Finite Group Databasebeta

← #27206655

Subgroups — #27206655

Order 13184.

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×#15693052C211yesmaximal, characteristic, complemented
2C22×#13110092C211yesmaximal, characteristic, complemented
3#20268437C211yesmaximal, characteristic
4#20268183C211yesmaximal, characteristic, complemented
5#20268039C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268013C211yesmaximal, characteristic, complemented
8#20267993C211yesmaximal, characteristic, complemented
9#20267951C211yesmaximal, characteristic, complemented
10#20267947C211yesmaximal, characteristic, complemented
11#20267941C211yesmaximal, characteristic, complemented
12#20267930C211yesmaximal, characteristic, complemented
13#20267889C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15D4×Q8×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18#15693052—24no—
19C2×#13110095C2211yescharacteristic, complemented
20C2×#13110095C2211yescharacteristic, complemented
21C2×#13110095C2211yescharacteristic, complemented
22C2×#13110092—24no—
23C2×#13110092C2211yescharacteristic
24C2×#13110092C2211yescharacteristic
25C2×#13110092C2211yescharacteristic
26C2×#13110092C2211yescharacteristic
27C2×#13110092C2211yescharacteristic
28C2×#13110092C2211yescharacteristic
29C2×#13110089C2211yescharacteristic, complemented
30C22×C103⋊C8C2211yescharacteristic
31#15693009C2211yescharacteristic
32#15693006—21no—
33#15693000C2211yescharacteristic
34#15692995C2211yescharacteristic
35#15692994—21no—
36#15692989—21no—
37C4×D412C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692954C2211yescharacteristic, complemented
40C4⋊(C103⋊C8)C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692941C2211yescharacteristic
46#15692941C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C22⋊(C103⋊C8)C2211yescharacteristic, complemented
49#15692932C2211yescharacteristic, complemented
50C22×Q8×C103C2211yescharacteristic
51C22×Q8×C103C2211yescharacteristic, complemented
52C4⋊Q8×C103—21no—
53C4⋊Q8×C103C2211yescharacteristic, complemented
54C22⋊Q8×C103—21no—
55C22⋊Q8×C103—21no—
56C22⋊Q8×C103C2211yescharacteristic
57C22⋊Q8×C103C2211yescharacteristic, complemented
58C4×Q8×C103C2211yescharacteristic, complemented
59C4×D4×C103—21no—
60C4×D4×C103C2211yescharacteristic
61C23×D103—21no—
62#13110105—22no—
63#13110105—41no—
64C2×Dic206C2311yescharacteristic
65C2×D412—22no—
66C2×D412—21no—
67C2×D412—41no—
68C2×D412C2311yescharacteristic
69C2×D412C2311yescharacteristic
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74#13110095—22no—
75#13110095—22no—
76#13110095—41no—
77#13110092—22no—
78#13110092—22no—
79#13110092—22no—
80#13110092—22no—
81#13110092—41no—
82#13110092D414yescomplemented
83#13110089—22no—
84C2×C103⋊C8—22no—
85C2×C103⋊C8C2311yescharacteristic
86C2×C103⋊C8C2311yescharacteristic
87C2×C103⋊C8C2311yescharacteristic
88C2×C103⋊C8C2311yescharacteristic
89C4⋊Dic103C2311yescharacteristic
90Dic103⋊C4—21no—
91C22⋊Dic103—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96C2×Q8×C103—21no—
97C2×Q8×C103—21no—
98C2×Q8×C103—22no—
99C2×Q8×C103—22no—
100C2×Q8×C103—41no—
101C2×Q8×C103—41no—
102C2×Q8×C103C2311yescharacteristic
103C2×Q8×C103C2311yescharacteristic
104C2×Q8×C103C2311yescharacteristic
105C2×D4×C103D411yescharacteristic
106C22×C4×C103—21no—
107C22×C4×C103—21no—
108C22×C4×C103C2311yescharacteristic
109C22×C4×C103C2311yescharacteristic
110C4⋊C4×C103—21no—
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103D411yescharacteristic
