Finite Group Databasebeta

← #29575999

Subgroups — #29575999

Order 15616.

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

normal subgroups only

This group has 478 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#21454904C211yesmaximal, characteristic, complemented
2#21451679C211yesmaximal, characteristic
3#21444416C212yesmaximal
4#21443684C212yesmaximal, complemented
5C4×#101×C61C211yesmaximal, characteristic, complemented
6C2×#14519765C2211yescharacteristic
7#16839893—24no—
8#16839819—21no—
9#16839819C2212yes—
10#16839815—21no—
11#16839697—21no—
12#16839682C411yescharacteristic
13#16839682C411yescharacteristic
14#16839679C411yescharacteristic
15#16839679C411yescharacteristic
16#16839673—21no—
17#16839653—21no—
18#16839653—21no—
19#16839630C2211yescharacteristic
20#16839501—24no—
21C2×C4×Q8×C61C2211yescharacteristic
22C2×#101×C61—21no—
23C4×M16×C61C2212yes—
24C61×#343—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27#14519765—22no—
28#14519765—22no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758198—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C4⋊#92418—22no—
38C4⋊#92418—22no—
39C4⋊#92418—22no—
40C22⋊#92418—22no—
41#14519688—22no—
42#14519688D414yes—
43C4×#92418—22no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×Q8×C61D411yescharacteristic
51C2×M16×C61—22no—
52C4×Q8×C61—22no—
53C4×Q8×C61—22no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#101×C61—24no—
61#97×C61—22no—
62C4×C8×C61—22no—
63C23×D61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×D244—22no—
78C2×D244—81no—
79C2×Dic122—22no—
80C2×Dic122—81no—
81M16×C61—24no—
82M16×C61—42no—
83C2×C8×C61—42no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—22no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61C2×D412yes—
92C42×C61#4112yes—
93#11758198—42no—
94#11758198—42no—
95#11758198—41no—
96#11758198—42no—
97#11758198—41no—
98#11758198—81no—
99#11758198—81no—
100#11758196—81no—
101#11758196—81no—
102C2×#92418—24no—
103C23×C61C2×C22⋊C411yescharacteristic
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111Q8×C61—44no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#10412yes—
126C2×C4×C61C4×D412yes—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61#12112yes—
129C2×C4×C61#12311yescharacteristic
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139D244—82no—
140Dic122—82no—
141C8×C61—44no—
142#92418—44no—
143#9188—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61#38611yescharacteristic
147C22×C61C2×#10411yescharacteristic
148C22×C61#42111yescharacteristic
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—81no—
155C2×D61—81no—
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—22no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167#2983—611no—
168#2632—611no—
169C4×#101D6111yescharacteristic, complemented
170#1527—612no—
171#1288—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61#187111yescharacteristic
175C2×C61#191211yescharacteristic
176C2×C61#191411yescharacteristic
177D61—161no—
178C2×#124—611no—
179C2×C4×Q8C2×D6111yescharacteristic
180#446—1224no—
181#432—612no—
182#432—1221no—
183#431—1221no—
184C2×#101—21no—
185C4×M16C2×D6112yes—
186#399—1221no—
187#395—611no—
188#395—611no—
189#394—611no—
190#394—611no—
191#393—1221no—
192#388—1221no—
193#388—1221no—
194#383—611no—
195#343—21no—
196#329—1224no—
197C61#918811yescharacteristic, complemented, Sylow
198C22×Q8—611no—
199C22×Q8C22⋊D6111yescharacteristic
200C22×D4—611no—
201C2×M16—22no—
202#124—1222no—
203#124—1222no—
204C4×Q8—22no—
205C4×Q8—22no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4C4×D6111yescharacteristic
209C2×C4⋊C4C4×D6111yescharacteristic
210C2×C4⋊C4C22⋊D6111yescharacteristic
211C2×C22⋊C4—1221no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C42D24411yescharacteristic
218C2×C42D24411yescharacteristic
219C2×C42C22×D6111yescharacteristic
220C4⋊C8—1222no—
221C4⋊C8—1222no—
222C4⋊C8—1222no—
223#101—24no—
224C22⋊C8—1222no—
225#97—22no—
226#97—614no—
227#97—1222no—
228C4×C8—22no—
229C4×C8—1222no—
230#95—611no—
231#95—611no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236C24—1221no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—1222no—
241C2×Q8—4881no—
242C2×D4—1222no—
243C2×D4—4881no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4#1175819811yescharacteristic
251C22×C4C2×C4×D6111yescharacteristic
252C22×C4C2×D24411yescharacteristic
253C22×C4C2×C22⋊D6111yescharacteristic
254M16—24no—
255M16—42no—
256C2×C8—42no—
257C2×C8—1224no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—4881no—
262C4⋊C4—4881no—
263C22⋊C4—4881no—
264C22⋊C4—4881no—
265C22⋊C4—2442no—
266C22⋊C4—2442no—
267C22⋊C4—2441no—
268C22⋊C4—2442no—
269C22⋊C4—2441no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42D4×D6112yes—
275C42#1175822412yes—
276C23—2441no—
277C23—2441no—
278C23—2441no—
279C23—2441no—
280C23—2441no—
281C23—2441no—
282C23—2441no—
283C23C2×#1175819811yescharacteristic
284Q8—44no—
285Q8—4882no—
286D4—4882no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451970512yes—
310C2×C4#1451973712yes—
311C2×C4#1451974711yescharacteristic
312C2×C4#1451974912yes—
313C2×C4#1451976111yescharacteristic
314C8—44no—
315C8—2444no—
316C22—21no—
317C22—21no—
318C22—4881no—
319C22—4881no—
320C22—4881no—
321C22—4881no—
322C22—4881no—
323C22—4881no—
324C22—4881no—
325C22#1683963911yescharacteristic
326C22C2×#1451970511yescharacteristic
327C22#1683978011yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—4881no—
337C4—4881no—
338C4—4881no—
339C2—21no—
340C2—21no—
341C2—9761no—
342C2#2144611911yescharacteristic
343C2#2144635411yescharacteristic
344C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#101×C61C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC4×#101D61
hypocenterC61#9188
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #21454904C2semidirect
4. #21443684C2semidirect
5. C4×#101×C61C2semidirect
169. C4×#101D61semidirect
197. C61#9188semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214516792
#214444162
#214436842
C4×#101×C612
#918861