Finite Group Databasebeta

← #28399857

Subgroups — #28399857

Order 14464.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813669C211yesmaximal, characteristic, complemented
2C2×#16813646C211yesmaximal, characteristic, complemented
3C2×SD16×D113C211yesmaximal, characteristic, complemented
4#20299164C211yesmaximal, characteristic, complemented
5#20298744C211yesmaximal, characteristic, complemented
6#20298743C211yesmaximal, characteristic, complemented
7#20298740C211yesmaximal, characteristic, complemented
8#20298739C211yesmaximal, characteristic, complemented
9#20298738C211yesmaximal, characteristic, complemented
10#20298736C211yesmaximal, characteristic, complemented
11#20298735C211yesmaximal, characteristic, complemented
12#20298605C211yesmaximal, characteristic, complemented
13#20298591C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16#16813669—24no—
17#16813669—24no—
18C2×#14268647—21no—
19C2×#14268647C2211yescharacteristic
20C2×#14268646—21no—
21C2×#14268646—21no—
22C2×#14268646C2211yescharacteristic
23C2×#14268646C2211yescharacteristic, complemented
24C22×Dic226—21no—
25C22×Dic226C2211yescharacteristic, complemented
26C2×Q8×D113C2211yescharacteristic
27C2×Q8×D113C2211yescharacteristic, complemented
28C2×D4×D113C2211yescharacteristic
29#16813646—24no—
30C2×#14268636C2211yescharacteristic
31C2×#14268636C2211yescharacteristic
32C2×#14268635C2211yescharacteristic
33C2×#14268635C2211yescharacteristic
34C2×#14268634C2211yescharacteristic
35SD16×D113—24no—
36C2×#14268632C2211yescharacteristic
37C2×#14268630C2211yescharacteristic
38C2×C8×D113C2211yescharacteristic
39#16813618—21no—
40#16813608—21no—
41#16813597C2211yescharacteristic
42#16813596C2211yescharacteristic
43#16813593C2211yescharacteristic
44#16813592—21no—
45#16813590—21no—
46#16813580C2211yescharacteristic
47#16813547C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813545C2211yescharacteristic, complemented
52#16813543C2211yescharacteristic, complemented
53C22⋊#11744751C2211yescharacteristic, complemented
54#16813534C2211yescharacteristic, complemented
55#16813534C2211yescharacteristic, complemented
56C2×#41×C113C2211yescharacteristic, complemented
57C2×SD16×C113C2211yescharacteristic
58C2×D8×C113C2211yescharacteristic
59#121×C113C2211yescharacteristic
60#103×C113C2211yescharacteristic, complemented
61#102×C113C2211yescharacteristic, complemented
62C22⋊C8×C113C2211yescharacteristic, complemented
63C23×D113—21no—
64#14268647—28no—
65#14268647—22no—
66#14268647—22no—
67#14268646—28no—
68#14268646—28no—
69#14268646—22no—
70#14268646—22no—
71#14268646—22no—
72#14268646D414yescomplemented
73C2×Dic226—28no—
74C2×Dic226—21no—
75C2×Dic226—21no—
76C2×Dic226—21no—
77C2×Dic226—22no—
78C2×Dic226—22no—
79C2×Dic226D411yescharacteristic
80C2×Dic226C2311yescharacteristic
81C2×Dic226C2311yescharacteristic
82Q8×D113—22no—
83Q8×D113—22no—
84Q8×D113—22no—
85Q8×D113D414yescomplemented
86C2×D452—21no—
