Finite Group Databasebeta

← #29577307

Subgroups — #29577307

Order 15616.

424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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#21457025C211yesmaximal, characteristic
2#21446762C211yesmaximal, characteristic
3#21444421C211yesmaximal, characteristic
4#21444369C211yesmaximal, characteristic
5#21443683C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic
7C61×#2336C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840172C412yescomplemented
10#16840132C412yescomplemented
11#16840097—21no—
12#16840092—21no—
13#16840066—22no—
14#16839819C2211yescharacteristic
15#16839819C2211yescharacteristic
16C4×#11758194C2211yescharacteristic
17#16839522—21no—
18#16839522—21no—
19#16839504—22no—
20#16839498—21no—
21#16839498—21no—
22C2×#125×C61C2211yescharacteristic
23C61×#389—21no—
24C61×#387—21no—
25C61×#387—21no—
26C61×#387—21no—
27C61×#387—21no—
28C61×#383C2211yescharacteristic
29C4×C4⋊C4×C61—21no—
30C4×C4⋊C4×C61C2211yescharacteristic
31C2×#11758194—21no—
32#14519777C2×C411yescharacteristic
33#14519777C2×C411yescharacteristic
34#14519769—21no—
35#14519756—21no—
36#14519756—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39#14519736—21no—
40#14519710—22no—
41#14519708—22no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44#14519700—22no—
45#14519700—22no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519688—21no—
49#14519688—21no—
50#14519688C2×C412yes—
51C4×#92418—21no—
52#125×C61—21no—
53#125×C61—21no—
54#125×C61C2×C412yes—
55#125×C61D412yes—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61—21no—
65C2×C42×C61D411yescharacteristic
66C2×C42×C61D411yescharacteristic
67C2×C42×C61C2311yescharacteristic
68#95×C61—21no—
69#95×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72#95×C61—21no—
73#95×C61—21no—
74#95×C61—21no—
75#95×C61D411yescharacteristic
76#95×C61D411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C2×Dic122—21no—
87C2×Dic122—21no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—42no—
95C4⋊C4×C61—42no—
96C4⋊C4×C61—81no—
97C4⋊C4×C61C22⋊C412yes—
98C4⋊C4×C61C22⋊C412yes—
99C42×C61—42no—
100C42×C61—41no—
101C42×C61—41no—
102C42×C61—81no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107C22⋊Dic61—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—41no—
115#11758194—22no—
116#11758194—41no—
117C2×#92418—22no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61#12011yescharacteristic
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
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—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×Dic61—41no—
150C2×Dic61—41no—
151Dic122—42no—
152Dic122—81no—
153#92418—42no—
154#92418—42no—
155#92418—81no—
156#9380—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#38611yescharacteristic
160C22×C61#45511yescharacteristic
161C22×C61#45611yescharacteristic
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—42no—
169C4×C61—42no—
170C4×C61—42no—
171C4×C61—81no—
172C4×C61—81no—
173C4×C61—81no—
174Dic61—81no—
175Dic61—81no—
176#3236—611no—
177#2336D6111yescharacteristic
178#1986—611no—
179#1528—611no—
180#1515—611no—
181#1288—611no—
182#1285—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#188211yescharacteristic
186C2×C61#190611yescharacteristic
187C2×C61#191211yescharacteristic
188#533—611no—
189C2×#125C2×D6111yescharacteristic
190#501—612no—
191#491—612no—
192#484—1221no—
193#483—1221no—
194#479—1222no—
195#432—611no—
196#432—611no—
197C4×M16—611no—
198#389—21no—
199#387—21no—
200#387—21no—
201#387—21no—
202#387—21no—
203#383C2×D6111yescharacteristic
204C4×C4⋊C4—21no—
205C4×C4⋊C4C2×D6111yescharacteristic
206#339—1221no—
207#339—1221no—
208#330—1222no—
209#328—1221no—
210#328—1221no—
211C61#938011yescharacteristic, complemented, Sylow
212C2×M16—1221no—
213C4⋊Q8—611no—
214C4⋊Q8—611no—
215#125—21no—
216#125—21no—
217#125—1221no—
218#125C4×D6112yes—
219#125D24412yes—
220C22⋊Q8—1221no—
221C22⋊Q8—1221no—
222C4×Q8—1221no—
223C4×Q8—1221no—
224#117—1221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D6111yescharacteristic
231C2×C4⋊C4C22⋊D6111yescharacteristic
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C22⋊D6111yescharacteristic
235C2×C42C22⋊D6111yescharacteristic
236C2×C42C22×D6111yescharacteristic
237#107—1222no—
238#106—1222no—
239C4⋊C8—1221no—
240C4⋊C8—1221no—
241#103—1222no—
242#103—1222no—
243C22⋊C8—1221no—
244C22⋊C8—1221no—
245#97—612no—
246#97—1221no—
247#97—1221no—
248C4×C8—1221no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95C22⋊D6111yescharacteristic
257#95C22⋊D6111yescharacteristic
258C2×Q8—1221no—
259C2×Q8—1221no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4C2×C22⋊D6111yescharacteristic
267C22×C4C2×C22⋊D6111yescharacteristic
268C22×C4C2×C22⋊D6111yescharacteristic
269M16—1222no—
270M16—2441no—
271C2×C8—1222no—
272C2×C8—2441no—
273C2×C8—2441no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—81no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4#1175819812yes—
290C4⋊C4#1175819812yes—
291C22⋊C4—2441no—
292C42—41no—
293C42—41no—
294C42—42no—
295C42—81no—
296C42—2441no—
297C42C2×C4×D6111yescharacteristic
298C42C2×D24411yescharacteristic
299C42#1175822211yescharacteristic
300C42#1175822211yescharacteristic
301C23#1451974611yescharacteristic
302Q8—4881no—
303Q8—2442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4C2×#1175819811yescharacteristic
329C2×C4C4×C22⋊D6111yescharacteristic
330C2×C4C4×C22⋊D6111yescharacteristic
331C2×C4#1451975111yescharacteristic
332C2×C4#1451975111yescharacteristic
333C2×C4#1451976011yescharacteristic
334C8—4881no—
335C8—2442no—
336C8—2442no—
337C22—21no—
338C22—21no—
339C22#1683964111yescharacteristic
340C22#1683994011yescharacteristic
341C22#1683994511yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—42no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—4881no—
355C4—4881no—
356C2—21no—
357C2—21no—
358C2#2144618811yescharacteristic
359C2#2144632011yescharacteristic
360C2#2144635611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2336C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#2336D61
hypocenterC61#9380
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2336

Complements

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

NH ≅ G/Ntype
9. #16840172C4semidirect
10. #16840132C4semidirect
211. C61#9380semidirect

Maximal subgroups

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

subgroupindex
#214570252
#214467622
#214444212
#214443692
#214436832
#214436752
C61×#23362
#938061