Finite Group Databasebeta

← #29591171

Subgroups — #29591171

Order 15616.

440 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 77 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#21451000C211yesmaximal, characteristic
2#21445810C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443847C211yesmaximal, characteristic, complemented
6#21443845C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic
9C2×#14519739C2211yescharacteristic
10#16839785—21no—
11C2×#14519693—21no—
12C22⋊C8×D61—21no—
13#16839701C2211yescharacteristic
14#16839699C411yescharacteristic
15#16839673C411yescharacteristic
16#16839645—21no—
17#16839640—21no—
18#16839633—21no—
19#16839619—21no—
20#95×D61C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×C8×D61—41no—
33#14519753—41no—
34#14519753—41no—
35#14519739—41no—
36#14519739—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519706—41no—
48#14519693—42no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C23×D61C22⋊C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—41no—
66C2×Q8×C61—81no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×D244—41no—
77C2×D244—41no—
78C2×D244SD1612yes—
79C2×D244Q1612yes—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88C2×C4×D61—81no—
89M16×C61—41no—
90M16×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—81no—
95#11758198—41no—
96#11758198—41no—
97#11758198—42no—
98#11758198—42no—
99#11758198—81no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106#11758194—41no—
107#11758194—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C8×D61—82no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61#10312yes—
121C22×D61#10312yes—
122Q8×C61—82no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
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×C61C2×SD1611yescharacteristic
136C2×C4×C61C2×Q1611yescharacteristic
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#9911yescharacteristic
147C2×Dic61#9911yescharacteristic
148D244—42no—
149D244—42no—
150C4×D61—42no—
151C4×D61—81no—
152C4×D61—81no—
153C4×D61—81no—
154C4×D61—84no—
155C8×C61—81no—
156C8×C61—81no—
157#92418—81no—
158#92418—81no—
159#11906—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#10311yescharacteristic
164C22×C61#42111yescharacteristic
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—42no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—81no—
181Dic61—21no—
182Dic61—21no—
183Dic61—41no—
184Dic61—81no—
185Dic61—81no—
186#2564—611no—
187#1800—611no—
188#1459—611no—
189#1354—611no—
190#1354D6111yescharacteristic, complemented
191#1353—611no—
192#1353—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#152011yescharacteristic
196C2×C61#212111yescharacteristic
197C2×C61#213211yescharacteristic
198D61—42no—
199D61—42no—
200C2×C22⋊Q8—611no—
201C2×C4×D4—611no—
202#423—1221no—
203C2×#100—1221no—
204C2×C22⋊C8—1221no—
205#400—611no—
206#399—611no—
207#395C2×D6111yescharacteristic
208#393—611no—
209#387—1221no—
210#386—1221no—
211#385—1221no—
212#380—1221no—
213C2×#95—611no—
214#343—611no—
215#343C2×D6111yescharacteristic
216#324—611no—
217#324C2×D6111yescharacteristic
218#323—1221no—
219C61#1190611yescharacteristic, complemented, Sylow
220C22×Q8C4×D6111yescharacteristic
221C22×D4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4—1221no—
225C2×M16—21no—
226C2×M16—1221no—
227C22×C8—2441no—
228C22⋊Q8—2441no—
229C22⋊Q8—2441no—
230C4×D4—2441no—
231C4×D4—2441no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4C22×D6111yescharacteristic
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—611no—
243C4⋊C8—2441no—
244C4⋊C8—2441no—
245#100—2442no—
246C22⋊C8—21no—
247C22⋊C8—1221no—
248C22⋊C8—2441no—
249#95—21no—
250#95—611no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95C4×D6111yescharacteristic
256C24—611no—
257C24—611no—
258C2×Q8—41no—
259C2×Q8—81no—
260C2×D4—612no—
261C2×D4—612no—
262C2×D4—2441no—
263C2×D4—2441no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—4881no—
275C22×C4—4881no—
276C22×C4—4881no—
277C22×C4—2442no—
278C22×C4—2442no—
279C22×C4C2×C4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282M16—41no—
283M16—41no—
284M16—2441no—
285M16—2441no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—4882no—
289C2×C8—2441no—
290C2×C8—2441no—
291C4⋊C4—41no—
292C4⋊C4—81no—
293C4⋊C4—2441no—
294C4⋊C4—2442no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—4881no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C42—1221no—
303C42—1221no—
304C23—612no—
305C23—612no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23C22⋊C4×D6111yescharacteristic
315Q8—82no—
316D4—2442no—
317D4—2442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1221no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4884no—
337C2×C4—2442no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4SD16×D6111yescharacteristic
347C2×C4Q16×D6111yescharacteristic
348C8—81no—
349C8—81no—
350C8—4881no—
351C8—4881no—
352C22—21no—
353C22—21no—
354C22—1222no—
355C22—1222no—
356C22—4881no—
357C22—2442no—
358C22—2442no—
359C22—2442no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22#99×D6111yescharacteristic
365C22#103×D6111yescharacteristic
366C22#1683977711yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—1221no—
374C4—1221no—
375C4—4881no—
376C4—4881no—
377C4—2441no—
378C2—21no—
379C2—21no—
380C2—2442no—
381C2—2442no—
382C2#2144438911yescharacteristic
383C2#2144746211yescharacteristic
384C2#2144750311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11906
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #21443849C2semidirect
5. #21443847C2semidirect
6. #21443845C2semidirect
7. C61×#1354C2semidirect
190. #1354D61semidirect
219. C61#11906semidirect

Maximal subgroups

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

subgroupindex
#214510002
#214458102
#214441362
#214438492
#214438472
#214438452
C61×#13542
#1190661