Finite Group Databasebeta

← #29590758

Subgroups — #29590758

Order 15616.

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

normal subgroups only

This group has 386 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#21451633C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic
3#21444147C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443846C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839725—21no—
11#16839724—21no—
12#16839700C411yescharacteristic
13#16839696—21no—
14#16839694—21no—
15#16839683C411yescharacteristic
16#16839682C2211yescharacteristic
17#16839636—21no—
18#16839624—21no—
19#16839621C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758189—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—
46C22⋊#92418—21no—
47#14519689—41no—
48#14519689—41no—
49#14519689—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—21no—
59#95×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—
92#11758198—42no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—42no—
97C4⋊Dic61—81no—
98#11758196—41no—
99#11758196—41no—
100#11758196—81no—
101#11758196—81no—
102#11758194—41no—
103#11758194—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106#11758189—82no—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61#9911yescharacteristic
113C22×D61#9911yescharacteristic
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#13711yescharacteristic
126C2×C4×C61#13711yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—41no—
143C4×D61—41no—
144C4×D61—42no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61—81no—
148Dic122—82no—
149C8×C61—81no—
150C8×C61—81no—
151#92418—81no—
152#92418—81no—
153#11817—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61C2×#9911yescharacteristic
157C22×C61#41911yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—42no—
166C2×D61—42no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—81no—
172C4×C61—81no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178#2627—611no—
179#1821—611no—
180#1463—611no—
181#1354—611no—
182#1354—611no—
183#1353—611no—
184#1353D6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#151111yescharacteristic
188C2×C61#212111yescharacteristic
189C2×C61#213311yescharacteristic
190D61—41no—
191D61—41no—
192C2×C22⋊Q8—611no—
193C22×C4⋊C4—611no—
194#407—1221no—
195#407—1221no—
196#400—611no—
197#400C2×D6111yescharacteristic
198#398—1221no—
199#398—1221no—
200#395—611no—
201#395—611no—
202#385—1221no—
203#381—1221no—
204#380—611no—
205#343—611no—
206#343—1221no—
207#343C2×D6111yescharacteristic
208#324—611no—
209#324—1221no—
210#324C2×D6111yescharacteristic
211C61#1181711yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C23×C4—611no—
214C23×C4—611no—
215C23×C4—611no—
216C2×M16—21no—
217C2×M16—1221no—
218C2×M16—2441no—
219C22⋊Q8—2441no—
220C22⋊Q8—2441no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—2441no—
229C2×C4⋊C4—2441no—
230C2×C4⋊C4C4×D6111yescharacteristic
231C2×C4⋊C4C22×D6111yescharacteristic
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C22⋊C8—21no—
235C22⋊C8—1221no—
236C22⋊C8—2441no—
237C22⋊C8—2441no—
238C22⋊C8—2441no—
239#95—21no—
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—4881no—
249C2×Q8—2441no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—4881no—
266C22×C4—4881no—
267C22×C4—2441no—
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4D4×D6111yescharacteristic
270C22×C4D4×D6111yescharacteristic
271M16—41no—
272M16—41no—
273M16—4882no—
274M16—2441no—
275M16—2441no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—2441no—
279C2×C8—2441no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—4881no—
283C4⋊C4—4881no—
284C4⋊C4—4881no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2442no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C22⋊C4—2442no—
292C23—611no—
293C23—611no—
294C23—1221no—
295C23—1221no—
296C23—2441no—
297C23—2441no—
298C23C22⋊C4×D6111yescharacteristic
299Q8—4882no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2442no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451980611yescharacteristic
333C2×C4#1451980911yescharacteristic
334C8—81no—
335C8—81no—
336C8—4881no—
337C8—4881no—
338C22—21no—
339C22—21no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—2442no—
347C22—2442no—
348C22#99×D6111yescharacteristic
349C22#1683976911yescharacteristic
350C22#1683977711yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—4881no—
358C4—4881no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C2—21no—
363C2—21no—
364C2—2441no—
365C2—2441no—
366C2#2144435011yescharacteristic
367C2#2144746411yescharacteristic
368C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11817
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #21443850C2semidirect
5. #21443848C2semidirect
6. #21443846C2semidirect
7. C61×#1353C2semidirect
184. #1353D61semidirect
211. C61#11817semidirect

Maximal subgroups

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

subgroupindex
#214516332
#214458982
#214441472
#214438502
#214438482
#214438462
C61×#13532
#1181761