Finite Group Databasebeta

← #29576934

Subgroups — #29576934

Order 15616.

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

normal subgroups only

This group has 492 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#21455918C211yesmaximal, characteristic
2#21448462C211yesmaximal, characteristic
3#21446763C211yesmaximal, characteristic, complemented
4#21444332C211yesmaximal, characteristic, complemented
5#21443713C211yesmaximal, characteristic, complemented
6#21443674C211yesmaximal, characteristic, complemented
7C61×#1490C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840097—21no—
10#16840042C412yescomplemented
11#16839967C412yescomplemented
12#16839913—21no—
13#16839862—22no—
14#16839819C2211yescharacteristic
15#16839665—21no—
16#16839661—21no—
17#16839655—22no—
18#16839625—21no—
19#16839622—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839608C2211yescharacteristic
22#16839523—22no—
23#16839500—21no—
24#16839500—21no—
25C2×C4×D4×C61C2211yescharacteristic
26C61×#432C2211yescharacteristic
27C4×M16×C61C2211yescharacteristic
28C61×D4⋊C8—22no—
29C2×#11758200—22no—
30#14519777C2×C411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519769—21no—
33#14519756—21no—
34#14519756—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37#14519736—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—22no—
40C2×C22⋊Dic61—22no—
41C2×C22⋊Dic61—22no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61D412yes—
44#14519710—22no—
45C4⋊#92418C2×C412yes—
46#14519700—22no—
47#14519698—22no—
48C22⋊#92418—21no—
49#14519688—21no—
50#14519684—22no—
51#14519684—21no—
52#14519684—21no—
53#14519684D411yescharacteristic
54#14519684D411yescharacteristic
55C22×D4×C61D411yescharacteristic
56C23×C4×C61—21no—
57C2×M16×C61—21no—
58C4×D4×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61C2×C412yes—
61C4×D4×C61D412yes—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C22⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#97×C61—21no—
68#97×C61—21no—
69C4×C8×C61—21no—
70C24×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—42no—
73C2×D4×C61C22⋊C412yes—
74C22×C4×C61—21no—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—82no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—21no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86M16×C61—22no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61C22⋊C412yes—
92C22⋊C4×C61—22no—
93C22⋊C4×C61—22no—
94C42×C61C22×C411yescharacteristic
95C42×C61C2×D411yescharacteristic
96C42×C61#4111yescharacteristic
97C42×C61#4111yescharacteristic
98C22⋊Dic61—41no—
99C22⋊Dic61—82no—
100C22⋊Dic61—82no—
101#11758200—44no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—42no—
107C4⋊Dic61—82no—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—42no—
111C4×Dic61—41no—
112C4×Dic61—42no—
113C2×#92418—22no—
114C23×C61—22no—
115C23×C61—42no—
116C23×C61—42no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61#12011yescharacteristic
120D4×C61—22no—
121D4×C61—22no—
122D4×C61—42no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—82no—
130C2×C4×C61—82no—
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148Dic122—42no—
149Dic122—81no—
150C8×C61—42no—
151C8×C61—81no—
152#92418—42no—
153#9327—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—42no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—82no—
160C22×C61—82no—
161C22×C61#38611yescharacteristic
162C22×C61#45511yescharacteristic
163C22×C61#45611yescharacteristic
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—42no—
170C4×C61#42112yes—
171Dic61—81no—
172Dic61—82no—
173Dic61—81no—
174Dic61—81no—
175Dic61—81no—
176#3110—611no—
177#2319—611no—
178#1986—611no—
179#1506—611no—
180#1490D6111yescharacteristic
181#1300—611no—
182#1285—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—82no—
