Finite Group Databasebeta

← #29568396

Subgroups — #29568396

Order 15616.

438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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#21454183C211yesmaximal, characteristic
2#21445934C211yesmaximal, characteristic, complemented
3#21445563C211yesmaximal, characteristic, complemented
4#21443643C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic
7C61×#1270C211yesmaximal, characteristic
8C2×#14519770—21no—
9C2×#14519706—21no—
10C2×C8×Dic61—21no—
11#16839665C411yescharacteristic
12#16839665C411yescharacteristic
13#16839661C411yescharacteristic
14#16839660C2211yescharacteristic
15#16839658C411yescharacteristic
16#16839656—21no—
17#16839655—21no—
18#16839650—21no—
19C42×Dic61C2211yescharacteristic
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28C22×#92418—21no—
29#14519770—42no—
30#14519770—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—42no—
47C8×Dic61—24no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61C2×C411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C24×C61—21no—
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C8×C61—22no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C42×C61—41no—
85C22⋊Dic61—42no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C22⋊Dic61—42no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—42no—
92C4⋊Dic61—41no—
93#11758196—41no—
94#11758196—41no—
95#11758196—42no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C4×Dic61D812yes—
104C4×Dic61SD1612yes—
105C2×#92418—22no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119D4×C61—81no—
120D4×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#13111yescharacteristic
131C2×C4×C61#13111yescharacteristic
132C2×C4×C61C2×D811yescharacteristic
133C2×C4×C61C2×SD1611yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61#10212yes—
152C2×Dic61#10212yes—
153C2×Dic61#10412yes—
154C8×C61—42no—
155C8×C61—81no—
156#92418—42no—
157#92418—81no—
158#7666—611nomaximal, Sylow
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61#40811yescharacteristic
167C22×C61#41011yescharacteristic
168C22×C61#41311yescharacteristic
169C22×C61C2×#10211yescharacteristic
170C22×C61#41611yescharacteristic
171C22×C61C2×#10411yescharacteristic
172C22×C61#42111yescharacteristic
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—81no—
180Dic61—22no—
181Dic61—22no—
182Dic61—22no—
183Dic61—41no—
184Dic61—81no—
185Dic61—81no—
186#2860—611no—
187#1831—611no—
188#1744—611no—
189#1271—611no—
190#1271—611no—
191#1270—611no—
192#1270D6111yescharacteristic
193C2×C61—161no—
194C2×C61#147311yescharacteristic
195C2×C61#148211yescharacteristic
196C2×C61#149211yescharacteristic
197C2×C61#150011yescharacteristic
198C2×C61#151711yescharacteristic
199C2×C61#153211yescharacteristic
200C2×C61#154011yescharacteristic
201C2×#126—1221no—
202C2×C4⋊C8—1221no—
203C2×C4×C8—1221no—
204#390—611no—
205#390—611no—
206#390C2×D6111yescharacteristic
207#389—611no—
208#389—611no—
209#389—611no—
210#388—1221no—
211#388—1221no—
212#388—1221no—
213C43—611no—
214#336—611no—
215#336—611no—
216#336—1221no—
217#336—1221no—
218#336C2×D6111yescharacteristic
219#336C2×D6111yescharacteristic
220C61#766611yescharacteristic, complemented, Sylow
221C22×D4C4×D6111yescharacteristic
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1221no—
225C22×C8—1221no—
226#126—2442no—
227#126—2442no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4C4×D6111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42C22×D6111yescharacteristic
247C4⋊C8—2442no—
248C4×C8—1224no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252C24—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4C2×C4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—1222no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8—2441no—
278C2×C8—2441no—
279C4⋊C4—41no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—2441no—
283C4⋊C4—2442no—
284C4⋊C4—2442no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—2442no—
292C22⋊C4—2442no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C42—41no—
296C42—612no—
297C42—612no—
298C42—1222no—
299C42—1221no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—2441no—
304C42—2441no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23C22⋊C4×D6111yescharacteristic
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—612no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451978311yescharacteristic
343C2×C4#1451978511yescharacteristic
344C2×C4D8×D6111yescharacteristic
345C2×C4SD16×D6111yescharacteristic
346C2×C4#1451979611yescharacteristic
347C2×C4#1451979811yescharacteristic
348C8—42no—
349C8—81no—
350C8—4881no—
351C8—2442no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22#1683972711yescharacteristic
360C22#1683973411yescharacteristic
361C22#1683974311yescharacteristic
362C22#102×D6111yescharacteristic
363C22#1683975511yescharacteristic
364C22#104×D6111yescharacteristic
365C22#1683977711yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—81no—
373C4—1222no—
374C4—1222no—
375C4—1222no—
376C4—4881no—
377C4—4881no—
378C4—2441no—
379C2—161no—
380C2#2144418511yescharacteristic
381C2#2144422411yescharacteristic
382C2#2144426811yescharacteristic
383C2#2144430211yescharacteristic
384C2#2144437711yescharacteristic
385C2#2144443611yescharacteristic
386C2#2144446511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C42×C61C23
hypercenter#1270D61
hypocenterC61#7666
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21445934C2semidirect
3. #21445563C2semidirect
4. #21443643C2semidirect
5. #21443641C2semidirect
220. C61#7666semidirect

Maximal subgroups

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

subgroupindex
#214541832
#214459342
#214455632
#214436432
#214436412
#214436402
C61×#12702
#766661