Finite Group Databasebeta

← #29570396

Subgroups — #29570396

Order 15616.

522 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454451C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic
3#432×D61C211yesmaximal, characteristic
4#21443730C211yesmaximal, characteristic, complemented
5#21443729C211yesmaximal, characteristic, complemented
6#21443729C211yesmaximal, characteristic, complemented
7C61×#1307C211yesmaximal, characteristic, complemented
8C2×C42×D61C2211yescharacteristic
9#16839819C2211yescharacteristic
10#16839819C2211yescharacteristic
11#16839818—21no—
12#16839818—21no—
13#16839818—21no—
14#16839817—21no—
15#16839817—21no—
16#16839816C412yes—
17#16839814—21no—
18#16839814—21no—
19#16839814—21no—
20#16839812C412yes—
21#16839786C2211yescharacteristic
22#16839784—21no—
23C4⋊C8×D61—21no—
24#16839725C412yes—
25#16839724C412yes—
26C22⋊C8×D61C412yes—
27#16839714—21no—
28M16×Dic61C412yes—
29#97×D61—21no—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C61×#423C2211yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61C2×C411yescharacteristic
36C2×#11758194C2×C412yes—
37C2×#11758189—22no—
38C2×C8×D61—22no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C42×D61D411yescharacteristic
43C42×D61D411yescharacteristic
44C42×D61D411yescharacteristic
45C42×D61D411yescharacteristic
46C42×D61D411yescharacteristic
47C42×D61D411yescharacteristic
48C42×D61Q811yescharacteristic
49C42×D61Q811yescharacteristic
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54#14519706—22no—
55#14519706—22no—
56C22⋊#92418C2×C412yes—
57C22⋊#92418C2×C412yes—
58#14519689—22no—
59#14519689—22no—
60#14519689—22no—
61#14519689—22no—
62#14519688—21no—
63#14519688—21no—
64#14519687—22no—
65#14519687—22no—
66C8×Dic61—22no—
67C8×Dic61—22no—
68C2×M16×C61C2×C412yes—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C22⋊C8×C61C2×C412yes—
75C22⋊C8×C61C2×C412yes—
76#97×C61—21no—
77#97×C61—21no—
78C23×D61C4211yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C22×C411yescharacteristic
82C22×Dic61C4211yescharacteristic
83C22×Dic61C4211yescharacteristic
84C22×Dic61C4211yescharacteristic
85C2×C4×D61—42no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—42no—
89C2×C4×D61C22⋊C411yescharacteristic
90C2×C4×D61C22⋊C411yescharacteristic
91C2×C4×D61C22⋊C411yescharacteristic
92C2×C4×D61C22⋊C411yescharacteristic
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61C22⋊C411yescharacteristic
95C2×C4×D61C4⋊C411yescharacteristic
96C2×C4×D61C4⋊C411yescharacteristic
97C2×C4×D61C4⋊C411yescharacteristic
98C2×C4×D61C4⋊C411yescharacteristic
99C2×C4×D61C4⋊C411yescharacteristic
100C2×C4×D61C4⋊C411yescharacteristic
101M16×C61—42no—
102C2×C8×C61—22no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×Q811yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C22⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C4⋊C411yescharacteristic
121#11758194—42no—
122C2×#92418—22no—
123C2×#92418—22no—
124C2×#92418—22no—
125#11758189—44no—
126C8×D61—44no—
127C23×C61C2×C4211yescharacteristic
128C22×D61—22no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#9511yescharacteristic
132C22×D61#9511yescharacteristic
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C4⋊C411yescharacteristic
141C2×C4×C61C2×C4⋊C411yescharacteristic
142C2×C4×C61C2×C4⋊C411yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61#9511yescharacteristic
147C2×Dic61#9511yescharacteristic
148C2×Dic61#9511yescharacteristic
149C2×Dic61#9511yescharacteristic
150C2×Dic61#9511yescharacteristic
151C2×Dic61#9511yescharacteristic
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C8×C61—42no—
167C8×C61—42no—
168C8×C61—42no—
169#92418—42no—
170#92418—42no—
171#92418—42no—
