Finite Group Databasebeta

← #29592874

Subgroups — #29592874

Order 15616.

520 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 59 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#21447172C211yesmaximal, characteristic, complemented
2#21444775C211yesmaximal, characteristic, complemented
3#21444741C211yesmaximal, characteristic
4#21443840C211yesmaximal, characteristic, complemented
5#21443816C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic, complemented
7C61×#2463C211yesmaximal, characteristic
8#16840388C2211yescharacteristic
9#16839918—21no—
10#16839913—21no—
11#16839635—21no—
12#16839529C2211yescharacteristic
13#16839528—21no—
14#16839498—21no—
15#16839498—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C2×C22⋊Q8×C61—21no—
19C2×C4×D4×C61—21no—
20C61×#394—21no—
21C61×#393C2211yescharacteristic
22C61×#392C2211yescharacteristic
23C61×#388—21no—
24C61×#387—21no—
25C61×#386—21no—
26C61×#385C2211yescharacteristic
27C2×#11758202—41no—
28C2×#11758200—41no—
29#14519756—21no—
30#14519756—21no—
31#14519754—41no—
32#14519754—41no—
33C2×#11758196—41no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36#14519701—41no—
37#14519698—41no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519684—41no—
41C22×Q8×C61D411yescharacteristic
42C22×D4×C61—21no—
43C22×D4×C61D411yescharacteristic
44C23×C4×C61—21no—
45C23×C4×C61D411yescharacteristic
46C22⋊Q8×C61—44no—
47C4×D4×C61—44no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61C2311yescharacteristic
58C2×C42×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61D411yescharacteristic
63#95×C61D411yescharacteristic
64C24×C61—21no—
65C24×C61C2×D411yescharacteristic
66C2×Q8×C61—42no—
67C2×Q8×C61—41no—
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—42no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—42no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—42no—
80C22×C4×C61—42no—
81C22×C4×C61—42no—
82C22×C4×C61—41no—
83C22×C4×C61—81no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—41no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C4⋊C4×C61—24no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—42no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C42×C61—42no—
103C22⋊Dic61—22no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107#11758202—82no—
108#11758200—82no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111#11758196—41no—
112#11758196—41no—
113#11758196—82no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—22no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61#12011yescharacteristic
128C23×C61#13511yescharacteristic
129C23×C61#13711yescharacteristic
130Q8×C61—42no—
131Q8×C61—81no—
132D4×C61—42no—
133D4×C61—44no—
134D4×C61—44no—
135D4×C61—81no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—81no—
157C2×C4×C61—84no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—81no—
162C2×Dic61—81no—
163C2×Dic61—81no—
164C2×Dic61—81no—
165Dic122—81no—
166Dic122—81no—
167#92418—81no—
168#92418—81no—
169#12227—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—42no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61#45211yescharacteristic
187C22×C61#45611yescharacteristic
188C22×C61B(4,𝔽2)11yescharacteristic
189C4×C61—42no—
190C4×C61—41no—
191C4×C61—42no—
192C4×C61—42no—
193C4×C61—41no—
194C4×C61—81no—
195C4×C61—81no—
196Dic61—82no—
197Dic61—81no—
198Dic61—81no—
199#2463D6111yescharacteristic
200#2062—611no—
201#1602—611no—
202#1596—611no—
203#1351—611no—
204#1343—611no—
205#1326—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—41no—
209C2×C61—41no—
210C2×C61—82no—
211C2×C61#160311yescharacteristic
212C2×C61#219611yescharacteristic
213C2×C61#219711yescharacteristic
214#543—611no—
215C2×C22⋊Q8—21no—
216C2×C4×D4—21no—
217#451—1221no—
218#450—1221no—
219#394—21no—
220#393C2×D6111yescharacteristic
221#392C2×D6111yescharacteristic
222#388—21no—
223#387—21no—
224#386—21no—
225#385—1221no—
226#385C2×D6111yescharacteristic
227#342—611no—
228#342—1221no—
229#328—1221no—
230#328—1221no—
231#323—611no—
232#323—611no—
233C61#1222711yescharacteristic, complemented, Sylow
234C22×Q8C22⋊D6111yescharacteristic
235C22×D4—21no—
236C22×D4C22⋊D6111yescharacteristic
237C23×C4—21no—
238C23×C4C22⋊D6111yescharacteristic
239C2×Q16—2441no—
240C2×SD16—2441no—
241C22⋊Q8—44no—
242C22⋊Q8—1221no—
243C22⋊Q8—1221no—
244C22⋊Q8—2441no—
245C22⋊Q8—2441no—
246C4×D4—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—2441no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4C22⋊D6111yescharacteristic
259C2×C22⋊C4C22×D6111yescharacteristic
260C2×C42—21no—
261#103—2441no—
262#102—2441no—
263C22⋊C8—1221no—
264C22⋊C8—1221no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—2441no—
269#95C22⋊D6111yescharacteristic
270#95C22⋊D6111yescharacteristic
271C24—21no—
272C24C2×C22⋊D6111yescharacteristic
273C2×Q8—42no—
274C2×Q8—41no—
275C2×Q8—1221no—
276C2×Q8—1221no—
277C2×D4—42no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—81no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—2441no—
296C22×C4C2×C22⋊D6111yescharacteristic
297C22×C4C2×C22⋊D6111yescharacteristic
298Q16—4882no—
299SD16—4882no—
300C2×C8—2441no—
301C2×C8—2441no—
302C4⋊C4—24no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—4882no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—1222no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C42—42no—
323C23—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#1451974611yescharacteristic
335C23#1451979711yescharacteristic
336C23#1451980711yescharacteristic
337Q8—42no—
338Q8—81no—
339Q8—4881no—
340Q8—4881no—
341D4—42no—
342D4—44no—
343D4—44no—
344D4—81no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—84no—
367C2×C4—4881no—
368C2×C4—4881no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4—2441no—
373C2×C4—2441no—
374C8—4881no—
375C8—4881no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—42no—
384C22—41no—
385C22—41no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22#1683992411yescharacteristic
393C22#1683994511yescharacteristic
394C22#1683994911yescharacteristic
395C4—42no—
396C4—41no—
397C4—42no—
398C4—42no—
399C4—41no—
400C4—81no—
401C4—81no—
402C4—4882no—
403C4—4881no—
404C4—4881no—
405C2—21no—
406C2—21no—
407C2—41no—
408C2—41no—
409C2—82no—
410C2#2144478211yescharacteristic
411C2#2144780311yescharacteristic
412C2#2144780911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2463C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#392C22
hypercenter#2463D61
hypocenterC61#12227
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2463

Complements

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

NH ≅ G/Ntype
1. #21447172C2semidirect
2. #21444775C2semidirect
4. #21443840C2semidirect
6. #21443767C2semidirect
233. C61#12227semidirect

Maximal subgroups

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

subgroupindex
#214471722
#214447752
#214447412
#214438402
#214438162
#214437672
C61×#24632
#1222761