Finite Group Databasebeta

← #13126581

Subgroups — #13126581

Order 1664.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D13C211yesmaximal, characteristic
2C22×#6107C211yesmaximal, characteristic, complemented
3C2×Q16×D13C211yesmaximal, characteristic, complemented
4#11719337C211yesmaximal, characteristic
5C13×#451C211yesmaximal, characteristic, complemented
6#11718847C211yesmaximal, characteristic, complemented
7#11718843C211yesmaximal, characteristic, complemented
8#11718842C211yesmaximal, characteristic, complemented
9#11718712C211yesmaximal, characteristic, complemented
10#11718474C211yesmaximal, characteristic, complemented
11#11718469C211yesmaximal, characteristic, complemented
12#11718454C211yesmaximal, characteristic, complemented
13#11718451C211yesmaximal, characteristic, complemented
14#11718400C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic
16C22×Q8×C13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×Q16C2211yescharacteristic
21C2×C13×Q16C2211yescharacteristic
22C13×C22⋊Q8C2211yescharacteristic
23#88200—21no—
24#88200C2211yescharacteristic
25Q8×Dic13C2211yescharacteristic
26#88198—21no—
27#88198C2211yescharacteristic
28#88198C2211yescharacteristic
29C2×#6107—24no—
30C2×#6107C2211yescharacteristic
31C2×#6107C2211yescharacteristic
32C2×#6107C2211yescharacteristic
33C2×#6107C2211yescharacteristic
34C2×#6107C2211yescharacteristic
35C4×C22⋊D13—21no—
36C4×C22⋊D13C2211yescharacteristic
37#88178—21no—
38#88178C2211yescharacteristic
39C22×#1055C2211yescharacteristic
40Q16×D13—24no—
41C2×Dic52C2211yescharacteristic
42C2×Dic52C2211yescharacteristic
43C2×C8×D13C2211yescharacteristic
44#88151C2211yescharacteristic
45#88150—21no—
46#88142—21no—
47#88141C2211yescharacteristic
48#88135—21no—
49#88132—21no—
50C13×#103C2211yescharacteristic
51C13×#103C2211yescharacteristic
52C13×C22⋊C8C2211yescharacteristic
53#88075C2211yescharacteristic
54#88060C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88054C2211yescharacteristic
58C8×Dic13C2211yescharacteristic
59#88050C2211yescharacteristic
60#88047C2211yescharacteristic
61C2×Q8×C13—21no—
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13C2311yescharacteristic
65C2×Q8×C13C2311yescharacteristic
66C2×Q8×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13D411yescharacteristic
70C22×Dic13—21no—
71Q8×D13—22no—
72Q8×D13—22no—
73Q8×D13—41no—
74Q8×D13—41no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26—22no—
79C2×Dic26—21no—
80C2×Dic26—21no—
81C2×Dic26—21no—
82C2×Dic26—41no—
83C2×Dic26C2311yescharacteristic
84C2×Dic26C2311yescharacteristic
85C2×Dic26C2311yescharacteristic
86C13×Q16—22no—
87C13×Q16—41no—
88C2×C8×C13C2311yescharacteristic
89C2×C8×C13C2311yescharacteristic
90C13×C4⋊C4—21no—
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13D411yescharacteristic
95#6107—22no—
96#6107—22no—
97#6107—22no—
98#6107—22no—
99#6107D414yescomplemented
100#6103—21no—
101#6103—21no—
102#6103D411yescharacteristic
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107#6101—21no—
108#6101—21no—
109#6101—21no—
110#6101—21no—
111#6101—21no—
112#6101—21no—
113#6101D411yescharacteristic
114C4×Dic13—21no—
115C4×Dic13—21no—
116C4×Dic13C2311yescharacteristic
117C2×#1055—22no—
118C2×#1055C2311yescharacteristic
119C2×#1055C2311yescharacteristic
120Dic52—22no—
121Dic52—41no—
122C8×D13—22no—
123D4×Q16—131nomaximal, Sylow
124C23×C13C2×D411yescharacteristic
125C22×D13C2×D411yescharacteristic
126Q8×C13—21no—
127Q8×C13—21no—
128Q8×C13—21no—
129Q8×C13—21no—
130Q8×C13—21no—
131Q8×C13—42no—
132Q8×C13C2×D412yes—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—42no—
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C22⋊D13Q1614yescomplemented
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—42no—
148C2×Dic13C2×D411yescharacteristic
149C2×Dic13C2×D411yescharacteristic
150C2×Dic13C2×D411yescharacteristic
151C4×D13—21no—
152C4×D13—21no—
153C4×D13—42no—
154C4×D13—42no—
155Dic26—21no—
156Dic26—21no—
157Dic26—21no—
158Dic26—21no—
159Dic26—21no—
160Dic26—42no—
161Dic26—42no—
162Dic26—42no—
163Dic26C2×D412yes—
164C8×C13—21no—
165C8×C13—21no—
166#1055—21no—
167#1055C2×D412yes—
168C22×Q16—131no—
169C22×Q16—131no—
170D4×Q8—131no—
171D4×Q8—131no—
172#494—131no—
173#467—131no—
174#467—131no—
175#462—131no—
176#462—131no—
177#451—131no—
178#451—131no—
179#451—131no—
180#451D1311yescharacteristic, complemented
