Finite Group Databasebeta

← #30599376

Subgroups — #30599376

Order 15616.

530 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461679C211yesmaximal, characteristic
2#21461054C211yesmaximal, characteristic
3#21460693C212yesmaximal, complemented
4#21460681C212yesmaximal, complemented
5#21448723C211yesmaximal, characteristic
6C2×#14519835—21no—
7D61⋊(C22⋊C8)C2212yes—
8#16840704C2212yes—
9#16840640—21no—
10#16840608—21no—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13C2×#14519737—21no—
14#16839657—21no—
15#16839634—21no—
16#16839633—21no—
17#16839626C411yescharacteristic, complemented
18#16839621C2211yescharacteristic
19#16839613C411yescharacteristic, complemented
20C2×#14519684C411yescharacteristic, complemented
21#95×D61C2211yescharacteristic
22C61×#380C411yescharacteristic, complemented
23C2×D61⋊C8—22no—
24C2×C4⋊#6923—22no—
25C2×C22⋊#6923—22no—
26#14519835—42no—
27#14519834—22no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—22no—
30C22×C22⋊D61D411yescharacteristic
31C23×Dic61—21no—
32C22×C4×D61—21no—
33C22×C4×D61C2311yescharacteristic
34C4×C22⋊D61—22no—
35C4×C22⋊D61—22no—
36#14519737—42no—
37#14519737—42no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51#14519684C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55#95×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C23×D61C2×D411yescharacteristic
59C22×#6923—42no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—81no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C2×C22⋊D61—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61D812yes—
70C2×C22⋊D61SD1612yes—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—42no—
74C22×Dic61—42no—
75C22×Dic61—81no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C2×C4×D61—42no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—81no—
83C2×C4×D61—81no—
84C2×C4×D61#4112yes—
85C2×C4×D61#4112yes—
86C22⋊#6923—42no—
87C22⋊#6923—42no—
88C2×#92420—42no—
89C4⋊#6923—82no—
90D61⋊C8—82no—
91C4⋊C4×C61—81no—
92C22⋊C4×C61—42no—
93C22⋊Dic61—22no—
94#11758198—22no—
95#11758198—41no—
96#11758198—41no—
97#11758196—22no—
98#11758196—42no—
99#11758196—42no—
100#11758196—81no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—42no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61#10212yes—
109C23×C61C2×C22⋊C411yescharacteristic
110C22×D61—41no—
111C22×D61—41no—
112C22×D61#12312yes—
113C22×D61C2×D811yescharacteristic
114C22×D61C2×SD1611yescharacteristic
115C22×D61#13712yes—
116C2×#6923—82no—
117C2×#6923—82no—
118C2×#6923—82no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
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—81no—
129C2×C4×C61—81no—
130C2×C4×C61#11711yescharacteristic
131C2×C4×C61#11711yescharacteristic
132C22⋊D61—24no—
133C22⋊D61—24no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—22no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—84no—
146C2×Dic61#10212yes—
147C2×Dic61#12312yes—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—82no—
151C4×D61—82no—
152#92420—82no—
153#8760—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61#38111yescharacteristic
162C22×C61C2×#10211yescharacteristic
163C22×C61#41911yescharacteristic
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—42no—
169C2×D61#48012yes—
170C2×D61#48312yes—
171#6923—162no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—81no—
176C4×C61—81no—
177Dic61—22no—
178Dic61—22no—
179Dic61—42no—
180Dic61—41no—
181Dic61—81no—
182#2349—611no—
183#1799—611no—
184#1459—611no—
185#1294—612no—
186#1289—612no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61#182311yescharacteristic
191C2×C61#182711yescharacteristic
192C2×C61#182811yescharacteristic
193D61—22no—
194D61—22no—
195C2×C4×D4—611no—
196C2×C4×D4—1221no—
197C2×#99—1221no—
198C2×C22⋊C8—612no—
199#389—1221no—
200#385—1221no—
201#385—1221no—
202#382—611no—
203#380—611no—
204#380—612no—
205#380#692311yescharacteristic, complemented
206C4×C4⋊C4—611no—
207C2×#95—611no—
208C2×#95—611no—
209#342—1221no—
210#324—1221no—
211#323—1221no—
212C61#876011yescharacteristic, complemented, Sylow
213C22×D4—611no—
214C23×C4—611no—
215C23×C4—1221no—
216C23×C4—1221no—
217C23×C4C2×#692311yescharacteristic
218C22×C8—1222no—
219C4×D4—1222no—
220C4×D4—1222no—
221C4×D4—2442no—
222C4×D4—2442no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1222no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1222no—
234C2×C42—611no—
235C2×C42—1221no—
236#99—2442no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239#95—611no—
240#95—611no—
241#95—1221no—
242#95—1221no—
243#95—1222no—
244#95—1221no—
245#95C2×#692311yescharacteristic
246#95C2×#692311yescharacteristic
247C24—611no—
248C24C22⋊#692311yescharacteristic
249C2×D4—612no—
250C2×D4—612no—
251C2×D4—1222no—
252C2×D4—1222no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—81no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—612no—
261C22×C4—612no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—4881no—
266C22×C4—4881no—
267C22×C4—4881no—
268C22×C4—2442no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4—2442no—
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22×#692311yescharacteristic
276C2×C8—4882no—
277C2×C8—2442no—
278C4⋊C4—81no—
279C4⋊C4—1222no—
280C4⋊C4—4881no—
281C4⋊C4—4882no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C22⋊C4—42no—
285C22⋊C4—1222no—
286C22⋊C4—1222no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C42—1221no—
292C42—1221no—
293C42—2442no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—612no—
299C23—611no—
300C23—611no—
301C23—612no—
302C23—2441no—
303C23—2441no—
304C23#1451983912yes—
305C23C2×C22⋊#692311yescharacteristic
306D4—1224no—
307D4—1224no—
308C2×C4—21no—
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—81no—
318C2×C4—81no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1222no—
324C2×C4—1221no—
325C2×C4—4882no—
326C2×C4—4882no—
327C2×C4—4882no—
328C2×C4—4882no—
329C2×C4—4882no—
330C2×C4—4884no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451985611yescharacteristic
341C2×C4#1451985611yescharacteristic
342C8—4882no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—612no—
351C22—612no—
352C22—1222no—
353C22—1222no—
354C22—2441no—
355C22—2441no—
356C22—2442no—
357C22#1684070511yescharacteristic
358C22C2×#1451983911yescharacteristic
359C22#1684075511yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—1222no—
366C4—1222no—
367C4—9762no—
368C4—4881no—
369C4—2442no—
370C4—2441no—
371C2—21no—
372C2—21no—
373C2—42no—
374C2—1222no—
375C2—1222no—
376C2#2146172211yescharacteristic
377C2#2146172911yescharacteristic
378C2#2146173011yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC22×C4×D61C23
hypercenter#380#6923
hypocenterC61#8760
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460693C2semidirect
4. #21460681C2semidirect
17. #16839626C4semidirect
19. #16839613C4semidirect
20. C2×#14519684C4semidirect
22. C61×#380C4semidirect
205. #380#6923semidirect
212. C61#8760semidirect

Maximal subgroups

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

subgroupindex
#214616792
#214610542
#214606932
#214606812
#214487232
#876061