87C2×D452D411yescharacteristic
88C2×D452C2311yescharacteristic
89C2×C22⋊D113—21no—
90C2×C22⋊D113—21no—
91C2×C22⋊D113—21no—
92C2×C22⋊D113—21no—
93C2×C22⋊D113—21no—
94C2×C22⋊D113D411yescharacteristic
95C2×C22⋊D113D411yescharacteristic
96D4×D113—22no—
97D4×D113—22no—
98C22×Dic113—21no—
99C22×Dic113—21no—
100C22×Dic113—21no—
101C2×C4×D113—21no—
102C2×C4×D113—21no—
103C2×C4×D113C2311yescharacteristic
104C2×C4×D113C2311yescharacteristic
105#14268636—22no—
106#14268636—22no—
107#14268635—22no—
108#14268635—22no—
109#14268634—22no—
110#14268632—22no—
111#14268630—22no—
112C2×#11744751C2311yescharacteristic
113C2×#11744751C2311yescharacteristic
114C8×D113—22no—
115C4⋊Dic113C2311yescharacteristic
116C22⋊Dic113—21no—
117#14268624—21no—
118#14268624—21no—
119#14268624—21no—
120C4×Dic113—21no—
121#41×C113—22no—
122#41×C113—22no—
123C2×Q8×C113C2311yescharacteristic
124C2×D4×C113—21no—
125C2×D4×C113—21no—
126C2×D4×C113C2311yescharacteristic
127C2×D4×C113C2311yescharacteristic
128C22×C4×C113—21no—
129C22×C4×C113C2311yescharacteristic
130SD16×C113—22no—
131D8×C113—22no—
132C2×C8×C113C2311yescharacteristic
133C2×C8×C113C2311yescharacteristic
134C4⋊C4×C113C2311yescharacteristic
135C22⋊C4×C113—21no—
136C23×C113—21no—
137C23×C113—21no—
138C23×C113C2×D411yescharacteristic
139C22×D113—21no—
140C22×D113—42no—
141C22×D113—81no—
142C22×D113—81no—
143C22×D113C2×D411yescharacteristic
144C22×D113C2×D411yescharacteristic
145Q8×C113—21no—
146Q8×C113C2×D412yes—
147D4×C113—24no—
148D4×C113—21no—
149D4×C113—21no—
150D4×C113—21no—
151D4×C113—81no—
152D4×C113C2×D412yes—
153C2×C4×C113—24no—
154C2×C4×C113—21no—
155C2×C4×C113—21no—
156C2×C4×C113—21no—
157C2×C4×C113—21no—
158C2×C4×C113C2×D411yescharacteristic
159C2×C4×C113C2411yescharacteristic
160C22⋊D113—24no—
161C22⋊D113—24no—
162C22⋊D113—22no—
163C22⋊D113—22no—
164C22⋊D113—42no—
165C22⋊D113—81no—
166C22⋊D113—81no—
167C2×Dic113—24no—
168C2×Dic113—24no—
169C2×Dic113—21no—
170C2×Dic113—21no—
171C2×Dic113—24no—
172C2×Dic113—21no—
173C2×Dic113C2×D411yescharacteristic
174C2×Dic113C2×D411yescharacteristic
175D452—22no—
176D452—21no—
177D452—21no—
178D452—81no—
179C4×D113—24no—
180C4×D113—24no—
181C4×D113—21no—
182C4×D113—21no—
183C4×D113C2×D412yes—
184C4×D113C2×D412yes—
185Dic226—24no—
186Dic226—24no—
187Dic226—21no—
188Dic226—21no—
189Dic226—24no—
190Dic226—22no—
191Dic226C2×D412yes—
192Dic226C2×D412yes—
193C8×C113—21no—
194C8×C113—21no—
195#11744751—21no—
196#11744751—21no—
197C22×C113—21no—
198C22×C113—22no—
199C22×C113—21no—
200C22×C113—21no—
201C22×C113—41no—
202C22×C113—41no—
203C22×C113—41no—
204C22×C113—41no—
205C22×C113—41no—
206C22×C113C22×D411yescharacteristic
207C2×D113—21no—
208C2×D113—21no—
209C2×D113—21no—
210C2×D113—21no—
211C2×D113—21no—
212C2×D113—41no—
213C2×D113—41no—
214C2×D113—41no—
215C2×D113—84no—
216C2×D113#12012yes—
217C4×C113—21no—
218C4×C113—22no—
219C4×C113—41no—
220C4×C113C22×D411yescharacteristic
221C4×C113C22×D411yescharacteristic
