Finite Group Databasebeta

← #30596785

Subgroups — #30596785

Order 15616.

906 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 166 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×#16840733C212yesmaximal
2#21460691C214yesmaximal, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic
4C22×#11758213—22no—
5#16840733—22no—
6#16840733—22no—
7#16840733C414yes—
8#16840733C2214yes—
9C2×#14519834C414yes—
10C2×C22⋊#92420—22no—
11C23×C4×D61C2211yescharacteristic
12C22×C8×D61C412yes—
13C2×C22⋊#92418C411yescharacteristic
14C2×#14519689C2212yes—
15C22⋊C8×D61—22no—
16C22⋊C8×D61—22no—
17C2×C22⋊C8×C61C411yescharacteristic
18C2×#11758213—24no—
19C2×#11758213—24no—
20C2×#11758213—48no—
21C22×#92420—24no—
22#14519834—24no—
23#14519834C2×C418yes—
24C22⋊#92420—24no—
25C22⋊#92420—24no—
26C24×D61Q811yescharacteristic
27C23×Dic61D411yescharacteristic
28C22×C4×D61—44no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61C2×C412yes—
31C22×C4×D61C2×C412yes—
32C22×C4×D61D412yes—
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D412yes—
35C22×C4×D61Q811yescharacteristic
36C22×C4×D61C2311yescharacteristic
37C22×#92418C2×C412yes—
38C2×C8×D61—22no—
39C2×C8×D61—22no—
40C2×C8×D61—44no—
41C22⋊#92418—22no—
42#14519689—24no—
43C23×C4×C61C2×C411yescharacteristic
44C22×C8×C61C2×C412yes—
45C22⋊C8×C61—22no—
46C24×C61C4⋊C411yescharacteristic
47C23×D61—22no—
48C23×D61—22no—
49C23×D61—42no—
50C23×D61—42no—
51C23×D61C4⋊C411yescharacteristic
52C23×D61C4⋊C412yes—
53C23×D61C4⋊C412yes—
54C23×D61C2×Q811yescharacteristic
55C22×C4×C61—42no—
56C22×C4×C61C4212yes—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C4⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—42no—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C22⋊C412yes—
63C22×Dic61C4⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×C4×D61—24no—
66C2×C4×D61—28no—
67C2×C4×D61—44no—
68C2×C4×D61—42no—
69C2×C4×D61—44no—
70C2×C4×D61—42no—
71C2×C4×D61—44no—
72C2×C4×D61—42no—
73C2×C4×D61C4211yescharacteristic
74C2×C4×D61C4211yescharacteristic
75C2×C4×D61C22⋊C411yescharacteristic
76C2×C4×D61C22⋊C412yes—
77C2×C4×D61C22⋊C412yes—
78C2×C4×D61C22⋊C411yescharacteristic
79C2×C4×D61C4⋊C412yes—
80C2×C4×D61C4⋊C412yes—
81C2×C4×D61C22×C412yes—
82C2×C4×D61C2×D412yes—
83C2×#92420—28no—
84C2×#92420—48no—
85#11758213—48no—
86#11758213—48no—
87C2×C8×C61—22no—
88C2×C8×C61—42no—
89C2×#92418—22no—
90C2×#92418—42no—
91C8×D61—44no—
92C8×D61—44no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61#9512yes—
96C23×C61#10812yes—
97C23×C61#10812yes—
98C23×C61C2×C4⋊C411yescharacteristic
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—22no—
102C22×D61—22no—
103C22×D61—24no—
104C22×D61—24no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—24no—
108C22×D61—24no—
109C22×D61—42no—
110C22×D61—41no—
111C22×D61—42no—
112C22×D61—41no—
113C22×D61—48no—
114C22×D61—48no—
115C22×D61#9511yescharacteristic
116C22×D61#9511yescharacteristic
117C22×D61C2×C4⋊C412yes—
118C2×C4×C61—22no—
119C2×C4×C61—24no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61#9512yes—
123C2×C4×C61C2×C4211yescharacteristic
124C2×C4×C61C2×C22⋊C411yescharacteristic
125C2×Dic61—24no—
126C2×Dic61—22no—
127C2×Dic61—42no—
128C2×Dic61—41no—
129C2×Dic61#9511yescharacteristic
130C2×Dic61#9511yescharacteristic
131C2×Dic61C2×C22⋊C412yes—
132C4×D61—24no—
133C4×D61—22no—
134C4×D61—22no—
135C4×D61—24no—
136C4×D61—22no—
137C4×D61—24no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61#9914yes—
142#92420—48no—
143C8×C61—42no—
144#92418—42no—
145#8008—611nomaximal, Sylow
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—22no—
149C22×C61—21no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61#34114yes—
153C22×C61C2×#9511yescharacteristic
154C22×C61C2×#10811yescharacteristic
155C22×C61C2×#10811yescharacteristic
156C2×D61—24no—
157C2×D61—24no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—48no—
166C2×D61—48no—
167C2×D61—42no—
168C2×D61—42no—
