Finite Group Databasebeta

← #30599237

Subgroups — #30599237

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—42no—
32#14519733—42no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—24no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
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—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—41no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61D812yes—
73C22×Dic61SD1612yes—
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×#92420—24no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—22no—
84C22⋊C4×C61—42no—
85C22⋊Dic61—42no—
86C4⋊Dic61—22no—
87C4⋊Dic61—22no—
88#11758196—42no—
89#11758196—42no—
90#11758196—42no—
91#11758196—42no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61#4114yes—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61#10212yes—
107C23×C61C2×C22⋊C411yescharacteristic
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#11712yes—
119C2×C4×C61#13112yes—
120C2×C4×C61#13112yes—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—24no—
128C2×Dic61—24no—
129C2×Dic61—44no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61#10212yes—
137C2×Dic61#10412yes—
138C2×Dic61#12312yes—
139C2×Dic61#12312yes—
140C2×Dic61C2×D811yescharacteristic
141C2×Dic61C2×SD1611yescharacteristic
142C2×Dic61#13712yes—
143#92420—44no—
144#92420—82no—
145#8709—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#38111yescharacteristic
154C22×C61#40811yescharacteristic
155C22×C61#40811yescharacteristic
156C22×C61C2×#10211yescharacteristic
157C22×C61#41911yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C22×C61#42111yescharacteristic
160C4×C61—41no—
161C4×C61—81no—
162C4×C61—81no—
163C4×C61#43314yes—
164Dic61—22no—
165Dic61—22no—
166Dic61—22no—
167Dic61—81no—
168Dic61—81no—
169Dic61#48012yes—
170Dic61#48312yes—
171#2285—611no—
172#1797—611no—
173C4×C22⋊C8—611no—
174#1279—612no—
175#1279—612no—
176C2×C61—42no—
177C2×C61#148011yescharacteristic
178C2×C61#148511yescharacteristic
179C2×C61#149211yescharacteristic
180C2×C61#149711yescharacteristic
181C2×C61#181811yescharacteristic
182C2×C61#182311yescharacteristic
183C2×C61#182611yescharacteristic
184C2×#117—1221no—
185C22×C42—611no—
186C2×C4⋊C8—612no—
187C2×C22⋊C8—1221no—
188C2×C22⋊C8—1221no—
189C2×C4×C8—612no—
190#384—611no—
191#384—611no—
192#382—1221no—
193#380—611no—
194#380—1221no—
195#380#692311yescharacteristic
196C4×C4⋊C4—611no—
197C4×C4⋊C4—611no—
198C4×C4⋊C4—1221no—
199#336—1221no—
200#336—1221no—
201C61#870911yescharacteristic, complemented, Sylow
202C23×C4—611no—
203C23×C4—611no—
204C23×C4C2×#692311yescharacteristic
205C22×C8—1222no—
206C22×C8—1222no—
207#117—2442no—
208#117—2442no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4C2×#692311yescharacteristic
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—1221no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—1224no—
224C2×C42—1221no—
225C2×C42—1221no—
226C4⋊C8—1224no—
227C22⋊C8—1224no—
228C22⋊C8—2442no—
229C4×C8—1224no—
230#95—21no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234C24C22⋊#692311yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—611no—
241C22×C4—612no—
242C22×C4—612no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—2441no—
253C22×C4C22⋊#692311yescharacteristic
254C22×C4C22×#692311yescharacteristic
255C2×C8—1224no—
256C2×C8—2442no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—42no—
270C22⋊C4—2442no—
271C42—614no—
272C42—1222no—
273C42—1222no—
274C42—1222no—
275C42—2441no—
276C42—2441no—
277C42—2441no—
278C42—2441no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#1451983912yes—
286C23C2×C22⋊#692311yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—612no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—612no—
303C2×C4—612no—
304C2×C4—1224no—
305C2×C4—1224no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—2444no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451985612yes—
320C2×C4#1451986412yes—
321C2×C4#1451986412yes—
322C8—4882no—
323C8—2444no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22#1684070511yescharacteristic
332C22#1684073511yescharacteristic
333C22#1684073511yescharacteristic
334C22C2×#1451983911yescharacteristic
335C22#1684075511yescharacteristic
336C22D61⋊#10411yescharacteristic
337C22#1684075911yescharacteristic
338C4—41no—
339C4—81no—
340C4—81no—
341C4—612no—
342C4—612no—
343C4—1222no—
344C4—1222no—
345C4—1222no—
346C4—4881no—
347C4—4881no—
348C4#1684078614yes—
349C2—42no—
350C2#2146112411yescharacteristic
351C2#2146114111yescharacteristic
352C2#2146116411yescharacteristic
353C2#2146118111yescharacteristic
354C2#2146171211yescharacteristic
355C2#2146172211yescharacteristic
356C2#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#8709
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
201. C61#8709semidirect

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
#870961