Finite Group Databasebeta

← #29596021

Subgroups — #29596021

Order 15616.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448535C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal
3#21445815C211yesmaximal, characteristic
4#21443945C212yesmaximal
5C61×#1801C211yesmaximal, characteristic
6C2×#14519775C2211yescharacteristic
7C2×C4×Dic122C411yescharacteristic
8#16839786—21no—
9C2×#14519696C2212yes—
10#16839669C2211yescharacteristic
11#16839667C411yescharacteristic
12#16839646—21no—
13#16839646—21no—
14#16839643—21no—
15#16839643—21no—
16#16839627C411yescharacteristic
17#16839608C411yescharacteristic
18#16839560—24no—
19#16839531—21no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#423—21no—
22C2×#101×C61C2212yes—
23C61×#343—21no—
24C22×Dic122C2×C411yescharacteristic
25C2×#11758194—22no—
26#14519775—21no—
27#14519775—21no—
28#14519775D412yes—
29#14519775Q812yes—
30C4×Dic122—42no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61C2×C411yescharacteristic
38C4⋊#92418—42no—
39#14519696—22no—
40#14519696—22no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×Q8×C61C2311yescharacteristic
50C2×M16×C61—22no—
51C4×Q8×C61—42no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56C2×C42×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C4⋊C8×C61—42no—
59#101×C61—22no—
60#101×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C2×Q8×C61C2×D411yescharacteristic
64C2×Q8×C61C2×Q811yescharacteristic
65C2×Q8×C61#4111yescharacteristic
66C2×Q8×C61#4111yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×Dic122—21no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122C4⋊C412yes—
82M16×C61—42no—
83M16×C61—42no—
84C2×C8×C61—42no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C42×C61—22no—
89C42×C61—22no—
90C42×C61—22no—
91C4⋊Dic61—41no—
92#11758196—22no—
93#11758196—22no—
94#11758196—22no—
95#11758196—22no—
96#11758196—42no—
97C4×Dic61—21no—
98C4×Dic61—42no—
99C4×Dic61—41no—
100C4×Dic61C4⋊C412yes—
101#11758194—42no—
102#11758194—42no—
103C2×#92418—42no—
104C23×C61C2×C22⋊C411yescharacteristic
105Q8×C61—41no—
106Q8×C61—41no—
107Q8×C61—41no—
108Q8×C61—41no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61#9912yes—
123C2×C4×C61C2×C4⋊C411yescharacteristic
124C2×C4×C61#11711yescharacteristic
125C2×C4×C61#12111yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61C22⋊Q811yescharacteristic
128C2×C4×C61C22⋊Q811yescharacteristic
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140Dic122—42no—
141Dic122—42no—
142C8×C61—82no—
143#92418—82no—
144#12804—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#38011yescharacteristic
148C22×C61C2×#9911yescharacteristic
149C22×C61#41011yescharacteristic
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—22no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160Dic61—42no—
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164#2327—611no—
165C2×#356—612no—
166#1801—611no—
167#1801D6111yescharacteristic
168#1394—612no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61#179911yescharacteristic
172C2×C61#213311yescharacteristic
173C2×C61#213511yescharacteristic
174C2×C4⋊Q8—611no—
175C2×C4×Q8—611no—
176C2×C4×Q8C2×D6111yescharacteristic
177#423—21no—
178#423—1221no—
179C2×#101—612no—
180C2×#101C2×D6112yes—
181#391—611no—
182#391—611no—
183#387—1221no—
184#387—1221no—
185#387—1221no—
186#387—1221no—
187#382—611no—
188#376—611no—
189#356—1224no—
190#343—21no—
191#343—1221no—
192C61#1280411yescharacteristic, complemented, Sylow
193C22×Q8—611no—
194C22×Q8C22×D6111yescharacteristic
195C2×M16—22no—
196C2×M16—1222no—
197C4⋊Q8—612no—
198C4⋊Q8—612no—
199C4⋊Q8—1221no—
200C4⋊Q8—1221no—
201C4×Q8—42no—
202C4×Q8—2442no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4C4×D6111yescharacteristic
208C2×C4⋊C4D24411yescharacteristic
209C2×C4⋊C4C22⋊D6111yescharacteristic
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—1221no—
213C2×C42C4×D6111yescharacteristic
214C2×C42D24411yescharacteristic
215C2×C42C22⋊D6111yescharacteristic
216C4⋊C8—42no—
217C4⋊C8—2442no—
218#101—22no—
219#101—22no—
220#101—1222no—
221#101—1222no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—612no—
233C2×Q8—1221no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×Q8D4×D6111yescharacteristic
237C2×Q8#1175822411yescharacteristic
238C2×Q8Q8×D6111yescharacteristic
239C2×Q8#1175822611yescharacteristic
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4#1175819811yescharacteristic
245C22×C4#1175819811yescharacteristic
246C22×C4#1175819811yescharacteristic
247C22×C4#1175819811yescharacteristic
248C22×C4C2×C4×D6111yescharacteristic
249C22×C4C2×D24411yescharacteristic
250C22×C4C2×C22⋊D6111yescharacteristic
251M16—42no—
252M16—42no—
253M16—2442no—
254M16—2442no—
255C2×C8—42no—
256C2×C8—2442no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—612no—
270C42—1221no—
271C42—2441no—
272C42—2442no—
273C23C2×#1175819811yescharacteristic
274Q8—41no—
275Q8—41no—
276Q8—41no—
277Q8—41no—
278Q8—2442no—
279Q8—2442no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2442no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4#1451969112yes—
305C2×C4C4⋊C4×D6111yescharacteristic
306C2×C4#1451973511yescharacteristic
307C2×C4#1451974811yescharacteristic
308C2×C4#1451975211yescharacteristic
309C2×C4#1451975311yescharacteristic
310C2×C4#1451975711yescharacteristic
311C8—82no—
312C8—4882no—
313C22—21no—
314C22—21no—
315C22#1683961911yescharacteristic
316C22C2×#1451969111yescharacteristic
317C22#1683973511yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—4881no—
329C4—4881no—
330C4—2442no—
331C4—2442no—
332C2—21no—
333C2—21no—
334C2#2144580411yescharacteristic
335C2#2144750611yescharacteristic
336C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1801C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1801D61
hypocenterC61#12804
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
192. C61#12804semidirect

Maximal subgroups

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

subgroupindex
#214485352
C2×#168395602
#214458152
#214439452
C61×#18012
#1280461