Finite Group Databasebeta

← #29590636

Subgroups — #29590636

Order 15616.

462 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 462 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#21450996C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic
3#21444158C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443840C211yesmaximal, characteristic, complemented
7C61×#1351C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10#16839816—21no—
11C2×#14519691—21no—
12#16839702C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839681C411yescharacteristic, complemented
15#16839644—21no—
16#16839638—21no—
17#16839634—21no—
18#16839621—21no—
19C22⋊C4×Dic61—21no—
20#95×D61C411yescharacteristic, complemented
21#16839529C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#393C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31#14519753—41no—
32#14519753—41no—
33#14519737—41no—
34#14519737—41no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—41no—
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519691—24no—
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—22no—
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—42no—
88C2×C4×D61—42no—
89C2×C4×D61—81no—
90C2×C4×D61—81no—
91C2×C8×C61—41no—
92C22⋊C4×C61—22no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—81no—
96C22⋊Dic61—22no—
97C22⋊Dic61—42no—
98C22⋊Dic61—41no—
99#11758198—41no—
100#11758198—42no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—42no—
104#11758196—41no—
105#11758196—41no—
106#11758196—81no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—82no—
110C2×#92418—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61#13711yescharacteristic
117C23×C61#13711yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61#10412yes—
123Q8×C61—82no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61—81no—
156C2×Dic61#9911yescharacteristic
157C2×Dic61#9911yescharacteristic
158C4×D61—81no—
159C4×D61—81no—
160C4×D61—84no—
161C8×C61—81no—
162#92418—81no—
163#11789—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—81no—
173C22×C61C2×#9911yescharacteristic
174C22×C61#41911yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C2×D61—22no—
177C2×D61—42no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—42no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184C4×C61—82no—
185C4×C61—81no—
186Dic61—21no—
187Dic61—21no—
188Dic61—42no—
189Dic61—41no—
190Dic61—41no—
191Dic61—82no—
192Dic61—81no—
193#2564—611no—
194C4×#99—611no—
195#1466—611no—
196#1352—611no—
197#1352—611no—
198#1351—611no—
199#1351D6111yescharacteristic, complemented
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—41no—
203C2×C61—41no—
204C2×C61#150811yescharacteristic
205C2×C61#212111yescharacteristic
206C2×C61#212611yescharacteristic
207D61—42no—
208C2×C22⋊Q8—611no—
209C2×C4×D4—611no—
210#432—1221no—
211C2×#99—1221no—
212#400—611no—
213#399—611no—
214#395—611no—
215#393C2×D6111yescharacteristic
216#387—1221no—
217#386—1221no—
218#385—1221no—
219#380—1221no—
220C4×C22⋊C4—1221no—
221C2×#95—611no—
222#342—611no—
223#342C2×D6111yescharacteristic
224#323—611no—
225#323—1221no—
226#323C2×D6111yescharacteristic
227C61#1178911yescharacteristic, complemented, Sylow
228C22×Q8C4×D6111yescharacteristic
229C22×D4—611no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—1221no—
233C22⋊Q8—2441no—
234C22⋊Q8—2441no—
235C4×D4—2441no—
236C4×D4—2441no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4C22×D6111yescharacteristic
249C2×C42—611no—
250C2×C42—2441no—
251C4⋊C8—2441no—
252#99—1224no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255#97—2441no—
256#95—21no—
257#95—611no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—2441no—
263#95C4×D6111yescharacteristic
264C24—611no—
265C24D4×D6111yescharacteristic
266C2×Q8—41no—
267C2×Q8—81no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—4881no—
285C22×C4—4881no—
286C22×C4—4881no—
287C22×C4—2442no—
288C22×C4—2442no—
289C22×C4—2441no—
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C2×C8—41no—
293C2×C8—2441no—
294C4⋊C4—4881no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2442no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C22⋊C4—1222no—
305C22⋊C4—2441no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2441no—
309C42—1221no—
310C42—1221no—
311C42—4882no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—612no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23C22⋊C4×D6111yescharacteristic
322C23#1451980611yescharacteristic
323C23#1451980911yescharacteristic
324Q8—82no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1222no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—4884no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C8—81no—
363C8—4881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—1222no—
374C22—2442no—
375C22—2442no—
376C22—2441no—
377C22—2441no—
378C22#99×D6111yescharacteristic
379C22#1683976911yescharacteristic
380C22#104×D6111yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—82no—
385C4—81no—
386C4—1221no—
387C4—1221no—
388C4—4882no—
389C4—4881no—
390C4—2442no—
391C4—2441no—
392C4—2441no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—2442no—
398C2#2144433711yescharacteristic
399C2#2144746211yescharacteristic
400C2#2144748311yescharacteristic
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#11789
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. #21443844C2semidirect
5. #21443842C2semidirect
6. #21443840C2semidirect
7. C61×#1351C2semidirect
8. C2×#14519753C4semidirect
12. #16839702C4semidirect
14. #16839681C4semidirect
20. #95×D61C4semidirect
199. #1351D61semidirect
227. C61#11789semidirect

Maximal subgroups

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

subgroupindex
#214509962
#214456062
#214441582
#214438442
#214438422
#214438402
C61×#13512
#1178961