116C4⋊C4×C103C2311yescharacteristic
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103D411yescharacteristic
120C22⋊C4×C103D411yescharacteristic
121C42×C103—21no—
122C42×C103C2311yescharacteristic
123C23×C103C2×D411yescharacteristic
124C23×C103C2×D411yescharacteristic
125C22×D103—21no—
126C22×D103—21no—
127C22×D103—42no—
128C22×D103—42no—
129C22×D103—81no—
130Q8×C103—21no—
131Q8×C103—21no—
132Q8×C103—21no—
133Q8×C103—21no—
134Q8×C103—21no—
135Q8×C103—42no—
136Q8×C103—42no—
137Q8×C103C2×D412yes—
138D4×C103—22no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—21no—
147C2×C4×C103—42no—
148C2×C4×C103—42no—
149C2×C4×C103C2×D411yescharacteristic
150C2×C4×C103C2×D411yescharacteristic
151C2×C4×C103C2×D411yescharacteristic
152C2×C4×C103C2×D411yescharacteristic
153C2×C4×C103C2411yescharacteristic
154C22⋊D103—42no—
155C22⋊D103—81no—
156C2×Dic103—21no—
157C2×Dic103—21no—
158D412—21no—
159D412—21no—
160D412—21no—
161D412—42no—
162D412C2×D412yes—
163C4×D103—42no—
164C4×D103—81no—
165Dic206—21no—
166Dic206—21no—
167C103⋊C8—21no—
168C103⋊C8—21no—
169C103⋊C8—21no—
170C103⋊C8C2×D412yes—
171C22×C103—21no—
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—21no—
175C22×C103—21no—
176C22×C103#13712yescomplemented
177C22×C103C22×D411yescharacteristic
178C2×D103—22no—
179C2×D103—41no—
180C2×D103—41no—
181C2×D103—41no—
182C2×D103—41no—
183C2×D103—41no—
184C2×D103—84no—
185C4×C103—21no—
186C4×C103—21no—
187C4×C103—22no—
188C4×C103—21no—
189C4×C103—21no—
190C4×C103—41no—
191C4×C103—41no—
192C4×C103—41no—
193C4×C103C22×D411yescharacteristic
194C4×C103H(5,𝔽2)11yescharacteristic
195Dic103—41no—
196Dic103—41no—
197C2×C103—22no—
198C2×C103—41no—
199C2×C103D4211yescharacteristic
200C2×C103C2×#13711yescharacteristic
201C2×C103#57711yescharacteristic
202D103—42no—
203D103—81no—
204#3266—1031nomaximal, Sylow
205C103#326611yescharacteristic, complemented, Sylow
206C2×#137—1031no—
207C22×SD16—1031no—
208D4×Q8D10311yescharacteristic, complemented
209#546—1031no—
210#497—1031no—
211#468—1031no—
212#467—1031no—
213#464—1031no—
214#461—1031no—
215#452—1031no—
216#451—1031no—
217#450—1031no—
218#448—1031no—
219#440—1031no—
220#435—1031no—
221C2×#41—1031no—
222C22×Q8C2×D10311yescharacteristic
223C22×Q8C2×D10311yescharacteristic, complemented
224C22×D4—1031no—
225#137—2064no—
226C2×Q16—1031no—
227C2×Q16—1031no—
228C2×Q16—1031no—
229C2×SD16—1031no—
230C2×SD16—1031no—
231C2×SD16—1031no—
232C2×SD16—1031no—
233C2×SD16—1031no—
234C2×SD16—1031no—
235C2×SD16—2064no—
236C2×M16—1031no—
237C22×C8—1031no—
238C4⋊Q8—21no—
239C4⋊Q8C2×D10311yescharacteristic, complemented
240#124—1031no—
241#123—2061no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—1031no—
245C22⋊Q8C2×D10311yescharacteristic
246C22⋊Q8C2×D10311yescharacteristic, complemented
247#121—1031no—
248#121—2061no—
249#120—2061no—
250C4×Q8C2×D10311yescharacteristic, complemented
251C4×D4—21no—
252C4×D4—1031no—
253C4×D4C2×D10311yescharacteristic
254C2×C22⋊C4—2061no—
255#107—1031no—
256C4⋊C8—1031no—
257#103—1031no—
258#103—1031no—
259#103—1031no—
260#103—1031no—
261#102—1031no—
262#102—1031no—
263C22⋊C8—1031no—
264C22⋊C8—1031no—
265#97—1031no—
266C24—2061no—
267#41—4121no—
268#41—2062no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—1031no—
276C2×Q8C22×D10311yescharacteristic
277C2×Q8C22×D10311yescharacteristic
278C2×Q8C22×D10311yescharacteristic
279C2×D4—1031no—
280C2×D4—1031no—
281C2×D4—4121no—
282C2×D4—2062no—
283C2×D4—2061no—
284C2×D4—2061no—
285C2×D4—2061no—
286C2×D4C22⋊D10311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—2061no—