222Dic113—21no—
223Dic113—22no—
224Dic113—22no—
225Dic113—41no—
226Dic113#12012yes—
227C2×C113—41no—
228C2×C113—42no—
229C2×C113—81no—
230C2×C113C2×#12011yescharacteristic
231C2×C113#57711yescharacteristic
232C2×C113#57711yescharacteristic
233D113—22no—
234D113—41no—
235D113—81no—
236#3010—1131nomaximal, Sylow
237C113#301011yescharacteristic, complemented, Sylow
238C2×2−1+4—1131no—
239C2×AGL(1,ℤ/8)—1131no—
240C22×SD16—1131no—
241#535—1131no—
242#449—1131no—
243#449—1131no—
244#449—1131no—
245#449D11311yescharacteristic, complemented
246#448—1131no—
247#448—1131no—
248#448—1131no—
249#448—1131no—
250#419—1131no—
251#416—1131no—
252#408—1131no—
2532−1+4—2264no—
2542−1+4—2264no—
255C2×#41—1131no—
256C2×#41—1131no—
257C2×#41—1131no—
258C2×#41—2261no—
259C2×#41—2261no—
260C2×#41—2261no—
261C2×#41C2×D11311yescharacteristic, complemented
262C22×Q8—1131no—
263C22×Q8—1131no—
264C22×Q8—1131no—
265C22×Q8—2261no—
266C22×D4—1131no—
267AGL(1,ℤ/8)—2264no—
268C2×SD16—1131no—
269C2×SD16—1131no—
270C2×SD16—1131no—
271C2×SD16—1131no—
272C2×SD16—1131no—
273C2×SD16—2264no—
274C2×SD16C2×D11311yescharacteristic
275C2×D8—1131no—
276C2×D8C2×D11311yescharacteristic
277C2×M16—1131no—
278C22×C8—1131no—
279#127—2261no—
280#124—2261no—
281#121—1131no—
282#121—1131no—
283#121—1131no—
284#121C2×D11311yescharacteristic
285#120—2261no—
286#120—2261no—
287#117—1131no—
288#103—1131no—
289#103—1131no—
290#103—1131no—
291#103—1131no—
292#103—1131no—
293#103C2×D11311yescharacteristic, complemented
294#102—1131no—
295#102C2×D11311yescharacteristic, complemented
296C22⋊C8—1131no—
297C22⋊C8—1131no—
298C22⋊C8—1131no—
299C22⋊C8C2×D11311yescharacteristic, complemented
300C24—2261no—
301#41—22no—
302#41—22no—
303#41—1134no—
304#41—2262no—
305#41—2262no—
306#41—2268no—
307#41—2262no—
308#41—2262no—
309#41—2268no—
310#41—2268no—
311#41—2262no—
312C2×Q8—1131no—
313C2×Q8—1134no—
314C2×Q8—1131no—
315C2×Q8—1131no—
316C2×Q8—2261no—
317C2×Q8—2261no—
318C2×Q8—2262no—
319C2×Q8—2262no—
320C2×Q8—2268no—
321C2×Q8—2262no—
322C2×Q8—2262no—
323C2×Q8—2262no—
324C2×Q8—2261no—
325C2×Q8C22×D11311yescharacteristic
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—1131no—
329C2×D4—1131no—
330C2×D4—1131no—
331C2×D4—1131no—
332C2×D4—2261no—
333C2×D4—2262no—
334C2×D4—2262no—
335C2×D4—2261no—
336C2×D4—2261no—
337C2×D4—2261no—
338C2×D4—2261no—
339C2×D4—2261no—
340C2×D4C22×D11311yescharacteristic
341C2×D4C22×D11311yescharacteristic
342C22×C4—21no—
343C22×C4—1131no—
344C22×C4—1131no—
345C22×C4—2261no—
346C22×C4—2261no—
347C22×C4—2261no—
348C22×C4—2261no—
349C22×C4—2261no—
350C22×C4C22×D11311yescharacteristic
351SD16—22no—
352SD16—2262no—
353SD16—2262no—
354SD16—2262no—
355SD16—2262no—
356SD16—2262no—
357D8—22no—
358D8—2262no—
359M16—2262no—
360C2×C8—1131no—
361C2×C8—1131no—
362C2×C8—2262no—
363C2×C8C22×D11311yescharacteristic
364C2×C8C22×D11311yescharacteristic
365C4⋊C4—1131no—
366C4⋊C4C22×D11311yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—2261no—
