Finite Group Databasebeta

← #29590943

Subgroups — #29590943

Order 15616.

412 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451193C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic
3#324×D61C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443825C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839725—21no—
11C22⋊C8×D61—21no—
12#16839693C411yescharacteristic
13#16839683C411yescharacteristic
14#16839682C2211yescharacteristic
15#16839661—21no—
16#16839659—21no—
17#16839636—21no—
18#16839633—21no—
19#16839609C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×C8×D61—41no—
33#14519757—41no—
34#14519757—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196D411yescharacteristic
42C4⋊C4×D61—41no—
43C4⋊C4×D61—41no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C22⋊#92418—21no—
48#14519689—41no—
49#14519689—41no—
50#14519689—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61C22⋊C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—41no—
82C2×C4×D61—81no—
83C2×C4×D61—81no—
84C2×Dic122—41no—
85C2×Dic122—81no—
86M16×C61—41no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94#11758198—24no—
95#11758198—41no—
96#11758198—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—42no—
99C4⋊Dic61—81no—
100#11758196—41no—
101#11758196—41no—
102#11758196—42no—
103#11758196—81no—
104C4×Dic61—81no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C8×D61—82no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—41no—
115C22×D61#9911yescharacteristic
116C22×D61#9911yescharacteristic
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
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#13511yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C4×D61—41no—
145C4×D61—41no—
146C4×D61—41no—
147C4×D61—41no—
148C4×D61—42no—
149C4×D61—81no—
150C4×D61—81no—
151C4×D61—81no—
152Dic122—82no—
153C8×C61—81no—
154C8×C61—81no—
155#92418—81no—
156#92418—81no—
157#11854—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61C2×#9911yescharacteristic
161C22×C61#41611yescharacteristic
162C22×C61#42111yescharacteristic
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61#35612yes—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—42no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—81no—
177Dic61—42no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—81no—
182#2583—611no—
183#1821—611no—
184C2×#324—611no—
185#1354—611no—
186#1354—611no—
187#1346—611no—
188#1346D6111yescharacteristic, complemented
189C2×C61—21no—
190C2×C61—21no—
191C2×C61#151611yescharacteristic
192C2×C61#212111yescharacteristic
193C2×C61C2×#35611yescharacteristic
194D61—22no—
195D61—41no—
196C2×C22⋊Q8—611no—
197C22×C4⋊C4—611no—
198#407—1221no—
199C2×C22⋊C8—1221no—
200#398—611no—
201#398C2×D6111yescharacteristic
202#395—611no—
203#395—611no—
204#389—1221no—
205#389—1221no—
206#385—1221no—
207#385—1221no—
208C4×C22⋊C4—611no—
209#343—611no—
210#343—1221no—
211#343C2×D6111yescharacteristic
212#324—611no—
213#324—1221no—
214#324C2×D6111yescharacteristic
215C61#1185411yescharacteristic, complemented, Sylow
216C22×Q8—611no—
217C23×C4—611no—
218C23×C4—611no—
219C23×C4—611no—
220C2×M16—21no—
221C2×M16—1221no—
222C22×C8—2441no—
223C22⋊Q8—2441no—
224C22⋊Q8—2441no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—2441no—
234C2×C4⋊C4—2441no—
235C2×C4⋊C4C4×D6111yescharacteristic
236C2×C4⋊C4C22×D6111yescharacteristic
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C42—1221no—
240C22⋊C8—21no—
241C22⋊C8—1221no—
242C22⋊C8—2441no—
243C22⋊C8—2441no—
244C22⋊C8—2441no—
245#95—21no—
246#95—611no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95C4×D6111yescharacteristic
251C24—611no—
252C2×Q8—4881no—
253C2×Q8—2441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—4881no—
270C22×C4—4881no—
271C22×C4—2441no—
272C22×C4C2×C4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275M16—41no—
276M16—41no—
277M16—2441no—
278M16—2441no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—4882no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—4881no—
289C4⋊C4—4881no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2442no—
294C4⋊C4—2442no—
295C22⋊C4—1224no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C42—4881no—
299C23—611no—
300C23—611no—
301C23—1222no—
302C23—1221no—
303C23—1221no—
304C23—2441no—
305C23C22⋊C4×D6111yescharacteristic
306Q8—4882no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451979611yescharacteristic
341C2×C4#1451979811yescharacteristic
342C8—81no—
343C8—81no—
344C8—4881no—
345C8—4881no—
346C22—21no—
347C22—21no—
348C22—612no—
349C22—1221no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—2442no—
355C22—2442no—
356C22#99×D6111yescharacteristic
357C22#1683975511yescharacteristic
358C22#1683977711yescharacteristic
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—4881no—
366C4—2442no—
367C4—2441no—
368C4—2441no—
369C4—2441no—
370C2—21no—
371C2—21no—
372C2—1222no—
373C2—2441no—
374C2#2144437211yescharacteristic
375C2#2144746411yescharacteristic
376C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11854
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #21443850C2semidirect
5. #21443848C2semidirect
6. #21443825C2semidirect
7. C61×#1346C2semidirect
188. #1346D61semidirect
215. C61#11854semidirect

Maximal subgroups

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

subgroupindex
#214511932
#214458982
#324×D612
#214438502
#214438482
#214438252
C61×#13462
#1185461