Finite Group Databasebeta

← #29568945

Subgroups — #29568945

Order 15616.

422 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453801C211yesmaximal, characteristic
2#21447062C211yesmaximal, characteristic, complemented
3#21446952C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2024C211yesmaximal, characteristic, complemented
8C2×#14519701—21no—
9C2×#14519701—21no—
10C2×#14519697—21no—
11#16839689—21no—
12#16839680—21no—
13#16839673—21no—
14#16839664C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839654—21no—
17#16839652—21no—
18#16839649—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#103×C61—21no—
24C61×#391C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61—21no—
41#14519701—42no—
42#14519701—42no—
43#14519697—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61—21no—
49C22×Q8×C61D411yescharacteristic
50C22×C8×C61—21no—
51C4⋊Q8×C61—42no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#103×C61—42no—
57#95×C61—21no—
58#95×C61—21no—
59C23×D61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—41no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—41no—
82C2×D244—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—81no—
97#11758198—81no—
98#11758198—81no—
99#11758198—81no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—81no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121Q8×C61—42no—
122Q8×C61—42no—
123Q8×C61—42no—
124Q8×C61—81no—
125Q8×C61—81no—
126Q8×C61—81no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157D244—42no—
158D244—81no—
159C8×C61—81no—
160#92418—81no—
161#92418—81no—
162#7773—611nomaximal, Sylow
163C22×C61#44911yescharacteristic
164C22×C61#45211yescharacteristic
165C22×C61#45211yescharacteristic
166C22×C61#45411yescharacteristic
167C22×C61#45511yescharacteristic
168C22×C61#45511yescharacteristic
169C22×C61B(4,𝔽2)11yescharacteristic
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—82no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—81no—
187Dic61—81no—
188Dic61—81no—
189#2808—611no—
190#2043—611no—
191#2024D6111yescharacteristic, complemented
192#2023—611no—
193#1272—611no—
194#1271—611no—
195#1270—611no—
196C2×C61#159711yescharacteristic
197C2×C61#160611yescharacteristic
198C2×C61#160611yescharacteristic
199C2×C61#163811yescharacteristic
200C2×C61#164011yescharacteristic
201C2×C61#164611yescharacteristic
202C2×C61#166211yescharacteristic
203D61—161no—
204C2×C4⋊Q8C2×D6111yescharacteristic
205C2×#103—21no—
206C2×#103—1221no—
207C2×#103—1221no—
208C2×#102—1221no—
209#397—1221no—
210#394—1221no—
211#393—1221no—
212#391C2×D6111yescharacteristic
213#390—611no—
214#389—611no—
215#388—1221no—
216#388—1221no—
217#387—1221no—
218#340—21no—
219#340—1221no—
220#336—611no—
221#336—611no—
222#336C2×D6111yescharacteristic
223C61#777311yescharacteristic, complemented, Sylow
224C22×Q8—21no—
225C22×Q8C22⋊D6111yescharacteristic
226C22×D4—611no—
227C22×C8—21no—
228C22×C8—1221no—
229C22×C8—1221no—
230C4⋊Q8—42no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4C22⋊D6111yescharacteristic
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—1221no—
245C2×C42C22×D6111yescharacteristic
246#103—42no—
247#103—2442no—
248#103—2442no—
249#102—2442no—
250#95—21no—
251#95—21no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256C24—1221no—
257C2×Q8—22no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—2441no—
270C2×D4—2441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4D4×D6111yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—2441no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8—2441no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C22⋊C4—4881no—
301C22⋊C4—4881no—
302C22⋊C4—4881no—
303C22⋊C4—4881no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42—41no—
309C42—4881no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23#1451974511yescharacteristic
318Q8—42no—
319Q8—42no—
320Q8—42no—
321Q8—81no—
322Q8—81no—
323Q8—81no—
324D4—4881no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4#1451979711yescharacteristic
351C2×C4#1451979811yescharacteristic
352C2×C4#1451980011yescharacteristic
353C2×C4#1451980411yescharacteristic
354C2×C4#1451980811yescharacteristic
355C2×C4#1451980911yescharacteristic
356C8—81no—
357C8—4881no—
358C8—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22#1683990611yescharacteristic
367C22#1683992211yescharacteristic
368C22#1683992311yescharacteristic
369C22#1683993311yescharacteristic
370C22#1683993811yescharacteristic
371C22#1683993911yescharacteristic
372C22#1683994811yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—81no—
380C4—82no—
381C4—81no—
382C4—4881no—
383C4—4881no—
384C4—4881no—
385C2—9761no—
386C2#2144474711yescharacteristic
387C2#2144479711yescharacteristic
388C2#2144479811yescharacteristic
389C2#2144499011yescharacteristic
390C2#2144500411yescharacteristic
391C2#2144504411yescharacteristic
392C2#2144514111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2024C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2024D61
hypocenterC61#7773
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. #21447062C2semidirect
4. #21443645C2semidirect
5. #21443641C2semidirect
7. C61×#2024C2semidirect
191. #2024D61semidirect
223. C61#7773semidirect

Maximal subgroups

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

subgroupindex
#214538012
#214470622
#214469522
#214436452
#214436412
#214436392
C61×#20242
#777361