Finite Group Databasebeta

← #28402078

Subgroups — #28402078

Order 14464.

494 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×SD16×D113C211yesmaximal, characteristic, complemented
2Q8×C22⋊D113C211yesmaximal, characteristic, complemented
3#20299236C211yesmaximal, characteristic
4#20298991C211yesmaximal, characteristic, complemented
5#20298844C211yesmaximal, characteristic, complemented
6#20298836C211yesmaximal, characteristic, complemented
7#20298822C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298737C211yesmaximal, characteristic, complemented
13#20298699C211yesmaximal, characteristic, complemented
14#20298667C211yesmaximal, characteristic, complemented
15C2×#137×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268636C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23SD16×D113—24no—
24C2×C8×D113C2211yescharacteristic
25#16813620—21no—
26#16813620C2211yescharacteristic, complemented
27#16813611C2211yescharacteristic
28#16813605—21no—
29#16813601—21no—
30#16813601C2211yescharacteristic, complemented
31#16813598—21no—
32#16813598C2211yescharacteristic
33#16813598C2211yescharacteristic
34#16813596C2211yescharacteristic
35#16813594—21no—
36#16813590—21no—
37Q8×Dic113C2211yescharacteristic, complemented
38D4×Dic113C2211yescharacteristic
39C4×C22⋊D113—21no—
40C4×C22⋊D113C2211yescharacteristic
41C2×#14268624—21no—
42#16813556C2211yescharacteristic, complemented
43#16813551C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813546C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic
49#16813543C2211yescharacteristic
50C22⋊#11744751C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic
52#16813532C2211yescharacteristic, complemented
53C2×#41×C113C2211yescharacteristic
54C22×Q8×C113C2211yescharacteristic, complemented
55#137×C113—24no—
56C2×Q16×C113C2211yescharacteristic, complemented
57C2×Q16×C113C2211yescharacteristic, complemented
58C2×SD16×C113C2211yescharacteristic
59C2×SD16×C113C2211yescharacteristic
60C2×M16×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—41no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70D4×D113—22no—
71D4×D113—41no—
72C22×Dic113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268637—41no—
76#14268636—22no—
77#14268635—22no—
78#14268634—22no—
79#14268634—41no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C8×D113—22no—
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626D411yescharacteristic
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113D411yescharacteristic
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624D411yescharacteristic
101C4×Dic113—21no—
102C4×Dic113C2311yescharacteristic
103#41×C113—22no—
104#41×C113—41no—
105C2×Q8×C113—21no—
106C2×Q8×C113—22no—
107C2×Q8×C113—41no—
108C2×Q8×C113C2311yescharacteristic
109C2×Q8×C113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117Q16×C113—22no—
118SD16×C113—22no—
119SD16×C113D414yescomplemented
120M16×C113—22no—
121C2×C8×C113C2311yescharacteristic
122C2×C8×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—42no—
128C22×D113—81no—
129C22×D113C2×D411yescharacteristic
130Q8×C113—21no—
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135Q8×C113—42no—
136Q8×C113C2×D412yes—
137D4×C113—21no—
138D4×C113—42no—
139D4×C113C2×D412yes—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—42no—
146C2×C4×C113—42no—
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2411yescharacteristic
149C22⋊D113—22no—
150C22⋊D113—42no—
151C22⋊D113—81no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—81no—
156C2×Dic113C2×D411yescharacteristic
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159D452—21no—
160D452—21no—
161C4×D113—21no—
162C4×D113—21no—
163C4×D113—42no—
164Dic226—21no—
165Dic226—21no—
166Dic226—42no—
167C8×C113—21no—
168C8×C113C2×D412yes—
169#11744751—21no—
170#11744751—21no—
171C22×C113—22no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
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#13712yescomplemented
185C4×C113—22no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113C22×D411yescharacteristic
190C4×C113H(5,𝔽2)11yescharacteristic
191Dic113—21no—
192Dic113—21no—
193Dic113—21no—
194Dic113—41no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—42no—
198C2×C113—41no—
199C2×C113D4211yescharacteristic
200C2×C113C2×#13711yescharacteristic
201C2×C113#57711yescharacteristic
202D113—22no—
203D113—81no—
204#3266—1131nomaximal, Sylow
205C113#326611yescharacteristic, complemented, Sylow
206C2×#137D11311yescharacteristic, complemented
207C22×SD16—1131no—
208D4×Q8—1131no—
209#546—1131no—
210#497—1131no—
211#468—1131no—
212#467—1131no—
213#464—1131no—
214#461—1131no—
