Finite Group Databasebeta

← #30599394

Subgroups — #30599394

Order 15616.

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

normal subgroups only

This group has 498 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#21461683C211yesmaximal, characteristic
2#21461058C211yesmaximal, characteristic
3#21460717C212yesmaximal, complemented
4#21460672C212yesmaximal, complemented
5#21448723C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519837—21no—
9#16840642—21no—
10#16840606—21no—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13C2×#14519737—21no—
14#16839657—21no—
15#16839634—21no—
16#16839633—21no—
17#16839626C2211yescharacteristic
18#16839621C411yescharacteristic
19#16839613C2211yescharacteristic
20C2×#14519684C411yescharacteristic
21#95×D61C411yescharacteristic
22C61×#380C411yescharacteristic
23C2×#11758217—22no—
24#14519844—22no—
25#14519844—22no—
26C4⋊#92420—22no—
27#14519837—42no—
28C22⋊#92420—22no—
29C4×#92420—22no—
30C22×C22⋊D61D411yescharacteristic
31C23×Dic61—21no—
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C4×C22⋊D61—22no—
35C4×C22⋊D61—22no—
36#14519737—44no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61D411yescharacteristic
42C2×#11758198—21no—
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—81no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C2×C22⋊D61—22no—
66C2×C22⋊D61—22no—
67C2×C22⋊D61SD1612yes—
68C2×C22⋊D61Q1612yes—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61—81no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—81no—
82C2×C4×D61—81no—
83#11758217—42no—
84#11758217—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊C4×C61—81no—
88C22⋊C4×C61—42no—
89C22⋊Dic61—22no—
90#11758198—22no—
91#11758198—42no—
92#11758196—22no—
93#11758196—42no—
94#11758196—42no—
95#11758196—81no—
96C4×Dic61—42no—
97C4×Dic61#4112yes—
98C4×Dic61#4112yes—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61#10312yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61#10312yes—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—81no—
120C2×C4×C61—81no—
121C2×C4×C61#11711yescharacteristic
122C2×C4×C61#11711yescharacteristic
123C22⋊D61—24no—
124C22⋊D61—24no—
125C2×Dic61—22no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—84no—
135C2×Dic61#12312yes—
136C2×Dic61#12312yes—
137C2×Dic61C2×SD1611yescharacteristic
138C2×Dic61C2×Q1611yescharacteristic
139C2×Dic61AGL(1,ℤ/8)12yes—
140C4×D61—81no—
141C4×D61—81no—
142C4×D61—84no—
143#92420—82no—
144#92420—82no—
145#8765—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—22no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61#38111yescharacteristic
154C22×C61C2×#10311yescharacteristic
155C22×C61#41811yescharacteristic
156C2×D61—22no—
157C2×D61—42no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—42no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—81no—
165C4×C61—81no—
166Dic61—22no—
167Dic61—42no—
168Dic61—41no—
169Dic61—81no—
170Dic61#48112yes—
171Dic61#48412yes—
172#2349—611no—
173#1800—611no—
174#1460—611no—
175#1303—612no—
176#1286—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—42no—
180C2×C61#182411yescharacteristic
181C2×C61#182711yescharacteristic
182C2×C61#182911yescharacteristic
183D61—42no—
184C2×C4×D4—611no—
185C2×C4×D4—1221no—
186#431—612no—
187#423—612no—
188C2×#100—1221no—
189#389—1221no—
190#385—1221no—
191#385—1221no—
192#382—611no—
193#380—611no—
194#380#692311yescharacteristic
195C4×C4⋊C4—611no—
196C2×#95—611no—
197C2×#95—611no—
198#343—1221no—
199#323—1221no—
200#323—1221no—
201C61#876511yescharacteristic, complemented, Sylow
202C22×D4—611no—
203C23×C4—611no—
204C23×C4—1221no—
205C23×C4—1221no—
206C23×C4C2×#692311yescharacteristic
207C2×M16—1222no—
208C4×D4—1222no—
209C4×D4—1222no—
210C4×D4—2444no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—611no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—1221no—
222C4⋊C8—1222no—
223C4⋊C8—1222no—
224C4⋊C8—1222no—
225#100—2442no—
226C22⋊C8—1222no—
227C4×C8—1222no—
228#95—611no—
229#95—611no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95C2×#692311yescharacteristic
234#95C2×#692311yescharacteristic
235C24—611no—
236C24C22⋊#692311yescharacteristic
237C2×D4—612no—
238C2×D4—612no—
239C2×D4—1222no—
240C2×D4—1222no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—81no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—4881no—
254C22×C4—4881no—
255C22×C4—4881no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4—2442no—
259C22×C4—2442no—
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22×#692311yescharacteristic
262M16—2442no—
263M16—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C4⋊C4—81no—
267C4⋊C4—1222no—
268C4⋊C4—4881no—
269C4⋊C4—2442no—
270C4⋊C4—2442no—
271C22⋊C4—42no—
272C22⋊C4—1222no—
273C22⋊C4—1222no—
274C22⋊C4—2442no—
275C42—612no—
276C42—612no—
277C42—2442no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—612no—
283C23—1221no—
284C23—1221no—
285C23—2441no—
286C23—2441no—
287C23#1451984012yes—
288C23C2×C22⋊#692311yescharacteristic
289D4—1224no—
290D4—1224no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—612no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—612no—
307C2×C4—1222no—
308C2×C4—1221no—
309C2×C4—4881no—
310C2×C4—4881no—
311C2×C4—4884no—
312C2×C4—4884no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451985611yescharacteristic
321C2×C4#1451985611yescharacteristic
322C8—4882no—
323C8—4882no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—42no—
328C22—42no—
329C22—41no—
330C22—41no—
331C22—1222no—
332C22—2442no—
333C22—2442no—
334C22—2441no—
335C22—2441no—
336C22#1684070511yescharacteristic
337C22C2×#1451984011yescharacteristic
338C22#1684075411yescharacteristic
339C4—21no—
340C4—21no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—612no—
345C4—612no—
346C4—1222no—
347C4—4881no—
348C4—2442no—
349C4—2441no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—2442no—
354C2#2146172311yescharacteristic
355C2#2146172911yescharacteristic
356C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#8765
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. #21460717C2semidirect
4. #21460672C2semidirect
201. C61#8765semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214610582
#214607172
#214606722
#214487232
#876561