Finite Group Databasebeta

← #28400072

Subgroups — #28400072

Order 14464.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299161C211yesmaximal, characteristic, complemented
4#20299070C211yesmaximal, characteristic, complemented
5#20298814C211yesmaximal, characteristic, complemented
6#20298813C211yesmaximal, characteristic, complemented
7#20298812C211yesmaximal, characteristic, complemented
8#20298811C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298791C211yesmaximal, characteristic, complemented
11#20298790C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813646—24no—
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic
23C2×#14268632C2211yescharacteristic
24C2×#14268632C2211yescharacteristic
25C2×#14268632C2211yescharacteristic, complemented
26D8×D113—24no—
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813618C2211yescharacteristic, complemented
30#16813610C2211yescharacteristic, complemented
31#16813609C2211yescharacteristic, complemented
32#16813594—21no—
33#16813594—21no—
34#16813590—21no—
35#16813590—21no—
36C4×D452C2211yescharacteristic, complemented
37D4×Dic113C2211yescharacteristic, complemented
38#16813584C2211yescharacteristic, complemented
39C4×C22⋊D113—21no—
40#16813582—21no—
41#16813580C2211yescharacteristic
42#16813579C2211yescharacteristic
43C2×#14268624—21no—
44C22⋊C4×D113—21no—
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813543C2211yescharacteristic, complemented
53#16813542C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic, complemented
56#127×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268646—22no—
64#14268646—22no—
65C2×Dic226C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73D4×D113—22no—
74D4×D113—22no—
75D4×D113—22no—
76D4×D113D414yescomplemented
77C22×Dic113—21no—
78C22×Dic113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113C2311yescharacteristic
82#14268636—22no—
83#14268635—22no—
84D904—22no—
85#14268632—22no—
86#14268632—22no—
87#14268632—22no—
88#14268630—22no—
89C2×#11744751C2311yescharacteristic
90C2×#11744751C2311yescharacteristic
91C8×D113—22no—
92C4⋊Dic113C2311yescharacteristic
93#14268626D411yescharacteristic
94#14268626D411yescharacteristic
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624D411yescharacteristic
104#14268624D411yescharacteristic
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—24no—
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—81no—
128C22×D113—81no—
129C22×D113—81no—
130C22×D113—81no—
131C22×D113C2×D411yescharacteristic
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—81no—
138D4×C113—81no—
139D4×C113C2×D412yes—
140C2×C4×C113—21no—
141C2×C4×C113—81no—
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2411yescharacteristic
145C22⋊D113—24no—
146C22⋊D113—42no—
147C22⋊D113—42no—
148C22⋊D113—81no—
149C22⋊D113—81no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—42no—
153C2×Dic113—81no—
154C2×Dic113C2×D411yescharacteristic
155C2×Dic113C2×D411yescharacteristic
156C2×Dic113C2×D411yescharacteristic
157D452—21no—
158D452—21no—
159D452—21no—
160D452C2×D412yes—
161C4×D113—81no—
162C4×D113—81no—
163C4×D113C2×D412yes—
164C4×D113#4112yes—
165Dic226—21no—
166Dic226—21no—
167C8×C113—21no—
168C8×C113—21no—
169#11744751—21no—
170#11744751—21no—
171C22×C113—22no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113C22×D411yescharacteristic
181C2×D113—21no—
182C2×D113—21no—
183C2×D113—22no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—84no—
190C2×D113—84no—
191C2×D113#12112yes—
192C4×C113—21no—
193C4×C113—21no—
194C4×C113—41no—
195C4×C113C22×D411yescharacteristic
196C4×C113C2×#4111yescharacteristic
197Dic113—21no—
198Dic113—21no—
199Dic113—41no—
200Dic113—41no—
201Dic113#12112yes—
202C2×C113—42no—
203C2×C113—81no—
204C2×C113—81no—
205C2×C113C2×#12111yescharacteristic
206C2×C113#57611yescharacteristic
207C2×C113#57611yescharacteristic
208D113—22no—
209D113—42no—
210D113—81no—
211#3041—1131nomaximal, Sylow
212C113#304111yescharacteristic, complemented, Sylow
213C2×AGL(1,ℤ/8)—1131no—
214C22×D8—1131no—
215#535—1131no—
216#518—1131no—
217#463—1131no—
218#463—1131no—
219#463—1131no—
220#463—1131no—
221#459—1131no—
222#459—1131no—
223#459—1131no—
224#459D11311yescharacteristic, complemented
225#424—1131no—
226#418—1131no—
227#416—1131no—
228C2×#41—1131no—
229C22×D4—1131no—
230C22×D4—1131no—
231AGL(1,ℤ/8)—2264no—
232C2×SD16—1131no—
233C2×SD16—1131no—
234C2×D8—1131no—
235C2×D8—1131no—
236C2×D8—1131no—
237C2×D8—1131no—
238C2×D8—2264no—
