Finite Group Databasebeta

← #29569070

Subgroups — #29569070

Order 15616.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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#21447377C211yesmaximal, characteristic, complemented
2#21447295C211yesmaximal, characteristic, complemented
3#21447222C211yesmaximal, characteristic
4#21443642C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic
7C61×#2683C211yesmaximal, characteristic
8C2×#14519708—21no—
9C2×#14519698—21no—
10#16839632C2211yescharacteristic
11#16839524—21no—
12#16839524—21no—
13#16839524—21no—
14#16839524—21no—
15#16839517C2211yescharacteristic
16#16839517C2211yescharacteristic
17#16839517C2211yescharacteristic
18C2×C22⋊Q8×C61—21no—
19C2×C22⋊Q8×C61—21no—
20C61×#396—21no—
21C61×#396—21no—
22C61×#395—21no—
23C61×#390C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#389C2211yescharacteristic
26C61×#386—21no—
27C22×#92418—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33#14519708—42no—
34#14519698—42no—
35C22×Q8×C61—21no—
36C22×D4×C61D411yescharacteristic
37C23×C4×C61—21no—
38C22⋊Q8×C61—42no—
39C22⋊Q8×C61—42no—
40C22⋊Q8×C61—42no—
41C22⋊Q8×C61—42no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60C24×C61—21no—
61C2×Q8×C61—42no—
62C2×Q8×C61—42no—
63C2×Q8×C61—81no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61SD1612yes—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—42no—
74C22×C4×C61—42no—
75C22×C4×C61—81no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—41no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61D812yes—
92C4⋊C4×C61SD1612yes—
93C22⋊C4×C61—42no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—81no—
100C42×C61—41no—
101C4⋊Dic61—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C2×#92418—22no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61#12011yescharacteristic
123Q8×C61—84no—
124D4×C61—42no—
125D4×C61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—84no—
148C2×C4×C61C2×D811yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×Dic61—81no—
155C2×Dic61—81no—
156C2×Dic61—81no—
157#92418—42no—
158#92418—81no—
159#92418—81no—
160#7791—611nomaximal, Sylow
161C22×C61—42no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61#44711yescharacteristic
169C22×C61#44811yescharacteristic
170C22×C61#45011yescharacteristic
171C22×C61#45411yescharacteristic
172C22×C61#45511yescharacteristic
173C22×C61#45611yescharacteristic
174C22×C61#45811yescharacteristic
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—42no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—161no—
187#2683D6111yescharacteristic
188#2099—611no—
189#2084—611no—
190#2071—611no—
191#1271—611no—
192#1271—611no—
193#1270—611no—
194C2×C61—82no—
195C2×C61#160811yescharacteristic
196C2×C61#161011yescharacteristic
197C2×C61#161611yescharacteristic
198C2×C61#162711yescharacteristic
199C2×C61#163911yescharacteristic
200C2×C61#165111yescharacteristic
201C2×C61#166411yescharacteristic
202C2×C22⋊Q8—21no—
203C2×C22⋊Q8—21no—
204C2×#106—1221no—
205C2×#102—1221no—
206#396—21no—
207#396—21no—
208#395—21no—
209#390C2×D6111yescharacteristic
210#389C2×D6111yescharacteristic
211#389C2×D6111yescharacteristic
212#386—21no—
213#384—611no—
214#340—1221no—
215#340—1221no—
216#340—1221no—
217#340—1221no—
218#336—611no—
219#336—611no—
220#336—611no—
221C61#779111yescharacteristic, complemented, Sylow
222C22×Q8—21no—
223C22×D4C22⋊D6111yescharacteristic
224C23×C4—21no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22×C8—1221no—
228C22⋊Q8—42no—
229C22⋊Q8—42no—
230C22⋊Q8—42no—
231C22⋊Q8—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4C22⋊D6111yescharacteristic
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C4⋊C4C22⋊D6111yescharacteristic
242C2×C4⋊C4C22⋊D6111yescharacteristic
243C2×C4⋊C4C22⋊D6111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C42C22×D6111yescharacteristic
250#106—2442no—
251#102—2442no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24—21no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—81no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4#1175820112yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—81no—
271C22×C4—2441no—
272C22×C4C2×C22⋊D6111yescharacteristic
273C22×C4C2×C22⋊D6111yescharacteristic
274C22×C4C2×C22⋊D6111yescharacteristic
275C2×C8—1222no—
276C2×C8—2441no—
277C2×C8—2441no—
278C2×C8—2441no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—2442no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4#1175819912yes—
301C4⋊C4#1175820012yes—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C42—41no—
310C23—22no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#1451974611yescharacteristic
318Q8—84no—
319D4—42no—
320D4—81no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—84no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4C2×#1175819911yescharacteristic
347C2×C4C2×#1175820111yescharacteristic
348C2×C4C2×#1175820011yescharacteristic
349C2×C4#1451980311yescharacteristic
350C2×C4#1451980311yescharacteristic
351C2×C4#1451980811yescharacteristic
352C8—4881no—
353C8—4881no—
354C8—2442no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22#1683989611yescharacteristic
363C22#1683990111yescharacteristic
364C22#1683991311yescharacteristic
365C22#1683993511yescharacteristic
366C22#1683994011yescharacteristic
367C22#1683994511yescharacteristic
368C22#1683995211yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—9761no—
381C2—82no—
382C2#2144481011yescharacteristic
383C2#2144482211yescharacteristic
384C2#2144485611yescharacteristic
385C2#2144492211yescharacteristic
386C2#2144499811yescharacteristic
387C2#2144508211yescharacteristic
388C2#2144515311yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2683C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#2683D61
hypocenterC61#7791
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
1. #21447377C2semidirect
2. #21447295C2semidirect
4. #21443642C2semidirect
5. #21443642C2semidirect
221. C61#7791semidirect

Maximal subgroups

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

subgroupindex
#214473772
#214472952
#214472222
#214436422
#214436402
C61×#26832
#779161