Finite Group Databasebeta

← #30599312

Subgroups — #30599312

Order 15616.

514 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#16840608C211yesmaximal, characteristic
2C2×#16840608C211yesmaximal, characteristic
3#21460662C212yesmaximal
4#21460662C212yesmaximal
5#21448174C211yesmaximal, characteristic
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8#16840608—21no—
9#16840608—21no—
10#16840608—21no—
11#16840608—21no—
12C2×#14519733C411yescharacteristic
13C2×#14519733C411yescharacteristic
14C22×#11758196C2211yescharacteristic
15C4×#11758196—21no—
16C4×#11758196—21no—
17#16839613—21no—
18#16839613—21no—
19C22⋊C4×Dic61C2211yescharacteristic
20C22⋊C4×Dic61C2211yescharacteristic
21C4×C22⋊Dic61C411yescharacteristic
22C4×C22⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2311yescharacteristic
31#14519733—22no—
32#14519733—22no—
33#14519733—22no—
34#14519733C814yescomplemented
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—22no—
38C2×#11758196—22no—
39C2×#11758196D411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61—21no—
57#95×C61—21no—
58C24×C61C22×C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—81no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—81no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×C812yes—
76C22×Dic61M1612yes—
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C22×Dic61#4112yes—
80C22×Dic61#4112yes—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—82no—
84C2×#92420—82no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61C2×C812yes—
88C22⋊C4×C61M1612yes—
89C42×C61—81no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61C2×C812yes—
93C22⋊Dic61M1612yes—
94#11758196—24no—
95#11758196—24no—
96#11758196—22no—
97#11758196—22no—
98#11758196—22no—
99#11758196—22no—
100C4×Dic61—24no—
101C4×Dic61—24no—
102C4×Dic61—81no—
103C4×Dic61—81no—
104C4×Dic61—81no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108C23×C61#11711yescharacteristic
109C23×C61#11711yescharacteristic
110C23×C61C22×C811yescharacteristic
111C23×C61C2×M1611yescharacteristic
112C23×C61C2×M1611yescharacteristic
113C23×C61C2×M1611yescharacteristic
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61C22⋊C812yes—
145C2×Dic61C22⋊C812yes—
146C2×Dic61#12312yes—
147C2×Dic61#12312yes—
148#92420—82no—
149#92420—82no—
150#8735—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61#38111yescharacteristic
162C22×C61C2×C22⋊C811yescharacteristic
163C22×C61#40711yescharacteristic
164C22×C61#43111yescharacteristic
165C22×C61#43111yescharacteristic
166C22×C61#43211yescharacteristic
167C22×C61#43211yescharacteristic
168C4×C61—42no—
169C4×C61—42no—
170C4×C61—41no—
171C4×C61—41no—
172Dic61—22no—
173Dic61—22no—
174Dic61—22no—
175Dic61—22no—
176Dic61—42no—
177Dic61—42no—
178#2274—611no—
179C2×#324—611no—
180C2×#324—611no—
181#1282—612no—
182#1282—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61#181711yescharacteristic
190C2×C61#182811yescharacteristic
191C2×C61#183011yescharacteristic
192C2×#117—611no—
193C2×#117—611no—
194C22×C4⋊C4—611no—
195C2×C22⋊C8—612no—
196C2×C22⋊C8—612no—
197C4×C4⋊C4—1221no—
198C4×C4⋊C4—1221no—
199C4×C4⋊C4—1221no—
200C4×C4⋊C4—1221no—
201C4×C22⋊C4—611no—
202C4×C22⋊C4—611no—
203C4×C22⋊C4—611no—
204C4×C22⋊C4#692311yescharacteristic
205#324—1221no—
206#324—1221no—
207#324—1221no—
208#324—1221no—
209C61#873511yescharacteristic, complemented, Sylow
210C23×C4—611no—
211C23×C4—611no—
212C23×C4C2×#692311yescharacteristic
213C22×C8—1222no—
214C22×C8—1222no—
215#117—614no—
216#117—1222no—
217#117—1222no—
218#117—1222no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1222no—
224C2×C4⋊C4—1222no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4C2×#692311yescharacteristic
231C2×C42—21no—
232C2×C42—1221no—
233C2×C42—1221no—
234C2×C42—1221no—
235C2×C42—1221no—
236C2×C42—1221no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239C22⋊C8—1222no—
240C22⋊C8—1222no—
241#95—21no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245C24C22×#692311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—81no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—612no—
258C22×C4—612no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—4881no—
266C22×C4C22⋊#692311yescharacteristic
267C22×C4C22⋊#692311yescharacteristic
268C2×C8—4882no—
269C2×C8—4882no—
270C2×C8—2442no—
271C2×C8—2442no—
272C4⋊C4—1222no—
273C4⋊C4—1222no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1224no—
277C4⋊C4—1224no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—612no—
281C22⋊C4—612no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4D61⋊C812yes—
285C22⋊C4#1175821312yes—
286C42—81no—
287C42—1224no—
288C42—1224no—
289C42—4881no—
290C42—4881no—
291C42—4881no—
292C23—41no—
293C23—41no—
294C23C2×C22⋊#692311yescharacteristic
295C23#1451985611yescharacteristic
296C23#1451985611yescharacteristic
297C23C2×D61⋊C811yescharacteristic
298C23D61⋊M1611yescharacteristic
299C23D61⋊M1611yescharacteristic
300C23C2×#1175821311yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—612no—
314C2×C4—612no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C8—4882no—
336C8—4882no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22#1684070511yescharacteristic
348C22D61⋊(C22⋊C8)11yescharacteristic
349C22#1684073311yescharacteristic
350C22#1684078011yescharacteristic
351C22#1684078111yescharacteristic
352C22#1684078411yescharacteristic
353C22#1684078511yescharacteristic
354C4—42no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—1222no—
359C4—1222no—
360C4—1222no—
361C4—1222no—
362C4—2442no—
363C4—2442no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#2146171111yescharacteristic
371C2#2146173011yescharacteristic
372C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8735
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
34. #14519733C8semidirect
209. C61#8735semidirect

Maximal subgroups

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

subgroupindex
C2×#168406082
#214606622
#214481742
#873561