Finite Group Databasebeta

← #29568320

Subgroups — #29568320

Order 15616.

500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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#21448349C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic
3#21445798C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443642C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic
9C2×#14519742C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519706—21no—
12C2×#14519689—21no—
13C2×#14519689—21no—
14#16839668C2211yescharacteristic
15#16839645—21no—
16#16839633—21no—
17#16839619C411yescharacteristic
18C4⋊C4×Dic61—21no—
19C4⋊C4×Dic61C411yescharacteristic
20#16839609—21no—
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×#92418—21no—
32C22×#92418—21no—
33#14519757—22no—
34#14519757—22no—
35#14519742—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C42×D61—42no—
47#14519706—42no—
48#14519689—42no—
49#14519689—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#95×C61—21no—
61C23×D61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61SD1612yes—
83C2×C4×D61Q1612yes—
84C2×Dic122—21no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×Dic122M1612yes—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61M1612yes—
99C42×C61—41no—
100#11758198—24no—
101#11758198—42no—
102C4⋊Dic61—24no—
103C4⋊Dic61—41no—
104#11758196—42no—
105C4×Dic61—22no—
106C4×Dic61—22no—
107C4×Dic61—41no—
108C4×Dic61—42no—
109C4×Dic61—42no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61#10312yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61C2×M1611yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61C2×Q1611yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61#9912yes—
156C2×Dic61#10312yes—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—42no—
163Dic122—42no—
164Dic122—42no—
165C8×C61—81no—
166C8×C61—81no—
167#92418—81no—
168#92418—81no—
169#7648—611nomaximal, Sylow
170C22×C61#40711yescharacteristic
171C22×C61C2×#9911yescharacteristic
172C22×C61#41311yescharacteristic
173C22×C61C2×#10311yescharacteristic
174C22×C61#41611yescharacteristic
175C22×C61#42111yescharacteristic
176C22×C61#42111yescharacteristic
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—42no—
191C4×C61—81no—
192Dic61—22no—
193Dic61—22no—
194Dic61—42no—
195Dic61—41no—
196Dic61—81no—
197C4×C22⋊Q8—611no—
198#1817—611no—
199#1797—611no—
200#1272—611no—
201#1272—611no—
202#1271—611no—
203#1271D6111yescharacteristic, complemented
204C2×C61#146511yescharacteristic
205C2×C61#148711yescharacteristic
206C2×C61#148811yescharacteristic
207C2×C61#151611yescharacteristic
208C2×C61#152011yescharacteristic
209C2×C61#153511yescharacteristic
210C2×C61#154211yescharacteristic
211D61—42no—
212C2×C22⋊Q8—611no—
213C2×C4×Q8—611no—
214C22×C42—611no—
215C2×C4⋊C8—1221no—
216C2×C22⋊C8—1221no—
217C2×C22⋊C8—1221no—
218#391—611no—
219#389C2×D6111yescharacteristic
220#387—1221no—
221#385—1221no—
222#380—611no—
223C4×C4⋊C4—611no—
224C4×C4⋊C4—1221no—
225C4×C22⋊C4—1221no—
226#336—611no—
227#336—611no—
228#336—1221no—
229#336C2×D6111yescharacteristic
230#336C2×D6111yescharacteristic
231C61#764811yescharacteristic, complemented, Sylow
232C22×Q8—611no—
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—1221no—
239C22×C8—1221no—
240C22⋊Q8—1222no—
241C22⋊Q8—1222no—
242C4×Q8—2442no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4C4×D6111yescharacteristic
248C2×C4⋊C4C4×D6111yescharacteristic
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42—2442no—
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—2442no—
259C22⋊C8—2442no—
260C22⋊C8—2442no—
261#95—21no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266C24—611no—
267C2×Q8—612no—
268C2×Q8—1221no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—611no—
278C22×C4—1222no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—2441no—
300C2×C8—2441no—
301C2×C8—2441no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—1224no—
310C4⋊C4—2441no—
311C4⋊C4—2442no—
312C4⋊C4#1175818912yes—
313C22⋊C4—1224no—
314C22⋊C4—2442no—
315C42—41no—
316C42—1222no—
317C42—1222no—
318C42—2441no—
319C42—2442no—
320C42—2442no—
321C23—612no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23C22⋊C4×D6111yescharacteristic
329Q8—2442no—
330Q8—2442no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1222no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4M16×D6111yescharacteristic
365C2×C4C2×#1175818911yescharacteristic
366C2×C4SD16×D6111yescharacteristic
367C2×C4Q16×D6111yescharacteristic
368C2×C4#1451979611yescharacteristic
369C2×C4#1451979811yescharacteristic
370C8—81no—
371C8—81no—
372C8—4881no—
373C8—4881no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22#1683972411yescharacteristic
382C22#99×D6111yescharacteristic
383C22#1683974511yescharacteristic
384C22#103×D6111yescharacteristic
385C22#1683975511yescharacteristic
386C22#1683977711yescharacteristic
387C22#1683977711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—1222no—
397C4—1222no—
398C4—4881no—
399C4—2441no—
400C4—2442no—
401C2—2442no—
402C2#2144415611yescharacteristic
403C2#2144424611yescharacteristic
404C2#2144425011yescharacteristic
405C2#2144437211yescharacteristic
406C2#2144438911yescharacteristic
407C2#2144444911yescharacteristic
408C2#2144447511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7648
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #21443644C2semidirect
5. #21443644C2semidirect
6. #21443642C2semidirect
7. C61×#1271C2semidirect
203. #1271D61semidirect
231. C61#7648semidirect

Maximal subgroups

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

subgroupindex
#214483492
#214458862
#214457982
#214436442
#214436422
C61×#12712
#764861