186C2×C61#188211yescharacteristic
187C2×C61#189711yescharacteristic
188C2×C61#190411yescharacteristic
189#533—611no—
190C2×C4×D4C2×D6111yescharacteristic
191#484—1221no—
192#474—612no—
193#461—612no—
194#450—1221no—
195#440—1222no—
196#432—611no—
197#432C2×D6111yescharacteristic
198C4×M16C2×D6111yescharacteristic
199#390—1221no—
200#389—1221no—
201#388—1222no—
202#381—1221no—
203#380—1221no—
204C4×C4⋊C4—611no—
205#376—611no—
206#339—1222no—
207#328—1221no—
208#328—1221no—
209D4⋊C8—22no—
210C61#932711yescharacteristic, complemented, Sylow
211C22×D4D24411yescharacteristic
212C23×C4—21no—
213C2×SD16—1222no—
214C2×M16—21no—
215C4⋊Q8—611no—
216C4⋊Q8—611no—
217#125—1221no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220C4×Q8—1221no—
221C4×Q8—1221no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4C4×D6112yes—
225C4×D4C22⋊D6112yes—
226#117—1221no—
227C2×C4⋊C4—1222no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4D24411yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—1222no—
232C2×C22⋊C4—1222no—
233C2×C42—612no—
234C2×C42—1221no—
235C2×C42C22×D6111yescharacteristic
236#107—1222no—
237C4⋊C8—21no—
238C4⋊C8—612no—
239#103—1222no—
240#102—1222no—
241C22⋊C8—21no—
242C22⋊C8—1221no—
243#97—21no—
244#97—21no—
245#97—1221no—
246C4×C8—21no—
247#95—611no—
248#95—611no—
249#95—1222no—
250#95—1221no—
251#95—1221no—
252C24—21no—
253C2×Q8—1221no—
254C2×Q8—1221no—
255C2×D4—21no—
256C2×D4—42no—
257C2×D4#1175819812yes—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—82no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1222no—
265C22×C4C2×D24411yescharacteristic
266C22×C4D4×D6111yescharacteristic
267C22×C4D4×D6111yescharacteristic
268SD16—2444no—
269M16—22no—
270M16—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—1222no—
274C4⋊C4—21no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—4882no—
280C4⋊C4—2442no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4#1175819812yes—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—4882no—
287C22⋊C4—4882no—
288C22⋊C4—2441no—
289C42—2442no—
290C42—2442no—
291C42—2441no—
292C42C2×C4×D6111yescharacteristic
293C42#1175822411yescharacteristic
294C42#1175822411yescharacteristic
295C42C2×C22⋊D6111yescharacteristic
296C23—22no—
297C23—42no—
298C23—42no—
299C23—41no—
300C23—41no—
301C23#1451974711yescharacteristic
302Q8—4881no—
303Q8—2442no—
304D4—22no—
305D4—22no—
306D4—42no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2442no—
319C2×C4—2441no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4C2×#1175819811yescharacteristic
327C2×C4#1451973711yescharacteristic
328C2×C4#1451973711yescharacteristic
329C2×C4#1451974911yescharacteristic
330C2×C4#1451974911yescharacteristic
331C2×C4#1451976111yescharacteristic
332C8—42no—
333C8—81no—
334C8—2442no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—82no—
342C22#1683963911yescharacteristic
343C22#1683994111yescharacteristic
344C22#1683994611yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—4881no—
352C4—4882no—
353C4—4881no—
354C4—4881no—
355C4—4881no—
356C4#1683977812yes—
357C2—21no—
358C2—21no—
359C2—82no—
360C2#2144618611yescharacteristic
361C2#2144626511yescharacteristic
362C2#2144630411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1490C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#1490D61
hypocenterC61#9327
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
3. #21446763C2semidirect
4. #21444332C2semidirect
5. #21443713C2semidirect
6. #21443674C2semidirect
10. #16840042C4semidirect
11. #16839967C4semidirect
210. C61#9327semidirect

Maximal subgroups

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

subgroupindex
#214559182
#214484622
#214467632
#214443322
#214437132
#214436742
C61×#14902
#932761