Finite Group Databasebeta

← #30601204

Subgroups — #30601204

Order 15616.

542 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 94 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#21462714C211yesmaximal, characteristic, complemented
2#21461686C211yesmaximal, characteristic, complemented
3#21461146C212yesmaximal
4#21460672C212yesmaximal, complemented
5#21450725C211yesmaximal, characteristic
6#16840811—24no—
7#16840779—21no—
8#16840779C2212yes—
9#16840778—21no—
10#16840765C2212yes—
11C2×#14519838—21no—
12#16840642—21no—
13#16840610—24no—
14C2×#14519755—21no—
15C2×#14519742C2211yescharacteristic
16C2×#14519739C2211yescharacteristic
17#16839693C411yescharacteristic
18#16839680C411yescharacteristic
19#16839679C411yescharacteristic
20#16839652—21no—
21#16839651—21no—
22#16839626C2211yescharacteristic
23#16839621—21no—
24C61×#398C411yescharacteristic
25C2×#11758217—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844—22no—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31#14519838—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C4×#92420—22no—
35C4×#92420D414yes—
36C22×Dic122D411yescharacteristic
37C22×D244C2×C411yescharacteristic
38C22×C4×D61—21no—
39#14519755—42no—
40#14519755—42no—
41#14519742—22no—
42#14519742—22no—
43#14519739—22no—
44#14519739—22no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196C2×C411yescharacteristic
48C2×#11758196D411yescharacteristic
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61C2311yescharacteristic
57#14519684—21no—
58#14519684—21no—
59#14519684C2×C411yescharacteristic
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63#95×C61—21no—
64#95×C61C2×C411yescharacteristic
65C23×D61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×D244—22no—
77C2×D244—42no—
78C2×C4×D61—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—42no—
82C2×Dic122—22no—
83C2×Dic122—22no—
84C2×Dic122D812yes—
85C2×Dic122SD1612yes—
86#11758217—42no—
87#11758217—42no—
88C2×#92420—24no—
89C2×#92420—42no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—42no—
93#11758198—42no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—41no—
98#11758198—41no—
99#11758196—22no—
100#11758196—22no—
101#11758196—42no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61C2×D412yes—
109C4×Dic61#4112yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—22no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
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—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#10212yes—
130C2×C4×C61C4×D412yes—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#10212yes—
140C2×Dic61#12011yescharacteristic
141C2×Dic61#12112yes—
142C2×Dic61#12311yescharacteristic
143C2×Dic61C2×D811yescharacteristic
144C2×Dic61C2×SD1611yescharacteristic
145C2×Dic61#13512yes—
146D244—24no—
147D244—42no—
148C4×D61—82no—
149C4×D61—82no—
150Dic122—24no—
151Dic122—24no—
152#92420—44no—
153#92420—82no—
154#9486—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61#38611yescharacteristic
158C22×C61C2×#10211yescharacteristic
159C22×C61#41611yescharacteristic
160C2×D61—42no—
161C2×D61—42no—
162C2×D61—42no—
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—22no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—81no—
177Dic61#46512yes—
178Dic61#46612yes—
179#2982—611no—
180#2536—611no—
181#1801—611no—
182#1486—612no—
183#1286—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#189111yescharacteristic
187C2×C61#189311yescharacteristic
188C2×C61#191211yescharacteristic
189D61—82no—
190C2×C22⋊Q8—1221no—
191C2×C4×Q8—611no—
192C2×C4×D4—611no—
193C8×Q8—1224no—
194#431—612no—
195#431—1221no—
196#431—1221no—
197#423—612no—
198C2×#101—1221no—
199#398—611no—
200#398#692311yescharacteristic
201#394—611no—
202#394—611no—
203#388—1221no—
204#388—1221no—
205#382—611no—
206#380—1221no—
207#343—1221no—
208D4⋊C8—1224no—
209C61#948611yescharacteristic, complemented, Sylow
210C22×Q8—611no—
211C22×D4—611no—
212C23×C4—1221no—
213C2×M16—1222no—
214C22⋊Q8—2442no—
215C22⋊Q8—2442no—
216C4×Q8—1222no—
217C4×Q8—1222no—
218C4×D4—1222no—
219C4×D4—1222no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4C2×#692311yescharacteristic
226C2×C4⋊C4C2×#692311yescharacteristic
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C4⋊C8—1222no—
236C4⋊C8—1222no—
237C4⋊C8—1222no—
238C4⋊C8—1222no—
239C4⋊C8—1222no—
240#101—2442no—
241C22⋊C8—1222no—
242C4×C8—614no—
243C4×C8—1222no—
244C4×C8—1222no—
245#95—21no—
246#95—611no—
247#95—1221no—
248#95—1221no—
249#95C2×#692311yescharacteristic
250C24—1221no—
251C2×Q8—612no—
252C2×Q8—612no—
253C2×Q8—1222no—
254C2×Q8—1222no—
255C2×D4—1222no—
256C2×D4—2442no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—2442no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2442no—
268C22×C4C22⋊#692311yescharacteristic
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271M16—2442no—
272M16—2442no—
273C2×C8—1224no—
274C2×C8—2442no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—1222no—
279C4⋊C4—1222no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C42—612no—
290C42—612no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C23—1222no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23C2×C22⋊#692311yescharacteristic
303Q8—1224no—
304Q8—1224no—
305D4—1224no—
306D4—2442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
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—612no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—612no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—612no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—4882no—
329C2×C4—4882no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4#1451983912yes—
336C2×C4D4×#692312yes—
337C8—4882no—
338C8—2444no—
339C22—21no—
340C22—21no—
341C22—4881no—
342C22—4881no—
343C22—4881no—
344C22—4881no—
345C22—2442no—
346C22—2442no—
347C22—2442no—
348C22#1684071011yescharacteristic
349C22C2×#1451983911yescharacteristic
350C22#1684075211yescharacteristic
351C4—22no—
352C4—22no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—612no—
357C4—612no—
358C4—1222no—
359C4—1221no—
360C4—1221no—
361C4—4881no—
362C4—2441no—
363C2—21no—
364C2—21no—
365C2—4882no—
366C2#2146183111yescharacteristic
367C2#2146183311yescharacteristic
368C2#2146186611yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#398#6923
hypocenterC61#9486
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #21462714C2semidirect
2. #21461686C2semidirect
4. #21460672C2semidirect
209. C61#9486semidirect

Maximal subgroups

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

subgroupindex
#214627142
#214616862
#214611462
#214606722
#214507252
#948661