Finite Group Databasebeta

← #29590895

Subgroups — #29590895

Order 15616.

432 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451507C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic, complemented
3#21444130C211yesmaximal, characteristic, complemented
4#21443840C211yesmaximal, characteristic, complemented
5#21443817C211yesmaximal, characteristic
6#21443815C211yesmaximal, characteristic
7C61×#1351C211yesmaximal, characteristic, complemented
8C2×#14519766C411yescharacteristic, complemented
9C2×#14519733C2211yescharacteristic
10#16839812—21no—
11#16839681C411yescharacteristic, complemented
12#16839680C411yescharacteristic, complemented
13#16839671C2211yescharacteristic
14#16839662—21no—
15#16839651—21no—
16#16839651—21no—
17#16839639—21no—
18#16839623—21no—
19#16839607C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#393C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30#14519766—41no—
31#14519766—41no—
32#14519733—41no—
33#14519733—41no—
34C2×#11758196—21no—
35C2×#11758196C2×C411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—41no—
48C22⋊#92418—21no—
49C8×Dic61—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53#14519684—41no—
54#14519684C2×C411yescharacteristic
55C22×Q8×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C23×D61—21no—
64C2×Q8×C61—41no—
65C2×Q8×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C2×C22⋊D61—42no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—81no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C2×D244—41no—
87C2×D244—81no—
88C2×C8×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—81no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96#11758198—42no—
97#11758198—42no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758196—41no—
103#11758196—41no—
104#11758196—81no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—42no—
110C2×#92418—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61#13511yescharacteristic
117C23×C61#13511yescharacteristic
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125Q8×C61—82no—
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×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C22⋊D61—82no—
140C22⋊D61—82no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—22no—
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—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—81no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160C2×Dic61#9911yescharacteristic
161C2×Dic61#9911yescharacteristic
162D244—82no—
163C8×C61—81no—
164#92418—81no—
165#11844—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—81no—
175C22×C61C2×#9911yescharacteristic
176C22×C61#41611yescharacteristic
177C22×C61#42111yescharacteristic
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—81no—
188C4×C61—81no—
189C4×C61—161no—
190Dic61—21no—
191Dic61—21no—
192Dic61—42no—
193Dic61—41no—
194Dic61—41no—
195Dic61—41no—
196Dic61—161no—
197#2610—611no—
198#1820—611no—
199#1458—611no—
200#1351—611no—
201#1351D6111yescharacteristic, complemented
202#1343—611no—
203#1343—611no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—41no—
207C2×C61—41no—
208C2×C61#151611yescharacteristic
209C2×C61#212211yescharacteristic
210C2×C61#212611yescharacteristic
211D61—161no—
212C2×#124—611no—
213C2×#117—611no—
214#431—1221no—
215#395—611no—
216#394—611no—
217#393C2×D6111yescharacteristic
218#392—611no—
219#390—1221no—
220#388—1221no—
221#388—1221no—
222#386—1221no—
223#381—1221no—
224#376—611no—
225#342—611no—
226#342—1221no—
227#342C2×D6111yescharacteristic
228#324—1221no—
229#323—611no—
230#323C2×D6111yescharacteristic
231C61#1184411yescharacteristic, complemented, Sylow
232C22×Q8C4×D6111yescharacteristic
233C22×D4—611no—
234C22×D4—1221no—
235C23×C4—611no—
236#124—2441no—
237#124—2441no—
238#117—2441no—
239#117—2441no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1221no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4C22×D6111yescharacteristic
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—1221no—
256C4⋊C8—2441no—
257C22⋊C8—21no—
258C22⋊C8—1221no—
259C4×C8—2441no—
260#95—21no—
261#95—611no—
262#95—1221no—
263#95—1221no—
264#95—2441no—
265#95—2441no—
266#95C4×D6111yescharacteristic
267C24—1221no—
268C24D4×D6111yescharacteristic
269C2×Q8—41no—
270C2×Q8—81no—
271C2×D4—4881no—
272C2×D4—4881no—
273C2×D4—2441no—
274C2×D4—2442no—
275C2×D4—2441no—
276C2×D4—2441no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4C2×C4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C2×C8—41no—
294C2×C8—2441no—
295C4⋊C4—4881no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—81no—
302C22⋊C4—4881no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C42—1221no—
315C42—2442no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23C22⋊C4×D6111yescharacteristic
328C23#1451979811yescharacteristic
329C23#1451980011yescharacteristic
330Q8—82no—
331D4—4882no—
332D4—4882no—
333D4—4882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1222no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C8—81no—
369C8—4881no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22#99×D6111yescharacteristic
387C22#1683975711yescharacteristic
388C22#1683977711yescharacteristic
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—1221no—
395C4—1221no—
396C4—9761no—
397C4—2442no—
398C4—2441no—
399C4—2441no—
400C4—2441no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—9761no—
406C2#2144437411yescharacteristic
407C2#2144746711yescharacteristic
408C2#2144748311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1351C2
socleC22×C61C2×#99
prime radical#16839671C22
cosocleC2×C22⋊C4×C61C23
hypercenter#1351D61
hypocenterC61#11844
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. #21445895C2semidirect
3. #21444130C2semidirect
4. #21443840C2semidirect
7. C61×#1351C2semidirect
8. C2×#14519766C4semidirect
11. #16839681C4semidirect
12. #16839680C4semidirect
19. #16839607C4semidirect
201. #1351D61semidirect
231. C61#11844semidirect

Maximal subgroups

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

subgroupindex
#214515072
#214458952
#214441302
#214438402
#214438172
#214438152
C61×#13512
#1184461