Finite Group Databasebeta

← #29568446

Subgroups — #29568446

Order 15616.

458 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454193C211yesmaximal, characteristic
2#21445667C211yesmaximal, characteristic, complemented
3#21445566C211yesmaximal, characteristic, complemented
4#21443645C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic
6#21443639C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic, complemented
8C2×#14519768C411yescharacteristic
9C2×#14519766C411yescharacteristic
10C2×#14519706—21no—
11C2×#14519687—21no—
12C2×C8×Dic61—21no—
13#16839669C411yescharacteristic
14#16839664C2211yescharacteristic
15#16839663C411yescharacteristic
16#16839654—21no—
17#16839654—21no—
18#16839651—21no—
19#16839651—21no—
20C42×Dic61C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30#14519768—42no—
31#14519766—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—24no—
48#14519687—24no—
49C8×Dic61—42no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61C2×C411yescharacteristic
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59C23×D61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—41no—
77C2×D244—41no—
78C2×C8×C61—22no—
79C2×C8×C61—22no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—41no—
85C42×C61—41no—
86#11758198—42no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—42no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C2×#92418—22no—
107C2×#92418—22no—
108C2×#92418—41no—
109C2×#92418—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—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#13111yescharacteristic
135C2×C4×C61#13111yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#10012yes—
153C2×Dic61#10412yes—
154C2×Dic61#10412yes—
155D244—81no—
156D244—81no—
157C8×C61—42no—
158C8×C61—42no—
159#92418—42no—
160#92418—42no—
161#7676—611nomaximal, Sylow
162C22×C61#40811yescharacteristic
163C22×C61#41011yescharacteristic
164C22×C61C2×#10011yescharacteristic
165C22×C61#41611yescharacteristic
166C22×C61#41711yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C22×C61C2×#10411yescharacteristic
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—81no—
183C4×C61—81no—
184Dic61—22no—
185Dic61—22no—
186Dic61—22no—
187Dic61—41no—
188Dic61—81no—
189#2861—611no—
190C4×C4⋊C8—611no—
191#1745—611no—
192#1272—611no—
193#1272D6111yescharacteristic, complemented
194#1270—611no—
195#1270—611no—
196C2×C61#146911yescharacteristic
197C2×C61#148311yescharacteristic
198C2×C61#149411yescharacteristic
199C2×C61#150011yescharacteristic
200C2×C61#150911yescharacteristic
201C2×C61#152511yescharacteristic
202C2×C61#155111yescharacteristic
203D61—161no—
204C2×#125—611no—
205C2×#124—611no—
206C2×C4⋊C8—1221no—
207C2×#97—1221no—
208C2×C4×C8—1221no—
209#391—611no—
210#391C2×D6111yescharacteristic
211#390—611no—
212#390—611no—
213#388—1221no—
214#388—1221no—
215#388—1221no—
216#388—1221no—
217C43—611no—
218#336—611no—
219#336—611no—
220#336—1221no—
221#336C2×D6111yescharacteristic
222#336C2×D6111yescharacteristic
223C61#767611yescharacteristic, complemented, Sylow
224C22×Q8C4×D6111yescharacteristic
225C22×D4—611no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—1221no—
229C22×C8—1221no—
230#125—2442no—
231#124—2442no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4C4×D6111yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42C22×D6111yescharacteristic
249C4⋊C8—1224no—
250#97—1224no—
251C4×C8—2442no—
252#95—21no—
253#95—21no—
254#95—1221no—
255#95—1221no—
256C24—1221no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—2441no—
264C2×D4—2441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4C2×C4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—1222no—
282C2×C8—1222no—
283C2×C8—2441no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8—2441no—
287C4⋊C4—41no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C22⋊C4—2442no—
292C22⋊C4—2442no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C42—41no—
300C42—1222no—
301C42—1222no—
302C42—1222no—
303C42—1221no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C42—1221no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23C22⋊C4×D6111yescharacteristic
317Q8—81no—
318Q8—81no—
319D4—4881no—
320D4—4881no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—612no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4#1451978311yescharacteristic
349C2×C4#1451978511yescharacteristic
350C2×C4#1451979811yescharacteristic
351C2×C4#1451980011yescharacteristic
352C2×C4#1451980411yescharacteristic
353C2×C4#1451980911yescharacteristic
354C8—42no—
355C8—42no—
356C8—2442no—
357C8—2442no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22#1683972711yescharacteristic
366C22#1683973411yescharacteristic
367C22#100×D6111yescharacteristic
368C22#1683975711yescharacteristic
369C22#1683976211yescharacteristic
370C22#104×D6111yescharacteristic
371C22#104×D6111yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—81no—
379C4—81no—
380C4—1222no—
381C4—1222no—
382C4—1222no—
383C4—4881no—
384C4—2441no—
385C2—9761no—
386C2#2144416911yescharacteristic
387C2#2144423111yescharacteristic
388C2#2144427811yescharacteristic
389C2#2144430411yescharacteristic
390C2#2144434311yescharacteristic
391C2#2144440911yescharacteristic
392C2#2144451311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7676
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21445667C2semidirect
3. #21445566C2semidirect
4. #21443645C2semidirect
7. C61×#1272C2semidirect
193. #1272D61semidirect
223. C61#7676semidirect

Maximal subgroups

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

subgroupindex
#214541932
#214456672
#214455662
#214436452
#214436392
C61×#12722
#767661