22no—
86#14268632—22no—
87#14268630—22no—
88C2×#11744751C2311yescharacteristic
89C2×#11744751C2311yescharacteristic
90C8×D113—22no—
91C4⋊Dic113C2311yescharacteristic
92#14268626—21no—
93#14268626—21no—
94#14268626—21no—
95#14268626D411yescharacteristic
96#14268626D411yescharacteristic
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624D411yescharacteristic
103#14268624D411yescharacteristic
104C4×Dic113—21no—
105C4×Dic113—21no—
106C4×Dic113C2311yescharacteristic
107C2×D4×C113—21no—
108C2×D4×C113—21no—
109C2×D4×C113C2311yescharacteristic
110C2×D4×C113C2311yescharacteristic
111C2×D4×C113C2311yescharacteristic
112C22×C4×C113—21no—
113D8×C113—22no—
114D8×C113—22no—
115C2×C8×C113C2311yescharacteristic
116C2×C8×C113C2311yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C23×C113—21no—
122C23×C113—21no—
123C22×D113—21no—
124C22×D113—42no—
125C22×D113—81no—
126C22×D113—81no—
127C22×D113C2×D411yescharacteristic
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—81no—
134D4×C113—81no—
135D4×C113C2×D412yes—
136C2×C4×C113—21no—
137C2×C4×C113—81no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2411yescharacteristic
141C22⋊D113—24no—
142C22⋊D113—42no—
143C22⋊D113—42no—
144C22⋊D113—81no—
145C22⋊D113—81no—
146C2×Dic113—21no—
147C2×Dic113—24no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—42no—
151C2×Dic113—81no—
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154C2×Dic113C2×D411yescharacteristic
155D452—21no—
156D452—21no—
157C4×D113—81no—
158C4×D113C2×D412yes—
159C4×D113#4112yes—
160Dic226—21no—
161Dic226—21no—
162Dic226—21no—
163Dic226C2×D412yes—
164C8×C113—21no—
165C8×C113—21no—
166#11744751—21no—
167#11744751—21no—
168C22×C113—22no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113C22×D411yescharacteristic
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C2×D113#12112yes—
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113C22×D411yescharacteristic
189C4×C113C2×#4111yescharacteristic
190Dic113—22no—
191Dic113—21no—
192Dic113—21no—
193Dic113—41no—
194Dic113—41no—
195Dic113#12112yes—
196C2×C113—42no—
197C2×C113—81no—
198C2×C113—81no—
199C2×C113C2×#12111yescharacteristic
200C2×C113#57611yescharacteristic
201C2×C113#57711yescharacteristic
202D113—22no—
203D113—81no—
204#3045—1131nomaximal, Sylow
205C113#304511yescharacteristic, complemented, Sylow
206C2×AGL(1,ℤ/8)—1131no—
207C2×#135—1131no—
208#535—1131no—
209#520—1131no—
210#464—1131no—
211#464—1131no—
212#463—1131no—
213#463—1131no—
214#460—1131no—
215#460—1131no—
216#459—1131no—
217#459D11311yescharacteristic, complemented
218#424—1131no—
219#417—1131no—
220C2×#102—1131no—
221C2×#41—1131no—
222C2×#41—1131no—
223C22×D4—1131no—
224AGL(1,ℤ/8)—2264no—
225#135—2264no—
226C2×Q16—1131no—
227C2×SD16—1131no—
228C2×SD16—1131no—
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×D8—1131no—
232C2×D8C2×D11311yescharacteristic
233C2×D8C2×D11311yescharacteristic, complemented
234C2×M16—1131no—
235C22×C8—1131no—
236#127—1131no—
237#127C2×D11311yescharacteristic
238#124—1131no—
239#124—1131no—
240#121—2261no—
241#121—2261no—
242#120—2261no—
243#120—2261no—
244C4×Q8—1131no—
245C4×Q8—1131no—
246C4×D4—1131no—
247C4×D4—2261no—
248C4×D4—2261no—
249C4×D4C2×D11311yescharacteristic, complemented
250#117—1131no—
251#117—2261no—
252C2×C4⋊C4—1131no—
253C2×C4⋊C4—2261no—
254C4⋊C8—1131no—
255C4⋊C8—1131no—
256C4⋊C8—1131no—
257C4⋊C8C2×D11311yescharacteristic, complemented
258#103—1131no—
259#103—1131no—
260#102—1131no—
261#102—1131no—
262#102—1131no—
263#102—1131no—
