Finite Group Databasebeta

← #30599240

Subgroups — #30599240

Order 15616.

540 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461673C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460655C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448221C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519733—21no—
13C22×C4×Dic61C2211yescharacteristic
14#16839631C411yescharacteristic
15#16839631C411yescharacteristic
16#16839626—21no—
17#16839622C411yescharacteristic
18#16839620—21no—
19C4⋊C4×Dic61C2211yescharacteristic
20C4⋊C4×Dic61C2211yescharacteristic
21#16839613—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C22⋊#92420—24no—
27C22⋊#92420—42no—
28C4×#92420—24no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519733—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C4×Dic61—24no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53#95×C61—21no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—41no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61SD1612yes—
72C22×Dic61Q1612yes—
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×#92420—24no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83C22⋊C4×C61—42no—
84C22⋊Dic61—42no—
85C4⋊Dic61—22no—
86C4⋊Dic61—22no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90#11758196—42no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—42no—
95C4×Dic61—42no—
96C4×Dic61#4114yes—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61#10312yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—44no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#11712yes—
116C2×C4×C61#13112yes—
117C2×C4×C61#13112yes—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—24no—
125C2×Dic61—24no—
126C2×Dic61—44no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61#10312yes—
134C2×Dic61#10412yes—
135C2×Dic61#12312yes—
136C2×Dic61#12312yes—
137C2×Dic61C2×SD1611yescharacteristic
138C2×Dic61C2×Q1611yescharacteristic
139C2×Dic61AGL(1,ℤ/8)12yes—
140#92420—44no—
141#92420—82no—
142#8710—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61#38111yescharacteristic
151C22×C61#40811yescharacteristic
152C22×C61#40811yescharacteristic
153C22×C61C2×#10311yescharacteristic
154C22×C61#41811yescharacteristic
155C22×C61C2×#10411yescharacteristic
156C22×C61#42111yescharacteristic
157C4×C61—41no—
158C4×C61—81no—
159C4×C61—81no—
160C4×C61#43314yes—
161Dic61—22no—
162Dic61—22no—
163Dic61—22no—
164Dic61—81no—
165Dic61—81no—
166Dic61#48112yes—
167Dic61#48412yes—
168#2285—611no—
169#1797—611no—
170C4×C22⋊C8—611no—
171#1279—612no—
172#1279—612no—
173C2×C61—42no—
174C2×C61#148111yescharacteristic
175C2×C61#148411yescharacteristic
176C2×C61#149311yescharacteristic
177C2×C61#149611yescharacteristic
178C2×C61#181811yescharacteristic
179C2×C61#182411yescharacteristic
180C2×C61#182611yescharacteristic
181C2×#117—1221no—
182C22×C42—611no—
183C2×C4⋊C8—612no—
184C2×C22⋊C8—1221no—
185C2×C22⋊C8—1221no—
186C2×C4×C8—612no—
187#384—611no—
188#384—611no—
189#382—1221no—
190#380—611no—
191#380—1221no—
192#380#692311yescharacteristic
193C4×C4⋊C4—611no—
194C4×C4⋊C4—611no—
195C4×C4⋊C4—1221no—
196#336—1221no—
197#336—1221no—
198C61#871011yescharacteristic, complemented, Sylow
199C23×C4—611no—
200C23×C4—611no—
201C23×C4C2×#692311yescharacteristic
202C22×C8—1222no—
203C22×C8—1222no—
204#117—2444no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C2×#692311yescharacteristic
212C2×C4⋊C4C2×#692311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—1221no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—1224no—
220C2×C42—1221no—
221C2×C42—1221no—
222C4⋊C8—1224no—
223C22⋊C8—1224no—
224C22⋊C8—2442no—
225C4×C8—1224no—
226#95—21no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C24C22⋊#692311yescharacteristic
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—611no—
237C22×C4—612no—
238C22×C4—612no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4—1222no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—2441no—
249C22×C4C22⋊#692311yescharacteristic
250C22×C4C22×#692311yescharacteristic
251C2×C8—1224no—
252C2×C8—2442no—
253C2×C8—2442no—
254C2×C8—2442no—
255C2×C8—2442no—
256C2×C8—2442no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—1222no—
260C4⋊C4—1222no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4—2442no—
264C4⋊C4—2442no—
265C22⋊C4—42no—
266C22⋊C4—2442no—
267C42—614no—
268C42—1222no—
269C42—1222no—
270C42—1222no—
271C42—2442no—
272C42—2442no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#1451984012yes—
280C23C2×C22⋊#692311yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—44no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—612no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—612no—
295C2×C4—612no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—1224no—
299C2×C4—1224no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2444no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4#1451985612yes—
314C2×C4#1451986412yes—
315C2×C4#1451986412yes—
316C8—4882no—
317C8—2444no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22#1684070511yescharacteristic
326C22#1684073511yescharacteristic
327C22#1684073511yescharacteristic
328C22C2×#1451984011yescharacteristic
329C22#1684075411yescharacteristic
330C22D61⋊#10411yescharacteristic
331C22#1684075911yescharacteristic
332C4—41no—
333C4—81no—
334C4—81no—
335C4—612no—
336C4—612no—
337C4—1222no—
338C4—1222no—
339C4—1222no—
340C4—4881no—
341C4—4881no—
342C4#1684078614yes—
343C2—42no—
344C2#2146112711yescharacteristic
345C2#2146113811yescharacteristic
346C2#2146116711yescharacteristic
347C2#2146117811yescharacteristic
348C2#2146171211yescharacteristic
349C2#2146172311yescharacteristic
350C2#2146172711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#8710
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
4. #21460655C2semidirect
198. C61#8710semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606552
#214482212
#871061