Finite Group Databasebeta

← #30607966

Subgroups — #30607966

Order 15616.

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

normal subgroups only

This group has 466 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
1#21462153C211yesmaximal, characteristic, complemented
2C2×#16840659C212yesmaximal, complemented
3C2×#16840658C212yesmaximal, complemented
4#21462025C211yesmaximal, characteristic, complemented
5C2×#16839837C211yesmaximal, characteristic
6C2×#14519851C2212yes—
7C2×#14519851C2212yes—
8#16840683—21no—
9#16840683—21no—
10#16840659—24no—
11#16840658—24no—
12#16840651—21no—
13#16840648—21no—
14C22×#11758194C2211yescharacteristic
15C22×#11758189C2211yescharacteristic
16C2×C4×C22⋊D61C411yescharacteristic
17#16839837—21no—
18#16839837—21no—
19#16839837—21no—
20#16839837—21no—
21C2×#14519706C411yescharacteristic
22C2×#14519689C411yescharacteristic
23C2×C8×Dic61C2211yescharacteristic
24C2×C22⋊C8×C61C411yescharacteristic
25#14519851—22no—
26#14519851—22no—
27#14519851—22no—
28#14519851D414yescomplemented
29C2×#11758187—22no—
30C2×#11758187—22no—
31C22×C22⋊D61C811yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35C2×#11758194—22no—
36C2×#11758194—22no—
37C2×#11758189—21no—
38C2×#11758189—21no—
39C2×#11758189—22no—
40C2×#11758189—22no—
41C22×#92418C2×C411yescharacteristic
42C22×#92418C2311yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47C2×#11758196C811yescharacteristic
48C2×C22⋊Dic61C811yescharacteristic
49C2×#11758198C811yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51#14519706—21no—
52#14519706—21no—
53#14519689—21no—
54#14519689—21no—
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C8×Dic61D411yescharacteristic
58C8×Dic61D411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C22×C8×C61C2×C411yescharacteristic
61C22×C8×C61C2×C411yescharacteristic
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C24×C61C2×C811yescharacteristic
65C23×D61C2×C811yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61C2×C811yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—42no—
75C22×Dic61C2×C811yescharacteristic
76C22×Dic61C2×C811yescharacteristic
77C22×Dic61C2×C811yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C8×C61—22no—
83C2×C8×C61—21no—
84C2×C8×C61—22no—
85C2×C8×C61C22⋊C411yescharacteristic
86C2×C8×C61C22⋊C411yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758198—21no—
90#11758198—21no—
91#11758196—21no—
92#11758196—21no—
93C4×Dic61C22⋊C411yescharacteristic
94C4×Dic61C22⋊C411yescharacteristic
95C4×Dic61M1611yescharacteristic
96C4×Dic61M1611yescharacteristic
97#11758194—42no—
98#11758194—41no—
99#11758194—41no—
100C2×#92418—21no—
101C2×#92418—22no—
102C2×#92418C2×D411yescharacteristic
103C2×#92418C2×D412yes—
104C2×#92418C2×D411yescharacteristic
105C2×#92418#4112yes—
106#11758189—42no—
107#11758189—41no—
108#11758189—41no—
109#11758187—24no—
110#11758187—42no—
111C23×C61—21no—
112C23×C61—22no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C22×C811yescharacteristic
116C22×D61—21no—
117C22×D61—22no—
118C22×D61—41no—
119C22×D61—41no—
120C2×C4×C61—21no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61C4×D412yes—
127C2×C4×C61C2×M1611yescharacteristic
128C2×C4×C61#13112yes—
129C22⋊D61—42no—
130C22⋊D61—42no—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61C22⋊C811yescharacteristic
136C2×Dic61C22⋊C811yescharacteristic
137C2×Dic61C22⋊C811yescharacteristic
138C2×Dic61C22⋊C811yescharacteristic
139C4×D61—41no—
140C4×D61—41no—
141C4×D61—42no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61—41no—
145#92418—41no—
146#92418#12112yes—
147#92418#12411yescharacteristic
148#92418#12711yescharacteristic
149#13194—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—82no—
156C22×C61C2×C22⋊C811yescharacteristic
