Finite Group Databasebeta

← #16789329

Subgroups — #16789329

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719089C211yesmaximal, characteristic
2#13131064C211yesmaximal, characteristic
3C2×#11718217C211yesmaximal, characteristic, complemented
4C2×#11718218C211yesmaximal, characteristic, complemented
5#13129876C211yesmaximal, characteristic, complemented
6#13129876C211yesmaximal, characteristic, complemented
7#13116445C211yesmaximal, characteristic
8C2×#88237C411yescharacteristic
9C2×D13⋊M16C411yescharacteristic
10C22×C8×D13C2211yescharacteristic
11#11719089—22no—
12#11719089—22no—
13C2×#88100C2211yescharacteristic
14C2×#88100C2211yescharacteristic
15C2×C8×#261C411yescharacteristic
16C2×C8×#261C411yescharacteristic
17C2×#88098C2211yescharacteristic
18C2×#88098C2211yescharacteristic
19C2×#88038C2211yescharacteristic
20C2×#88038C2211yescharacteristic
21C22⋊#6092C412yescomplemented
22#11718259C412yescomplemented
23#11718218—22no—
24#11718217—22no—
25C13×C22⋊C16C411yescharacteristic, complemented
26C22⋊#6090C411yescharacteristic, complemented
27#11718099C411yescharacteristic, complemented
28#11718099C411yescharacteristic, complemented
29C22×C4×D13C2×C411yescharacteristic
30C2×C22⋊#261—21no—
31C2×#6122—21no—
32#88237—22no—
33#88237—22no—
34C2×C4⋊#261—21no—
35C2×C4×#261C2×C411yescharacteristic
36C2×C4×#261C2×C411yescharacteristic
37D13⋊M16—22no—
38D13⋊M16—22no—
39C2×#6118—21no—
40C2×D13⋊C8C2×C411yescharacteristic
41C2×D13⋊C8C2×C411yescharacteristic
42C22×C8×C13C2×C411yescharacteristic
43C22×#1055C2×C411yescharacteristic
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C2×C8×D13—21no—
47C2×C8×D13—21no—
48C2×C8×D13C2×C411yescharacteristic
49C2×C8×D13C2×C411yescharacteristic
50C2×C8×D13C2×C411yescharacteristic
51C2×C8×D13C2311yescharacteristic
52C2×#6092C2×C412yes—
53C2×#6092C2×C412yes—
54#88100—21no—
55#88100—21no—
56#88100D412yes—
57#88100D412yes—
58C8×#261—22no—
59C8×#261—22no—
60#88098—21no—
61#88098—21no—
62#88098—21no—
63#88098—21no—
64C2×C13×C16C2×C411yescharacteristic
65C2×C13×C16C2×C411yescharacteristic
66C2×#6090C2×C411yescharacteristic
67C2×#6090C2×C411yescharacteristic
68#88038—21no—
69#88038—21no—
70#88038—21no—
71#88038—21no—
72#12606—131nomaximal, Sylow
73C23×D13M1611yescharacteristic
74C22×#261—21no—
75C22×#261—21no—
76C22×C4×C13C4211yescharacteristic
77C22×Dic13M1611yescharacteristic
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13C4211yescharacteristic
83C2×C4×D13M1611yescharacteristic
84C2×C4×D13M1611yescharacteristic
85C2×C4×D13C22×C411yescharacteristic
86C22⋊#261—24no—
87#6122—24no—
88C2×#1057—21no—
89C2×#1057—21no—
90C4⋊#261—24no—
91C4×#261—21no—
92C4×#261—21no—
93C4×#261C22⋊C412yes—
94C4×#261M1612yes—
95#6118—24no—
96D13⋊C8—21no—
97D13⋊C8—21no—
98D13⋊C8C22⋊C412yes—
99D13⋊C8M1612yes—
100C2×C8×C13—21no—
101C2×C8×C13—21no—
102C2×C8×C13C4211yescharacteristic
103C2×C8×C13C22×C411yescharacteristic
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055C4211yescharacteristic
107C2×#1055C22×C411yescharacteristic
108C8×D13—21no—
109C8×D13—21no—
110C8×D13—21no—
111C8×D13—21no—
112C8×D13—21no—
113C8×D13—21no—
114C8×D13C2×D411yescharacteristic
115C8×D13C2×D411yescharacteristic
116C8×D13#4111yescharacteristic
117C8×D13#4111yescharacteristic
118#6092—22no—
119#6092—22no—
120C13×C16—21no—
121C13×C16—21no—
122#6090—21no—
123#6090—21no—
124C2×#405—131no—
125#2112—131no—
126#2112—131no—
127C2×#347—131no—
128C2×#347—131no—
129#1375—131no—
130#1375—131no—
131C23×C13#9711yescharacteristic
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13#9711yescharacteristic
137C22×D13C2×M1611yescharacteristic
138C2×#261—22no—
139C2×#261—22no—
140C2×#261—41no—
141C2×#261—41no—
142C2×#261—41no—
143C2×#261—41no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13#9711yescharacteristic
147C2×C4×C13C2×C4211yescharacteristic
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13#9711yescharacteristic
151C2×Dic13C2×M1611yescharacteristic
152C4×D13—21no—
153C4×D13—21no—
154C4×D13—21no—
155C4×D13—21no—
156C4×D13—21no—
157C4×D13—21no—
158C4×D13C2×C22⋊C411yescharacteristic
159C4×D13#11711yescharacteristic
160C4×D13C2×M1611yescharacteristic
161C4×D13C2×M1611yescharacteristic
162#1057—22no—
163#1057—22no—
164C8×C13—21no—
165C8×C13C4×D411yescharacteristic
166C8×C13C4×D411yescharacteristic
167#1055—21no—
168#1055C4×D411yescharacteristic
