Finite Group Databasebeta

← #29590873

Subgroups — #29590873

Order 15616.

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

normal subgroups only

This group has 446 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#21451378C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic, complemented
3#21444130C211yesmaximal, characteristic, complemented
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic
7C61×#1343C211yesmaximal, characteristic
8C2×D4×Dic61C411yescharacteristic, complemented
9C2×#14519733C2211yescharacteristic
10#16839812—21no—
11#16839702C411yescharacteristic, complemented
12#16839698C2211yescharacteristic
13#16839676C411yescharacteristic, complemented
14#16839656—21no—
15#16839642—21no—
16#16839642—21no—
17#16839634—21no—
18#16839629C411yescharacteristic, complemented
19#16839623—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61—21no—
28C23×Dic61D411yescharacteristic
29D4×Dic61—41no—
30D4×Dic61—41no—
31#14519733—41no—
32#14519733—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196C2×C411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61D411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46C22⋊#92418—21no—
47C8×Dic61—41no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53#14519684—41no—
54#14519684C2×C411yescharacteristic
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61—21no—
63C24×C61C2×D411yescharacteristic
64C2×D4×C61—41no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—81no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—41no—
81C22×Dic61—42no—
82C22×Dic61—41no—
83C22×Dic61—81no—
84C22×Dic61—81no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C2×C8×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—81no—
94C22⋊Dic61—41no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—81no—
102C4⋊Dic61—41no—
103#11758196—41no—
104#11758196—41no—
105#11758196—81no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—22no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61#13511yescharacteristic
124C23×C61#13511yescharacteristic
125D4×C61—42no—
126D4×C61—42no—
127D4×C61—82no—
128D4×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—84no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162C2×Dic61#9911yescharacteristic
163C2×Dic61#9911yescharacteristic
164C8×C61—81no—
165#92418—81no—
166#11840—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—42no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61C2×#9911yescharacteristic
184C22×C61#41611yescharacteristic
185C22×C61#42111yescharacteristic
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61—161no—
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196Dic61—81no—
197Dic61—161no—
198#2598—611no—
199#1820—611no—
200#1458—611no—
201#1352—611no—
202#1352—611no—
203#1343—611no—
204#1343D6111yescharacteristic
205C2×C61—21no—
206C2×C61—21no—
207C2×C61—41no—
208C2×C61—41no—
209C2×C61—82no—
210C2×C61#151611yescharacteristic
211C2×C61#212011yescharacteristic
212C2×C61#212811yescharacteristic
213C2×C4×D4—611no—
214C2×#117—611no—
215#431—1221no—
216#400—611no—
217#399—611no—
218#394—611no—
219#392C2×D6111yescharacteristic
220#388—1221no—
221#386—1221no—
222#386—1221no—
223#385—1221no—
224#383—611no—
225#381—1221no—
226#342—611no—
227#342—1221no—
228#342C2×D6111yescharacteristic
229#324—1221no—
230#323—611no—
231#323C2×D6111yescharacteristic
232C61#1184011yescharacteristic, complemented, Sylow
233C22×D4—21no—
234C22×D4C4×D6111yescharacteristic
235C23×C4—611no—
236C23×C4—1221no—
237C4×D4—2441no—
238C4×D4—2441no—
239#117—2441no—
240#117—2441no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4C22×D6111yescharacteristic
254C2×C42—611no—
255C2×C42—611no—
256C4⋊C8—2441no—
257C22⋊C8—21no—
258C22⋊C8—1221no—
259C4×C8—2441no—
260#95—611no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—2441no—
266#95—2441no—
267#95C4×D6111yescharacteristic
268C24—21no—
269C24D4×D6111yescharacteristic
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—81no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—4881no—
289C22×C4—4881no—
290C22×C4—2441no—
291C22×C4—2442no—
292C22×C4—2441no—
293C22×C4C2×C4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C2×C8—41no—
296C2×C8—2441no—
297C4⋊C4—4881no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—81no—
305C22⋊C4—4881no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2442no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2442no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42—1221no—
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23C22⋊C4×D6111yescharacteristic
329C23#1451979611yescharacteristic
330C23#1451979811yescharacteristic
331D4—42no—
332D4—42no—
333D4—82no—
334D4—82no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—4884no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C8—81no—
371C8—4881no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22#99×D6111yescharacteristic
389C22#1683975511yescharacteristic
390C22#1683977711yescharacteristic
391C4—41no—
392C4—41no—
393C4—81no—
394C4—161no—
395C4—1221no—
396C4—1221no—
397C4—9761no—
398C4—4881no—
399C4—4881no—
400C4—2441no—
401C4—2441no—
402C4—2441no—
403C2—21no—
404C2—21no—
405C2—41no—
406C2—41no—
407C2—82no—
408C2#2144437211yescharacteristic
409C2#2144745711yescharacteristic
410C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radicalC61×#392C22
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11840
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445895C2semidirect
3. #21444130C2semidirect
4. #21443844C2semidirect
5. #21443842C2semidirect
8. C2×D4×Dic61C4semidirect
11. #16839702C4semidirect
13. #16839676C4semidirect
18. #16839629C4semidirect
232. C61#11840semidirect

Maximal subgroups

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

subgroupindex
#214513782
#214458952
#214441302
#214438442
#214438422
#214438162
C61×#13432
#1184061