Finite Group Databasebeta

← #13125056

Subgroups — #13125056

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719288C211yesmaximal, characteristic, complemented
2#11719279C211yesmaximal, characteristic
3C4×C13×Q16C211yesmaximal, characteristic, complemented
4#11718848C211yesmaximal, characteristic
5#11718843C211yesmaximal, characteristic, complemented
6#11718691C211yesmaximal, characteristic, complemented
7#11718687C211yesmaximal, characteristic, complemented
8#11718552C211yesmaximal, characteristic, complemented
9#11718545C211yesmaximal, characteristic, complemented
10#11718479C211yesmaximal, characteristic, complemented
11#11718471C211yesmaximal, characteristic
12#11718466C211yesmaximal, characteristic, complemented
13#11718460C211yesmaximal, characteristic, complemented
14C4×#6095C211yesmaximal, characteristic, complemented
15#11718351C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88198C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24C2×#6106C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26#88152—21no—
27#88151C2211yescharacteristic
28#88147—21no—
29#88147C2211yescharacteristic
30C4⋊C4×D13—21no—
31C4⋊C4×D13C2211yescharacteristic
32#88144C2211yescharacteristic
33#88143—21no—
34#88130—21no—
35C4×D52—21no—
36C4×D52C2211yescharacteristic
37#88126—21no—
38#88126C2211yescharacteristic
39#88124—21no—
40C4×Dic26C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C4×C8×C13C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88057C2211yescharacteristic
51#88056C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61#6131—22no—
62#6131—22no—
63C2×D52—21no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C13×Q16—22no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C42×C13—21no—
79C42×C13—21no—
80C42×C13C2311yescharacteristic
81#6107—22no—
82#6106—22no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103D411yescharacteristic
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3120—131nomaximal, Sylow
109C22×D13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13#4112yes—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—24no—
129D52—21no—
130D52#4112yes—
131C4×D13—24no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—81no—
135C4×D13—81no—
136C4×D13—81no—
137Dic26—21no—
138Dic26—21no—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#541—131no—
144#520—131no—
145#484—131no—
146#483—131no—
147#479—131no—
148#478—131no—
149#462—131no—
150#461—131no—
151#452—131no—
152#452—131no—
153#441—131no—
154#440—131no—
155C4×Q16D1311yescharacteristic, complemented
156C4×SD16—131no—
157#433—131no—
158C22×C13C22×D411yescharacteristic
159C2×D13—21no—
160C2×D13—22no—
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C13C2×#4111yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×#41—131no—
180C2×Q16—131no—
181C2×Q16C2×D1311yescharacteristic
182C2×SD16—131no—
183C2×SD16—131no—
184C4⋊Q8—131no—
185#126—261no—
186#126—261no—
187#125—131no—
188#125—261no—
189#125—261no—
190C22⋊Q8—131no—
191C22⋊Q8—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8C2×D1311yescharacteristic
195C4×Q8C2×D1311yescharacteristic
196C4×D4—131no—
197C4×D4—131no—
198C4×D4—261no—
199C4×D4—261no—
200#117—131no—
201#117—261no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204#107—131no—
205#107C2×D1311yescharacteristic
206#106—131no—
207#106—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218C22⋊C8—131no—
219C22⋊C8—131no—
220#97—131no—
221C4×C8C2×D1311yescharacteristic
222C2×C13#52511yescharacteristic
223C2×C13#57711yescharacteristic
224C2×C13#57811yescharacteristic
225D13—41no—
226D13—42no—
227#41—262no—
228#41—262no—
229C2×Q8—131no—
230C2×Q8C22×D1311yescharacteristic
231C2×Q8C22×D1311yescharacteristic
232C2×D4—131no—
233C2×D4—261no—
234C22×C4—131no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239Q16—22no—
240Q16—262no—
241SD16—262no—
242SD16—262no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—131no—
265C22⋊C4—131no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C42—21no—
271C42—21no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#312011yescharacteristic, complemented, Sylow
277C23—131no—
278C23—261no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—261no—
283Q8—261no—
284Q8#612712yes—
285D4—132no—
286D4—264no—
287D4—261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—264no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4D4×D1311yescharacteristic
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—261no—
310C8—261no—
311C22—261no—
312C22—261no—
313C22—262no—
314C22—261no—
315C22—521no—
316C22—521no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—261no—
325C4—261no—
326C4—261no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4C2×#612711yescharacteristic
331C4#41×D1311yescharacteristic
332C2—521no—
333C2—522no—
334C2#1171925211yescharacteristic
335C2#1171947111yescharacteristic
336C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×Q16C2
socleC22×C13C22×D4
prime radicalC2×#6131C22
hypercenterC4×Q16D13
hypocenterC13#3120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #11719288C2semidirect
3. C4×C13×Q16C2semidirect
5. #11718843C2semidirect
6. #11718691C2semidirect
7. #11718687C2semidirect
8. #11718552C2semidirect
9. #11718545C2semidirect
10. #11718479C2semidirect
12. #11718466C2semidirect
13. #11718460C2semidirect
14. C4×#6095C2semidirect
15. #11718351C2semidirect
155. C4×Q16D13semidirect
276. C13#3120semidirect

Maximal subgroups

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

subgroupindex
#117192882
#117192792
C4×C13×Q162
#117188482
#117188432
#117186912
#117186872
#117185522
#117185452
#117184792
#117184712
#117184662
#117184602
C4×#60952
#117183512
#312013