Finite Group Databasebeta

← #30606311

Subgroups — #30606311

Order 15616.

818 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 152 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⋊#101C212yesmaximal
2#21460917C212yesmaximal, complemented
3#21460916C212yesmaximal, complemented
4#391×D61C211yesmaximal, characteristic
5C2×D61⋊M16—22no—
6D61⋊#101—24no—
7D61⋊#101C418yescomplemented
8C2×#14519838—22no—
9C2×#14519838C2214yes—
10C22×Q8×D61C2211yescharacteristic
11C2×C4⋊C4×D61C411yescharacteristic
12C2×C42×D61C411yescharacteristic
13#16839669C411yescharacteristic
14#16839668C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839666—22no—
17#95×D61—22no—
18C61×#391C411yescharacteristic
19C2×#11758213—42no—
20D61⋊M16—28no—
21D61⋊M16—44no—
22C2×#11758217—24no—
23C2×D61⋊C8—42no—
24#14519838—28no—
25#14519838—24no—
26#14519838C2×C418yescomplemented
27C22×Dic122D412yes—
28C22×Dic122C2311yescharacteristic
29C2×Q8×D61—42no—
30C2×Q8×D61—41no—
31C2×Q8×D61—41no—
32C2×Q8×D61C2×C414yes—
33C2×Q8×D61D412yes—
34C2×Q8×D61Q812yes—
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D412yes—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C4⋊C4×D61—41no—
42C4⋊C4×D61—41no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C42×D61—42no—
46#14519684—22no—
47#14519684—22no—
48#14519684—22no—
49C22×Q8×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—22no—
53C23×D61C22⋊C411yescharacteristic
54C2×Q8×C61—41no—
55C2×Q8×C61—41no—
56C2×Q8×C61C4212yes—
57C2×Q8×C61C4⋊C412yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D412yes—
66Q8×D61—44no—
67Q8×D61—44no—
68Q8×D61—42no—
69Q8×D61—42no—
70Q8×D61—42no—
71Q8×D61—42no—
72C2×C4×D61—22no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—22no—
76C2×C4×D61—24no—
77C2×C4×D61—22no—
78C2×C4×D61—24no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—44no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61C4212yes—
85C2×C4×D61C22⋊C414yes—
86C2×C4×D61C4⋊C412yes—
87C2×C4×D61C4⋊C414yes—
88C2×Dic122—42no—
89C2×Dic122—42no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122C22⋊C414yes—
93C2×Dic122C4⋊C414yes—
94C2×Dic122C22×C412yes—
95C2×Dic122C2×D411yescharacteristic
96C2×Dic122C2×Q811yescharacteristic
97#11758217—28no—
98#11758217—44no—
99C2×#92420—44no—
100#11758213—48no—
101D61⋊C8—48no—
102C4⋊C4×C61—41no—
103C42×C61—41no—
104C4⋊Dic61—41no—
105#11758196—42no—
106C4×Dic61—42no—
107C4×Dic61—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61#9512yes—
112C22×D61#9911yescharacteristic
113C22×D61#9912yes—
114C22×D61#9911yescharacteristic
115Q8×C61—42no—
116Q8×C61—42no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61#9514yes—
127C2×C4×C61C2×C4211yescharacteristic
128C2×C4×C61C2×C4⋊C411yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61#9512yes—
139C2×Dic61C2×C22⋊C412yes—
140C2×Dic61C2×C4⋊C412yes—
141C4×D61—24no—
142C4×D61—24no—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—24no—
148C4×D61—24no—
149C4×D61—48no—
150C4×D61—82no—
151C4×D61—82no—
152Dic122—44no—
153Dic122—44no—
154Dic122—42no—
155Dic122—41no—
156Dic122—41no—
157#92420—48no—
158C2×#1394—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61C2×#9511yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—24no—
167C2×D61—24no—
168C2×D61#34212yes—
169C2×D61#34212yes—
170C2×D61#35512yes—
171C2×D61#35612yes—
172C4×C61—24no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—42no—
176C4×C61—81no—
177Dic61—22no—
178Dic61—22no—
179Dic61—22no—
180Dic61—42no—
181Dic61—81no—
182C22×#101—612no—
183C2×#391—611no—
184#1394—612no—
185#1394—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61C2×#34211yescharacteristic
189C2×C61C2×#35511yescharacteristic
