Finite Group Databasebeta

← #30602003

Subgroups — #30602003

Order 15616.

402 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462012C211yesmaximal, characteristic
2#21462011C211yesmaximal, characteristic
3#21461373C211yesmaximal, characteristic
4#21461334C211yesmaximal, characteristic
5#21461332C211yesmaximal, characteristic
6#21461028C211yesmaximal, characteristic
7C2×#16840111C211yesmaximal, characteristic
8#16840779C2211yescharacteristic
9#16840765C2211yescharacteristic
10#16840765C2211yescharacteristic
11C4×#11758217C2211yescharacteristic
12#16840642—22no—
13#16840642—22no—
14#16840624—21no—
15#16840623—21no—
16#16840622—22no—
17#16840621—22no—
18#92420⋊C8—21no—
19#16840603—21no—
20C2×#14519776C2211yescharacteristic
21C2×#14519775C2211yescharacteristic
22#16840111—21no—
23#16840111—21no—
24#16840111—21no—
25#16840111—21no—
26C2×#14519702C411yescharacteristic
27C2×#14519701C411yescharacteristic
28C2×#14519700C411yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×#103×C61C411yescharacteristic
31C2×#11758217—21no—
32C2×#11758217—21no—
33C2×#11758217D412yes—
34#14519844—21no—
35#14519844—21no—
36#14519844D412yes—
37C4⋊#92420—21no—
38C4⋊#92420—21no—
39C22⋊#92420—21no—
40#14519832—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43C22×Dic122—21no—
44C22×Dic122C2×C411yescharacteristic
45C22×#92418C2×C411yescharacteristic
46#14519776—21no—
47#14519776—21no—
48#14519776—21no—
49#14519776—21no—
50#14519775—21no—
51#14519775—21no—
52#14519775—21no—
53#14519775—21no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×C4×Dic61C2311yescharacteristic
59#14519702—21no—
60#14519702—21no—
61#14519701—21no—
62#14519701—21no—
63#14519700—21no—
64#14519700—21no—
65C8×Dic61D411yescharacteristic
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C8×Dic61D411yescharacteristic
69C22×Q8×C61C2×C411yescharacteristic
70C22×C8×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72#103×C61—21no—
73#103×C61—21no—
74C2×Q8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C22×C411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61#4111yescharacteristic
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—82no—
92#11758217—22no—
93#11758217—22no—
94#11758217—42no—
95#11758217—42no—
96C2×#92420—22no—
97C2×#92420—22no—
98C2×#92420—41no—
99C2×#92420—41no—
100C2×C8×C61—41no—
101C2×C8×C61C22⋊C411yescharacteristic
102C2×C8×C61C22⋊C411yescharacteristic
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107#11758196—41no—
108#11758196—41no—
109#11758196—41no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113C4×Dic61C2×D411yescharacteristic
114C4×Dic61C2×D411yescharacteristic
115C4×Dic61C2×D411yescharacteristic
116C4×Dic61#4111yescharacteristic
117C2×#92418—41no—
118C2×#92418C22⋊C411yescharacteristic
119C2×#92418C22⋊C411yescharacteristic
120C23×C61C4×D411yescharacteristic
121Q8×C61—41no—
122Q8×C61—41no—
123Q8×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×Dic61—22no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61#12111yescharacteristic
138C2×Dic61#12111yescharacteristic
139C2×Dic61#12411yescharacteristic
140C2×Dic61#12711yescharacteristic
141C2×Dic61#13712yes—
142C2×Dic61#13712yes—
143Dic122—41no—
144Dic122—41no—
145Dic122—82no—
146Dic122—82no—
147Dic122—81no—
148#92420—42no—
149#92420—42no—
150#92420—81no—
151#92420—81no—
152C8×C61—21no—
153C8×C61—21no—
154#92418—21no—
155#92418—21no—
156#9803—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#39011yescharacteristic
