Finite Group Databasebeta

← #29596296

Subgroups — #29596296

Order 15616.

334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454466C211yesmaximal, characteristic
2#21445924C211yesmaximal, characteristic
3#21445920C211yesmaximal, characteristic
4#21443948C211yesmaximal, characteristic
5#21443941C211yesmaximal, characteristic
6#21443939C211yesmaximal, characteristic
7C61×#1395C211yesmaximal, characteristic
8#41×Dic61C2211yescharacteristic
9#16839820—21no—
10#16839820—21no—
11#16839816—21no—
12#16839816—21no—
13#16839790C411yescharacteristic, complemented
14#16839788C411yescharacteristic, complemented
15#16839746C2211yescharacteristic
16#16839736C2211yescharacteristic
17#16839729C2211yescharacteristic
18M16×Dic61C411yescharacteristic, complemented
19C2×#14519687C411yescharacteristic, complemented
20#16839523—21no—
21#16839521—21no—
22#16839519—21no—
23#16839518—21no—
24C61×#413C2211yescharacteristic
25C61×#410C2211yescharacteristic
26C61×#408C2211yescharacteristic
27C2×#11758194—21no—
28C2×#11758194C2×C411yescharacteristic
29C22×#92418C2×C411yescharacteristic
30Q8×Dic61—21no—
31D4×Dic61—21no—
32D4×Dic61—21no—
33D4×Dic61—21no—
34#14519736—21no—
35#14519736C2×C411yescharacteristic
36#14519736D411yescharacteristic
37#14519736D411yescharacteristic
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41#14519706—21no—
42#14519706—21no—
43#14519706—21no—
44#14519706—21no—
45#14519696—21no—
46#14519694—21no—
47#14519692—21no—
48#14519692—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519687—21no—
52#14519687—21no—
53#14519687—21no—
54C8×Dic61—21no—
55C2×#41×C61C2311yescharacteristic
56C2×M16×C61—21no—
57C2×M16×C61C2×C411yescharacteristic
58C22×C8×C61C2×C411yescharacteristic
59#117×C61—21no—
60#101×C61—21no—
61#100×C61—21no—
62#99×C61—21no—
63#99×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#41×C61—41no—
67#41×C61—41no—
68C2×Q8×C61#4111yescharacteristic
69C2×D4×C61#4111yescharacteristic
70C2×D4×C61#4111yescharacteristic
71C2×D4×C61#4111yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78M16×C61—41no—
79M16×C61—41no—
80M16×C61—41no—
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—41no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—41no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—41no—
100C4×Dic61C22⋊C411yescharacteristic
101C4×Dic61C22⋊C411yescharacteristic
102C4×Dic61C22⋊C411yescharacteristic
103C4×Dic61C22⋊C411yescharacteristic
104#11758194—41no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61#11711yescharacteristic
112C23×C61#12311yescharacteristic
113C23×C61#12311yescharacteristic
114Q8×C61—41no—
115D4×C61—41no—
116D4×C61—41no—
117D4×C61—41no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—81no—
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61#11711yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×C4×C61#12311yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C8×C61—41no—
138C8×C61—41no—
139C8×C61—81no—
140#92418—41no—
141#92418—41no—
142#92418—81no—
143#12865—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61#38111yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—161no—
155C4×C61#41011yescharacteristic
156C4×C61#41011yescharacteristic
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61—161no—
162#2923—611no—
163#1827—611no—
164#1827—611no—
165#1395—611no—
166#1395D6111yescharacteristic
167#1392—611no—
168#1391—611no—
169C2×C61—21no—
170C2×C61—41no—
171C2×C61—41no—
172C2×C61—41no—
173C2×C61#182011yescharacteristic
174C4×#41—611no—
175#433—1221no—
176#433—1221no—
177#432—1221no—
178#432—1221no—
179#424—611no—
180#424—611no—
181#413—611no—
182#413C2×D6111yescharacteristic
183#410—611no—
184#410C2×D6111yescharacteristic
185#408—611no—
186#408C2×D6111yescharacteristic
187C4×M16—611no—
188C2×#97—611no—
189#339—1221no—
190#339—1221no—
191H(3,ℤ/4)—1221no—
192H(3,ℤ/4)—1221no—
193C61#1286511yescharacteristic, complemented, Sylow
194C2×#41C22×D6111yescharacteristic
195C2×M16—21no—
196C2×M16—611no—
197C2×M16—1221no—
198C2×M16C4×D6111yescharacteristic
199C22×C8—611no—
200C22×C8C4×D6111yescharacteristic
201C4×Q8—1221no—
202C4×D4—1221no—
203C4×D4—1221no—
204C4×D4—1221no—
205#117—21no—
206#117—611no—
207#117—611no—
208#117—611no—
209#117—1221no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—1221no—
216C4⋊C8—1221no—
217#101—21no—
218#101—1221no—
219#100—21no—
220#100—1221no—
221#99—21no—
222#99—21no—
223#99—1221no—
224#99—1221no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—1221no—
228C22⋊C8—1221no—
229#97—1221no—
230#97—1221no—
231#97—1221no—
232C4×C8—1221no—
233#41—41no—
234#41—41no—
235C2×Q8#1175822211yescharacteristic
236C2×D4#1175822211yescharacteristic
237C2×D4#1175822411yescharacteristic
238C2×D4#1175822611yescharacteristic
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4C2×C4×D6111yescharacteristic
243C22×C4D4×D6111yescharacteristic
244C22×C4D4×D6111yescharacteristic
245M16—41no—
246M16—41no—
247M16—41no—
248M16—2441no—
249M16—2441no—
250M16—2441no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—1221no—
256C2×C8—1221no—
257C2×C8—2441no—
258C2×C8—2441no—
259C4⋊C4—41no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—2441no—
264C22⋊C4—41no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—2441no—
269C42—41no—
270C42—611no—
271C42—611no—
272C42—611no—
273C42—611no—
274C42—1221no—
275C42—1221no—
276C42—1221no—
277C42—2441no—
278C23#1451973511yescharacteristic
279C23#1451975911yescharacteristic
280C23#1451976211yescharacteristic
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—4881no—
297C2×C4—4881no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4C22⋊C4×D6111yescharacteristic
301C2×C4#1451973411yescharacteristic
302C2×C4#1451975911yescharacteristic
303C2×C4#1451976211yescharacteristic
304C8—41no—
305C8—41no—
306C8—81no—
307C8—4881no—
308C8—2441no—
309C8—2441no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22#1683962411yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—161no—
321C4—9761no—
322C4—2441no—
323C4—2441no—
324C4—2441no—
325C4—2441no—
326C4#1683973411yescharacteristic
327C4#1683973411yescharacteristic
328C2—21no—
329C2—41no—
330C2—41no—
331C2—41no—
332C2#2144589511yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#1395C2
socleC2×C61#1820
prime radical, cosocleC2×#41×C61C23
hypercenter#1395D61
hypocenterC61#12865
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1395

Complements

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

NH ≅ G/Ntype
13. #16839790C4semidirect
14. #16839788C4semidirect
18. M16×Dic61C4semidirect
19. C2×#14519687C4semidirect
193. C61#12865semidirect

Maximal subgroups

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

subgroupindex
#214544662
#214459242
#214459202
#214439482
#214439412
#214439392
C61×#13952
#1286561