215#452—1131no—
216#451—1131no—
217#450—1131no—
218#448—1131no—
219#440—1131no—
220#435—1131no—
221C2×#41C2×D11311yescharacteristic
222C22×Q8—1131no—
223C22×Q8C2×D11311yescharacteristic, complemented
224C22×D4—1131no—
225#137—24no—
226C2×Q16—1131no—
227C2×Q16C2×D11311yescharacteristic, complemented
228C2×Q16C2×D11311yescharacteristic, complemented
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16—1131no—
233C2×SD16—2264no—
234C2×SD16C2×D11311yescharacteristic
235C2×SD16C2×D11311yescharacteristic
236C2×M16C2×D11311yescharacteristic, complemented
237C22×C8—1131no—
238C4⋊Q8—1131no—
239C4⋊Q8—2261no—
240#124—1131no—
241#123—2261no—
242C22⋊Q8—1131no—
243C22⋊Q8—1131no—
244C22⋊Q8—1131no—
245C22⋊Q8—2261no—
246C22⋊Q8—2261no—
247#121—1131no—
248#121—2261no—
249#120—2261no—
250C4×Q8—1131no—
251C4×D4—1131no—
252C4×D4—1131no—
253C4×D4—2261no—
254C2×C22⋊C4—2261no—
255#107—1131no—
256C4⋊C8—1131no—
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103—1131no—
261#102—1131no—
262#102—1131no—
263C22⋊C8—1131no—
264C22⋊C8—1131no—
265#97—1131no—
266C24—2261no—
267#41—22no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1131no—
273C2×Q8—4521no—
274C2×Q8—2261no—
275C2×Q8—2262no—
276C2×Q8C22×D11311yescharacteristic
277C2×Q8C22×D11311yescharacteristic
278C2×Q8C22×D11311yescharacteristic
279C2×D4—21no—
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—4521no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4—2262no—
286C2×D4C22×D11311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—1131no—
290C22×C4—2261no—
291C22×C4—2261no—
292C22×C4C22×D11311yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—4521no—
296SD16—22no—
297SD16—4521no—
298SD16—2262no—
299SD16—2262no—
300SD16—2262no—
301SD16C22⋊D11314yescomplemented
302M16—22no—
303C2×C8—1131no—
304C2×C8—1131no—
305C2×C8—2262no—
306C2×C8C22×D11311yescharacteristic
307C2×C8C22×D11311yescharacteristic
308C4⋊C4—1131no—
309C4⋊C4—1131no—
310C4⋊C4—1131no—
311C4⋊C4—2261no—
312C4⋊C4—2261no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4—2261no—
317C22⋊C4—1131no—
318C22⋊C4—1131no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C42—1131no—
327C42—2261no—
328C23—21no—
329C23—1131no—
330C23—9041no—
331C23—4522no—
332C23—4522no—
333C23—2261no—
334C23D4×D11311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—4522no—
342Q8—2261no—
343Q8—2261no—
344Q8C2×C22⋊D11312yes—
345D4—21no—
346D4—42no—
347D4—9041no—
348D4—4522no—
349D4—2262no—
350D4—2261no—
351D4—2261no—
352D4C2×C22⋊D11312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—1131no—
361C2×C4—1131no—
362C2×C4—1131no—
363C2×C4—9041no—
364C2×C4—4522no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4D4×D11311yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—21no—
373C8—2261no—
374C8—2261no—
375C8C2×C22⋊D11312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—1132no—
383C22—9044no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22—2261no—
388C22—2261no—
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—4521no—
395C4—4521no—
396C4—4521no—
397C4—2261no—
398C4—2261no—
399C4—2261no—
400C4C22×C22⋊D11311yescharacteristic
401C4#1681366711yescharacteristic
402C2—41no—
403C2—42no—
404C2—9041no—
405C2—2262no—
406C2D4×C22⋊D11311yescharacteristic
407C2#137×D11311yescharacteristic
408C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
prime radical#20299236C2
hypercenterC2×#137D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. Q8×C22⋊D113C2semidirect
4. #20298991C2semidirect
5. #20298844C2semidirect
6. #20298836C2semidirect
7. #20298822C2semidirect
8. #20298801C2semidirect
9. #20298760C2semidirect
10. #20298752C2semidirect
11. #20298747C2semidirect
12. #20298737C2semidirect
13. #20298699C2semidirect
14. #20298667C2semidirect
15. C2×#137×C113C2semidirect
18. C2×#14268637C22semidirect
26. #16813620C22semidirect
30. #16813601C22semidirect
37. Q8×Dic113C22semidirect
42. #16813556C22semidirect
43. #16813551C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
47. #16813546C22semidirect
50. C22⋊#11744751C22semidirect
52. #16813532C22semidirect
54. C22×Q8×C113C22semidirect
56. C2×Q16×C113C22semidirect
57. C2×Q16×C113C22semidirect
60. C2×M16×C113C22semidirect
119. SD16×C113D4semidirect
184. C2×D113#137semidirect
205. C113#3266semidirect
206. C2×#137D113semidirect
223. C22×Q8C2×D113semidirect
227. C2×Q16C2×D113semidirect
228. C2×Q16C2×D113semidirect
236. C2×M16C2×D113semidirect
301. SD16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
Q8×C22⋊D1132
#202992362
#202989912
#202988442
#202988362
#202988222
#202988012
#202987602
#202987522
#202987472
#202987372
#202986992
#202986672
C2×#137×C1132
#3266113