264#102C2×D11311yescharacteristic
265#102C2×D11311yescharacteristic, complemented
266C24—2261no—
267#41—1134no—
268#41—2262no—
269#41—2262no—
270#41—2262no—
271C2×Q8—1131no—
272C2×Q8—1131no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—1131no—
276C2×D4—2262no—
277C2×D4—2262no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4C22×D11311yescharacteristic
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—21no—
287C22×C4—1131no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4—2261no—
292Q16—2262no—
293SD16—2262no—
294SD16—2262no—
295SD16—2262no—
296SD16—2262no—
297D8—22no—
298D8—22no—
299D8—2262no—
300M16—2262no—
301C2×C8—1131no—
302C2×C8—1131no—
303C2×C8—2262no—
304C2×C8C22×D11311yescharacteristic
305C2×C8C22×D11311yescharacteristic
306C4⋊C4—1131no—
307C4⋊C4—1131no—
308C4⋊C4—1131no—
309C4⋊C4—2261no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4C22×D11311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—1131no—
315C22⋊C4—1131no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C42—1131no—
322C42—2261no—
323C42—2261no—
324C42C22×D11311yescharacteristic
325C23—21no—
326C23—21no—
327C23—21no—
328C23—1131no—
329C23—9041no—
330C23—9041no—
331C23—4522no—
332C23—2261no—
333Q8—1132no—
334Q8—2261no—
335Q8—2261no—
336Q8—2261no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—9041no—
345D4—9041no—
346D4—4522no—
347D4—4522no—
348D4—2264no—
349D4—2261no—
350D4—2261no—
351D4D4×D11312yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—1131no—
355C2×C4—1132no—
356C2×C4—1132no—
357C2×C4—1131no—
358C2×C4—1131no—
359C2×C4—9041no—
360C2×C4—9041no—
361C2×C4—4522no—
362C2×C4—2264no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4D4×D11311yescharacteristic
367C2×C4D4×D11311yescharacteristic
368C2×C4C23×D11311yescharacteristic
369C8—21no—
370C8—21no—
371C8—2261no—
372C8—2261no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—1132no—
383C22—9044no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22—2261no—
388C22—2261no—
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—1132no—
394C4—4521no—
395C4—4521no—
396C4—2262no—
397C4—2261no—
398C4—2261no—
399C4C2×D4×D11311yescharacteristic
400C4#41×D11311yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—9041no—
405C2—2262no—
406C2#121×D11311yescharacteristic
407C2#2029939911yescharacteristic
408C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3045
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×#16813641C2semidirect
3. #20299161C2semidirect
4. #20299077C2semidirect
5. #20298821C2semidirect
6. #20298819C2semidirect
7. #20298813C2semidirect
8. #20298811C2semidirect
9. #20298797C2semidirect
10. #20298795C2semidirect
11. #20298791C2semidirect
12. #20298623C2semidirect
13. #20298596C2semidirect
14. #102×D113C2semidirect
15. #459×C113C2semidirect
21. C2×Dic452C22semidirect
24. C2×#14268635C22semidirect
25. C2×#14268635C22semidirect
36. C4×Dic226C22semidirect
37. #16813587C22semidirect
38. D4×Dic113C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813545C22semidirect
52. #16813543C22semidirect
55. C2×D8×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
60. #102×C113C22semidirect
65. #14268646D4semidirect
205. C113#3045semidirect
217. #459D113semidirect
233. C2×D8C2×D113semidirect
249. C4×D4C2×D113semidirect
257. C4⋊C8C2×D113semidirect
265. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×#168136412
#202991612
#202990772
#202988212
#202988192
#202988132
#202988112
#202987972
#202987952
#202987912
#202986232
#202985962
#102×D1132
#459×C1132
#3045113