Finite Group Databasebeta

← #30607486

Subgroups — #30607486

Order 15616.

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

normal subgroups only

This group has 494 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×D61⋊M32C211yesmaximal, characteristic, complemented
2C2×#16840660C212yesmaximal, complemented
3C2×#16840657C211yesmaximal, characteristic, complemented
4#21460874C212yesmaximal, complemented
5#21454516C211yesmaximal, characteristic
6C2×#14519852—21no—
7D61⋊M32—24no—
8C2×#14519851C2212yes—
9C2×D61⋊C16—21no—
10C22×#11758187C2212yes—
11#16840660—24no—
12#16840657—21no—
13#16840657—21no—
14C2×#14519784C2211yescharacteristic
15C22×C8×D61C2211yescharacteristic
16#16840269C411yescharacteristic
17#16839836—21no—
18#16839836—21no—
19#16839825—21no—
20#16839825—21no—
21#16839788C411yescharacteristic
22#16839725C411yescharacteristic
23#16839720C2211yescharacteristic
24C61×#408C411yescharacteristic
25#14519852—24no—
26#14519851—22no—
27#14519851D414yescomplemented
28D61⋊C16—24no—
29C2×#11758187—22no—
30C2×#11758187—22no—
31C2×#11758187—22no—
32C2×#11758187—22no—
33C22×C4×D61C2×C411yescharacteristic
34#14519784—22no—
35#14519784—22no—
36C2×#11758194—21no—
37C2×#11758194C2×C411yescharacteristic
38C22×#92418—21no—
39C22×#92418C2311yescharacteristic
40C2×C8×D61—22no—
41C2×C8×D61—22no—
42C2×C8×D61D411yescharacteristic
43C2×C8×D61D411yescharacteristic
44C2×C8×D61D411yescharacteristic
45C2×C8×D61D411yescharacteristic
46#14519758—21no—
47#14519753C811yescharacteristic
48#14519753C811yescharacteristic
49#14519748C811yescharacteristic
50#14519748C811yescharacteristic
51#14519745—21no—
52C4×C22⋊D61—21no—
53C4×C22⋊D61—21no—
54#14519736C2×C411yescharacteristic
55#14519706—21no—
56#14519706—21no—
57#14519689—21no—
58#14519689—21no—
59#14519687—21no—
60C8×Dic61—21no—
61C2×#41×C61C2×C411yescharacteristic
62C2×M16×C61C2×C411yescharacteristic
63C22×C8×C61C2×C411yescharacteristic
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C23×D61M1611yescharacteristic
67#41×C61—22no—
68#41×C61—22no—
69C2×Q8×C61C2×C811yescharacteristic
70C2×D4×C61—21no—
71C2×D4×C61C2×C811yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61C22×C411yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C22×Dic61M1611yescharacteristic
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61C22⋊C411yescharacteristic
80C2×C4×D61C22⋊C411yescharacteristic
81C2×C4×D61C2×C811yescharacteristic
82C2×C4×D61C2×C811yescharacteristic
83M16×C61—22no—
84C2×C8×C61—22no—
85C2×C8×C61—21no—
86C2×C8×C61C22⋊C411yescharacteristic
87C2×C8×C61C22⋊C411yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61C2×C811yescharacteristic
94C4⋊Dic61C2×C811yescharacteristic
95#11758196—21no—
96#11758196—21no—
97C4×Dic61—21no—
98#11758194—22no—
99#11758194—42no—
100C2×#92418—21no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418C2×D412yes—
104C2×#92418C2×D411yescharacteristic
105C2×#92418C2×D411yescharacteristic
106C2×#92418#4112yes—
107C8×D61—21no—
108C8×D61—21no—
109C8×D61—22no—
110C8×D61—22no—
111C8×D61—21no—
112C8×D61—21no—
113#11758187—24no—
114#11758187—42no—
115C23×C61—21no—
116C23×C61C2×M1611yescharacteristic
117C22×D61—22no—
118C22×D61—22no—
119C22×D61—41no—
120C22×D61C22⋊C811yescharacteristic
121C22×D61C22⋊C811yescharacteristic
122Q8×C61—22no—
123D4×C61—22no—
124D4×C61—42no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61C4×D412yes—
130C2×C4×C61C22×C811yescharacteristic
131C2×C4×C61#13112yes—
132C22⋊D61—42no—
133C22⋊D61—42no—
134C2×Dic61—22no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61C22⋊C811yescharacteristic
138C2×Dic61C22⋊C811yescharacteristic
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—22no—
144C4×D61—22no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—41no—
148#92418—41no—
149#92418#12011yescharacteristic
150#92418#12112yes—
151#92418#12311yescharacteristic
