Finite Group Databasebeta

← #29568964

Subgroups — #29568964

Order 15616.

446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452779C211yesmaximal, characteristic
2#21447149C211yesmaximal, characteristic, complemented
3#21446952C211yesmaximal, characteristic
4#21443642C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2043C211yesmaximal, characteristic, complemented
8C2×#14519772—21no—
9C2×#14519708—21no—
10C2×#14519697—21no—
11#16839697—21no—
12#16839684—21no—
13#16839680—21no—
14#16839664C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839659—21no—
17#16839652—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#103×C61—21no—
24C2×#103×C61—21no—
25C61×#389C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30#14519772—42no—
31#14519772—42no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45#14519708—42no—
46#14519697—42no—
47#14519684—21no—
48#14519684—21no—
49C22×Q8×C61—21no—
50C22×C8×C61—21no—
51C4⋊Q8×C61—42no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#103×C61—42no—
59#103×C61—42no—
60#95×C61—21no—
61C23×D61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—41no—
80C2×D244—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C42×C61—41no—
94#11758198—42no—
95#11758198—42no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—81no—
101#11758198—81no—
102C4⋊Dic61—21no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61SD1612yes—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109#11758196—81no—
110C4×Dic61—42no—
111C2×#92418—22no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61#12011yescharacteristic
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125Q8×C61—42no—
126Q8×C61—42no—
127Q8×C61—81no—
128Q8×C61—81no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
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—42no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C2×Dic61—22no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159D244—42no—
160D244—81no—
161C8×C61—81no—
162#92418—42no—
163#92418—81no—
164#7776—611nomaximal, Sylow
165C22×C61#44911yescharacteristic
166C22×C61#45011yescharacteristic
167C22×C61#45211yescharacteristic
168C22×C61#45411yescharacteristic
169C22×C61#45511yescharacteristic
170C22×C61#45611yescharacteristic
171C22×C61B(4,𝔽2)11yescharacteristic
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—82no—
186C4×C61—81no—
187C4×C61—81no—
188Dic61—42no—
189Dic61—81no—
190Dic61—81no—
191#2727—611no—
192#2058—611no—
193#2043D6111yescharacteristic, complemented
194#2023—611no—
195#1271—611no—
196#1271—611no—
197#1270—611no—
198C2×C61#159711yescharacteristic
199C2×C61#160411yescharacteristic
200C2×C61#160611yescharacteristic
201C2×C61#163511yescharacteristic
202C2×C61#164211yescharacteristic
203C2×C61#165211yescharacteristic
204C2×C61#166411yescharacteristic
205D61—161no—
206C2×C4⋊Q8C2×D6111yescharacteristic
207C2×#126—1221no—
208C2×#106—1221no—
209C2×#103—21no—
210C2×#103—21no—
211C2×#102—1221no—
212#399—1221no—
213#396—1221no—
214#394—1221no—
215#390—611no—
216#389—611no—
217#389—1221no—
218#389C2×D6111yescharacteristic
219#388—1221no—
220#340—1221no—
221#340—1221no—
222#336—611no—
223#336—611no—
224#336C2×D6111yescharacteristic
225C61#777611yescharacteristic, complemented, Sylow
226C22×Q8—21no—
227C22×D4—611no—
228C22×C8—21no—
229C22×C8—1221no—
230C22×C8—1221no—
231C4⋊Q8—42no—
232#126—2442no—
233#126—2442no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4C22⋊D6111yescharacteristic
244C2×C4⋊C4C22⋊D6111yescharacteristic
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42—1221no—
252C2×C42C22×D6111yescharacteristic
253#106—2442no—
254#103—42no—
255#103—42no—
256#102—2442no—
257#95—21no—
258#95—1221no—
259#95—1221no—
260C24—1221no—
261C2×Q8—22no—
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—1222no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8—2441no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—612no—
299C4⋊C4—1221no—
300C4⋊C4—4881no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2442no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—4881no—
307C22⋊C4—4881no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C42—41no—
315C42—2442no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23#1451974511yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—81no—
327Q8—81no—
328D4—4881no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—1222no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4SD16×D6111yescharacteristic
355C2×C4#1451979711yescharacteristic
356C2×C4#1451980011yescharacteristic
357C2×C4#1451980311yescharacteristic
358C2×C4#1451980411yescharacteristic
359C2×C4#1451980911yescharacteristic
360C8—81no—
361C8—4881no—
362C8—2442no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22#1683990511yescharacteristic
371C22#1683991111yescharacteristic
372C22#1683992311yescharacteristic
373C22#1683993411yescharacteristic
374C22#1683993811yescharacteristic
375C22#1683994311yescharacteristic
376C22#1683994811yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—81no—
385C4—81no—
386C4—4881no—
387C4—4881no—
388C4—2442no—
389C2—9761no—
390C2#2144474611yescharacteristic
391C2#2144478611yescharacteristic
392C2#2144479811yescharacteristic
393C2#2144496711yescharacteristic
394C2#2144501711yescharacteristic
395C2#2144508711yescharacteristic
396C2#2144515011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2043C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2043D61
hypocenterC61#7776
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. #21447149C2semidirect
4. #21443642C2semidirect
5. #21443641C2semidirect
7. C61×#2043C2semidirect
193. #2043D61semidirect
225. C61#7776semidirect

Maximal subgroups

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

subgroupindex
#214527792
#214471492
#214469522
#214436422
#214436412
#214436392
C61×#20432
#777661