Finite Group Databasebeta

← #29590399

Subgroups — #29590399

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#21451684C211yesmaximal, characteristic
2#21445614C211yesmaximal, characteristic, complemented
3#21444141C211yesmaximal, characteristic, complemented
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic
7C61×#1345C211yesmaximal, characteristic
8C2×#14519764C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839812—21no—
11C2×#14519695—21no—
12M16×Dic61—21no—
13#16839698—21no—
14#16839683C411yescharacteristic
15#16839682C2211yescharacteristic
16#16839676C411yescharacteristic
17#16839674—21no—
18#16839656—21no—
19#16839655—21no—
20#16839629C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×Dic122D411yescharacteristic
29C2×#11758194—21no—
30#14519764—41no—
31#14519764—41no—
32#14519742—41no—
33#14519742—41no—
34C2×C4⋊Dic61—21no—
35C2×#11758196—21no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46#14519695—24no—
47C22⋊#92418—21no—
48#14519687—41no—
49C8×Dic61—41no—
50C8×Dic61—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×D4×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—81no—
82M16×C61—22no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—81no—
90C22⋊Dic61—42no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—42no—
94C22⋊Dic61—81no—
95C4⋊Dic61—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×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117D4×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#13511yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61#9911yescharacteristic
144C2×Dic61#9911yescharacteristic
145C2×Dic61#10412yes—
146Dic122—42no—
147Dic122—42no—
148Dic122—82no—
149C8×C61—42no—
150C8×C61—81no—
151#92418—42no—
152#92418—81no—
153#11738—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61C2×#9911yescharacteristic
164C22×C61#41611yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—81no—
171Dic61—21no—
172Dic61—21no—
173Dic61—22no—
174Dic61—41no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178#2632—611no—
179C4×#101—611no—
180#1461—611no—
181#1354—611no—
182#1354—611no—
183#1345—611no—
184#1345D6111yescharacteristic
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—161no—
188C2×C61#150111yescharacteristic
189C2×C61#212211yescharacteristic
190C2×C61#213311yescharacteristic
191C2×#124—611no—
192C2×C4×Q8—611no—
193#431—1221no—
194C2×#101—1221no—
195C4×M16—1221no—
196#399—1221no—
197#395—611no—
198#395—611no—
199#394—611no—
200#394C2×D6111yescharacteristic
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×Q8—611no—
213C22×D4C4×D6111yescharacteristic
214C2×M16—21no—
215C2×M16—1221no—
216#124—2441no—
217#124—2441no—
218C4×Q8—2441no—
219C4×Q8—2441no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4C22×D6111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
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—611no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95C4×D6111yescharacteristic
247C24—21no—
248C2×Q8—1222no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C2×Q8—4881no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×D4—41no—
255C2×D4—81no—
256C22×C4—21no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
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—4881no—
276C4⋊C4—4881no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—81no—
282C22⋊C4—4881no—
283C22⋊C4—2442no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2442no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C42—1221no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C22⋊C4×D6111yescharacteristic
301Q8—4882no—
302Q8—2442no—
303Q8—2442no—
304D4—82no—
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—611no—
315C2×C4—611no—
316C2×C4—612no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451979611yescharacteristic
332C2×C4#1451979811yescharacteristic
333C8—42no—
334C8—81no—
335C8—4881no—
336C8—2442no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#99×D6111yescharacteristic
347C22#1683975511yescharacteristic
348C22#104×D6111yescharacteristic
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—81no—
354C4—1221no—
355C4—1221no—
356C4—1222no—
357C4—4881no—
358C4—4881no—
359C4—2441no—
360C4—2441no—
361C2—21no—
362C2—21no—
363C2—161no—
364C2#2144430711yescharacteristic
365C2#2144746711yescharacteristic
366C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11738
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445614C2semidirect
3. #21444141C2semidirect
4. #21443850C2semidirect
5. #21443848C2semidirect
210. C61#11738semidirect

Maximal subgroups

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

subgroupindex
#214516842
#214456142
#214441412
#214438502
#214438482
#214438222
C61×#13452
#1173861