Finite Group Databasebeta

← #29568513

Subgroups — #29568513

Order 15616.

530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454128C211yesmaximal, characteristic
2#21445580C211yesmaximal, characteristic
3#336×D61C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519768C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12C2×#14519687—21no—
13#16839660C2211yescharacteristic
14#16839648—21no—
15#16839644—21no—
16#16839636—21no—
17#16839633—21no—
18#16839627C411yescharacteristic
19#16839619C411yescharacteristic
20#16839619C411yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32C2×C8×D61—24no—
33C2×C8×D61—42no—
34C2×C8×D61—42no—
35#14519768—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C42×D61—42no—
47#14519689—24no—
48#14519687—42no—
49#14519684—21no—
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—22no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C8×C61—22no—
85C2×C8×C61—22no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C42×C61—41no—
96#11758198—42no—
97#11758198—42no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—41no—
104#11758196—42no—
105C4×Dic61—22no—
106C4×Dic61—22no—
107C4×Dic61—41no—
108C2×#92418—22no—
109C2×#92418—22no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C8×D61—48no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61#10112yes—
121C22×D61#10412yes—
122C22×D61#10412yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#13111yescharacteristic
136C2×C4×C61#13111yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61#9912yes—
156C4×D61—24no—
157C4×D61—24no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162C8×C61—42no—
163C8×C61—42no—
164#92418—42no—
165#92418—42no—
166#7691—611nomaximal, Sylow
167C22×C61#40811yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61C2×#10111yescharacteristic
170C22×C61#41611yescharacteristic
171C22×C61#41711yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C22×C61C2×#10411yescharacteristic
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61#33014yes—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—81no—
188C4×C61—81no—
189Dic61—22no—
190Dic61—41no—
191Dic61—41no—
192Dic61—81no—
193Dic61—81no—
194#2851—611no—
195#1749—611no—
196C2×#336—611no—
197#1271—611no—
198#1271—611no—
199#1271—611no—
200#1271D6111yescharacteristic, complemented
201C2×C61#147211yescharacteristic
202C2×C61#148311yescharacteristic
203C2×C61#149411yescharacteristic
204C2×C61#150111yescharacteristic
205C2×C61#150411yescharacteristic
206C2×C61C2×#33011yescharacteristic
207C2×C61#155211yescharacteristic
208D61—24no—
209C23×C8—1221no—
210C2×#125—611no—
211C22×C42—611no—
212C2×C22⋊C8—1221no—
213C2×#97—1221no—
214#389—611no—
215#389C2×D6111yescharacteristic
216#387—1221no—
217#387—1221no—
218#385—1221no—
219#385—1221no—
220#382—611no—
221#380—611no—
222#380—611no—
223#336—611no—
224#336—611no—
225#336—1221no—
226#336C2×D6111yescharacteristic
227#336C2×D6111yescharacteristic
228C61#769111yescharacteristic, complemented, Sylow
229C23×C4—611no—
230C23×C4—611no—
231C23×C4—611no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—1224no—
235C22×C8—1221no—
236C22×C8—1221no—
237C22×C8—2442no—
238C22×C8—2442no—
239#125—2442no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4C4×D6111yescharacteristic
247C2×C4⋊C4C4×D6111yescharacteristic
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—2442no—
254C2×C42C22×D6111yescharacteristic
255C22⋊C8—1224no—
256#97—2442no—
257#95—21no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263C24—611no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1222no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—1222no—
293C2×C8—1222no—
294C2×C8—2448no—
295C2×C8—2441no—
296C2×C8—2441no—
297C2×C8—2441no—
298C2×C8—2441no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—2441no—
307C4⋊C4—2442no—
308C4⋊C4—2442no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C42—41no—
314C42—1222no—
315C42—1222no—
316C42—2441no—
317C23—612no—
318C23—612no—
319C23—612no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23C22⋊C4×D6111yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—612no—
338C2×C4—1224no—
339C2×C4—1224no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4#1451978311yescharacteristic
359C2×C4#1451978511yescharacteristic
360C2×C4#1451979811yescharacteristic
361C2×C4#1451980011yescharacteristic
362C2×C4#1451980111yescharacteristic
363C2×C4#1451980611yescharacteristic
364C8—42no—
365C8—42no—
366C8—2442no—
367C8—2442no—
368C22—614no—
369C22—1222no—
370C22—1222no—
371C22—1222no—
372C22—1222no—
373C22—1222no—
374C22—1222no—
375C22#1683972711yescharacteristic
376C22#99×D6111yescharacteristic
377C22#101×D6111yescharacteristic
378C22#1683975711yescharacteristic
379C22#1683976011yescharacteristic
380C22#104×D6111yescharacteristic
381C22#104×D6111yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—1222no—
391C4—4881no—
392C4—4881no—
393C4—2441no—
394C4—2441no—
395C2—1224no—
396C2#2144418111yescharacteristic
397C2#2144422911yescharacteristic
398C2#2144427811yescharacteristic
399C2#2144430911yescharacteristic
400C2#2144432011yescharacteristic
401C2#330×D6111yescharacteristic
402C2#2144451811yescharacteristic
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#7691
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. #21443643C2semidirect
5. #21443642C2semidirect
6. #21443641C2semidirect
7. C61×#1271C2semidirect
200. #1271D61semidirect
228. C61#7691semidirect

Maximal subgroups

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

subgroupindex
#214541282
#214455802
#336×D612
#214436432
#214436422
#214436412
C61×#12712
#769161