152#12978—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C2×C22⋊C811yescharacteristic
159C22×C61#43512yes—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—44no—
166C2×D61#35012yescomplemented
167C4×C61—41no—
168C4×C61#38611yescharacteristic
169C4×C61#40811yescharacteristic
170C4×C61C8×D412yes—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175C22×M32—611no—
176#2929—611no—
177C2×#350—612no—
178C2×C22⋊C16—611no—
179#1379—612no—
180C2×C61—22no—
181C2×C61—81no—
182C2×C61#186911yescharacteristic
183C2×C61C2×#35011yescharacteristic
184C2×C61#211711yescharacteristic
185D61—22no—
186D61—41no—
187C2×#131—611no—
188C23×C8—611no—
189#525—611no—
190C2×M32—612no—
191C2×M32—1224no—
192C2×M32—1221no—
193C22×C16—612no—
194C22×C16—1221no—
195#435—1221no—
196#435—1221no—
197C8×D4—1221no—
198C8×D4—1221no—
199#424—611no—
200#408#692311yescharacteristic
201#407—611no—
202#405—611no—
203#350—1224no—
204C22⋊C16—1221no—
205C22⋊C16—1221no—
206C61#1297811yescharacteristic, complemented, Sylow
207C2×#41C2×#692311yescharacteristic
208C23×C4—611no—
209#131—1222no—
210#131—1222no—
211C2×M16—611no—
212C2×M16—1221no—
213C2×M16C2×#692311yescharacteristic
214C22×C8—611no—
215C22×C8—611no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8—611no—
219C22×C8—1222no—
220C22×C8—1222no—
221C22×C8—1221no—
222C22×C8C2×#692311yescharacteristic
223#123—1221no—
224C22⋊Q8—611no—
225C22⋊Q8—611no—
226#121—611no—
227#121—611no—
228#120—1221no—
229C4×D4—1221no—
230C4×D4—1221no—
231#117—611no—
232M32—614no—
233M32—1222no—
234M32—1224no—
235C2×C16—1222no—
236C2×C16—1224no—
237C2×C16—1222no—
238C2×C16—1222no—
239C2×C16—1222no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—1221no—
245C22⋊C8—1221no—
246#97—1221no—
247C4×C8—1221no—
248C24—611no—
249#41—22no—
250#41—22no—
251C2×Q8D61⋊C811yescharacteristic
252C2×D4—21no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4D61⋊C811yescharacteristic
256C22×C4—21no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4C22×#692311yescharacteristic
265M16—22no—
266M16—1222no—
267M16—2442no—
268C2×C8—22no—
269C2×C8—21no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—612no—
273C2×C8—612no—
274C2×C8—1221no—
275C2×C8—1221no—
276C2×C8—1222no—
277C2×C8—1222no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8C22⋊#692311yescharacteristic
284C2×C8C22⋊#692311yescharacteristic
285C4⋊C4—611no—
286C4⋊C4—611no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—1221no—
295C16—1224no—
296C16—2442no—
297C23—21no—
298C23—611no—
299C23—611no—
300C23—1222no—
301C23—1222no—
302C23—2441no—
303C23D61⋊M1611yescharacteristic
304Q8—22no—
305D4—22no—
306D4—42no—
307D4—2442no—
308D4—2442no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1222no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4C2×C22⋊#692311yescharacteristic
324C2×C4D4×#692312yes—
325C2×C4C2×D61⋊C811yescharacteristic
326C2×C4#1451986412yes—
327C8—21no—
328C8—21no—
329C8—41no—
330C8—611no—
331C8—612no—
332C8—611no—
333C8—2441no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—612no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—2444no—
346C22D61⋊(C22⋊C8)11yescharacteristic
347C22#1684079412yes—
348C4—41no—
349C4—1221no—
350C4—1221no—
351C4—2441no—
352C4—2441no—
353C4#1684071011yescharacteristic
354C4#1684073611yescharacteristic
355C4#1684078912yes—
356C2—22no—
357C2—81no—
358C2—1222no—
359C2—2441no—
360C2#2146179311yescharacteristic
361C2D61⋊#35011yescharacteristic
362C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61C2×C22⋊C8
prime radical#16840269C4
cosocleC22×#92418C23
hypercenter#408#6923
hypocenterC61#12978
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊M32C2semidirect
2. C2×#16840660C2semidirect
3. C2×#16840657C2semidirect
4. #21460874C2semidirect
27. #14519851D4semidirect
166. C2×D61#350semidirect
206. C61#12978semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊M322
C2×#168406602
C2×#168406572
#214608742
#214545162
#1297861