Finite Group Databasebeta

← #30595917

Subgroups — #30595917

Order 15616.

494 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461710C211yesmaximal, characteristic
2#21461673C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#21454169C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519754—21no—
14C22×C4×Dic61C2211yescharacteristic
15#16839666—21no—
16#16839661C2211yescharacteristic
17#16839659—21no—
18#16839658C2211yescharacteristic
19#16839631C411yescharacteristic
20#16839622C411yescharacteristic
21#16839620—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—42no—
27C22⋊#92420—42no—
28C22×Dic122—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519776—42no—
32#14519754—44no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—42no—
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—21no—
58C22×C4×C61—21no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—41no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61SD1612yes—
72C22×Dic61Q1612yes—
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—42no—
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—42no—
87C22⋊Dic61—42no—
88C4⋊Dic61—22no—
89C4⋊Dic61—42no—
90C4⋊Dic61—41no—
91#11758196—42no—
92#11758196—42no—
93#11758196—42no—
94#11758196—42no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61#10312yes—
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—44no—
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#10112yes—
119C2×C4×C61#13112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—44no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61#9912yes—
138C2×Dic61#10312yes—
139C2×Dic61C2×SD1611yescharacteristic
140C2×Dic61C2×Q1611yescharacteristic
141C2×Dic61AGL(1,ℤ/8)12yes—
142Dic122—84no—
143#92420—82no—
144#92420—82no—
145#7725—611nomaximal, Sylow
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61#40811yescharacteristic
154C22×C61C2×#9911yescharacteristic
155C22×C61C2×#10111yescharacteristic
156C22×C61C2×#10311yescharacteristic
157C22×C61#41811yescharacteristic
158C22×C61#42111yescharacteristic
159C22×C61#42111yescharacteristic
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—81no—
163C4×C61—81no—
164Dic61—22no—
165Dic61—22no—
166Dic61—21no—
167Dic61—22no—
168Dic61—21no—
169Dic61—81no—
170Dic61—81no—
171#2857—611no—
172#1817—611no—
173#1797—611no—
174#1271—612no—
175#1271—612no—
176C2×C61—42no—
177C2×C61#147211yescharacteristic
178C2×C61#148111yescharacteristic
179C2×C61#149611yescharacteristic
180C2×C61#151011yescharacteristic
181C2×C61#152011yescharacteristic
182C2×C61#153711yescharacteristic
183C2×C61#154911yescharacteristic
184C2×C4⋊Q8—611no—
185C2×C22⋊Q8—1221no—
186C22×C42—611no—
187C2×C4⋊C8—1221no—
188C2×C22⋊C8—1221no—
189C2×C22⋊C8—1221no—
190#391—1221no—
191#389—611no—
192#389—611no—
193#389—1221no—
194#384—611no—
195#380—611no—
196#380—1221no—
197#380#692311yescharacteristic
198#336—612no—
199#336—612no—
200#336—1221no—
201C61#772511yescharacteristic, complemented, Sylow
202C22×Q8—1221no—
203C23×C4—611no—
204C23×C4—611no—
205C23×C4C2×#692311yescharacteristic
206C22×C8—1222no—
207C22×C8—1222no—
208C4⋊Q8—2442no—
209C22⋊Q8—2444no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C4⋊C4C2×#692311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—1221no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—2442no—
226C4⋊C8—2442no—
227C22⋊C8—2442no—
228C22⋊C8—2442no—
229#95—21no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C24C22⋊#692311yescharacteristic
234C2×Q8—2442no—
235C2×Q8—2442no—
236C2×Q8—2442no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—612no—
247C22×C4—612no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—2441no—
253C22×C4—2441no—
254C22×C4—2441no—
255C22×C4C22⋊#692311yescharacteristic
256C22×C4C22×#692311yescharacteristic
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—1222no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C4⋊C4—2442no—
270C4⋊C4—2442no—
271C4⋊C4—2442no—
272C22⋊C4—42no—
273C22⋊C4—2442no—
274C42—1222no—
275C42—1222no—
276C42—2441no—
277C42—2441no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#1451984012yes—
285C23C2×C22⋊#692311yescharacteristic
286Q8—4884no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—612no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2444no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451983812yes—
321C2×C4#1451986412yes—
322C8—4882no—
323C8—4882no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22#1684073511yescharacteristic
332C22D61⋊#9911yescharacteristic
333C22C2×#1451983811yescharacteristic
334C22C2×#1451984011yescharacteristic
335C22#1684075411yescharacteristic
336C22#1684075911yescharacteristic
337C22#1684075911yescharacteristic
338C4—22no—
339C4—22no—
340C4—81no—
341C4—81no—
342C4—1221no—
343C4—1222no—
344C4—1221no—
345C4—1222no—
346C4—1222no—
347C4—4881no—
348C4—4881no—
349C2—42no—
350C2#2146109811yescharacteristic
351C2#2146112711yescharacteristic
352C2#2146117811yescharacteristic
353C2#2146122511yescharacteristic
354C2#2146125711yescharacteristic
355C2#2146131011yescharacteristic
356C2#2146133411yescharacteristic
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#7725
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460638C2semidirect
4. #21460637C2semidirect
201. C61#7725semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214616732
#214606382
#214606372
#214541692
#772561