181C4×Q16—131no—
182C8×D4—131no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13C2×Q1612yescomplemented
186C22×C13C22×D411yescharacteristic
187C2×D13—21no—
188C2×D13—21no—
189C2×D13C2×Q1612yescomplemented
190C4×C13—21no—
191C4×C13—22no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13C22×D411yescharacteristic
196C4×C13H(5,𝔽2)11yescharacteristic
197Dic13—22no—
198Dic13—21no—
199Dic13—21no—
200Dic13—41no—
201Dic13—41no—
202Dic13—41no—
203Dic13C2×Q1612yescomplemented
204C22×Q8—131no—
205C22×Q8—131no—
206C22×Q8—131no—
207C22×Q8C2×D1311yescharacteristic
208C2×Q16—131no—
209C2×Q16—131no—
210C2×Q16—131no—
211C2×Q16—131no—
212C2×Q16—131no—
213C2×Q16—131no—
214C2×Q16—131no—
215C2×Q16—264no—
216C2×Q16—264no—
217C2×Q16C2×D1311yescharacteristic
218C2×Q16C2×D1311yescharacteristic
219C22×C8—131no—
220C22×C8—131no—
221C4⋊Q8—131no—
222C4⋊Q8—131no—
223C4⋊Q8—261no—
224C4⋊Q8—261no—
225C22⋊Q8—131no—
226C22⋊Q8—131no—
227C22⋊Q8—131no—
228C22⋊Q8—261no—
229C22⋊Q8—261no—
230C22⋊Q8—261no—
231C22⋊Q8—261no—
232C22⋊Q8C2×D1311yescharacteristic
233C4×Q8—131no—
234C4×Q8—131no—
235C4×D4—131no—
236C4×D4—261no—
237C4×D4—261no—
238#107—131no—
239C4⋊C8—131no—
240#103—131no—
241#103—131no—
242#103—131no—
243#103—131no—
244#103C2×D1311yescharacteristic
245#103C2×D1311yescharacteristic
246C22⋊C8—131no—
247C22⋊C8C2×D1311yescharacteristic
248C4×C8—131no—
249C2×C13—22no—
250C2×C13D4211yescharacteristic
251C2×C13C22×Q1611yescharacteristic
252C2×C13#57811yescharacteristic
253D13—22no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—131no—
258C2×Q8—131no—
259C2×Q8—131no—
260C2×Q8—261no—
261C2×Q8—261no—
262C2×Q8—262no—
263C2×Q8—261no—
264C2×Q8—262no—
265C2×Q8—262no—
266C2×Q8—521no—
267C2×Q8—521no—
268C2×Q8—521no—
269C2×Q8C22×D1311yescharacteristic
270C2×Q8C22×D1311yescharacteristic
271C2×Q8C22×D1311yescharacteristic
272C2×D4—131no—
273C22×C4—21no—
274C22×C4—131no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4C22×D1311yescharacteristic
279Q16—22no—
280Q16—41no—
281Q16—134no—
282Q16—262no—
283Q16—262no—
284Q16—262no—
285Q16—262no—
286Q16—262no—
287Q16—521no—
288C2×C8—131no—
289C2×C8—131no—
290C2×C8—262no—
291C2×C8—262no—
292C2×C8C22×D1311yescharacteristic
293C2×C8C22×D1311yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4—261no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4C22×D1311yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—131no—
309C22⋊C4—131no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C22⋊C4—261no—
313C42—131no—
314C42—261no—
315C42—261no—
316C13D4×Q1611yescharacteristic, complemented, Sylow
317C23—131no—
318C23D4×D1311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—132no—
326Q8—261no—
327Q8—261no—
328Q8—261no—
329Q8—261no—
330Q8—261no—
331Q8—522no—
332Q8—522no—
333Q8—522no—
334Q8D4×D1312yes—
335D4—134no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—131no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4D4×D1311yescharacteristic
356C2×C4C23×D1311yescharacteristic
357C8—21no—
358C8—21no—
359C8—132no—
360C8—261no—
361C22—21no—
362C22—21no—
363C22—132no—
364C22—261no—
365C22—261no—
366C22Q16×D1312yescomplemented
367C22C2×D4×D1311yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—132no—
374C4—261no—
375C4—261no—
376C4—262no—
377C4—521no—
378C4—521no—
379C4—521no—
380C4C2×D4×D1311yescharacteristic
381C4#8825111yescharacteristic
382C2—22no—
383C2—262no—
384C2#1171929511yescharacteristic
385C2C2×Q16×D1311yescharacteristic
386C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#451C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#451D13
hypocenterC13D4×Q16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C22×#6107C2semidirect
3. C2×Q16×D13C2semidirect
5. C13×#451C2semidirect
6. #11718847C2semidirect
7. #11718843C2semidirect
8. #11718842C2semidirect
9. #11718712C2semidirect
10. #11718474C2semidirect
11. #11718469C2semidirect
12. #11718454C2semidirect
13. #11718451C2semidirect
14. #11718400C2semidirect
99. #6107D4semidirect
142. C22⋊D13Q16semidirect
180. #451D13semidirect
185. C22×C13C2×Q16semidirect
189. C2×D13C2×Q16semidirect
203. Dic13C2×Q16semidirect
316. C13D4×Q16semidirect
366. C22Q16×D13semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D132
C22×#61072
C2×Q16×D132
#117193372
C13×#4512
#117188472
#117188432
#117188422
#117187122
#117184742
#117184692
#117184542
#117184512
#117184002
#117183862
D4×Q1613