Finite Group Databasebeta

← #29589692

Subgroups — #29589692

Order 15616.

424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451169C211yesmaximal, characteristic
2#21444154C211yesmaximal, characteristic
3#21444138C211yesmaximal, characteristic
4#21443768C211yesmaximal, characteristic, complemented
5#21443767C211yesmaximal, characteristic, complemented
6#21443766C211yesmaximal, characteristic, complemented
7C61×#1326C211yesmaximal, characteristic, complemented
8C2×#14519737C2211yescharacteristic
9C22×C4⋊Dic61C411yescharacteristic
10#16839812—21no—
11#16839724—21no—
12#16839696—21no—
13#16839684—21no—
14#16839648—21no—
15#16839641C411yescharacteristic
16#16839639C411yescharacteristic
17#16839636—21no—
18#16839634C2211yescharacteristic
19#16839620C411yescharacteristic
20#16839487—21no—
21#16839486C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#385C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C23×Dic61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32#14519737—41no—
33#14519737—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—41no—
37C2×C4⋊Dic61—41no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61C2×C411yescharacteristic
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49#14519689—41no—
50C8×Dic61—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C23×C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60C22⋊C8×C61—21no—
61#95×C61—21no—
62C24×C61C22×C411yescharacteristic
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—41no—
79C22×Dic61—81no—
80C22×Dic61—81no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—81no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—42no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758198—41no—
96#11758198—42no—
97#11758198—81no—
98C4⋊Dic61—42no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101#11758196—41no—
102#11758196—81no—
103#11758196—81no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C2×#92418—41no—
107C2×#92418—41no—
108#11758189—82no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61#13111yescharacteristic
115C23×C61#13111yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—41no—
120C22×D61—41no—
121C2×C4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—82no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
151C2×Dic61#10112yes—
152C4×D61—42no—
153C4×D61—81no—
154C8×C61—81no—
155C8×C61—81no—
156#92418—81no—
157#92418—81no—
158#11577—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—42no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61#40811yescharacteristic
169C22×C61C2×#9911yescharacteristic
170C22×C61C2×#10111yescharacteristic
171C2×D61—42no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—81no—
176C4×C61—41no—
177C4×C61—42no—
178C4×C61—41no—
179C4×C61—81no—
180Dic61—21no—
181Dic61—21no—
182Dic61—22no—
183Dic61—41no—
184Dic61—81no—
185Dic61—81no—
186#2579—611no—
187#1465—611no—
188#1460—611no—
189#1326—611no—
190#1326—611no—
191#1326—611no—
192#1326D6111yescharacteristic, complemented
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—41no—
196C2×C61—41no—
197C2×C61#147211yescharacteristic
198C2×C61#212011yescharacteristic
199C2×C61#212111yescharacteristic
200D61—81no—
201C2×C4×D4—611no—
202C22×C4⋊C4—611no—
203#431—1221no—
204#407—1221no—
205#398—1221no—
206#396—1221no—
207#387—1221no—
208#386—611no—
209#386—611no—
210#385—611no—
211#385—1221no—
212#385C2×D6111yescharacteristic
213#380—611no—
214#324—1221no—
215#323—611no—
216#323—611no—
217#323—1221no—
218#323C2×D6111yescharacteristic
219#323C2×D6111yescharacteristic
220C61#1157711yescharacteristic, complemented, Sylow
221C22×D4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4—611no—
225C23×C4C4×D6111yescharacteristic
226C2×M16—2441no—
227C4×D4—2441no—
228C4×D4—2441no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—2441no—
236C2×C4⋊C4—2441no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4C22×D6111yescharacteristic
243C2×C42—611no—
244C4⋊C8—2441no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—1221no—
248C22⋊C8—1221no—
249C22⋊C8—2441no—
250C4×C8—2441no—
251#95—21no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256C24—611no—
257C24C2×C4×D6111yescharacteristic
258C2×D4—1222no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—2441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—4881no—
276C22×C4—4881no—
277C22×C4—4881no—
278C22×C4—2441no—
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281M16—4882no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—2441no—
285C2×C8—2441no—
286C4⋊C4—42no—
287C4⋊C4—4881no—
288C4⋊C4—4881no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2442no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—4881no—
299C22⋊C4—2441no—
300C22⋊C4—2442no—
301C42—1221no—
302C42—1221no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—2441no—
311C23—2441no—
312C23C22⋊C4×D6111yescharacteristic
313C23#1451978311yescharacteristic
314C23#1451978511yescharacteristic
315D4—2442no—
316D4—2442no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—612no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—4882no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C8—81no—
349C8—81no—
350C8—4881no—
351C8—4881no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—4881no—
362C22—2442no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22#1683972711yescharacteristic
367C22#99×D6111yescharacteristic
368C22#101×D6111yescharacteristic
369C4—41no—
370C4—42no—
371C4—41no—
372C4—81no—
373C4—1221no—
374C4—1221no—
375C4—1222no—
376C4—4881no—
377C4—4881no—
378C4—2441no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—4881no—
384C2#2144418111yescharacteristic
385C2#2144745711yescharacteristic
386C2#2144746411yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1326C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1326D61
hypocenterC61#11577
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
4. #21443768C2semidirect
5. #21443767C2semidirect
6. #21443766C2semidirect
7. C61×#1326C2semidirect
192. #1326D61semidirect
220. C61#11577semidirect

Maximal subgroups

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

subgroupindex
#214511692
#214441542
#214441382
#214437682
#214437672
#214437662
C61×#13262
#1157761