160C22×C61#44112yes—
161C4×C61—21no—
162C4×C61—81no—
163C4×C61—81no—
164C4×C61#41311yescharacteristic
165C4×C61#41311yescharacteristic
166Dic61—21no—
167Dic61—81no—
168Dic61—81no—
169Dic61#47012yes—
170Dic61#47112yes—
171Dic61#49711yescharacteristic
172Dic61#49711yescharacteristic
173C2×#487—611no—
174#1997—611no—
175#1997—611no—
176#1566—611no—
177#1549—611no—
178#1548—611no—
179#1451—611no—
180C2×C61—22no—
181C2×C61#196711yescharacteristic
182C2×C61#197111yescharacteristic
183C2×C61#197711yescharacteristic
184C2×C4⋊Q8—611no—
185C2×C4⋊Q8—611no—
186#487—1221no—
187#487—1221no—
188#487—1221no—
189#487—1221no—
190#431—611no—
191#423—611no—
192#423—611no—
193C2×#103—611no—
194C2×#103—611no—
195C2×#103—611no—
196C2×#103#692311yescharacteristic
197C4×M16—611no—
198C2×C4×C8—611no—
199#343—1222no—
200#343—1222no—
201#334—1221no—
202#334—1221no—
203#333—1222no—
204#332—1222no—
205#322—1221no—
206#322—1221no—
207C61#980311yescharacteristic, complemented, Sylow
208C22×Q8—611no—
209C22×Q8—1221no—
210C22×Q8C2×#692311yescharacteristic
211C2×M16—612no—
212C2×M16—1221no—
213C2×M16—1221no—
214C22×C8—611no—
215C22×C8C2×#692311yescharacteristic
216C4⋊Q8—1221no—
217C4⋊Q8—1221no—
218C4⋊Q8—1221no—
219C4⋊Q8—1221no—
220C4⋊Q8—1221no—
221C4⋊Q8—1221no—
222C4⋊Q8—1221no—
223C4⋊Q8—1221no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C42—611no—
230C4⋊C8—612no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233C4⋊C8—1221no—
234C4⋊C8—1221no—
235#103—21no—
236#103—21no—
237#103—1221no—
238#103—1221no—
239#103—1221no—
240#103—1221no—
241#103—1221no—
242#103—1221no—
243C22⋊C8—1221no—
244#97—1221no—
245C4×C8—611no—
246C4×C8—611no—
247C4×C8—611no—
248C4×C8—611no—
249C4×C8—1221no—
250C4×C8—1221no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—1221no—
256C2×Q8—1221no—
257C2×Q8—4882no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8—2441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4C22×#692311yescharacteristic
269M16—1222no—
270M16—1222no—
271M16—2442no—
272M16—2442no—
273C2×C8—41no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—1222no—
277C2×C8—1222no—
278C2×C8—2441no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8C22⋊#692311yescharacteristic
282C2×C8C22⋊#692311yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C42—611no—
294C42—611no—
295C42—611no—
296C42—611no—
297C23D4×#692311yescharacteristic
298Q8—41no—
299Q8—41no—
300Q8—81no—
301Q8—4881no—
302Q8—4882no—
303Q8—4882no—
304Q8—2441no—
305Q8—2441no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4C2×C22⋊#692311yescharacteristic
324C2×C4D4×#692311yescharacteristic
325C8—21no—
326C8—21no—
327C8—1221no—
328C8—1221no—
329C8—4881no—
330C8—4881no—
331C8—2442no—
332C8—2442no—
333C22—21no—
334C22—21no—
335C22#1684071411yescharacteristic
336C22#1684080212yes—
337C4—21no—
338C4—81no—
339C4—81no—
340C4—612no—
341C4—611no—
342C4—611no—
343C4—612no—
344C4—1221no—
345C4—4881no—
346C4—4881no—
347C4#1684074811yescharacteristic
348C4#1684074911yescharacteristic
349C2—22no—
350C2#2146196311yescharacteristic
351C2#2146196711yescharacteristic
352C2#2146197911yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#103×C61C4
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC2×#103#6923
hypocenterC61#9803
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
207. C61#9803semidirect

Maximal subgroups

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

subgroupindex
#214620122
#214620112
#214613732
#214613342
#214613322
#214610282
C2×#168401112
#980361