Finite Group Databasebeta

← #30595699

Subgroups — #30595699

Order 15616.

708 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 126 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#21461674C211yesmaximal, characteristic, complemented
2#21461480C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4#21454165C211yesmaximal, characteristic
5C22×D61⋊C8—21no—
6C2×C4⋊#92420—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519774C411yescharacteristic
12C2×#14519752—21no—
13C2×#14519752—21no—
14C2×#14519752C412yes—
15C2×C42×D61C2211yescharacteristic
16#16839663—21no—
17#16839663—21no—
18#16839663C2212yes—
19C61×#384C411yescharacteristic
20C2×D61⋊C8—24no—
21C2×D61⋊C8—42no—
22C2×D61⋊C8—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519834—42no—
27C22×D244—22no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244C2×C412yes—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519774—42no—
35#14519752—44no—
36#14519752—42no—
37#14519752—42no—
38#14519752—42no—
39#14519752—42no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—22no—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C42×D61—42no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61C2×C412yes—
50C2×C42×C61C2×C411yescharacteristic
51C23×D61—22no—
52C23×D61C22⋊C411yescharacteristic
53C22×C4×C61—22no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×D244—24no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—42no—
65C2×D244—44no—
66C2×D244—44no—
67C2×D244—44no—
68C2×D244—42no—
69C2×D244—42no—
70C2×D244—42no—
71C2×D244—42no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61D812yes—
80C2×C4×D61D812yes—
81C2×C4×D61SD1612yes—
82C2×C4×D61SD1612yes—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89D61⋊C8—48no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—42no—
93C42×C61—22no—
94#11758198—44no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—42no—
99C4×Dic61—22no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—42no—
108C22×D61—42no—
109C22×D61—42no—
110C22×D61—42no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61—42no—
114C22×D61#10012yes—
115C22×D61#10212yes—
116C22×D61#10212yes—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61#9912yes—
125C2×C4×C61#10212yes—
126C2×C4×C61#10212yes—
127C2×C4×C61#10412yes—
128C2×C4×C61#13112yes—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61C2×D811yescharacteristic
137C2×Dic61C2×D811yescharacteristic
138C2×Dic61C2×SD1611yescharacteristic
139C2×Dic61C2×SD1611yescharacteristic
140D244—84no—
141D244—84no—
142D244—88no—
143D244—84no—
144C4×D61—24no—
145C4×D61—24no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—44no—
149#92420—44no—
150#92420—82no—
151#7664—611nomaximal, Sylow
152C22×C61#40811yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61C2×#10011yescharacteristic
155C22×C61C2×#10211yescharacteristic
156C22×C61C2×#10211yescharacteristic
157C22×C61C2×#10411yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—82no—
166C2×D61—82no—
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—82no—
171C2×D61—82no—
172C2×D61#33114yes—
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—82no—
176C4×C61#32714yes—
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182#2856—611no—
183#1797—611no—
184C2×#336—611no—
185#1270—614no—
186C2×C61#147111yescharacteristic
187C2×C61#148011yescharacteristic
188C2×C61#149211yescharacteristic
189C2×C61C2×#32711yescharacteristic
190C2×C61#151911yescharacteristic
191C2×C61#153011yescharacteristic
192C2×C61C2×#33111yescharacteristic
193D61—24no—
194D61—162no—
195C23×C8—1221no—
196C2×#127—611no—
197C2×#121—612no—
198C2×#121—1221no—
199C2×#121—1221no—
200C22×C42—611no—
201C2×C4⋊C8—1221no—
202C2×C22⋊C8—1221no—
203#390—612no—
204#390—1221no—
205#390—1221no—
206#384#692311yescharacteristic
207#336—612no—
208#336—612no—
209#336—1221no—
210C61#766411yescharacteristic, complemented, Sylow
211C22×D4—612no—
212C22×D4—1222no—
213C22×D4—1221no—
214C22×D4—1221no—
215C23×C4—611no—
216C23×C4—611no—
217C23×C4—611no—
218C22×C8—1222no—
219C22×C8—1224no—
220C22×C8—1222no—
221C22×C8—2442no—
222C22×C8—2442no—
223#127—2442no—
224#121—2442no—
225#121—2442no—
226#121—2442no—
227#121—2442no—
228#121—2444no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C2×#692312yes—
232C2×C22⋊C4—1222no—
233C2×C22⋊C4—1222no—
234C2×C22⋊C4—1222no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—2442no—
239C2×C42C2×#692311yescharacteristic
240C4⋊C8—2442no—
241C22⋊C8—2442no—
242C24—611no—
243C24—1222no—
244C2×D4—1224no—
245C2×D4—2442no—
246C2×D4—2442no—
247C2×D4—2442no—
248C2×D4—2442no—
249C2×D4—2444no—
250C2×D4—2444no—
251C2×D4—2444no—
252C2×D4—2442no—
253C2×D4—2442no—
254C2×D4—2442no—
255C2×D4—2442no—
256C22×C4—22no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—612no—
260C22×C4—612no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—611no—
264C22×C4—1222no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4C22⋊#692311yescharacteristic
272C22×C4C22⋊#692311yescharacteristic
273C22×C4C22×#692311yescharacteristic
274C2×C8—1224no—
275C2×C8—2442no—
276C2×C8—2442no—
277C2×C8—2442no—
278C2×C8—2442no—
279C2×C8—2448no—
280C2×C8—2442no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C22⋊C4—2444no—
289C42—22no—
290C42—1222no—
291C42—2441no—
292C42—2441no—
293C23—612no—
294C23—612no—
295C23—612no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—2442no—
301C23—2442no—
302C23—2442no—
303C23—2442no—
304C23—2442no—
305C23—2442no—
306C23—2442no—
307C23C2×C22⋊#692311yescharacteristic
308D4—4884no—
309D4—4884no—
310D4—4888no—
311D4—4884no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1224no—
328C2×C4—1224no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2444no—
335C2×C4#1451983612yes—
336C2×C4#1451983912yes—
337C2×C4#1451983912yes—
338C2×C4#1451984212yes—
339C2×C4#1451986512yes—
340C8—4882no—
341C8—2444no—
342C22—614no—
343C22—1222no—
344C22—1222no—
345C22—1222no—
346C22—1222no—
347C22—1222no—
348C22—1222no—
349C22—4882no—
350C22—4882no—
351C22—4882no—
352C22—4882no—
353C22—4882no—
354C22—4882no—
355C22—4882no—
356C22#1684073711yescharacteristic
357C22C2×#1451983611yescharacteristic
358C22D61⋊#10011yescharacteristic
359C22C2×#1451983911yescharacteristic
360C22C2×#1451983911yescharacteristic
361C22C2×#1451984211yescharacteristic
362C22#1684076111yescharacteristic
363C4—22no—
364C4—22no—
365C4—82no—
366C4—1221no—
367C4—1221no—
368C4—1221no—
369C4—1221no—
370C4—2441no—
371C4#1684061414yes—
372C2—1224no—
373C2—9762no—
374C2#2146109611yescharacteristic
375C2#2146112611yescharacteristic
376C2#2146116611yescharacteristic
377C2C2×#1684061411yescharacteristic
378C2#2146125611yescharacteristic
379C2#2146129011yescharacteristic
380C2D61⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radical#21454165C2
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7664
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #21461674C2semidirect
2. #21461480C2semidirect
3. #21460636C2semidirect
210. C61#7664semidirect

Maximal subgroups

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

subgroupindex
#214616742
#214614802
#214606362
#214541652
#766461