Finite Group Databasebeta

← #29574337

Subgroups — #29574337

Order 15616.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454484C211yesmaximal, characteristic
2#21445840C211yesmaximal, characteristic
3#21444593C211yesmaximal, characteristic, complemented
4#21444575C211yesmaximal, characteristic, complemented
5#21444202C211yesmaximal, characteristic
6#21443722C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16839822—22no—
10#16839818—21no—
11#16839815C2211yescharacteristic
12#16839814—21no—
13#16839786C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519705—21no—
16#16839728—21no—
17#16839717—21no—
18#16839522—21no—
19#16839514—21no—
20#16839514—21no—
21#16839513—22no—
22#16839494C411yescharacteristic, complemented
23#16839494C411yescharacteristic, complemented
24#16839491C411yescharacteristic, complemented
25#16839491C411yescharacteristic, complemented
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C2×#11758222D411yescharacteristic
30C2×#11758194—21no—
31C2×#11758194—21no—
32C4×Dic122C2×C411yescharacteristic
33C4×Dic122Q811yescharacteristic
34C4×D244C2×C411yescharacteristic
35C4×D244Q811yescharacteristic
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38#14519736D411yescharacteristic
39#14519734—21no—
40C42×D61—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418C2×C411yescharacteristic
45C4⋊#92418C2×C411yescharacteristic
46C4⋊#92418D412yes—
47#14519705—42no—
48C22⋊#92418—21no—
49#14519689—22no—
50#14519689—22no—
51#14519687—22no—
52C4×#92418—21no—
53C8×Dic61—22no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61D411yescharacteristic
61C4⋊C8×C61D411yescharacteristic
62C4×C8×C61—21no—
63C4×C8×C61C2×C411yescharacteristic
64C4×C8×C61C2×C411yescharacteristic
65#95×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C2×C22⋊D61—21no—
71#11758222—21no—
72#11758222—21no—
73#11758222—21no—
74#11758222—21no—
75C2×D244C4⋊C411yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122C4⋊C411yescharacteristic
80C2×C8×C61—21no—
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—42no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—41no—
89C42×C61—41no—
90C42×C61—41no—
91C42×C61C22×C411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61C2×Q811yescharacteristic
95C22⋊Dic61—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61C4⋊C411yescharacteristic
99C4⋊Dic61C4⋊C411yescharacteristic
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105#11758194—41no—
106#11758194—41no—
107#11758194—41no—
108#11758194—41no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—22no—
112C2×#92418—41no—
113C23×C61#12311yescharacteristic
114C22×D61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—42no—
119C2×C4×C61—81no—
120C2×C4×C61—81no—
121C2×C4×C61C2×C4⋊C411yescharacteristic
122C2×C4×C61C4×D411yescharacteristic
123C2×C4×C61C4×D411yescharacteristic
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61C22⋊Q811yescharacteristic
126C2×C4×C61C22⋊Q811yescharacteristic
127C2×C4×C61#13511yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C22⋊D61—41no—
132C22⋊D61—41no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136D244—21no—
137D244—21no—
138C4×D61—41no—
139C4×D61—41no—
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—81no—
143Dic122—21no—
144Dic122—21no—
145C8×C61—22no—
146C8×C61—41no—
147C8×C61—41no—
148C8×C61—41no—
149#92418—41no—
150#92418—41no—
151#92418—42no—
152#92418—81no—
153#8905—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#38511yescharacteristic
157C22×C61#48211yescharacteristic
158C22×C61#48511yescharacteristic
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—82no—
166C4×C61#42711yescharacteristic
167C4×C61#42811yescharacteristic
168C4×C61#44311yescharacteristic
169C4×C61#44411yescharacteristic
170C4×C61#44911yescharacteristic
171C4×C61#45211yescharacteristic
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175#2925—611no—
176#1806—611no—
177#1571—611no—
178#1566—611no—
179#1476—611no—
