Finite Group Databasebeta

← #29590404

Subgroups — #29590404

Order 15616.

420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451744C211yesmaximal, characteristic
2#21445610C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443825C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic
9C2×#14519739C2211yescharacteristic
10C2×#14519693—21no—
11C22⋊C8×D61—21no—
12M16×Dic61—21no—
13#16839691—21no—
14#16839688C411yescharacteristic
15#16839682C2211yescharacteristic
16#16839679—21no—
17#16839675C411yescharacteristic
18#16839648—21no—
19#16839636—21no—
20#16839624C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×C8×D61—41no—
33#14519757—41no—
34#14519757—41no—
35#14519739—41no—
36#14519739—41no—
37C2×C4⋊Dic61—21no—
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519693—24no—
47C22⋊#92418—21no—
48#14519689—41no—
49#14519687—41no—
50C8×Dic61—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C23×D61C22⋊C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×D244—22no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—41no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—81no—
83C2×C4×D61—81no—
84C2×Dic122—41no—
85C2×Dic122—81no—
86M16×C61—22no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—42no—
97#11758198—42no—
98#11758198—81no—
99#11758198—81no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102#11758196—81no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105#11758194—22no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C8×D61—82no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61#10412yes—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9911yescharacteristic
145C2×Dic61#9911yescharacteristic
146D244—42no—
147D244—42no—
148C4×D61—42no—
149C4×D61—81no—
150C4×D61—81no—
151C4×D61—81no—
152Dic122—82no—
153C8×C61—42no—
154C8×C61—81no—
155#92418—42no—
156#92418—81no—
157#11739—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61C2×#9911yescharacteristic
161C22×C61#41611yescharacteristic
162C22×C61C2×#10411yescharacteristic
163C2×D61—22no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—81no—
178C4×C61—81no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—81no—
183Dic61—81no—
184#2638—611no—
185C4×#100—611no—
186#1459—611no—
187#1354—611no—
188#1354—611no—
189#1346—611no—
190#1346D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#150111yescharacteristic
194C2×C61#212111yescharacteristic
195C2×C61#213511yescharacteristic
196D61—42no—
197D61—81no—
198C2×C22⋊Q8—611no—
199C2×C4×D4—611no—
200C2×#100—1221no—
201C2×C22⋊C8—1221no—
202C4×M16—1221no—
203#398C2×D6111yescharacteristic
204#397—611no—
205#397—1221no—
206#395—611no—
207#394—1221no—
208#393—611no—
209#387—1221no—
210#385—1221no—
211#381—611no—
212#343—611no—
213#343C2×D6111yescharacteristic
214#324—611no—
215#324C2×D6111yescharacteristic
216#323—1221no—
217C61#1173911yescharacteristic, complemented, Sylow
218C22×Q8—611no—
219C22×D4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C2×M16—21no—
223C2×M16—1221no—
224C22×C8—2441no—
225C22⋊Q8—2441no—
226C22⋊Q8—2441no—
227C4×D4—2441no—
228C4×D4—2441no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4C4×D6111yescharacteristic
233C2×C4⋊C4C22×D6111yescharacteristic
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—611no—
241#100—1224no—
242C22⋊C8—21no—
243C22⋊C8—1221no—
244C22⋊C8—2441no—
245#97—2441no—
246C4×C8—2441no—
247#95—21no—
248#95—611no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95C4×D6111yescharacteristic
254C24—611no—
255C24—611no—
256C2×Q8—4881no—
257C2×Q8—2441no—
258C2×D4—1222no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—2441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—4881no—
273C22×C4—4881no—
274C22×C4C2×C4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4D4×D6111yescharacteristic
277M16—22no—
278M16—41no—
279M16—1222no—
280M16—2441no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—4882no—
284C2×C8—2441no—
285C2×C8—2441no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—4881no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C22⋊C4—4881no—
294C22⋊C4—4881no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2442no—
298C22⋊C4—2442no—
299C42—1221no—
300C42—1221no—
301C23—612no—
302C23—1221no—
303C23—1221no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23C22⋊C4×D6111yescharacteristic
312Q8—4882no—
313D4—2442no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—1221no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451979611yescharacteristic
343C2×C4#1451979811yescharacteristic
344C8—42no—
345C8—81no—
346C8—4881no—
347C8—2442no—
348C22—21no—
349C22—21no—
350C22—1222no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—2442no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22#99×D6111yescharacteristic
361C22#1683975511yescharacteristic
362C22#104×D6111yescharacteristic
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—1221no—
370C4—1221no—
371C4—4881no—
372C4—4881no—
373C4—2441no—
374C2—21no—
375C2—21no—
376C2—4881no—
377C2—2442no—
378C2#2144430711yescharacteristic
379C2#2144746411yescharacteristic
380C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11739
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #21443850C2semidirect
5. #21443848C2semidirect
6. #21443825C2semidirect
7. C61×#1346C2semidirect
190. #1346D61semidirect
217. C61#11739semidirect

Maximal subgroups

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

subgroupindex
#214517442
#214456102
#214441362
#214438502
#214438482
#214438252
C61×#13462
#1173961