Finite Group Databasebeta

← #29590803

Subgroups — #29590803

Order 15616.

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

normal subgroups only

This group has 414 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#21451742C211yesmaximal, characteristic
2#21445806C211yesmaximal, characteristic
3#21444158C211yesmaximal, characteristic
4#21443840C211yesmaximal, characteristic, complemented
5#21443820C211yesmaximal, characteristic, complemented
6#21443818C211yesmaximal, characteristic, complemented
7C61×#1351C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10#16839816—21no—
11C2×#14519691—21no—
12#16839694C411yescharacteristic, complemented
13#16839691—21no—
14#16839687C2211yescharacteristic
15#16839681C411yescharacteristic, complemented
16#16839678—21no—
17#16839645—21no—
18#16839634—21no—
19#16839624C411yescharacteristic, complemented
20#16839620—21no—
21#16839529C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#393C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30#14519753—41no—
31#14519753—41no—
32#14519737—41no—
33#14519737—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—41no—
39C2×#11758196C2×C411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519691—42no—
48C22⋊#92418—21no—
49#14519687—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—41no—
66C2×Q8×C61—81no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—41no—
81C22×Dic61—81no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—81no—
88C2×C8×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—81no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97#11758198—41no—
98#11758198—42no—
99#11758198—81no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—41no—
104#11758196—41no—
105#11758196—81no—
106#11758196—82no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C2×#92418—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61AGL(1,ℤ/8)11yescharacteristic
116C23×C61#13711yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122Q8×C61—82no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61#9911yescharacteristic
156C2×Dic61#9911yescharacteristic
157C4×D61—81no—
158C4×D61—81no—
159C8×C61—81no—
160#92418—81no—
161#11826—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—81no—
171C22×C61C2×#9911yescharacteristic
172C22×C61#41711yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—81no—
182C4×C61—81no—
183C4×C61—161no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190Dic61—161no—
191#2638—611no—
192#1799—611no—
193#1466—611no—
194#1351—611no—
195#1351D6111yescharacteristic, complemented
196#1344—611no—
197#1344—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—41no—
201C2×C61—41no—
202C2×C61#151311yescharacteristic
203C2×C61#212111yescharacteristic
204C2×C61#212911yescharacteristic
205D61—81no—
206C2×C22⋊Q8—611no—
207C2×C4×D4—611no—
208#432—1221no—
209C2×#99—1221no—
210#398—611no—
211#397—611no—
212#397—1221no—
213#395—611no—
214#394—1221no—
215#393C2×D6111yescharacteristic
216#387—1221no—
217#385—1221no—
218#381—611no—
219#380—1221no—
220#342—611no—
221#342C2×D6111yescharacteristic
222#323—611no—
223#323—1221no—
224#323C2×D6111yescharacteristic
225C61#1182611yescharacteristic, complemented, Sylow
226C22×Q8C4×D6111yescharacteristic
227C22×D4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C22⋊Q8—2441no—
231C22⋊Q8—2441no—
232C4×D4—2441no—
233C4×D4—2441no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2441no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4C22×D6111yescharacteristic
248C2×C42—611no—
249C4⋊C8—2441no—
250#99—2442no—
251C22⋊C8—21no—
252C22⋊C8—1221no—
253#97—2441no—
254#95—21no—
255#95—611no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—2441no—
261#95C4×D6111yescharacteristic
262C24—611no—
263C24D4×D6111yescharacteristic
264C2×Q8—41no—
265C2×Q8—81no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C2×D4—2441no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—4881no—
283C22×C4—4881no—
284C22×C4—2441no—
285C22×C4C2×C4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C2×C8—41no—
288C2×C8—2441no—
289C4⋊C4—4881no—
290C4⋊C4—4882no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2442no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—4881no—
301C22⋊C4—2441no—
302C22⋊C4—2442no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C42—1221no—
308C42—1221no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—2441no—
317C23—2441no—
318C23C22⋊C4×D6111yescharacteristic
319C23#1451980411yescharacteristic
320C23#1451980911yescharacteristic
321Q8—82no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—2441no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C8—81no—
359C8—4881no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—4881no—
370C22—4881no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#99×D6111yescharacteristic
375C22#1683976211yescharacteristic
376C22#1683977711yescharacteristic
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—161no—
382C4—1221no—
383C4—1221no—
384C4—9761no—
385C4—4881no—
386C4—4881no—
387C4—2441no—
388C4—2441no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—4881no—
394C2#2144436111yescharacteristic
395C2#2144746211yescharacteristic
396C2#2144749211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1351C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1351D61
hypocenterC61#11826
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #21443840C2semidirect
5. #21443820C2semidirect
6. #21443818C2semidirect
7. C61×#1351C2semidirect
8. C2×#14519753C4semidirect
12. #16839694C4semidirect
15. #16839681C4semidirect
19. #16839624C4semidirect
195. #1351D61semidirect
225. C61#11826semidirect

Maximal subgroups

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

subgroupindex
#214517422
#214458062
#214441582
#214438402
#214438202
#214438182
C61×#13512
#1182661