Finite Group Databasebeta

← #30595927

Subgroups — #30595927

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—42no—
33#14519754—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54#95×C61—21no—
55C24×C61C22⋊C411yescharacteristic
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61D812yes—
73C22×Dic61SD1612yes—
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×Dic122—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊Dic61—42no—
89C4⋊Dic61—22no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93#11758196—42no—
94#11758196—42no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61#10212yes—
109C23×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—44no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61#10112yes—
122C2×C4×C61#13112yes—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—44no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#9912yes—
141C2×Dic61#10212yes—
142C2×Dic61C2×D811yescharacteristic
143C2×Dic61C2×SD1611yescharacteristic
144C2×Dic61#13712yes—
145Dic122—84no—
146#92420—82no—
147#92420—82no—
148#7728—611nomaximal, Sylow
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61#40811yescharacteristic
157C22×C61C2×#9911yescharacteristic
158C22×C61C2×#10111yescharacteristic
159C22×C61C2×#10211yescharacteristic
160C22×C61#41911yescharacteristic
161C22×C61#42111yescharacteristic
162C22×C61#42111yescharacteristic
163C4×C61—22no—
164C4×C61—22no—
165C4×C61—81no—
166C4×C61—81no—
167Dic61—22no—
168Dic61—22no—
169Dic61—21no—
170Dic61—22no—
171Dic61—21no—
172Dic61—81no—
173Dic61—81no—
174#2857—611no—
175#1817—611no—
176#1797—611no—
177#1271—612no—
178#1271—612no—
179C2×C61—42no—
180C2×C61#147211yescharacteristic
181C2×C61#148011yescharacteristic
182C2×C61#149711yescharacteristic
183C2×C61#151111yescharacteristic
184C2×C61#151911yescharacteristic
185C2×C61#153711yescharacteristic
186C2×C61#154611yescharacteristic
187C2×C4⋊Q8—611no—
188C2×C22⋊Q8—1221no—
189C22×C42—611no—
190C2×C4⋊C8—1221no—
191C2×C22⋊C8—1221no—
192C2×C22⋊C8—1221no—
193#391—1221no—
194#389—611no—
195#389—611no—
196#389—1221no—
197#384—611no—
198#380—611no—
199#380—1221no—
200#380#692311yescharacteristic
201#336—612no—
202#336—612no—
203#336—1221no—
204C61#772811yescharacteristic, complemented, Sylow
205C22×Q8—1221no—
206C23×C4—611no—
207C23×C4—611no—
208C23×C4C2×#692311yescharacteristic
209C22×C8—1222no—
210C22×C8—1222no—
211C4⋊Q8—2442no—
212C22⋊Q8—2442no—
213C22⋊Q8—2442no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—1221no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—2442no—
230C4⋊C8—2442no—
231C22⋊C8—2442no—
232C22⋊C8—2442no—
233#95—21no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24C22⋊#692311yescharacteristic
238C2×Q8—2442no—
239C2×Q8—2442no—
240C2×Q8—2442no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22×#692311yescharacteristic
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2442no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—1222no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2442no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C22⋊C4—42no—
279C22⋊C4—2442no—
280C42—1222no—
281C42—1222no—
282C42—2441no—
283C42—2441no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23#1451983912yes—
291C23C2×C22⋊#692311yescharacteristic
292Q8—4884no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—612no—
305C2×C4—612no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—612no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2444no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451983812yes—
327C2×C4#1451986412yes—
328C8—4882no—
329C8—4882no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22#1684073511yescharacteristic
338C22D61⋊#9911yescharacteristic
339C22C2×#1451983811yescharacteristic
340C22C2×#1451983911yescharacteristic
341C22#1684075511yescharacteristic
342C22#1684075911yescharacteristic
343C22#1684075911yescharacteristic
344C4—22no—
345C4—22no—
346C4—81no—
347C4—81no—
348C4—1221no—
349C4—1221no—
350C4—1222no—
351C4—1222no—
352C4—1222no—
353C4—4881no—
354C4—4881no—
355C2—42no—
356C2#2146109811yescharacteristic
357C2#2146112411yescharacteristic
358C2#2146118111yescharacteristic
359C2#2146122811yescharacteristic
360C2#2146125411yescharacteristic
361C2#2146131011yescharacteristic
362C2#2146132811yescharacteristic
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#7728
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
204. C61#7728semidirect

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
#772861