Finite Group Databasebeta

← #29590401

Subgroups — #29590401

Order 15616.

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

normal subgroups only

This group has 400 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#21451685C211yesmaximal, characteristic
2#21445614C211yesmaximal, characteristic, complemented
3#21444141C211yesmaximal, characteristic, complemented
4#21443849C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic
6#21443821C211yesmaximal, characteristic
7C61×#1354C211yesmaximal, characteristic, complemented
8C2×#14519766C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839812—21no—
11C2×#14519695—21no—
12M16×Dic61—21no—
13#16839697—21no—
14#16839681C411yescharacteristic
15#16839680C411yescharacteristic
16#16839679C2211yescharacteristic
17#16839675—21no—
18#16839652—21no—
19#16839651—21no—
20#16839629C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C2×#11758194—21no—
30#14519766—41no—
31#14519766—41no—
32#14519742—41no—
33#14519742—41no—
34C2×#11758196—21no—
35C2×#11758196C2×C411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519695—24no—
48C22⋊#92418—21no—
49#14519687—41no—
50C8×Dic61—41no—
51C8×Dic61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C23×D61—21no—
64C2×Q8×C61—41no—
65C2×Q8×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×D244—41no—
77C2×D244—81no—
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122—22no—
81C2×Dic122—41no—
82M16×C61—22no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—81no—
88#11758198—42no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—42no—
94#11758198—81no—
95#11758198—81no—
96#11758196—41no—
97#11758196—41no—
98#11758196—81no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105#11758194—22no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117Q8×C61—82no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
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—41no—
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61#9911yescharacteristic
144C2×Dic61#9911yescharacteristic
145C2×Dic61#10412yes—
146D244—82no—
147Dic122—42no—
148Dic122—42no—
149C8×C61—42no—
150C8×C61—81no—
151#92418—42no—
152#92418—81no—
153#11738—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61C2×#9911yescharacteristic
157C22×C61#41611yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—21no—
173Dic61—21no—
174Dic61—22no—
175Dic61—41no—
176Dic61—41no—
177Dic61—81no—
178#2632—611no—
179C4×#101—611no—
180#1461—611no—
181#1354—611no—
182#1354D6111yescharacteristic, complemented
183#1345—611no—
184#1345—611no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#150111yescharacteristic
188C2×C61#212211yescharacteristic
189C2×C61#213311yescharacteristic
190D61—161no—
191C2×#124—611no—
192C2×C4×Q8—611no—
193#431—1221no—
194C2×#101—1221no—
195C4×M16—1221no—
196#399—1221no—
197#395—611no—
198#395C2×D6111yescharacteristic
199#394—611no—
200#394—611no—
201#393—1221no—
202#388—1221no—
203#388—1221no—
204#383—611no—
205#343—611no—
206#343C2×D6111yescharacteristic
207#324—611no—
208#324—1221no—
209#324C2×D6111yescharacteristic
210C61#1173811yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×Q8C4×D6111yescharacteristic
213C22×D4—611no—
214C2×M16—21no—
215C2×M16—1221no—
216#124—2441no—
217#124—2441no—
218C4×Q8—2441no—
219C4×Q8—2441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4C22×D6111yescharacteristic
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C4⋊C8—2441no—
235#101—1224no—
236C22⋊C8—21no—
237C22⋊C8—1221no—
238#97—2441no—
239C4×C8—2441no—
240C4×C8—2441no—
241#95—21no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95C4×D6111yescharacteristic
247C24—1221no—
248C2×Q8—41no—
249C2×Q8—81no—
250C2×Q8—1222no—
251C2×Q8—1221no—
252C2×Q8—1221no—
253C2×Q8—2441no—
254C2×D4—4881no—
255C2×D4—2441no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4C2×C4×D6111yescharacteristic
264C22×C4D4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266M16—22no—
267M16—41no—
268M16—1222no—
269M16—2441no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—2441no—
273C2×C8—2441no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—4881no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—4881no—
280C22⋊C4—4881no—
281C22⋊C4—2442no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2442no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C42—1221no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23C22⋊C4×D6111yescharacteristic
301Q8—82no—
302Q8—2442no—
303Q8—2442no—
304D4—4882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—612no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451979811yescharacteristic
332C2×C4#1451980011yescharacteristic
333C8—42no—
334C8—81no—
335C8—4881no—
336C8—2442no—
337C22—21no—
338C22—21no—
339C22—4881no—
340C22—4881no—
341C22—4881no—
342C22—4881no—
343C22—4881no—
344C22—4881no—
345C22—4881no—
346C22#99×D6111yescharacteristic
347C22#1683975711yescharacteristic
348C22#104×D6111yescharacteristic
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—81no—
354C4—81no—
355C4—1221no—
356C4—1221no—
357C4—1222no—
358C4—4881no—
359C4—2441no—
360C4—2441no—
361C2—21no—
362C2—21no—
363C2—9761no—
364C2#2144430911yescharacteristic
365C2#2144746711yescharacteristic
366C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11738
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
2. #21445614C2semidirect
3. #21444141C2semidirect
4. #21443849C2semidirect
7. C61×#1354C2semidirect
182. #1354D61semidirect
210. C61#11738semidirect

Maximal subgroups

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

subgroupindex
#214516852
#214456142
#214441412
#214438492
#214438232
#214438212
C61×#13542
#1173861