Finite Group Databasebeta

← #29589642

Subgroups — #29589642

Order 15616.

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

normal subgroups only

This group has 412 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#21450802C211yesmaximal, characteristic
2#21444161C211yesmaximal, characteristic, complemented
3#21444141C211yesmaximal, characteristic, complemented
4#21443753C211yesmaximal, characteristic, complemented
5#21443750C211yesmaximal, characteristic
6#21443750C211yesmaximal, characteristic
7C61×#1319C211yesmaximal, characteristic, complemented
8C2×#14519775C411yescharacteristic
9C2×#14519766C411yescharacteristic
10C2×#14519765C411yescharacteristic
11C2×#14519742C2211yescharacteristic
12#16839816—21no—
13#16839812—21no—
14#16839686—21no—
15#16839686—21no—
16#16839663C2211yescharacteristic
17#16839651—21no—
18#16839651—21no—
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#391C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29#14519775—42no—
30#14519766—41no—
31#14519766—41no—
32#14519765—42no—
33#14519742—41no—
34#14519742—41no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196D411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—41no—
51#14519706—41no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519687—41no—
55C8×Dic61—41no—
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×D61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—41no—
82C2×D244—41no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×Dic122—22no—
86C2×Dic122—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—42no—
98#11758196—41no—
99#11758196—41no—
100#11758196—42no—
101#11758196—42no—
102#11758196—42no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120Q8×C61—81no—
121Q8×C61—81no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
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#13111yescharacteristic
135C2×C4×C61#13111yescharacteristic
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—22no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9911yescharacteristic
148C2×Dic61#9911yescharacteristic
149C2×Dic61#10012yes—
150D244—81no—
151D244—81no—
152Dic122—42no—
153Dic122—42no—
154C8×C61—81no—
155C8×C61—81no—
156#92418—81no—
157#92418—81no—
158#11565—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#40811yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#10011yescharacteristic
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—81no—
176C4×C61—81no—
177Dic61—21no—
178Dic61—21no—
179Dic61—22no—
180Dic61—42no—
181Dic61—41no—
182Dic61—41no—
183#2545—611no—
184#1467—611no—
185#1461—611no—
186#1319—611no—
187#1319D6111yescharacteristic, complemented
188#1318—611no—
189#1318—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#147111yescharacteristic
193C2×C61#212611yescharacteristic
194C2×C61#213311yescharacteristic
195D61—161no—
196C2×C4⋊Q8—611no—
197C2×#124—611no—
198C2×#124—611no—
199C2×C4×Q8—611no—
200#432—1221no—
201#431—1221no—
202#396—1221no—
203#396—1221no—
204#391C2×D6111yescharacteristic
205#390—611no—
206#388—1221no—
207#388—1221no—
208C4×C4⋊C4—611no—
209#324—611no—
210#324—611no—
211#324—1221no—
212#324—1221no—
213#324C2×D6111yescharacteristic
214#324C2×D6111yescharacteristic
215C61#1156511yescharacteristic, complemented, Sylow
216C22×Q8—611no—
217C22×Q8C4×D6111yescharacteristic
218C22×D4—611no—
219C4⋊Q8—2442no—
220#124—2442no—
221#124—2441no—
222#124—2441no—
223C4×Q8—2441no—
224C4×Q8—2441no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4C22×D6111yescharacteristic
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42C4×D6111yescharacteristic
242C4⋊C8—2441no—
243C4⋊C8—2441no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—1221no—
247C22⋊C8—1221no—
248#97—2441no—
249C4×C8—2441no—
250#95—21no—
251#95—21no—
252#95—1221no—
253C24—1221no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—1222no—
259C2×Q8—1221no—
260C2×Q8—1221no—
261C2×Q8—2441no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—2441no—
265C2×D4—2441no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4C2×C4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—2441no—
279C2×C8—2441no—
280C4⋊C4—41no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2442no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C22⋊C4—2442no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C22⋊C4—2442no—
293C42—41no—
294C42—1221no—
295C42—1221no—
296C42—1221no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C42—2441no—
301C23—2441no—
302C23—2441no—
303C23—2441no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23C22⋊C4×D6111yescharacteristic
309Q8—81no—
310Q8—81no—
311Q8—2442no—
312Q8—2442no—
313D4—4881no—
314D4—4881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—612no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1222no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4#1451978311yescharacteristic
342C2×C4#1451978511yescharacteristic
343C8—81no—
344C8—81no—
345C8—4881no—
346C8—4881no—
347C22—21no—
348C22—21no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683972711yescharacteristic
357C22#99×D6111yescharacteristic
358C22#100×D6111yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—1222no—
366C4—1221no—
367C4—1221no—
368C4—2442no—
369C4—2441no—
370C4—2441no—
371C2—21no—
372C2—21no—
373C2—9761no—
374C2#2144417711yescharacteristic
375C2#2144748311yescharacteristic
376C2#2144750711yescharacteristic
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#11565
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
2. #21444161C2semidirect
3. #21444141C2semidirect
4. #21443753C2semidirect
7. C61×#1319C2semidirect
187. #1319D61semidirect
215. C61#11565semidirect

Maximal subgroups

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

subgroupindex
#214508022
#214441612
#214441412
#214437532
#214437502
C61×#13192
#1156561