Finite Group Databasebeta

← #29590715

Subgroups — #29590715

Order 15616.

388 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451587C211yesmaximal, characteristic
2#21445901C211yesmaximal, characteristic
3#21444152C211yesmaximal, characteristic
4#21443826C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443824C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×#14519776C411yescharacteristic
9C2×#14519755—21no—
10C2×#14519735C2211yescharacteristic
11#16839816—21no—
12#16839725—21no—
13#16839695—21no—
14#16839692C2211yescharacteristic
15#16839691—21no—
16#16839689C411yescharacteristic
17#16839688C411yescharacteristic
18#16839666—21no—
19#16839626C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×C4×D61D411yescharacteristic
29C2×#11758194—21no—
30#14519776—41no—
31#14519776—41no—
32#14519755—42no—
33#14519755—42no—
34#14519735—41no—
35#14519735—41no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—41no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519689—41no—
51#14519687—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
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
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—41no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84M16×C61—41no—
85M16×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—42no—
95#11758198—42no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98#11758196—42no—
99#11758196—42no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106#11758194—41no—
107#11758194—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
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×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#9911yescharacteristic
143C2×Dic61#9911yescharacteristic
144C4×D61—41no—
145C4×D61—41no—
146C4×D61—41no—
147C4×D61—41no—
148Dic122—82no—
149Dic122—82no—
150C8×C61—81no—
151C8×C61—81no—
152#92418—81no—
153#92418—81no—
154#11807—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61C2×#9911yescharacteristic
158C22×C61#41811yescharacteristic
159C22×C61#42111yescharacteristic
160C2×D61—42no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—81no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—81no—
170C4×C61—81no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61—81no—
176Dic61—81no—
177#2621—611no—
178#1822—611no—
179#1464—611no—
180#1346—611no—
181#1346—611no—
182#1346—611no—
183#1346D6111yescharacteristic, complemented
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#151011yescharacteristic
187C2×C61#212311yescharacteristic
188C2×C61#213511yescharacteristic
189D61—81no—
190C2×C4⋊Q8—611no—
191C2×C22⋊Q8—1221no—
192C2×#117—611no—
193#432—1221no—
194#407—1221no—
195#398—611no—
196#398—1221no—
197#398C2×D6111yescharacteristic
198#397—611no—
199#397—611no—
200#397—1221no—
201#391—1221no—
202#382—611no—
203#343—611no—
204#343—1221no—
205#343C2×D6111yescharacteristic
206#324—611no—
207#324C2×D6111yescharacteristic
208#323—1221no—
209C61#1180711yescharacteristic, complemented, Sylow
210C22×Q8—1221no—
211C23×C4—611no—
212C2×M16—21no—
213C2×M16—1221no—
214C4⋊Q8—2441no—
215C4⋊Q8—2441no—
216C22⋊Q8—2442no—
217C22⋊Q8—2442no—
218#117—2441no—
219#117—2441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C4×D6111yescharacteristic
227C2×C4⋊C4C22×D6111yescharacteristic
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C4⋊C8—2441no—
235C22⋊C8—21no—
236C22⋊C8—1221no—
237C22⋊C8—2441no—
238C22⋊C8—2441no—
239#97—2441no—
240#95—21no—
241#95—611no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95C4×D6111yescharacteristic
247C24—611no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8—2442no—
251C2×Q8—2442no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—2441no—
264C22×C4C2×C4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267M16—41no—
268M16—41no—
269M16—2441no—
270M16—2441no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—2441no—
274C2×C8—2441no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C42—1221no—
293C23—1221no—
294C23—1221no—
295C23—1221no—
296C23—2441no—
297C23—2441no—
298C23C22⋊C4×D6111yescharacteristic
299Q8—4882no—
300Q8—4882no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
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#1451980111yescharacteristic
332C2×C4#1451980411yescharacteristic
333C8—81no—
334C8—81no—
335C8—4881no—
336C8—4881no—
337C22—21no—
338C22—21no—
339C22—4881no—
340C22—2442no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22#99×D6111yescharacteristic
345C22#1683976511yescharacteristic
346C22#1683977711yescharacteristic
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—1221no—
354C4—1221no—
355C4—4881no—
356C4—4881no—
357C4—2441no—
358C4—2441no—
359C2—21no—
360C2—21no—
361C2—4881no—
362C2#2144434611yescharacteristic
363C2#2144747111yescharacteristic
364C2#2144751211yescharacteristic
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#11807
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. #21443826C2semidirect
5. #21443825C2semidirect
6. #21443824C2semidirect
7. C61×#1346C2semidirect
183. #1346D61semidirect
209. C61#11807semidirect

Maximal subgroups

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

subgroupindex
#214515872
#214459012
#214441522
#214438262
#214438252
#214438242
C61×#13462
#1180761