Finite Group Databasebeta

← #29589636

Subgroups — #29589636

Order 15616.

444 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450816C211yesmaximal, characteristic
2#21444156C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4#21443753C211yesmaximal, characteristic, complemented
5#21443752C211yesmaximal, characteristic, complemented
6#21443752C211yesmaximal, characteristic, complemented
7C61×#1319C211yesmaximal, characteristic, complemented
8C2×#14519775C411yescharacteristic
9C2×#14519766C411yescharacteristic
10C2×#14519765C411yescharacteristic
11C2×#14519739C2211yescharacteristic
12#16839724—21no—
13C22⋊C8×D61—21no—
14#16839691—21no—
15#16839691—21no—
16#16839667C2211yescharacteristic
17#16839621—21no—
18#16839621—21no—
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#391C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32C2×C8×D61—41no—
33#14519775—41no—
34#14519775—41no—
35#14519766—42no—
36#14519765—42no—
37#14519739—41no—
38#14519739—41no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C2×Q8×C61—21no—
67C2×Q8×C61—21no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×D244—22no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—41no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—41no—
96C42×C61—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—42no—
100#11758198—42no—
101#11758198—42no—
102#11758198—42no—
103#11758196—42no—
104#11758196—42no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112#11758189—82no—
113C8×D61—82no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61#10012yes—
125Q8×C61—81no—
126Q8×C61—81no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#13111yescharacteristic
140C2×C4×C61#13111yescharacteristic
141C2×Dic61—22no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61#9911yescharacteristic
151C2×Dic61#9911yescharacteristic
152D244—42no—
153D244—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—81no—
157C4×D61—81no—
158Dic122—81no—
159Dic122—81no—
160C8×C61—81no—
161C8×C61—81no—
162#92418—81no—
163#92418—81no—
164#11564—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#40811yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61C2×#10011yescharacteristic
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—81no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—21no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190Dic61#35412yes—
191#2547—611no—
192#1465—611no—
193#1459—611no—
194#1319—611no—
195#1319—611no—
196#1319—611no—
197#1319D6111yescharacteristic, complemented
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#147111yescharacteristic
201C2×C61C2×#35411yescharacteristic
202C2×C61#213511yescharacteristic
203D61—42no—
204D61—81no—
205C2×C4⋊Q8—611no—
206C2×#124—611no—
207C2×#124—611no—
208C2×C4×D4—611no—
209#407—1221no—
210C2×C22⋊C8—1221no—
211#397—1221no—
212#397—1221no—
213#391—611no—
214#391C2×D6111yescharacteristic
215#380—1221no—
216#380—1221no—
217C4×C4⋊C4—611no—
218#324—611no—
219#324—611no—
220#324C2×D6111yescharacteristic
221#324C2×D6111yescharacteristic
222#323—1221no—
223#323—1221no—
224C61#1156411yescharacteristic, complemented, Sylow
225C22×Q8—611no—
226C22×Q8C4×D6111yescharacteristic
227C22×D4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C2×M16—2441no—
231C22×C8—2441no—
232C4⋊Q8—2441no—
233C4⋊Q8—2441no—
234#124—2442no—
235#124—2442no—
236C4×D4—2441no—
237C4×D4—2441no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4C22×D6111yescharacteristic
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42C4×D6111yescharacteristic
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—1221no—
254C22⋊C8—1221no—
255C22⋊C8—2441no—
256C22⋊C8—2441no—
257#95—21no—
258#95—21no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262C24—611no—
263C24—611no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—1221no—
269C2×Q8—1221no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×D4—1222no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4C2×C4×D6111yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291M16—4882no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—4882no—
295C2×C8—2441no—
296C2×C8—2441no—
297C4⋊C4—41no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2442no—
301C4⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C42—41no—
309C42—1221no—
310C42—1221no—
311C42—2441no—
312C23—612no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23C22⋊C4×D6111yescharacteristic
323Q8—81no—
324Q8—81no—
325Q8—4881no—
326Q8—4881no—
327D4—2442no—
328D4—2442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1221no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4#1451978311yescharacteristic
357C2×C4#1451978511yescharacteristic
358C8—81no—
359C8—81no—
360C8—4881no—
361C8—4881no—
362C22—21no—
363C22—21no—
364C22—1222no—
365C22—4881no—
366C22—4881no—
367C22—2442no—
368C22—2442no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#1683972711yescharacteristic
375C22#99×D6111yescharacteristic
376C22#100×D6111yescharacteristic
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—612no—
384C4—1221no—
385C4—4881no—
386C4—4881no—
387C4—2441no—
388C2—21no—
389C2—21no—
390C2—4881no—
391C2—2442no—
392C2#2144417711yescharacteristic
393C2#354×D6111yescharacteristic
394C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1319D61
hypocenterC61#11564
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #21443753C2semidirect
5. #21443752C2semidirect
6. #21443752C2semidirect
7. C61×#1319C2semidirect
197. #1319D61semidirect
224. C61#11564semidirect

Maximal subgroups

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

subgroupindex
#214508162
#214441562
#214441362
#214437532
#214437522
C61×#13192
#1156461