239C2×D8C2×D11311yescharacteristic
240C2×D8C2×D11311yescharacteristic, complemented
241C2×M16—1131no—
242C22×C8—1131no—
243#127—1131no—
244#127C2×D11311yescharacteristic, complemented
245#124—1131no—
246#124—1131no—
247#121—2261no—
248#121—2261no—
249#120—2261no—
250#120—2261no—
251C4×D4—1131no—
252C4×D4—1131no—
253C4×D4—1131no—
254C4×D4—2261no—
255C4×D4—2261no—
256C4×D4C2×D11311yescharacteristic, complemented
257#117—1131no—
258#117—1131no—
259C2×C22⋊C4—2261no—
260C2×C22⋊C4—2261no—
261C4⋊C8—1131no—
262C4⋊C8—1131no—
263C4⋊C8—1131no—
264C4⋊C8C2×D11311yescharacteristic, complemented
265#103—1131no—
266#103—1131no—
267#102—1131no—
268#102—1131no—
269#102—1131no—
270#102—1131no—
271#102C2×D11311yescharacteristic, complemented
272#102C2×D11311yescharacteristic, complemented
273C24—2261no—
274C24—2261no—
275#41—2262no—
276#41—2262no—
277C2×Q8—1131no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—1134no—
281C2×D4—1131no—
282C2×D4—1131no—
283C2×D4—2262no—
284C2×D4—2262no—
285C2×D4—2262no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2261no—
290C2×D4—2261no—
291C2×D4C22×D11311yescharacteristic
292C2×D4C22×D11311yescharacteristic
293C2×D4C22×D11311yescharacteristic
294C22×C4—21no—
295C22×C4—1131no—
296C22×C4—2261no—
297C22×C4—2261no—
298C22×C4—2261no—
299C22×C4—2261no—
300SD16—2262no—
301SD16—2262no—
302D8—22no—
303D8—22no—
304D8—2262no—
305D8—2262no—
306D8—2262no—
307D8—2262no—
308M16—2262no—
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⋊C4C22×D11311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—1131no—
320C22⋊C4—1131no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C42—1131no—
330C42—2261no—
331C42C22×D11311yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—1131no—
336C23—9041no—
337C23—9041no—
338C23—9041no—
339C23—9041no—
340C23—4522no—
341C23—2264no—
342C23—2261no—
343C23—2261no—
344Q8—2261no—
345Q8—2261no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—1132no—
354D4—9041no—
355D4—9041no—
356D4—4522no—
357D4—4522no—
358D4—2264no—
359D4—2261no—
360D4—2261no—
361D4—2261no—
362D4D4×D11312yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—1131no—
366C2×C4—1132no—
367C2×C4—1132no—
368C2×C4—1131no—
369C2×C4—1131no—
370C2×C4—9041no—
371C2×C4—9041no—
372C2×C4—9041no—
373C2×C4—4522no—
374C2×C4—2261no—
375C2×C4—2261no—
376C2×C4D4×D11311yescharacteristic
377C2×C4D4×D11311yescharacteristic
378C2×C4C23×D11311yescharacteristic
379C8—21no—
380C8—21no—
381C8—2261no—
382C8—2261no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—1132no—
393C22—9044no—
394C22—9044no—
395C22—4521no—
396C22—4521no—
397C22—4521no—
398C22—4521no—
399C22—4521no—
400C22—2262no—
401C22—2261no—
402C22—2261no—
403C22C2×D4×D11311yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—1132no—
408C4—4521no—
409C4—4521no—
410C4—2261no—
411C4—2261no—
412C4C2×D4×D11311yescharacteristic
413C4#41×D11311yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—9041no—
418C2—4522no—
419C2—2262no—
420C2#121×D11311yescharacteristic
421C2#2029939911yescharacteristic
422C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3041
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×D8×D113C2semidirect
3. #20299161C2semidirect
4. #20299070C2semidirect
5. #20298814C2semidirect
6. #20298813C2semidirect
7. #20298812C2semidirect
8. #20298811C2semidirect
9. #20298792C2semidirect
10. #20298791C2semidirect
11. #20298790C2semidirect
12. #20298623C2semidirect
13. #20298601C2semidirect
14. #20298591C2semidirect
15. #459×C113C2semidirect
20. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
25. C2×#14268632C22semidirect
29. #16813618C22semidirect
30. #16813610C22semidirect
31. #16813609C22semidirect
36. C4×D452C22semidirect
37. D4×Dic113C22semidirect
38. #16813584C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813545C22semidirect
50. #16813544C22semidirect
51. #16813543C22semidirect
52. #16813543C22semidirect
53. #16813542C22semidirect
55. C2×D8×C113C22semidirect
56. #127×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #102×C113C22semidirect
60. #102×C113C22semidirect
76. D4×D113D4semidirect
212. C113#3041semidirect
224. #459D113semidirect
240. C2×D8C2×D113semidirect
244. #127C2×D113semidirect
256. C4×D4C2×D113semidirect
264. C4⋊C8C2×D113semidirect
271. #102C2×D113semidirect
272. #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×D8×D1132
#202991612
#202990702
#202988142
#202988132
#202988122
#202988112
#202987922
#202987912
#202987902
#202986232
#202986012
#202985912
#459×C1132
#3041113