Finite Group Databasebeta

← #29568651

Subgroups — #29568651

Order 15616.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454160C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic
3#21445886C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443643C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1272C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic
9C2×C42×D61C2211yescharacteristic
10C2×#14519689—21no—
11C2×#14519689—21no—
12#16839669C411yescharacteristic
13#16839661C411yescharacteristic
14#16839660C2211yescharacteristic
15#16839645—21no—
16#16839644—21no—
17#16839636—21no—
18#16839624—21no—
19#16839619C411yescharacteristic
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32#14519753—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C42×D61—42no—
44#14519689—42no—
45#14519689—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
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×C4×D61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—41no—
92C42×C61—41no—
93#11758198—42no—
94#11758198—42no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—42no—
98C4⋊Dic61—41no—
99#11758196—42no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61#9912yes—
119Q8×C61—81no—
120Q8×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#13111yescharacteristic
134C2×C4×C61#13111yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—42no—
160C8×C61—81no—
161C8×C61—81no—
162#92418—81no—
163#92418—81no—
164#7721—611nomaximal, Sylow
165C22×C61#40811yescharacteristic
166C22×C61C2×#9911yescharacteristic
167C22×C61#41311yescharacteristic
168C22×C61#41611yescharacteristic
169C22×C61#41911yescharacteristic
170C22×C61#42111yescharacteristic
171C22×C61#42111yescharacteristic
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—81no—
186C4×C61—81no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191Dic61—81no—
192#2855—611no—
193#1817—611no—
194#1817—611no—
195#1272—611no—
196#1272D6111yescharacteristic, complemented
197#1271—611no—
198#1271—611no—
199C2×C61#146811yescharacteristic
200C2×C61#148211yescharacteristic
201C2×C61#149711yescharacteristic
202C2×C61#151111yescharacteristic
203C2×C61#151611yescharacteristic
204C2×C61#153511yescharacteristic
205C2×C61#155411yescharacteristic
206D61—42no—
207C2×C22⋊Q8—611no—
208C22×C42—611no—
209C2×C22⋊C8—1221no—
210C2×C22⋊C8—1221no—
211#391—611no—
212#391C2×D6111yescharacteristic
213#389—611no—
214#389—611no—
215#387—1221no—
216#387—1221no—
217#385—1221no—
218#381—1221no—
219#380—611no—
220#336—611no—
221#336—611no—
222#336—1221no—
223#336—1221no—
224#336C2×D6111yescharacteristic
225#336C2×D6111yescharacteristic
226C61#772111yescharacteristic, complemented, Sylow
227C22×Q8C4×D6111yescharacteristic
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—1221no—
234C22×C8—1221no—
235C22⋊Q8—2442no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—2442no—
248C2×C42C22×D6111yescharacteristic
249C22⋊C8—2442no—
250C22⋊C8—2442no—
251#95—21no—
252#95—21no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258C24—611no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—41no—
262C2×Q8—41no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4C2×C4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C2×C8—2441no—
295C2×C8—2441no—
296C2×C8—2441no—
297C4⋊C4—41no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—2441no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C42—41no—
308C42—2441no—
309C42—2441no—
310C42—2441no—
311C23—612no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23C22⋊C4×D6111yescharacteristic
319Q8—81no—
320Q8—81no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4#1451978311yescharacteristic
355C2×C4#1451978511yescharacteristic
356C2×C4#1451979811yescharacteristic
357C2×C4#1451980011yescharacteristic
358C2×C4#1451980611yescharacteristic
359C2×C4#1451980911yescharacteristic
360C8—81no—
361C8—81no—
362C8—4881no—
363C8—4881no—
364C22—1222no—
365C22—1222no—
366C22—1222no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22#1683972711yescharacteristic
372C22#99×D6111yescharacteristic
373C22#1683974311yescharacteristic
374C22#1683975711yescharacteristic
375C22#1683976911yescharacteristic
376C22#1683977711yescharacteristic
377C22#1683977711yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—4881no—
387C4—4881no—
388C4—2441no—
389C4—2441no—
390C4—2441no—
391C2—2442no—
392C2#2144416411yescharacteristic
393C2#2144422611yescharacteristic
394C2#2144429011yescharacteristic
395C2#2144435011yescharacteristic
396C2#2144437411yescharacteristic
397C2#2144444711yescharacteristic
398C2#2144452811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7721
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #21443645C2semidirect
5. #21443643C2semidirect
6. #21443641C2semidirect
7. C61×#1272C2semidirect
196. #1272D61semidirect
226. C61#7721semidirect

Maximal subgroups

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

subgroupindex
#214541602
#214458862
#214436452
#214436432
#214436412
C61×#12722
#772161