Finite Group Databasebeta

← #29569047

Subgroups — #29569047

Order 15616.

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

normal subgroups only

This group has 418 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#21452748C211yesmaximal, characteristic
2#21447376C211yesmaximal, characteristic, complemented
3#21447223C211yesmaximal, characteristic
4#21443642C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2083C211yesmaximal, characteristic, complemented
8C2×#14519762—21no—
9C2×#14519697—21no—
10#16839695—21no—
11#16839689—21no—
12#16839688—21no—
13#16839664C2211yescharacteristic
14#16839660C2211yescharacteristic
15#16839636—21no—
16#16839633—21no—
17#16839524—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#107×C61—21no—
23C61×#389C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519762—42no—
32#14519762—42no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43#14519697—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×C8×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#107×C61—42no—
57#95×C61—21no—
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C2×D244—21no—
69C2×D244—41no—
70C2×D244—41no—
71C2×D244D812yes—
72C2×C4×D61—42no—
73C2×C4×D61—81no—
74C2×C4×D61—81no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C42×C61—41no—
89#11758198—42no—
90#11758198—42no—
91#11758198—42no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—81no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61#12011yescharacteristic
110C22×D61—22no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61C2×D811yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
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—41no—
147D244—42no—
148D244—81no—
149C4×D61—84no—
150C8×C61—42no—
151#92418—81no—
152#92418—81no—
153#7788—611nomaximal, Sylow
154C22×C61#44711yescharacteristic
155C22×C61#44911yescharacteristic
156C22×C61#45211yescharacteristic
157C22×C61#45411yescharacteristic
158C22×C61#45511yescharacteristic
159C22×C61#45611yescharacteristic
160C22×C61#45811yescharacteristic
161C2×D61—42no—
162C2×D61—42no—
163C2×D61—42no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—81no—
175C4×C61—81no—
176C4×C61—161no—
177Dic61—81no—
178Dic61—81no—
179Dic61—81no—
180#2724—611no—
181#2099—611no—
182#2083D6111yescharacteristic, complemented
183#2071—611no—
184#1271—611no—
185#1271—611no—
186#1270—611no—
187C2×C61#160711yescharacteristic
188C2×C61#160911yescharacteristic
189C2×C61#161511yescharacteristic
190C2×C61#162511yescharacteristic
191C2×C61#164011yescharacteristic
192C2×C61#164711yescharacteristic
193C2×C61#166411yescharacteristic
194D61—82no—
195C2×#123—1221no—
196C2×#107—21no—
197C2×#102—1221no—
198#398—1221no—
199#397—1221no—
200#397—1221no—
201#390—611no—
202#389—611no—
203#389C2×D6111yescharacteristic
204#385—1221no—
205#385—1221no—
206#384C2×D6111yescharacteristic
207#340—21no—
208#340—1221no—
209#340—1221no—
210#340—1221no—
211#336—611no—
212#336—611no—
213#336C2×D6111yescharacteristic
214C61#778811yescharacteristic, complemented, Sylow
215C22×D4—611no—
216C23×C4—1221no—
217C22×C8—21no—
218C22×C8—1221no—
219C22×C8—1221no—
220#123—2442no—
221#123—2442no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C22⋊D6111yescharacteristic
232C2×C4⋊C4C22⋊D6111yescharacteristic
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C42C22×D6111yescharacteristic
239#107—42no—
240#102—2442no—
241#95—21no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—1221no—
247C2×D4—612no—
248C2×D4—1221no—
249C2×D4—2441no—
250C2×D4—2441no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—4881no—
258C22×C4—4881no—
259C22×C4—2442no—
260C22×C4D4×D6111yescharacteristic
261C22×C4D4×D6111yescharacteristic
262C22×C4C2×C22⋊D6111yescharacteristic
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—2441no—
267C2×C8—2441no—
268C2×C8—2441no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—4881no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C42—41no—
297C23—1222no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23—2441no—
303C23—2441no—
304C23#1451974511yescharacteristic
305D4—4881no—
306D4—2442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—4884no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4D8×D6111yescharacteristic
333C2×C4#1451979711yescharacteristic
334C2×C4#1451980011yescharacteristic
335C2×C4#1451980111yescharacteristic
336C2×C4#1451980311yescharacteristic
337C2×C4#1451980911yescharacteristic
338C8—42no—
339C8—4881no—
340C8—4881no—
341C22—4881no—
342C22—4881no—
343C22—4881no—
344C22—4881no—
345C22—2442no—
346C22—2442no—
347C22—2442no—
348C22#1683989411yescharacteristic
349C22#1683990511yescharacteristic
350C22#1683992311yescharacteristic
351C22#1683993311yescharacteristic
352C22#1683993811yescharacteristic
353C22#1683994411yescharacteristic
354C22#1683995111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—81no—
363C4—161no—
364C4—4881no—
365C4—4881no—
366C4—4881no—
367C2—4882no—
368C2#2144480311yescharacteristic
369C2#2144481411yescharacteristic
370C2#2144484911yescharacteristic
371C2#2144490711yescharacteristic
372C2#2144500311yescharacteristic
373C2#2144505111yescharacteristic
374C2#2144515111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2083C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2083D61
hypocenterC61#7788
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
2. #21447376C2semidirect
4. #21443642C2semidirect
5. #21443641C2semidirect
7. C61×#2083C2semidirect
182. #2083D61semidirect
214. C61#7788semidirect

Maximal subgroups

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

subgroupindex
#214527482
#214473762
#214472232
#214436422
#214436412
#214436392
C61×#20832
#778861