172#8118—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61C2×#9511yescharacteristic
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—44no—
183C2×D61#34412yes—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61#41311yescharacteristic
190C4×C61#41311yescharacteristic
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61#34412yes—
197#2920—611no—
198#2920—611no—
199C2×#432—611no—
200#1307—611no—
201#1307—611no—
202#1307—611no—
203#1307D6111yescharacteristic, complemented
204C2×C61—41no—
205C2×C61#174211yescharacteristic
206C2×C61C2×#34411yescharacteristic
207C2×C61C2×#34411yescharacteristic
208D61—22no—
209D61—41no—
210C22×C42—611no—
211#432—611no—
212#432—611no—
213#432—612no—
214#432—1221no—
215#432—1221no—
216#432—1221no—
217#432—1221no—
218#432—1221no—
219#432C2×D6111yescharacteristic
220#432C2×D6111yescharacteristic
221#431—612no—
222#431—1221no—
223#431—1221no—
224#431—1221no—
225#423—611no—
226#423—1221no—
227#423C2×D6111yescharacteristic
228C2×C4⋊C8—1221no—
229#407—612no—
230#407—612no—
231C2×C22⋊C8—612no—
232C4×M16—612no—
233C4×M16—1221no—
234C2×#97—1221no—
235C61#811811yescharacteristic, complemented, Sylow
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C2×M16—612no—
240C2×M16—1222no—
241C2×M16C4×D6112yes—
242C22×C8—1222no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42C22×D6111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264C4⋊C8—1221no—
265C22⋊C8—612no—
266C22⋊C8—612no—
267C22⋊C8—1222no—
268C22⋊C8—1222no—
269C22⋊C8—1222no—
270C22⋊C8—1222no—
271C22⋊C8C4×D6112yes—
272C22⋊C8C4×D6112yes—
273#97—21no—
274#97—21no—
275#97—1222no—
276#97—1222no—
277#97—1221no—
278#97—1221no—
279C4×C8—1222no—
280C4×C8—1222no—
281C24—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2442no—
300C22×C4—2442no—
301C22×C4C2×C4×D6111yescharacteristic
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4C2×C4×D6111yescharacteristic
304M16—42no—
305M16—2444no—
306M16—2442no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—1222no—
311C2×C8—1222no—
312C2×C8—1222no—
313C2×C8—2444no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—611no—
326C42D4×D6111yescharacteristic
327C42D4×D6111yescharacteristic
328C42D4×D6111yescharacteristic
329C42Q8×D6111yescharacteristic
330C23—611no—
331C23—611no—
332C23—1222no—
333C23—2441no—
334C23—2441no—
335C23C42×D6111yescharacteristic
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4C22⋊C4×D6111yescharacteristic
364C2×C4C22⋊C4×D6111yescharacteristic
365C2×C4C22⋊C4×D6111yescharacteristic
366C2×C4C4⋊C4×D6111yescharacteristic
367C2×C4C4⋊C4×D6111yescharacteristic
368C2×C4C4⋊C4×D6111yescharacteristic
369C8—42no—
370C8—42no—
371C8—42no—
372C8—2442no—
373C8—2442no—
374C8—2442no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—612no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—2444no—
385C22#95×D6111yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—612no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4#1683974311yescharacteristic
398C4#1683974511yescharacteristic
399C2—41no—
400C2—1222no—
401C2—2441no—
402C2#2144555611yescharacteristic
403C2#344×D6111yescharacteristic
404C2#344×D6111yescharacteristic
subgroupG/H
centerC22#95×D61
commutatorC23×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#1307C2
socleC22×C61C2×#95
prime radicalC23×D61C42
cosocleC2×C42×C61C23
hypercenter#1307D61
hypocenterC61#8118
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
4. #21443730C2semidirect
5. #21443729C2semidirect
6. #21443729C2semidirect
7. C61×#1307C2semidirect
203. #1307D61semidirect
235. C61#8118semidirect

Maximal subgroups

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

subgroupindex
#214544512
#214544492
#432×D612
#214437302
#214437292
C61×#13072
#811861