Finite Group Databasebeta

← #29591061

Subgroups — #29591061

Order 15616.

460 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 79 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#21450122C211yesmaximal, characteristic
2#21445810C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4#21443826C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443824C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×#14519762—21no—
9C2×#14519739C2211yescharacteristic
10C2×C4⋊C4×D61C411yescharacteristic
11#16839785—21no—
12C2×#14519693—21no—
13C22⋊C8×D61—21no—
14#16839692C2211yescharacteristic
15#16839689C411yescharacteristic
16#16839688C411yescharacteristic
17#16839657—21no—
18#16839624—21no—
19#16839621—21no—
20#16839621C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#398C2211yescharacteristic
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#14519762—42no—
34#14519762—42no—
35#14519739—41no—
36#14519739—41no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C4⋊C4×D61—41no—
42C4⋊C4×D61—41no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50#14519706—41no—
51#14519693—42no—
52C22⋊#92418—21no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61C2×C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
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×D244D812yes—
79C2×D244SD1612yes—
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—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89M16×C61—41no—
90M16×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—42no—
100#11758198—42no—
101#11758198—42no—
102C4⋊Dic61—41no—
103#11758196—42no—
104#11758196—41no—
105#11758196—41no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110#11758194—41no—
111#11758194—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C8×D61—82no—
115C23×C61C2×C22⋊C411yescharacteristic
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#10212yes—
125C22×D61#10212yes—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
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×C61C2×D811yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×Dic61—22no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
151D244—42no—
152D244—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—81no—
157C4×D61—84no—
158C8×C61—81no—
159C8×C61—81no—
160#92418—81no—
161#92418—81no—
162#11881—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61C2×#9911yescharacteristic
166C22×C61C2×#10211yescharacteristic
167C22×C61#42111yescharacteristic
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—42no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183C4×C61—81no—
184Dic61—21no—
185Dic61—41no—
186Dic61—81no—
187Dic61—81no—
188Dic61#35212yes—
189#2486—611no—
190#1800—611no—
191#1459—611no—
192#1346—611no—
193#1346—611no—
194#1346—611no—
195#1346D6111yescharacteristic, complemented
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#151911yescharacteristic
199C2×C61C2×#35211yescharacteristic
200C2×C61#213511yescharacteristic
201D61—42no—
202D61—42no—
203C2×#123—1221no—
204C2×C4×D4—611no—
205C22×C4⋊C4—611no—
206#423—1221no—
207C2×#100—1221no—
208C2×C22⋊C8—1221no—
209#398—611no—
210#398C2×D6111yescharacteristic
211#397—611no—
212#397—611no—
213#389—1221no—
214#381—1221no—
215#380—611no—
216#380—1221no—
217#343—611no—
218#343C2×D6111yescharacteristic
219#324—611no—
220#324C2×D6111yescharacteristic
221#323—1221no—
222C61#1188111yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C23×C4—611no—
225C23×C4—611no—
226C23×C4—1221no—
227C2×M16—21no—
228C2×M16—1221no—
229C22×C8—2441no—
230#123—2442no—
231#123—2442no—
232C4×D4—2441no—
233C4×D4—2441no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2441no—
240C2×C4⋊C4—2441no—
241C2×C4⋊C4C4×D6111yescharacteristic
242C2×C4⋊C4C22×D6111yescharacteristic
243C2×C22⋊C4—611no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C42—611no—
249C4⋊C8—2441no—
250C4⋊C8—2441no—
251#100—2442no—
252C22⋊C8—21no—
253C22⋊C8—1221no—
254C22⋊C8—2441no—
255#95—21no—
256#95—611no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95C4×D6111yescharacteristic
261C24—611no—
262C24—611no—
263C2×D4—612no—
264C2×D4—612no—
265C2×D4—2441no—
266C2×D4—2441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—2442no—
278C22×C4—2442no—
279C22×C4—2442no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4C2×C4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285M16—41no—
286M16—41no—
287M16—2441no—
288M16—2441no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—4882no—
292C2×C8—2441no—
293C2×C8—2441no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2442no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C42—1221no—
310C42—1221no—
311C23—612no—
312C23—612no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23C22⋊C4×D6111yescharacteristic
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1222no—
339C2×C4—1221no—
340C2×C4—4881no—
341C2×C4—4884no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4D8×D6111yescharacteristic
353C2×C4SD16×D6111yescharacteristic
354C8—81no—
355C8—81no—
356C8—4881no—
357C8—4881no—
358C22—21no—
359C22—21no—
360C22—1222no—
361C22—1222no—
362C22—4881no—
363C22—2442no—
364C22—2442no—
365C22—2442no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22#99×D6111yescharacteristic
371C22#102×D6111yescharacteristic
372C22#1683977711yescharacteristic
373C4—21no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—612no—
380C4—1221no—
381C4—4881no—
382C4—4881no—
383C4—2441no—
384C2—21no—
385C2—21no—
386C2—2442no—
387C2—2442no—
388C2#2144438511yescharacteristic
389C2#352×D6111yescharacteristic
390C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11881
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #21443826C2semidirect
5. #21443825C2semidirect
6. #21443824C2semidirect
7. C61×#1346C2semidirect
195. #1346D61semidirect
222. C61#11881semidirect

Maximal subgroups

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

subgroupindex
#214501222
#214458102
#214441362
#214438262
#214438252
#214438242
C61×#13462
#1188161