Finite Group Databasebeta

← #29569043

Subgroups — #29569043

Order 15616.

430 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 85 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#21452837C211yesmaximal, characteristic
2#21447378C211yesmaximal, characteristic, complemented
3#21447227C211yesmaximal, characteristic, complemented
4#21447224C211yesmaximal, characteristic
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic, complemented
8C2×#14519753—21no—
9C2×#14519701—21no—
10C2×#14519699—21no—
11#16839699—21no—
12#16839694—21no—
13#16839684—21no—
14#16839664C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839640—21no—
17#16839636—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30#14519753—42no—
31#14519753—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519701—42no—
48#14519699—42no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61D411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C23×D61—21no—
59C2×Q8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61D812yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244SD1612yes—
76C2×C4×D61—42no—
77C2×C4×D61—81no—
78C2×C4×D61—81no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61—41no—
87#11758198—42no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—81no—
93#11758198—81no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—42no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—42no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—81no—
105#11758196—42no—
106#11758196—41no—
107#11758196—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61#12011yescharacteristic
112C22×D61—22no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119Q8×C61—42no—
120Q8×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×D811yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151D244—42no—
152D244—81no—
153C4×D61—84no—
154C8×C61—81no—
155C8×C61—81no—
156#92418—81no—
157#7787—611nomaximal, Sylow
158C22×C61#44711yescharacteristic
159C22×C61#44811yescharacteristic
160C22×C61#45211yescharacteristic
161C22×C61#45411yescharacteristic
162C22×C61#45511yescharacteristic
163C22×C61#45511yescharacteristic
164C22×C61#45811yescharacteristic
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—42no—
179C4×C61—81no—
180Dic61—81no—
181Dic61—81no—
182Dic61—81no—
183Dic61—161no—
184#2732—611no—
185#2099—611no—
186#2072—611no—
187#2071—611no—
188#1272D6111yescharacteristic, complemented
189#1271—611no—
190#1270—611no—
191C2×C61#160711yescharacteristic
192C2×C61#160811yescharacteristic
193C2×C61#161511yescharacteristic
194C2×C61#162711yescharacteristic
195C2×C61#164111yescharacteristic
196C2×C61#164311yescharacteristic
197C2×C61#166211yescharacteristic
198D61—82no—
199C2×C22⋊Q8—1221no—
200C2×#103—1221no—
201C2×#102—1221no—
202#399—1221no—
203#398—1221no—
204#396—1221no—
205#391C2×D6111yescharacteristic
206#390—611no—
207#389—611no—
208#386—1221no—
209#385—1221no—
210#384—611no—
211#340—1221no—
212#340—1221no—
213#340—1221no—
214#340—1221no—
215#336—611no—
216#336C2×D6111yescharacteristic
217#336C2×D6111yescharacteristic
218C61#778711yescharacteristic, complemented, Sylow
219C22×Q8D24411yescharacteristic
220C22×D4—611no—
221C23×C4—1221no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1221no—
225C22⋊Q8—2442no—
226C22⋊Q8—2442no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4D24411yescharacteristic
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C42C22×D6111yescharacteristic
244#103—2442no—
245#102—2442no—
246#95—21no—
247#95—21no—
248#95—1221no—
249#95—1221no—
250C24—1221no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8D48812yes—
255C2×D4—612no—
256C2×D4—1221no—
257C2×D4—2441no—
258C2×D4—2441no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—4881no—
265C22×C4—4881no—
266C22×C4—2442no—
267C22×C4—2441no—
268C22×C4C2×D24411yescharacteristic
269C22×C4D4×D6111yescharacteristic
270C22×C4D4×D6111yescharacteristic
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—2441no—
278C2×C8—2441no—
279C2×C8—2441no—
280C4⋊C4—41no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—4881no—
284C4⋊C4—2442no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C22⋊C4—4881no—
296C22⋊C4—4881no—
297C22⋊C4—2442no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—41no—
303C23—1222no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23#1451974711yescharacteristic
311Q8—42no—
312Q8—81no—
313D4—4881no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—4884no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4C2×D48811yescharacteristic
341C2×C4SD16×D6111yescharacteristic
342C2×C4#1451979811yescharacteristic
343C2×C4#1451980511yescharacteristic
344C2×C4#1451980911yescharacteristic
345C2×C4#1451980911yescharacteristic
346C8—81no—
347C8—81no—
348C8—4881no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—2442no—
354C22—2442no—
355C22—2442no—
356C22#1683989811yescharacteristic
357C22#1683990211yescharacteristic
358C22#1683992711yescharacteristic
359C22#1683993611yescharacteristic
360C22#1683994111yescharacteristic
361C22#1683994211yescharacteristic
362C22#1683995311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—9761no—
372C4—4881no—
373C4—4881no—
374C4—4881no—
375C2—4882no—
376C2#2144480711yescharacteristic
377C2#2144481111yescharacteristic
378C2#2144485311yescharacteristic
379C2#2144492411yescharacteristic
380C2#2144501411yescharacteristic
381C2#2144502711yescharacteristic
382C2#2144514411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1272D61
hypocenterC61#7787
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21447378C2semidirect
3. #21447227C2semidirect
5. #21443641C2semidirect
7. C61×#1272C2semidirect
188. #1272D61semidirect
218. C61#7787semidirect

Maximal subgroups

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

subgroupindex
#214528372
#214473782
#214472272
#214472242
#214436412
#214436392
C61×#12722
#778761