Finite Group Databasebeta

← #29590405

Subgroups — #29590405

Order 15616.

420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451736C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic
3#21443848C212yesmaximal, complemented
4#21443824C212yesmaximal, complemented
5C4×#100×C61C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C22⋊#92418—21no—
8#16839692C2211yescharacteristic
9#16839690—21no—
10#16839687C411yescharacteristic
11#16839682C2211yescharacteristic
12#16839676—21no—
13#16839674C411yescharacteristic
14#16839646—21no—
15#16839635—21no—
16#16839625C411yescharacteristic
17#16839488C2212yes—
18#16839486—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#100×C61—21no—
21C4×M16×C61—21no—
22C61×#343C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—41no—
25#14519756—41no—
26#14519756—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C22⋊#92418—22no—
36C22⋊#92418—41no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C2×M16×C61—22no—
48C4×D4×C61—41no—
49C4×D4×C61—41no—
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54#100×C61—24no—
55#97×C61—41no—
56C4×C8×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—81no—
67C22×C4×C61—81no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×Dic122—41no—
78C2×Dic122—81no—
79M16×C61—24no—
80M16×C61—42no—
81C2×C8×C61—42no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—21no—
86C42×C61—21no—
87C22⋊Dic61—42no—
88C22⋊Dic61—42no—
89C22⋊Dic61—81no—
90C22⋊Dic61—81no—
91C4⋊Dic61—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—42no—
95#11758196—81no—
96C2×#92418—42no—
97C2×#92418—82no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#10412yes—
108C23×C61C2×C22⋊C411yescharacteristic
109D4×C61—44no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—42no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—81no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61#9911yescharacteristic
124C2×C4×C61#9911yescharacteristic
125C2×C4×C61#13512yes—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138Dic122—82no—
139C8×C61—44no—
140#92418—82no—
141#11739—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—22no—
145C22×C61—42no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61C2×#9911yescharacteristic
155C22×C61#41611yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163Dic61—81no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167#2638—611no—
168C4×#100D6111yescharacteristic
169#1459—611no—
170#1354—612no—
171#1346—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61—42no—
175C2×C61—81no—
176C2×C61#150111yescharacteristic
177C2×C61#212111yescharacteristic
178C2×C61#213511yescharacteristic
179C2×C22⋊Q8—611no—
180C2×C4×D4C2×D6111yescharacteristic
181C2×#100—21no—
182C2×C22⋊C8—1221no—
183C4×M16—21no—
184#398—611no—
185#397—611no—
186#397—1221no—
187#395—611no—
188#394—1221no—
189#393—611no—
190#387—1221no—
191#385—1221no—
192#381—611no—
193#343C2×D6112yes—
194#324—612no—
195#323—1221no—
196C61#1173911yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×D4C22⋊D6111yescharacteristic
199C23×C4C4×D6111yescharacteristic
200C23×C4D24411yescharacteristic
201C2×M16—22no—
202C22×C8—2441no—
203C22⋊Q8—2441no—
204C22⋊Q8—2441no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C22×D6111yescharacteristic
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4C4×D6111yescharacteristic
217C2×C22⋊C4D24411yescharacteristic
218C2×C42C22⋊D6111yescharacteristic
219#100—24no—
220C22⋊C8—1222no—
221C22⋊C8—2441no—
222#97—41no—
223C4×C8—41no—
224#95—611no—
225#95—611no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C24#1175819811yescharacteristic
232C24#1175819811yescharacteristic
233C2×Q8—4881no—
234C2×Q8—2441no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4C2×C4×D6111yescharacteristic
251C22×C4C2×D24411yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—24no—
254M16—42no—
255C2×C8—42no—
256C2×C8—4882no—
257C2×C8—2442no—
258C4⋊C4—41no—
259C4⋊C4—4881no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2442no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—4881no—
267C22⋊C4—4881no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#1451970512yes—
282C23C2×#1175819811yescharacteristic
283Q8—4882no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4#1451969111yescharacteristic
311C2×C4#1451969111yescharacteristic
312C2×C4#1451979712yes—
313C8—44no—
314C8—4882no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#1451969111yescharacteristic
328C22#1683975611yescharacteristic
329C22C2×#1451970511yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—4881no—
337C4—4881no—
338C4—4881no—
339C4—4881no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#2144430811yescharacteristic
345C2#2144746611yescharacteristic
346C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC4×#100×C61C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C4⋊C4×C61C23
hypercenterC4×#100D61
hypocenterC61#11739
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #21443848C2semidirect
4. #21443824C2semidirect
196. C61#11739semidirect

Maximal subgroups

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

subgroupindex
#214517362
#214441372
#214438482
#214438242
C4×#100×C612
#1173961