Finite Group Databasebeta

← #29569045

Subgroups — #29569045

Order 15616.

430 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 83 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#21452835C211yesmaximal, characteristic
2#21447377C211yesmaximal, characteristic, complemented
3#21447229C211yesmaximal, characteristic, complemented
4#21447224C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519755—21no—
9C2×#14519702—21no—
10C2×#14519699—21no—
11#16839697—21no—
12#16839696—21no—
13#16839684—21no—
14#16839668C2211yescharacteristic
15#16839664C2211yescharacteristic
16#16839640—21no—
17#16839633—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839524—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31#14519755—42no—
32#14519755—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46#14519702—42no—
47#14519699—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C2×D244—21no—
69C2×D244—41no—
70C2×D244—41no—
71C2×D244SD1612yes—
72C2×C4×D61—42no—
73C2×C4×D61—81no—
74C2×C4×D61—81no—
75C2×Dic122—21no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122D812yes—
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—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91#11758198—42no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—81no—
97#11758198—81no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105#11758196—42no—
106#11758196—42no—
107#11758196—81no—
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—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
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×C61C2×D811yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149D244—42no—
150D244—81no—
151C4×D61—84no—
152Dic122—42no—
153Dic122—81no—
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—81no—
179C4×C61—81no—
180Dic61—42no—
181Dic61—81no—
182Dic61—81no—
183Dic61—161no—
184#2732—611no—
185#2099—611no—
186#2072—611no—
187#2071—611no—
188#1272—611no—
189#1271D6111yescharacteristic, complemented
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#391—611no—
206#390—611no—
207#389C2×D6111yescharacteristic
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×Q8—611no—
220C22×D4—611no—
221C23×C4—1221no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1221no—
225C22⋊Q8—2442no—
226C22⋊Q8—2442no—
227C2×C4⋊C4—21no—
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⋊C4D24411yescharacteristic
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—1221no—
248#95—1221no—
249#95—1221no—
250C24—1221no—
251C2×Q8—612no—
252C2×Q8—1221no—
253C2×Q8—2441no—
254C2×Q8—2441no—
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—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—4881no—
286C4⋊C4—2442no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
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—4881no—
312Q8—2442no—
313D4—4881no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—1222no—
328C2×C4—4884no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
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×C4D8×D6111yescharacteristic
341C2×C4SD16×D6111yescharacteristic
342C2×C4#1451979911yescharacteristic
343C2×C4#1451980411yescharacteristic
344C2×C4#1451980911yescharacteristic
345C2×C4#1451981011yescharacteristic
346C8—81no—
347C8—81no—
348C8—4881no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—2442no—
354C22—2442no—
355C22—2442no—
356C22#1683989711yescharacteristic
357C22#1683990211yescharacteristic
358C22#1683992611yescharacteristic
359C22#1683993711yescharacteristic
360C22#1683994111yescharacteristic
361C22#1683994111yescharacteristic
362C22#1683995311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—81no—
371C4—9761no—
372C4—4881no—
373C4—4881no—
374C4—2442no—
375C2—4882no—
376C2#2144480611yescharacteristic
377C2#2144481111yescharacteristic
378C2#2144485211yescharacteristic
379C2#2144492311yescharacteristic
380C2#2144501511yescharacteristic
381C2#2144502911yescharacteristic
382C2#2144514311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1271D61
hypocenterC61#7787
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #21447377C2semidirect
3. #21447229C2semidirect
5. #21443644C2semidirect
7. C61×#1271C2semidirect
189. #1271D61semidirect
218. C61#7787semidirect

Maximal subgroups

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

subgroupindex
#214528352
#214473772
#214472292
#214472242
#214436442
#214436392
C61×#12712
#778761