180#1303—611no—
181#1279D6111yescharacteristic, complemented
182C2×C61—21no—
183C2×C61—21no—
184C2×C61#185411yescharacteristic
185C2×C61#186111yescharacteristic
186C2×C61#186611yescharacteristic
187D61—81no—
188C4×#41—611no—
189#433—1222no—
190#432—1221no—
191#431—611no—
192#431—1221no—
193#423—611no—
194#423—611no—
195C2×C4⋊C8C2×D6111yescharacteristic
196C2×#104—1221no—
197#408—1221no—
198#405—1221no—
199C2×C4×C8C2×D6111yescharacteristic
200C4×C4⋊C4C2×D6111yescharacteristic
201#339—1221no—
202#335—1221no—
203#335—1221no—
204#334—1222no—
205Q8⋊C8—611no—
206Q8⋊C8—611no—
207D4⋊C8—611no—
208D4⋊C8—611no—
209C61#890511yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C2×M16—1221no—
212C2×M16—1221no—
213C22×C8—21no—
214C22×C8—21no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220C4×D4—1221no—
221#117—611no—
222#117—1221no—
223C2×C4⋊C4—21no—
224C2×C42—21no—
225C2×C42—1221no—
226C2×C42C22×D6111yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—611no—
229C4⋊C8—611no—
230C4⋊C8—612no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233C4⋊C8—1221no—
234C4⋊C8D24411yescharacteristic
235C4⋊C8D24411yescharacteristic
236#104—2442no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239C22⋊C8—1221no—
240#97—1222no—
241C4×C8—21no—
242C4×C8—1222no—
243C4×C8—1221no—
244C4×C8C4×D6111yescharacteristic
245C4×C8C4×D6111yescharacteristic
246#95—21no—
247#41—1221no—
248#41—1221no—
249#41—1221no—
250#41—1221no—
251C2×Q8—611no—
252C2×D4—611no—
253C2×D4—1221no—
254C22×C4—41no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4#1175822211yescharacteristic
259C22×C4D4×D6111yescharacteristic
260C22×C4#1175822411yescharacteristic
261M16—2441no—
262M16—2441no—
263M16—2441no—
264M16—2441no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—42no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—1221no—
273C2×C8—1221no—
274C2×C8—1222no—
275C2×C8—2441no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C42—41no—
286C42—41no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42C2×C4×D6111yescharacteristic
291C42C2×D24411yescharacteristic
292C42D4×D6111yescharacteristic
293C42Q8×D6111yescharacteristic
294C23—1221no—
295C23#1451975911yescharacteristic
296Q8—1221no—
297Q8—1221no—
298D4—1221no—
299D4—1221no—
300D4—2441no—
301D4—2441no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4C4⋊C4×D6111yescharacteristic
317C2×C4#1451973711yescharacteristic
318C2×C4C4×D24411yescharacteristic
319C2×C4#1451974711yescharacteristic
320C2×C4#1451975511yescharacteristic
321C2×C4#1451975711yescharacteristic
322C2×C4#1451979811yescharacteristic
323C2×C4#1451979811yescharacteristic
324C2×C4#1451980111yescharacteristic
325C2×C4#1451980911yescharacteristic
326C8—22no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—4881no—
331C8—2441no—
332C8—2441no—
333C8—2442no—
334C22—21no—
335C22—21no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22#1683963611yescharacteristic
340C22#1684008511yescharacteristic
341C22#1684010111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4#1683979711yescharacteristic
350C4#1683980311yescharacteristic
351C4#1683988011yescharacteristic
352C4#1683988511yescharacteristic
353C4#1683990811yescharacteristic
354C4#1683992711yescharacteristic
355C2—21no—
356C2—21no—
357C2—4881no—
358C2#2144601911yescharacteristic
359C2#2144606011yescharacteristic
360C2#2144609711yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC22×C61#385
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8905
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #21444593C2semidirect
4. #21444575C2semidirect
6. #21443722C2semidirect
7. C61×#1279C2semidirect
22. #16839494C4semidirect
23. #16839494C4semidirect
24. #16839491C4semidirect
25. #16839491C4semidirect
181. #1279D61semidirect
209. C61#8905semidirect

Maximal subgroups

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

subgroupindex
#214544842
#214458402
#214445932
#214445752
#214442022
#214437222
C61×#12792
#890561