Finite Group Databasebeta

← #16789386

Subgroups — #16789386

Order 3328.

420 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131064C211yesmaximal, characteristic
2C2×#11718217C211yesmaximal, characteristic, complemented
3C2×#11718218C211yesmaximal, characteristic, complemented
4#13130572C211yesmaximal, characteristic
5#13129876C211yesmaximal, characteristic, complemented
6#13129876C211yesmaximal, characteristic, complemented
7C2×D13×M32C211yesmaximal, characteristic
8C22×C8×D13C2211yescharacteristic
9C4×C22⋊#261C411yescharacteristic
10D13⋊(C22⋊C8)C411yescharacteristic
11C2×#88100C2211yescharacteristic
12C2×#88100C2211yescharacteristic
13C2×#88098C2211yescharacteristic
14C2×#88098C2211yescharacteristic
15C2×C13×M32C411yescharacteristic, complemented
16C2×#88052C411yescharacteristic, complemented
17D13×M32—22no—
18D13×M32—22no—
19C2×#88038C2211yescharacteristic
20C2×#88038C2211yescharacteristic
21C2×C16×D13C411yescharacteristic, complemented
22C2×C16×D13C411yescharacteristic, complemented
23C22⋊#6092C412yescomplemented
24(C2×#261)⋊C8C411yescharacteristic
25(C2×#261)⋊C8C411yescharacteristic
26#11718259C412yescomplemented
27#11718218—22no—
28#11718217—22no—
29C22×C4×D13C2×C411yescharacteristic
30C2×C22⋊#261—21no—
31C2×C4×#261C2×C411yescharacteristic
32C2×C4×#261C2×C411yescharacteristic
33C2×D13⋊C8C2×C411yescharacteristic
34C2×D13⋊C8C2×C411yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C2×C8×D13—21no—
38C2×C8×D13—21no—
39C2×C8×D13—21no—
40C2×C8×D13—21no—
41C2×C8×D13C2×C411yescharacteristic
42C2×C8×D13C2×C411yescharacteristic
43C2×C8×D13C2×C411yescharacteristic
44C2×C8×D13C2311yescharacteristic
45C22⋊#1057—21no—
46(C2×#261)⋊C4—21no—
47#88111—21no—
48C2×#6092C2×C412yes—
49C2×#6092C2×C412yes—
50#88100—21no—
51#88100—21no—
52#88100—21no—
53#88100—21no—
54#88098—21no—
55#88098—21no—
56#88098—21no—
57#88098—21no—
58C13×M32—22no—
59C2×C13×C16C2×C411yescharacteristic
60C2×C13×C16C2×C411yescharacteristic
61#88052—22no—
62C2×#6090C2×C411yescharacteristic
63C2×#6090C2×C411yescharacteristic
64#88038—21no—
65#88038—21no—
66#88038D412yes—
67#88038D412yes—
68C16×D13—22no—
69C16×D13—22no—
70#12616—131nomaximal, Sylow
71C23×D13M1611yescharacteristic
72C22×#261—21no—
73C22×#261—21no—
74C22×C4×C13C4211yescharacteristic
75C22×Dic13M1611yescharacteristic
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13C4211yescharacteristic
81C2×C4×D13M1611yescharacteristic
82C2×C4×D13M1611yescharacteristic
83C2×C4×D13C22×C411yescharacteristic
84C22⋊#261—42no—
85C2×#1057—21no—
86C2×#1057—21no—
87C4×#261—21no—
88C4×#261—21no—
89C4×#261—21no—
90C4×#261—21no—
91D13⋊C8—21no—
92D13⋊C8—21no—
93D13⋊C8—21no—
94D13⋊C8—21no—
95C2×C8×C13—21no—
96C2×C8×C13—21no—
97C2×C8×C13C4211yescharacteristic
98C2×C8×C13C22×C411yescharacteristic
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055C4211yescharacteristic
102C2×#1055C22×C411yescharacteristic
103C8×D13—21no—
104C8×D13—21no—
105C8×D13—21no—
106C8×D13—21no—
107C8×D13—21no—
108C8×D13—21no—
109C8×D13C2×D411yescharacteristic
110C8×D13C2×D411yescharacteristic
111C8×D13#4111yescharacteristic
112C8×D13#4111yescharacteristic
113#6092—22no—
114#6092—22no—
115C13×C16—21no—
116C13×C16C22⋊C412yescomplemented
117#6090—21no—
118#6090C22⋊C412yescomplemented
119C22×M32—131no—
120#2112—131no—
121C2×#347—131no—
122C2×#347—131no—
123#1752—131no—
124#1375—131no—
125#1375—131no—
126C23×C13#9711yescharacteristic
127C22×D13—22no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—41no—
131C22×D13#9711yescharacteristic
132C22×D13C2×M1611yescharacteristic
133C2×#261—41no—
134C2×#261—41no—
135C2×#261—41no—
136C2×#261—41no—
137C2×#261—41no—
138C2×#261—41no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13#9711yescharacteristic
142C2×C4×C13C2×C4211yescharacteristic
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13#9711yescharacteristic
146C2×Dic13C2×M1611yescharacteristic
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—21no—
152C4×D13—21no—
153C4×D13C4×D411yescharacteristic
154C4×D13C4×D411yescharacteristic
155C4×D13#13111yescharacteristic
156C4×D13#13111yescharacteristic
157#1057—41no—
158#1057—41no—
159C8×C13—21no—
160C8×C13C2×C22⋊C411yescharacteristic
161C8×C13#11711yescharacteristic
162#1055—21no—