169C2×D61#33812yes—
170C2×D61#34212yes—
171C4×C61—22no—
172C4×C61—21no—
173C4×C61C2×#9912yes—
174Dic61—22no—
175Dic61—21no—
176Dic61#34212yes—
177C2×#407—612no—
178C22×C22⋊C8—611no—
179#1293—614no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—24no—
183C2×C61C2×#33811yescharacteristic
184C2×C61C2×#34111yescharacteristic
185C2×C61C2×#34211yescharacteristic
186D61—22no—
187D61—22no—
188D61—42no—
189C24×C4—611no—
190C22×M16—1222no—
191C23×C8—612no—
192#407—614no—
193#407—614no—
194#407—1222no—
195#407—1222no—
196C2×C22⋊C8—614no—
197C2×C22⋊C8—611no—
198C2×C22⋊C8—612no—
199C2×C22⋊C8—1222no—
200C2×C22⋊C8—1222no—
201C2×C22⋊C8—1222no—
202C2×C22⋊C8#692311yescharacteristic
203C61#800811yescharacteristic, complemented, Sylow
204C25—611no—
205C23×C4—611no—
206C23×C4—612no—
207C23×C4—611no—
208C23×C4—612no—
209C23×C4—612no—
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—612no—
213C23×C4—611no—
214C23×C4—2444no—
215C23×C4C2×#692311yescharacteristic
216C2×M16—1224no—
217C2×M16—1224no—
218C2×M16—2448no—
219C22×C8—612no—
220C22×C8—1222no—
221C22×C8—1222no—
222C22×C8—1224no—
223C22×C8—2444no—
224C22×C8C2×#692312yes—
225C22⋊C8—22no—
226C22⋊C8—618no—
227C22⋊C8—1224no—
228C22⋊C8—1224no—
229C22⋊C8—1224no—
230C22⋊C8—1224no—
231C22⋊C8—1222no—
232C24—611no—
233C24—612no—
234C24—612no—
235C24—611no—
236C24—1222no—
237C24—1222no—
238C24—2442no—
239C24—2442no—
240C24C4⋊#692311yescharacteristic
241C22×C4—42no—
242C22×C4—611no—
243C22×C4—612no—
244C22×C4—611no—
245C22×C4—612no—
246C22×C4—611no—
247C22×C4—612no—
248C22×C4—612no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—612no—
252C22×C4—611no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—612no—
256C22×C4—1224no—
257C22×C4—1228no—
258C22×C4—2442no—
259C22×C4—2444no—
260C22×C4—2444no—
261C22×C4—2442no—
262C22×C4—2444no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4C4×#692312yes—
266C22×C4C4⋊#692311yescharacteristic
267C22×C4C22⋊#692312yes—
268C22×C4C22×#692311yescharacteristic
269M16—2448no—
270M16—2448no—
271C2×C8—22no—
272C2×C8—42no—
273C2×C8—1228no—
274C2×C8—1222no—
275C2×C8—2444no—
276C2×C8—2444no—
277C2×C8—2448no—
278C2×C8—2442no—
279C23—41no—
280C23—41no—
281C23—611no—
282C23—611no—
283C23—612no—
284C23—1222no—
285C23—1222no—
286C23—1224no—
287C23—1224no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291C23—1221no—
292C23—1224no—
293C23—1224no—
294C23—2442no—
295C23—2441no—
296C23—2442no—
297C23—2441no—
298C23—2448no—
299C23—2448no—
300C23(C2×#6923)⋊C412yes—
301C23#1451984712yes—
302C23#1451984812yes—
303C23C2×C4⋊#692311yescharacteristic
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—611no—
309C2×C4—614no—
310C2×C4—611no—
311C2×C4—612no—
312C2×C4—1224no—
313C2×C4—1222no—
314C2×C4—1224no—
315C2×C4—1222no—
316C2×C4—1224no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1224no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2441no—
324C2×C4—2442no—
325C2×C4(C2×#6923)⋊C412yes—
326C2×C4C2×C4×#692311yescharacteristic
327C2×C4C2×C22⋊#692311yescharacteristic
328C8—42no—
329C8—2448no—
330C8—2442no—
331C22—22no—
332C22—21no—
333C22—22no—
334C22—21no—
335C22—42no—
336C22—42no—
337C22—612no—
338C22—612no—
339C22—1224no—
340C22—1224no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—1222no—
346C22—1222no—
347C22—1222no—
348C22—2448no—
349C22—2448no—
350C22—2442no—
351C22—2442no—
352C22#1684063814yes—
353C22C2×(C2×#6923)⋊C411yescharacteristic
354C22C2×#1451984711yescharacteristic
355C22C2×#1451984811yescharacteristic
356C4—22no—
357C4—21no—
358C4—612no—
359C4—1222no—
360C4—1221no—
361C4D61⋊#9912yes—
362C2—21no—
363C2—21no—
364C2—24no—
365C2—1222no—
366C2—1222no—
367C2—2442no—
368C2D61⋊#33811yescharacteristic
369C2C2×#1684063811yescharacteristic
370C2#2146151611yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #21460691C2semidirect
203. C61#8008semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
#214606912
C2×C22⋊C8×D612
#800861