290C22×C4—2061no—
291C22×C4C22×D10311yescharacteristic
292C22×C4C22×D10311yescharacteristic
293Q16—4121no—
294Q16—2062no—
295Q16—2062no—
296SD16—1034no—
297SD16—4121no—
298SD16—2062no—
299SD16—2062no—
300SD16—2062no—
301SD16—2062no—
302M16—2062no—
303C2×C8—1031no—
304C2×C8—1031no—
305C2×C8—1031no—
306C2×C8—1031no—
307C2×C8—2062no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—1031no—
314C4⋊C4—2061no—
315C4⋊C4C22⋊D10311yescharacteristic
316C4⋊C4C22×D10311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—2061no—
320C22⋊C4—2061no—
321C22⋊C4—2061no—
322C22⋊C4—2061no—
323C22⋊C4—2061no—
324C22⋊C4C22⋊D10311yescharacteristic
325C22⋊C4C22⋊D10311yescharacteristic
326C42—21no—
327C42C22×D10311yescharacteristic
328C23—8241no—
329C23—4122no—
330C23—4122no—
331C23—2061no—
332C23—2061no—
333C23C2×C22⋊D10311yescharacteristic
334C23C2×C22⋊D10311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—42no—
342Q8—2061no—
343Q8—2061no—
344Q8D4×D10312yes—
345D4—22no—
346D4—8241no—
347D4—1032no—
348D4—4122no—
349D4—4122no—
350D4—2061no—
351D4—2061no—
352D4—2061no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—8241no—
364C2×C4—4122no—
365C2×C4—2061no—
366C2×C4—2061no—
367C2×C4C2×C22⋊D10311yescharacteristic
368C2×C4C2×C22⋊D10311yescharacteristic
369C2×C4C2×C22⋊D10311yescharacteristic
370C2×C4C2×C22⋊D10311yescharacteristic
371C2×C4C23×D10311yescharacteristic
372C8—1032no—
373C8—2061no—
374C8—2061no—
375C8—2061no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—8244no—
382C22—4121no—
383C22—4121no—
384C22—4121no—
385C22—4121no—
386C22—4121no—
387C22—2062no—
388C22#1569305212yescomplemented
389C22C22×C22⋊D10311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—4121no—
399C4—4121no—
400C4C2×D4×D10311yescharacteristic
401C4#1569306611yescharacteristic
402C2—22no—
403C2—41no—
404C2—8241no—
405C2—4122no—
406C2D4×C22⋊D10311yescharacteristic
407C2C2×#1569305211yescharacteristic
408C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingD4×Q8×C103C2
socleC22×C103C22×D4
prime radical#20268437C2
hypercenterD4×Q8D103
hypocenterC103#3266
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#15693052C2semidirect
2. C22×#13110092C2semidirect
4. #20268183C2semidirect
5. #20268039C2semidirect
6. #20268030C2semidirect
7. #20268013C2semidirect
8. #20267993C2semidirect
9. #20267951C2semidirect
10. #20267947C2semidirect
11. #20267941C2semidirect
12. #20267930C2semidirect
13. #20267889C2semidirect
14. #20267863C2semidirect
15. D4×Q8×C103C2semidirect
19. C2×#13110095C22semidirect
20. C2×#13110095C22semidirect
21. C2×#13110095C22semidirect
29. C2×#13110089C22semidirect
39. #15692954C22semidirect
40. C4⋊(C103⋊C8)C22semidirect
41. #15692945C22semidirect
42. #15692945C22semidirect
43. #15692945C22semidirect
44. #15692944C22semidirect
48. C22⋊(C103⋊C8)C22semidirect
49. #15692932C22semidirect
51. C22×Q8×C103C22semidirect
53. C4⋊Q8×C103C22semidirect
57. C22⋊Q8×C103C22semidirect
58. C4×Q8×C103C22semidirect
82. #13110092D4semidirect
176. C22×C103#137semidirect
205. C103#3266semidirect
208. D4×Q8D103semidirect
223. C22×Q8C2×D103semidirect
239. C4⋊Q8C2×D103semidirect
246. C22⋊Q8C2×D103semidirect
250. C4×Q8C2×D103semidirect
388. C22#15693052semidirect

Maximal subgroups

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

subgroupindex
C2×#156930522
C22×#131100922
#202684372
#202681832
#202680392
#202680302
#202680132
#202679932
#202679512
#202679472
#202679412
#202679302
#202678892
#202678632
D4×Q8×C1032
#3266103