Finite Group Databasebeta

← #29590946

Subgroups — #29590946

Order 15616.

412 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 91 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#21445899C211yesmaximal, characteristic
2C2×#16839488C211yesmaximal, characteristic
3#21443849C212yesmaximal, complemented
4#21443825C212yesmaximal, complemented
5C61×#2583C211yesmaximal, characteristic
6#16839726—21no—
7C2×C22⋊#92418—21no—
8#16839531—21no—
9#16839531C2212yes—
10#16839488—21no—
11#16839488C2212yes—
12C2×C22⋊Q8×C61C411yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C61×#398C411yescharacteristic
15C61×#398C2211yescharacteristic
16C61×#395C411yescharacteristic
17C61×#395C2211yescharacteristic
18C61×#389—21no—
19C61×#389—21no—
20C61×#385—21no—
21C61×#385—21no—
22C4×C22⋊C4×C61C411yescharacteristic
23C2×#11758194—22no—
24C22×#92418—41no—
25C22⋊#92418—22no—
26C22⋊#92418—41no—
27C22⋊#92418—41no—
28C22⋊#92418—41no—
29C22×Q8×C61C2×C411yescharacteristic
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61D411yescharacteristic
32C23×C4×C61D411yescharacteristic
33C22⋊Q8×C61—41no—
34C22⋊Q8×C61—41no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—41no—
41C2×C4⋊C4×C61—41no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C4⋊C4×C61C2311yescharacteristic
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C42×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C2×Q8×C61—41no—
58C2×Q8×C61—81no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61—81no—
72C22×C4×C61—81no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—42no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—81no—
88C4⋊C4×C61—81no—
89C22⋊C4×C61—24no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—81no—
93#11758194—42no—
94#11758194—42no—
95C2×#92418—42no—
96C2×#92418—42no—
97C2×#92418—82no—
98C23×C61—22no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—41no—
102C23×C61#9911yescharacteristic
103C23×C61#9911yescharacteristic
104C23×C61C2×C22⋊C411yescharacteristic
105Q8×C61—82no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
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—42no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61#13512yes—
138#92418—82no—
139#92418—82no—
140#11854—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—42no—
149C22×C61—42no—
150C22×C61#35612yes—
151C22×C61C2×#9911yescharacteristic
152C22×C61#41611yescharacteristic
153C22×C61#42111yescharacteristic
154C4×C61—22no—
155C4×C61—42no—
156C4×C61—42no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163C4×C61—81no—
164#2583D6111yescharacteristic
165#1821—611no—
166C2×#324—611no—
167#1354—612no—
168#1346—612no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61—22no—
172C2×C61—41no—
173C2×C61#151611yescharacteristic
174C2×C61#212111yescharacteristic
175C2×C61C2×#35611yescharacteristic
176C2×C22⋊Q8Dic6111yescharacteristic
177C22×C4⋊C4C2×D6111yescharacteristic
178#407—1221no—
179C2×C22⋊C8—1221no—
180#398Dic6111yescharacteristic
181#398C2×D6111yescharacteristic
182#395Dic6111yescharacteristic
183#395C2×D6111yescharacteristic
184#389—21no—
185#389—21no—
186#385—21no—
187#385—21no—
188C4×C22⋊C4Dic6111yescharacteristic
189#343—612no—
190#343—1221no—
191#324—612no—
192#324—1221no—
193C61#1185411yescharacteristic, complemented, Sylow
194C22×Q8C2×Dic6111yescharacteristic
195C23×C4C2×Dic6111yescharacteristic
196C23×C4C22⋊D6111yescharacteristic
197C23×C4C22⋊D6111yescharacteristic
198C2×M16—1222no—
199C22×C8—2441no—
200C22⋊Q8—41no—
201C22⋊Q8—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4C2×Dic6111yescharacteristic
210C2×C4⋊C4C2×Dic6111yescharacteristic
211C2×C4⋊C4C22⋊D6111yescharacteristic
212C2×C4⋊C4C22⋊D6111yescharacteristic
213C2×C4⋊C4C22×D6111yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42—21no—
217C22⋊C8—1222no—
218C22⋊C8—2441no—
219C22⋊C8—2441no—
220C22⋊C8—2441no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C2×Dic6111yescharacteristic
226#95C2×Dic6111yescharacteristic
227C24C22⋊Dic6111yescharacteristic
228C2×Q8—41no—
229C2×Q8—81no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4C22⋊Dic6111yescharacteristic
245C22×C4C22⋊Dic6111yescharacteristic
246C22×C4C22⋊Dic6111yescharacteristic
247C22×C4C22×Dic6111yescharacteristic
248C22×C4C2×C22⋊D6111yescharacteristic
249C22×C4C2×C22⋊D6111yescharacteristic
250M16—2442no—
251M16—2442no—
252C2×C8—4882no—
253C2×C8—2442no—
254C2×C8—2442no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C22⋊C4—24no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—81no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—41no—
273C23#1451969211yescharacteristic
274C23#1451969211yescharacteristic
275C23C2×C22⋊Dic6111yescharacteristic
276Q8—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4#1451979712yes—
309C8—4882no—
310C8—4882no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22#1683956112yes—
321C22C2×#1451969211yescharacteristic
322C22#1683975811yescharacteristic
323C22#1683977911yescharacteristic
324C4—22no—
325C4—42no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2#2144437511yescharacteristic
339C2#2144746511yescharacteristic
340C2C2×#1683956111yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2583C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2583D61
hypocenterC61#11854
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #21443849C2semidirect
4. #21443825C2semidirect
193. C61#11854semidirect

Maximal subgroups

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

subgroupindex
#214458992
C2×#168394882
#214438492
#214438252
C61×#25832
#1185461