369C22⋊C4—2261no—
370C22⋊C4—2261no—
371C22⋊C4—2261no—
372C42—2261no—
373C23—21no—
374C23—21no—
375C23—1131no—
376C23—1131no—
377C23—9041no—
378C23—9041no—
379C23—4522no—
380C23—2261no—
381C23D4×D11311yescharacteristic
382Q8—21no—
383Q8—1132no—
384Q8—1132no—
385Q8—2262no—
386Q8—2264no—
387Q8—2264no—
388Q8—2264no—
389Q8—2261no—
390Q8—2261no—
391Q8D4×D11312yes—
392D4—24no—
393D4—21no—
394D4—21no—
395D4—21no—
396D4—81no—
397D4—9041no—
398D4—9041no—
399D4—9041no—
400D4—4522no—
401D4—2262no—
402D4—2262no—
403D4—2262no—
404D4—2264no—
405D4—2264no—
406D4—2261no—
407D4—2261no—
408D4D4×D11312yes—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—1131no—
415C2×C4—1132no—
416C2×C4—1132no—
417C2×C4—1131no—
418C2×C4—2264no—
419C2×C4—2264no—
420C2×C4—2264no—
421C2×C4—2261no—
422C2×C4—2264no—
423C2×C4—2264no—
424C2×C4—2261no—
425C2×C4—2261no—
426C2×C4—2261no—
427C2×C4—2261no—
428C2×C4D4×D11311yescharacteristic
429C2×C4C23×D11311yescharacteristic
430C8—21no—
431C8—21no—
432C8—2261no—
433C8—2261no—
434C22—21no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—1132no—
444C22—9044no—
445C22—4521no—
446C22—4521no—
447C22—4521no—
448C22—2261no—
449C22—2261no—
450C22—2261no—
451C22—2261no—
452C22—2261no—
453C22C2×D4×D11311yescharacteristic
454C4—21no—
455C4—22no—
456C4—41no—
457C4—1132no—
458C4—4521no—
459C4—2261no—
460C4—2262no—
461C4—2262no—
462C4C2×D4×D11311yescharacteristic
463C4C2×D4×D11311yescharacteristic
464C2—41no—
465C2—42no—
466C2—81no—
467C2—9041no—
468C2—4521no—
469C2—2262no—
470C2#120×D11311yescharacteristic
471C2#2029940511yescharacteristic
472C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3010
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#16813669C2semidirect
2. C2×#16813646C2semidirect
3. C2×SD16×D113C2semidirect
4. #20299164C2semidirect
5. #20298744C2semidirect
6. #20298743C2semidirect
7. #20298740C2semidirect
8. #20298739C2semidirect
9. #20298738C2semidirect
10. #20298736C2semidirect
11. #20298735C2semidirect
12. #20298605C2semidirect
13. #20298591C2semidirect
14. #20298563C2semidirect
15. #449×C113C2semidirect
23. C2×#14268646C22semidirect
25. C22×Dic226C22semidirect
27. C2×Q8×D113C22semidirect
47. #16813547C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
51. #16813545C22semidirect
52. #16813543C22semidirect
53. C22⋊#11744751C22semidirect
54. #16813534C22semidirect
55. #16813534C22semidirect
56. C2×#41×C113C22semidirect
60. #103×C113C22semidirect
61. #102×C113C22semidirect
62. C22⋊C8×C113C22semidirect
72. #14268646D4semidirect
85. Q8×D113D4semidirect
237. C113#3010semidirect
245. #449D113semidirect
261. C2×#41C2×D113semidirect
293. #103C2×D113semidirect
295. #102C2×D113semidirect
299. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
C2×#168136462
C2×SD16×D1132
#202991642
#202987442
#202987432
#202987402
#202987392
#202987382
#202987362
#202987352
#202986052
#202985912
#202985632
#449×C1132
#3010113