Finite Group Databasebeta

← #29590930

Subgroups — #29590930

Order 15616.

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

normal subgroups only

This group has 418 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#21451501C211yesmaximal, characteristic
2#21445901C211yesmaximal, characteristic, complemented
3#21444132C211yesmaximal, characteristic, complemented
4#21443849C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C2×#14519766C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839812—21no—
11#16839725—21no—
12#16839679C2211yescharacteristic
13#16839673C411yescharacteristic
14#16839672C411yescharacteristic
15#16839663—21no—
16#16839654—21no—
17#16839652—21no—
18#16839640—21no—
19#16839607C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31#14519766—41no—
32#14519766—41no—
33#14519735—41no—
34#14519735—41no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198C2×C411yescharacteristic
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—41no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519689—41no—
51C8×Dic61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C22×Q8×C61C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61—21no—
63C23×D61C22⋊C411yescharacteristic
64C2×Q8×C61—41no—
65C2×Q8×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×D244—42no—
76C2×D244—41no—
77C2×D244—42no—
78C2×D244—81no—
79C2×D244—81no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—41no—
85M16×C61—41no—
86M16×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—81no—
91#11758198—41no—
92#11758198—41no—
93#11758198—42no—
94#11758198—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—81no—
100#11758198—81no—
101C4⋊Dic61—41no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—42no—
107#11758194—41no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124Q8×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
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#13511yescharacteristic
138C2×C4×C61#13511yescharacteristic
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—41no—
148C2×Dic61#9911yescharacteristic
149C2×Dic61#9911yescharacteristic
150D244—84no—
151D244—82no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C8×C61—81no—
157C8×C61—81no—
158#92418—81no—
159#92418—81no—
160#11851—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61C2×#9911yescharacteristic
164C22×C61#41611yescharacteristic
165C22×C61#42111yescharacteristic
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189#2610—611no—
190#1822—611no—
191#1458—611no—
192#1354—611no—
193#1354D6111yescharacteristic, complemented
194#1345—611no—
195#1345—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#151611yescharacteristic
199C2×C61#212211yescharacteristic
200C2×C61#213211yescharacteristic
201D61—81no—
202D61—161no—
203C2×#124—611no—
204C2×#117—611no—
205#431—1221no—
206#407—1221no—
207#395C2×D6111yescharacteristic
208#394—611no—
209#393—611no—
210#392—611no—
211#390—1221no—
212#388—1221no—
213#388—1221no—
214#386—1221no—
215#376—611no—
216#343—611no—
217#343—1221no—
218#343C2×D6111yescharacteristic
219#324—611no—
220#324C2×D6111yescharacteristic
221#323—1221no—
222C61#1185111yescharacteristic, complemented, Sylow
223C22×Q8C4×D6111yescharacteristic
224C22×D4—611no—
225C22×D4—1221no—
226C23×C4—611no—
227C2×M16—21no—
228C2×M16—1221no—
229#124—2441no—
230#124—2441no—
231#117—2441no—
232#117—2441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C22×D6111yescharacteristic
236C2×C22⋊C4—611no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—1221no—
247C4⋊C8—2441no—
248C22⋊C8—21no—
249C22⋊C8—1221no—
250C22⋊C8—2441no—
251C22⋊C8—2441no—
252C4×C8—2441no—
253#95—21no—
254#95—611no—
255#95—1221no—
256#95—1221no—
257#95C4×D6111yescharacteristic
258C24—611no—
259C24—1221no—
260C2×Q8—41no—
261C2×Q8—81no—
262C2×D4—4881no—
263C2×D4—4881no—
264C2×D4—2441no—
265C2×D4—2442no—
266C2×D4—2442no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—2441no—
278C22×C4C2×C4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281M16—41no—
282M16—41no—
283M16—2441no—
284M16—2441no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—2441no—
288C2×C8—2441no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—2441no—
292C22⋊C4—4881no—
293C22⋊C4—4881no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2442no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2442no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—1221no—
303C42—1221no—
304C42—1221no—
305C42—1221no—
306C42—2442no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23C22⋊C4×D6111yescharacteristic
320Q8—82no—
321D4—4882no—
322D4—4884no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
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—611no—
336C2×C4—611no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4#1451979811yescharacteristic
351C2×C4#1451980011yescharacteristic
352C8—81no—
353C8—81no—
354C8—4881no—
355C8—4881no—
356C22—21no—
357C22—21no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22—2442no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22#99×D6111yescharacteristic
371C22#1683975711yescharacteristic
372C22#1683977711yescharacteristic
373C4—21no—
374C4—21no—
375C4—42no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—1221no—
380C4—1221no—
381C4—4881no—
382C4—2441no—
383C4—2441no—
384C2—21no—
385C2—21no—
386C2—9761no—
387C2—4881no—
388C2#2144437411yescharacteristic
389C2#2144746711yescharacteristic
390C2#2144750311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radical#16839672C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11851
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
2. #21445901C2semidirect
3. #21444132C2semidirect
4. #21443849C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1354C2semidirect
193. #1354D61semidirect
222. C61#11851semidirect

Maximal subgroups

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

subgroupindex
#214515012
#214459012
#214441322
#214438492
#214438232
#214438212
C61×#13542
#1185161