Finite Group Databasebeta

← #29569273

Subgroups — #29569273

Order 15616.

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

normal subgroups only

This group has 446 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#21447381C211yesmaximal, characteristic, complemented
3#21447353C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443643C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2095C211yesmaximal, characteristic, complemented
8C2×#14519753—21no—
9C2×#14519708—21no—
10C2×#14519697—21no—
11#16839699—21no—
12#16839694—21no—
13#16839684—21no—
14#16839664C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839640—21no—
17#16839636—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#107×C61—21no—
23C2×#103×C61—21no—
24C61×#391C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519753—42no—
32#14519753—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45#14519708—42no—
46#14519697—42no—
47#14519684—21no—
48#14519684—21no—
49C22×Q8×C61D411yescharacteristic
50C22×C8×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#107×C61—42no—
57#103×C61—42no—
58#95×C61—21no—
59#95×C61—21no—
60C23×D61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C2×Q8×C61SD1612yes—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244Q1612yes—
78C2×C4×D61—42no—
79C2×C4×D61—81no—
80C2×C4×D61—81no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—42no—
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—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—81no—
104#11758196—42no—
105#11758196—41no—
106#11758196—41no—
107C2×#92418—22no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114C22×D61—22no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121Q8×C61—42no—
122Q8×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
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—
137C2×C4×C61—81no—
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61C2×Q1611yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153D244—42no—
154D244—81no—
155C4×D61—84no—
156C8×C61—42no—
157#92418—42no—
158#92418—81no—
159#7823—611nomaximal, Sylow
160C22×C61#45011yescharacteristic
161C22×C61#45111yescharacteristic
162C22×C61#45211yescharacteristic
163C22×C61#45311yescharacteristic
164C22×C61#45311yescharacteristic
165C22×C61#45411yescharacteristic
166C22×C61#45811yescharacteristic
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—81no—
182C4×C61—161no—
183Dic61—81no—
184Dic61—81no—
185Dic61—81no—
186#2732—611no—
187#2100—611no—
188#2095D6111yescharacteristic, complemented
189#2094—611no—
190#1272—611no—
191#1271—611no—
192#1270—611no—
193C2×C61#161311yescharacteristic
194C2×C61#161411yescharacteristic
195C2×C61#161511yescharacteristic
196C2×C61#163111yescharacteristic
197C2×C61#163211yescharacteristic
198C2×C61#163711yescharacteristic
199C2×C61#165611yescharacteristic
200D61—82no—
201C2×C22⋊Q8—1221no—
202C2×#107—21no—
203C2×#106—1221no—
204C2×#103—21no—
205C2×#102—1221no—
206#399—1221no—
207#398—1221no—
208#396—1221no—
209#391C2×D6111yescharacteristic
210#390—611no—
211#389—611no—
212#386—1221no—
213#385—1221no—
214#384C2×D6111yescharacteristic
215#340—1221no—
216#340—1221no—
217#336—611no—
218#336—611no—
219#336C2×D6111yescharacteristic
220C61#782311yescharacteristic, complemented, Sylow
221C22×Q8C22⋊D6111yescharacteristic
222C22×D4—611no—
223C23×C4—1221no—
224C22×C8—21no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22⋊Q8—2442no—
228C22⋊Q8—2442no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4C22⋊D6111yescharacteristic
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42C22×D6111yescharacteristic
246#107—42no—
247#106—2442no—
248#103—42no—
249#102—2442no—
250#95—21no—
251#95—21no—
252#95—1221no—
253#95—1221no—
254C24—1221no—
255C2×Q8—21no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8#1175820112yes—
259C2×D4—612no—
260C2×D4—1221no—
261C2×D4—2441no—
262C2×D4—2441no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—4881no—
270C22×C4—4881no—
271C22×C4—2442no—
272C22×C4D4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4C2×C22⋊D6111yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—1222no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—4881no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2442no—
296C4⋊C4—2442no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—4881no—
300C22⋊C4—4881no—
301C22⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—41no—
307C23—1222no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23#1451974511yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—4881no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—4884no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4C2×#1175820111yescharacteristic
345C2×C4Q16×D6111yescharacteristic
346C2×C4#1451980011yescharacteristic
347C2×C4#1451980211yescharacteristic
348C2×C4#1451980911yescharacteristic
349C2×C4#1451980911yescharacteristic
350C8—42no—
351C8—4881no—
352C8—2442no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22—4881no—
357C22—2442no—
358C22—2442no—
359C22—2442no—
360C22#1683991211yescharacteristic
361C22#1683991611yescharacteristic
362C22#1683992311yescharacteristic
363C22#1683992811yescharacteristic
364C22#1683992911yescharacteristic
365C22#1683993311yescharacteristic
366C22#1683995111yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—161no—
376C4—4881no—
377C4—4881no—
378C4—4881no—
379C2—4882no—
380C2#2144483811yescharacteristic
381C2#2144484211yescharacteristic
382C2#2144484911yescharacteristic
383C2#2144494411yescharacteristic
384C2#2144495011yescharacteristic
385C2#2144498211yescharacteristic
386C2#2144511011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2095C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2095D61
hypocenterC61#7823
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
2. #21447381C2semidirect
4. #21443645C2semidirect
5. #21443643C2semidirect
7. C61×#2095C2semidirect
188. #2095D61semidirect
220. C61#7823semidirect

Maximal subgroups

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

subgroupindex
#214528372
#214473812
#214473532
#214436452
#214436432
#214436392
C61×#20952
#782361