Finite Group Databasebeta

← #13124903

Subgroups — #13124903

Order 1664.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719283C211yesmaximal, characteristic, complemented
2C4×#6129C211yesmaximal, characteristic
3C4×C13×SD16C211yesmaximal, characteristic, complemented
4#11718834C211yesmaximal, characteristic
5#11718823C211yesmaximal, characteristic, complemented
6C4×#6107C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic, complemented
8#11718528C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718475C211yesmaximal, characteristic, complemented
11#11718454C211yesmaximal, characteristic, complemented
12#11718444C211yesmaximal, characteristic
13#11718420C211yesmaximal, characteristic, complemented
14C4×Dic52C211yesmaximal, characteristic, complemented
15#11718346C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25C4×C22⋊D13—21no—
26C2×C4×Dic13—21no—
27C2×Dic52C2211yescharacteristic
28#88151C2211yescharacteristic
29#88150—21no—
30#88146C2211yescharacteristic
31#88143—21no—
32#88142C2211yescharacteristic
33#88141C2211yescharacteristic
34#88135—21no—
35#88131—21no—
36#88126—21no—
37C42×D13C2211yescharacteristic
38C4×Dic26—21no—
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C4×C8×C13C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65#6129—22no—
66#6129—22no—
67C2×C4×D13D411yescharacteristic
68C2×C4×D13D411yescharacteristic
69C2×C4×D13C2311yescharacteristic
70C2×Dic26—21no—
71C2×Dic26C2311yescharacteristic
72C2×Dic26C2311yescharacteristic
73C13×SD16—22no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C42×C13—21no—
81C42×C13C2311yescharacteristic
82C22⋊Dic13—21no—
83#6107—22no—
84#6105—22no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13D411yescharacteristic
103C4×Dic13D411yescharacteristic
104C4×Dic13C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107Dic52—22no—
108#3107—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113D4×C13—21no—
114D4×C13#4112yes—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—24no—
123C2×Dic13—24no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—22no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—22no—
136Dic26—21no—
137Dic26—21no—
138Dic26—21no—
139Dic26—42no—
140Dic26#4112yes—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#533—131no—
146C4×#41—131no—
147#485—131no—
148#485—131no—
149#475—131no—
150#474—131no—
151#462—131no—
152#461—131no—
153#452—131no—
154#452—131no—
155C4×Q16—131no—
156C4×Q16—131no—
157C4×SD16—131no—
158C4×SD16D1311yescharacteristic, complemented
159#431—131no—
160C22×C13—22no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—21no—
165C2×D13—21no—
166C2×D13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13#13712yes—
172C4×C13C2×#4111yescharacteristic
173C4×C13C2×#4111yescharacteristic
174Dic13—22no—
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13#13512yes—
181C2×#41—131no—
182C2×Q16—131no—
183C2×Q16—131no—
184C2×SD16—131no—
185C2×SD16C2×D1311yescharacteristic
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188#125—261no—
189C22⋊Q8—131no—
190C22⋊Q8—131no—
191C22⋊Q8—261no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—261no—
196C4×Q8C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4—261no—
199C4×D4—261no—
200C4×D4C2×D1311yescharacteristic
201#117—131no—
202#117—261no—
203#117—261no—
204C2×C42—131no—
205C2×C42—261no—
206#107—131no—
207#107—131no—
208#106—131no—
209#106C2×D1311yescharacteristic
210C4⋊C8—131no—
211C4⋊C8—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#103C2×D1311yescharacteristic
218#102—131no—
219#102C2×D1311yescharacteristic
220C22⋊C8—131no—
221C22⋊C8—131no—
222C4×C8—131no—
223C4×C8C2×D1311yescharacteristic
224C2×C13—42no—
225C2×C13#52511yescharacteristic
226C2×C13C2×#13511yescharacteristic
227C2×C13C2×#13711yescharacteristic
228D13—41no—
229#41—262no—
230#41—262no—
231C2×Q8—131no—
232C2×Q8—131no—
233C2×Q8—261no—
234C2×Q8C22×D1311yescharacteristic
235C2×D4—261no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—21no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—261no—
242C22×C4—261no—
243Q16—262no—
244Q16—262no—
245SD16—22no—
246SD16—262no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8C22×D1311yescharacteristic
250C2×C8C22×D1311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—131no—
253C4⋊C4—131no—
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—21no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—21no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#310711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—131no—
281Q8—21no—
282Q8—21no—
283Q8—132no—
284Q8—261no—
285Q8—261no—
286Q8—261no—
287Q8—522no—
288D4—21no—
289D4—264no—
290D4#612712yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—262no—
299C2×C4—264no—
300C2×C4—261no—
301C2×C4—262no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4D4×D1311yescharacteristic
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—261no—
314C8—261no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—261no—
319C22—261no—
320C22—261no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—132no—
327C4—261no—
328C4—261no—
329C4—262no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#8816912yes—
334C4C2×#612711yescharacteristic
335C4#41×D1311yescharacteristic
336C2—42no—
337C2—521no—
338C2#1171925211yescharacteristic
339C2C2×#8816911yescharacteristic
340C2D13×#13511yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×SD16C2
socleC22×C13C22×D4
prime radicalC2×#6129C22
hypercenterC4×SD16D13
hypocenterC13#3107
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #11719283C2semidirect
3. C4×C13×SD16C2semidirect
5. #11718823C2semidirect
6. C4×#6107C2semidirect
7. C4×#6105C2semidirect
8. #11718528C2semidirect
9. #11718515C2semidirect
10. #11718475C2semidirect
11. #11718454C2semidirect
13. #11718420C2semidirect
14. C4×Dic52C2semidirect
15. #11718346C2semidirect
158. C4×SD16D13semidirect
278. C13#3107semidirect

Maximal subgroups

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

subgroupindex
#117192832
C4×#61292
C4×C13×SD162
#117188342
#117188232
C4×#61072
C4×#61052
#117185282
#117185152
#117184752
#117184542
#117184442
#117184202
C4×Dic522
#117183462
#310713