169#1055C4×D411yescharacteristic
170C22×M16—131no—
171C23×C8—131no—
172C2×#117—131no—
173C2×M32—131no—
174C2×M32—131no—
175C2×M32—131no—
176C2×M32—131no—
177#405—262no—
178#405—262no—
179C2×#97—131no—
180C2×#97—131no—
181C2×C4×C8—131no—
182C2×C4×C8—131no—
183C22⋊C16—132no—
184C22⋊C16—132no—
185C22⋊C16—131no—
186C22⋊C16—131no—
187C22⋊C16—131no—
188C22⋊C16#26111yescharacteristic, complemented
189#347—262no—
190#347—262no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13C2×#9711yescharacteristic
195C2×D13—21no—
196C2×D13—21no—
197C2×D13—21no—
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—42no—
201C2×D13—42no—
202C2×D13#40711yescharacteristic
203C2×D13#43211yescharacteristic
204#261—42no—
205#261—42no—
206C4×C13—21no—
207C4×C13C4×C22⋊C411yescharacteristic
208C4×C13C4×M1611yescharacteristic
209Dic13—21no—
210Dic13#40711yescharacteristic
211Dic13#43211yescharacteristic
212C23×C4—131no—
213C2×M16—262no—
214C2×M16—262no—
215C2×M16—261no—
216C2×M16—261no—
217C22×C8—131no—
218C22×C8—131no—
219C22×C8—131no—
220C22×C8—131no—
221C22×C8—131no—
222C22×C8—131no—
223C22×C8—131no—
224C22×C8—261no—
225C22×C8—261no—
226C22×C8—261no—
227C22×C8—261no—
228C22×C8C2×#26111yescharacteristic
229#117—262no—
230#117—262no—
231C2×C4⋊C4—261no—
232C2×C22⋊C4—261no—
233C2×C42—131no—
234C2×C42—131no—
235M32—261no—
236M32—261no—
237M32—261no—
238M32—261no—
239M32—261no—
240M32—261no—
241M32—261no—
242M32—261no—
243C2×C16—132no—
244C2×C16—132no—
245C2×C16—131no—
246C2×C16—131no—
247C2×C16C2×#26111yescharacteristic
248C2×C16C2×#26111yescharacteristic
249#97—132no—
250#97—132no—
251#97—261no—
252#97—261no—
253C4×C8—262no—
254C4×C8—262no—
255C2×C13—41no—
256C2×C13#174911yescharacteristic
257C2×C13#211011yescharacteristic
258C2×C13#211011yescharacteristic
259D13—21no—
260D13—21no—
261D13—41no—
262C24—131no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4C4×#26111yescharacteristic
275M16—264no—
276M16—264no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—131no—
280C2×C8—131no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8—132no—
285C2×C8—132no—
286C2×C8—131no—
287C2×C8—261no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8—261no—
291C2×C8—261no—
292C2×C8—261no—
293C2×C8—261no—
294C2×C8—261no—
295C2×C8—261no—
296C2×C8—261no—
297C2×C8—261no—
298C2×C8—261no—
299C2×C8C4×#26111yescharacteristic
300C2×C8C22×#26111yescharacteristic
301C4⋊C4—264no—
302C22⋊C4—264no—
303C42—132no—
304C42—132no—
305C42—261no—
306C42—261no—
307C16—21no—
308C16—21no—
309C16—262no—
310C16—262no—
311C16—261no—
312C16—261no—
313C13#1260611yescharacteristic, complemented, Sylow
314C23—131no—
315C23—131no—
316C23—261no—
317C23—261no—
318C23—521no—
319C23—521no—
320C23#8810011yescharacteristic
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—131no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—262no—
338C2×C4—262no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4#8810011yescharacteristic
344C2×C4C2×C4×#26111yescharacteristic
345C8—21no—
346C8—131no—
347C8—131no—
348C8—262no—
349C8—262no—
350C8—261no—
351C8D4×#26111yescharacteristic
352C8D4×#26111yescharacteristic
353C22—21no—
354C22—21no—
355C22—21no—
356C22—131no—
357C22—131no—
358C22—261no—
359C22—261no—
360C22—261no—
361C22—261no—
362C22—261no—
363C22—522no—
364C22—522no—
365C22C2×#8810011yescharacteristic
366C4—21no—
367C4—131no—
368C4—131no—
369C4—261no—
370C4—522no—
371C4—522no—
372C4C22⋊C4×#26111yescharacteristic
373C4M16×#26111yescharacteristic
374C2—41no—
375C2—261no—
376C2—261no—
377C2—521no—
378C2#1313056411yescharacteristic
379C2#1313105511yescharacteristic
380C2#1313105611yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC2×C8C22×#261
FittingC13×C22⋊C16C4
socleC22×C13C2×#97
prime radicalC23×D13M16
cosocleC2×C8×D13C23
hypercenterC22⋊C16#261
hypocenterC13#12606
LCSG ▷ C2×C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. C2×#11718217C2semidirect
4. C2×#11718218C2semidirect
5. #13129876C2semidirect
6. #13129876C2semidirect
21. C22⋊#6092C4semidirect
22. #11718259C4semidirect
25. C13×C22⋊C16C4semidirect
26. C22⋊#6090C4semidirect
27. #11718099C4semidirect
28. #11718099C4semidirect
188. C22⋊C16#261semidirect
313. C13#12606semidirect

Maximal subgroups

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

subgroupindex
C2×#117190892
#131310642
C2×#117182172
C2×#117182182
#131298762
#131164452
#1260613