163#1055C4×D411yescharacteristic
164#1055C4×D411yescharacteristic
165C23×C8—131no—
166C2×M32—131no—
167C2×M32—131no—
168C2×M32—131no—
169C2×M32—131no—
170C2×M32—131no—
171C2×M32—262no—
172C2×M32—262no—
173C2×M32#26111yescharacteristic, complemented
174C22×C16—131no—
175C22×C16—131no—
176C2×C22⋊C8—131no—
177C2×#97—131no—
178C2×#97—131no—
179C4×C22⋊C4—131no—
180C22⋊C16—132no—
181C22⋊C16—132no—
182#347—262no—
183#347—262no—
184#336—131no—
185#336—131no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13C2×#9711yescharacteristic
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—21no—
194C2×D13—42no—
195C2×D13—42no—
196C2×D13#34712yescomplemented
197C2×D13#43511yescharacteristic
198C2×D13#43511yescharacteristic
199#261—81no—
200#261—81no—
201C4×C13—21no—
202C4×C13C4×C22⋊C411yescharacteristic
203C4×C13#40511yescharacteristic
204Dic13—21no—
205Dic13#43511yescharacteristic
206Dic13#43511yescharacteristic
207C23×C4—131no—
208C22×C8—131no—
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—131no—
214C22×C8—131no—
215C22×C8—261no—
216C22×C8—261no—
217C22×C8—261no—
218C22×C8—261no—
219C22×C8C2×#26111yescharacteristic
220C2×C22⋊C4—261no—
221C2×C42—131no—
222C2×C42—131no—
223M32—22no—
224M32—132no—
225M32—132no—
226M32—261no—
227M32—261no—
228M32—262no—
229M32—261no—
230M32—261no—
231M32—261no—
232M32—261no—
233C2×C16—131no—
234C2×C16—132no—
235C2×C16—132no—
236C2×C16—131no—
237C2×C16—262no—
238C2×C16—262no—
239C2×C16C2×#26111yescharacteristic
240C2×C16C2×#26111yescharacteristic
241C22⋊C8—261no—
242C22⋊C8—261no—
243#97—261no—
244#97—261no—
245#97—261no—
246#97—261no—
247#95—261no—
248C2×C13—41no—
249C2×C13#175211yescharacteristic
250C2×C13C2×#34711yescharacteristic
251C2×C13#211011yescharacteristic
252D13—21no—
253D13—21no—
254D13—22no—
255C24—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4C4×#26111yescharacteristic
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8—131no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8—261no—
277C2×C8—261no—
278C2×C8—261no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8—261no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8C4×#26111yescharacteristic
291C2×C8C22×#26111yescharacteristic
292C22⋊C4—522no—
293C42—261no—
294C42—261no—
295C42—261no—
296C42—261no—
297C16—21no—
298C16—132no—
299C16—262no—
300C16—262no—
301C16—261no—
302C16C22⋊#26112yescomplemented
303C13#1261611yescharacteristic, complemented, Sylow
304C23—131no—
305C23—131no—
306C23—262no—
307C23—261no—
308C23—261no—
309C23—521no—
310C23#8810011yescharacteristic
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—131no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4#8810011yescharacteristic
334C2×C4C2×C4×#26111yescharacteristic
335C8—21no—
336C8—131no—
337C8—131no—
338C8—261no—
339C8—521no—
340C8—521no—
341C8#8823711yescharacteristic
342C8C2×C22⋊#26111yescharacteristic
343C22—21no—
344C22—21no—
345C22—21no—
346C22—132no—
347C22—131no—
348C22—131no—
349C22—261no—
350C22—261no—
351C22—261no—
352C22—261no—
353C22—522no—
354C22—522no—
355C22C2×#8810011yescharacteristic
356C4—21no—
357C4—131no—
358C4—131no—
359C4—261no—
360C4—1041no—
361C4—1041no—
362C4#1171908911yescharacteristic
363C4C4×C22⋊#26111yescharacteristic
364C2—41no—
365C2—261no—
366C2—261no—
367C2—262no—
368C2#1313057211yescharacteristic
369C2#1313105111yescharacteristic
370C2#1313105611yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC2×C8C22×#261
FittingC2×C13×M32C4
socleC22×C13C2×#97
prime radicalC23×D13M16
cosocleC2×C8×D13C23
hypercenterC2×M32#261
hypocenterC13#12616
LCSG ▷ C2×C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
2. C2×#11718217C2semidirect
3. C2×#11718218C2semidirect
5. #13129876C2semidirect
6. #13129876C2semidirect
15. C2×C13×M32C4semidirect
16. C2×#88052C4semidirect
21. C2×C16×D13C4semidirect
22. C2×C16×D13C4semidirect
23. C22⋊#6092C4semidirect
26. #11718259C4semidirect
116. C13×C16C22⋊C4semidirect
118. #6090C22⋊C4semidirect
173. C2×M32#261semidirect
196. C2×D13#347semidirect
302. C16C22⋊#261semidirect
303. C13#12616semidirect

Maximal subgroups

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

subgroupindex
#131310642
C2×#117182172
C2×#117182182
#131305722
#131298762
C2×D13×M322
#1261613