190C2×C61C2×#35611yescharacteristic
191D61—22no—
192D61#139414yescomplemented
193C23×Q8—611no—
194C22×M16—1222no—
195C22×C4⋊C4—611no—
196C22×C42—611no—
197C2×#101—614no—
198C2×#101—618no—
199C2×#101—1222no—
200C2×#101—1224no—
201#391—611no—
202#391—611no—
203#391—611no—
204#391—1222no—
205#391#692311yescharacteristic
206C2×#95—1222no—
207C61C2×#139411yescharacteristic, complemented, Sylow
208C22×Q8—614no—
209C22×Q8—612no—
210C22×Q8—612no—
211C22×Q8—612no—
212C22×Q8—611no—
213C22×Q8—2442no—
214C22×Q8—2441no—
215C22×Q8—2441no—
216C22×Q8C2×#692311yescharacteristic
217C23×C4—612no—
218C23×C4—611no—
219C23×C4—1221no—
220C23×C4—1221no—
221C2×M16—1224no—
222C2×M16—1228no—
223C2×M16—2444no—
224C2×M16—2442no—
225C22×C8—2442no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—2441no—
229C2×C4⋊C4—2441no—
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C42—611no—
232C2×C42—1221no—
233C2×C42—2442no—
234C2×C42C2×#692311yescharacteristic
235#101—618no—
236#101—1228no—
237#101—1224no—
238#95—22no—
239#95—1222no—
240#95—1222no—
241#95—1222no—
242C24—611no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—614no—
246C2×Q8—614no—
247C2×Q8—612no—
248C2×Q8—611no—
249C2×Q8—611no—
250C2×Q8—2441no—
251C2×Q8—2442no—
252C2×Q8—2441no—
253C2×Q8—2442no—
254C2×Q8—2442no—
255C2×Q8—2444no—
256C2×Q8—2442no—
257C2×Q8—2444no—
258C2×Q8—2442no—
259C2×Q8—2442no—
260C2×Q8C4×#692312yes—
261C2×Q8C4⋊#692312yes—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—612no—
265C22×C4—611no—
266C22×C4—614no—
267C22×C4—614no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—1222no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1222no—
274C22×C4—1224no—
275C22×C4—1222no—
276C22×C4—1224no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2444no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4C22⋊#692312yes—
285C22×C4C22×#692311yescharacteristic
286M16—1228no—
287M16—2448no—
288M16—2444no—
289C2×C8—2448no—
290C2×C8—2444no—
291C4⋊C4—41no—
292C4⋊C4—2441no—
293C4⋊C4—2442no—
294C42—41no—
295C42—2441no—
296C42—2442no—
297C23—611no—
298C23—612no—
299C23—611no—
300C23—612no—
301C23—1222no—
302C23—1222no—
303C23C2×C22⋊#692311yescharacteristic
304Q8—42no—
305Q8—42no—
306Q8—2444no—
307Q8—2444no—
308Q8—2442no—
309Q8—2441no—
310Q8—2441no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—612no—
323C2×C4—1224no—
324C2×C4—1224no—
325C2×C4—1224no—
326C2×C4—1224no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1221no—
332C2×C4—1222no—
333C2×C4—1221no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—4882no—
337C2×C4—4882no—
338C2×C4—2448no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4(C2×#6923)⋊C414yes—
344C2×C4C2×C4×#692311yescharacteristic
345C2×C4C2×C4⋊#692311yescharacteristic
346C8—2448no—
347C22—21no—
348C22—21no—
349C22—612no—
350C22—612no—
351C22—612no—
352C22—612no—
353C22—1224no—
354C22—1224no—
355C22—1221no—
356C22—1221no—
357C22C2×(C2×#6923)⋊C411yescharacteristic
358C22D61⋊#9911yescharacteristic
359C22D61⋊#9911yescharacteristic
360C4—24no—
361C4—21no—
362C4—21no—
363C4—42no—
364C4—81no—
365C4—1222no—
366C4—1222no—
367C4—1222no—
368C4—4881no—
369C4—2442no—
370C2—21no—
371C2—21no—
372C2—614no—
373C2—1222no—
374C2#2146151611yescharacteristic
375C2D61⋊#35511yescharacteristic
376C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC22×Dic122C23
hypercenter#391#6923
hypocenterC61C2×#1394
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #21460917C2semidirect
3. #21460916C2semidirect
7. D61⋊#101C4semidirect
26. #14519838C2×C4semidirect
192. D61#1394semidirect
207. C61C2×#1394semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1012
#214609172
#214609162
#391×D612
C2×#139461