157C22×C61C8×D412yes—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—82no—
162C4×C61—41no—
163C4×C61#39011yescharacteristic
164C4×C61#40811yescharacteristic
165C4×C61#43612yes—
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61#34912yescomplemented
171C2×#436—611no—
172#2150—611no—
173C2×#349—612no—
174C2×#349—612no—
175C4×M32—611no—
176C2×C61—22no—
177C2×C61—81no—
178C2×C61#195411yescharacteristic
179C2×C61C2×#34911yescharacteristic
180C2×C61#211511yescharacteristic
181D61—81no—
182C22×M16—611no—
183C22×M16—611no—
184C2×C4×D4—611no—
185C2×M32—612no—
186C2×M32—612no—
187#436—1221no—
188#436—1221no—
189#436—1221no—
190#436—1221no—
191C2×C4⋊C8—611no—
192C2×C22⋊C8—611no—
193C2×C22⋊C8#692311yescharacteristic
194C2×C4×C8—611no—
195C4⋊C16—1221no—
196C4⋊C16—1221no—
197#349—1224no—
198#349—1224no—
199#346—1221no—
200C4×C16—1221no—
201C61#1319411yescharacteristic, complemented, Sylow
202C22×D4—611no—
203C23×C4—611no—
204C23×C4C2×#692311yescharacteristic
205C2×M16—1222no—
206C2×M16—1221no—
207C2×M16—1221no—
208C2×M16—1222no—
209C2×M16—1222no—
210C2×M16—1221no—
211C2×M16—1221no—
212C2×M16—1222no—
213C22×C8—611no—
214C22×C8—611no—
215C22×C8C2×#692311yescharacteristic
216C22×C8C2×#692311yescharacteristic
217C4×D4—1221no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221C2×C4⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C42—611no—
225M32—614no—
226M32—1222no—
227M32—1222no—
228M32—1222no—
229C2×C16—1222no—
230C2×C16—1222no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—1221no—
236C22⋊C8—1221no—
237C4×C8—611no—
238C4×C8—611no—
239C4×C8—611no—
240C4×C8—611no—
241C24—611no—
242C24D61⋊C811yescharacteristic
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—2442no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1222no—
255C22×C4—1221no—
256C22×C4—1222no—
257C22×C4D61⋊C811yescharacteristic
258C22×C4C22×#692311yescharacteristic
259M16—2442no—
260M16—2441no—
261M16—2441no—
262M16—2442no—
263M16—2441no—
264M16—2441no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—612no—
271C2×C8—612no—
272C2×C8—1221no—
273C2×C8—1222no—
274C2×C8C22⋊#692311yescharacteristic
275C2×C8C22⋊#692311yescharacteristic
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C42—611no—
283C42—611no—
284C42—611no—
285C42—611no—
286C16—1224no—
287C16—2442no—
288C23—21no—
289C23—22no—
290C23—41no—
291C23—41no—
292C23—1222no—
293C23—1221no—
294C23—2441no—
295C23—2441no—
296C23C2×D61⋊C811yescharacteristic
297D4—2442no—
298D4—2442no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1222no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2442no—
315C2×C4C2×C22⋊#692311yescharacteristic
316C2×C4D4×#692312yes—
317C2×C4D61⋊M1611yescharacteristic
318C2×C4#1451986412yes—
319C8—21no—
320C8—21no—
321C8—41no—
322C8—612no—
323C8—611no—
324C8—611no—
325C8—2441no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—82no—
332C22—4882no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22D61⋊(C22⋊C8)11yescharacteristic
337C22#1684078912yes—
338C4—41no—
339C4—612no—
340C4—1221no—
341C4—1221no—
342C4—1221no—
343C4—2441no—
344C4#1684071411yescharacteristic
345C4#1684073511yescharacteristic
346C4#1684079512yes—
347C2—22no—
348C2—81no—
349C2—4881no—
350C2#2146194211yescharacteristic
351C2D61⋊#34911yescharacteristic
352C2#2146205611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC22×C22⋊D61C8
cosocleC22×#92418C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#13194
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21462153C2semidirect
2. C2×#16840659C2semidirect
3. C2×#16840658C2semidirect
4. #21462025C2semidirect
28. #14519851D4semidirect
170. Dic61#349semidirect
201. C61#13194semidirect

Maximal subgroups

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

subgroupindex
#214621532
C2×#168406592
C2×#168406582
#214620252
C2×#168398372
#1319461