Finite Group Databasebeta

← #29592895

Subgroups — #29592895

Order 15616.

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

normal subgroups only

This group has 422 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×#2824C211yesmaximal, 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
18C61×#400—21no—
19C61×#397—21no—
20C61×#394—21no—
21C61×#394—21no—
22C61×#393—21no—
23C61×#393C2211yescharacteristic
24C61×#392C2211yescharacteristic
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×C61D411yescharacteristic
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61C2311yescharacteristic
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C24×C61—21no—
63C24×C61C2×D411yescharacteristic
64C2×Q8×C61—41no—
65C2×Q8×C61—81no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—81no—
70C2×D4×C61—81no—
71C2×D4×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61—81no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—41no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86C4⋊C4×C61—81no—
87C4⋊C4×C61—81no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊C4×C61—81no—
93C22⋊C4×C61—81no—
94C22⋊C4×C61—81no—
95C22⋊C4×C61—81no—
96C22⋊C4×C61—81no—
97C22⋊Dic61—22no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101#11758202—82no—
102#11758200—82no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105#11758196—41no—
106#11758196—41no—
107#11758196—82no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61#12011yescharacteristic
122C23×C61#13511yescharacteristic
123C23×C61#13711yescharacteristic
124Q8×C61—42no—
125Q8×C61—81no—
126D4×C61—42no—
127D4×C61—81no—
128D4×C61—82no—
129D4×C61—82no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—81no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—81no—
155C2×Dic61—81no—
156C2×Dic61—81no—
157C2×Dic61—81no—
158Dic122—81no—
159Dic122—81no—
160#92418—81no—
161#92418—81no—
162#12230—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61#45211yescharacteristic
180C22×C61#45611yescharacteristic
181C22×C61B(4,𝔽2)11yescharacteristic
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61—81no—
186C4×C61—81no—
187C4×C61—81no—
188C4×C61—81no—
189Dic61—82no—
190Dic61—81no—
191Dic61—81no—
192#2824D6111yescharacteristic
193#2062—611no—
194#1602—611no—
195#1596—611no—
196#1351—611no—
197#1343—611no—
198#1326—611no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—41no—
202C2×C61—41no—
203C2×C61—161no—
204C2×C61#160311yescharacteristic
205C2×C61#219911yescharacteristic
206C2×C61#220011yescharacteristic
207#543—611no—
208#451—1221no—
209#450—1221no—
210#400—21no—
211#397—21no—
212#394—21no—
213#394—21no—
214#393—21no—
215#393C2×D6111yescharacteristic
216#392C2×D6111yescharacteristic
217#386—21no—
218#385—1221no—
219#385C2×D6111yescharacteristic
220#342—611no—
221#342—1221no—
222#328—1221no—
223#328—1221no—
224#323—611no—
225#323—611no—
226C61#1223011yescharacteristic, complemented, Sylow
227C22×Q8C22⋊D6111yescharacteristic
228C22×D4—21no—
229C22×D4C22⋊D6111yescharacteristic
230C23×C4C22⋊D6111yescharacteristic
231C2×Q16—2441no—
232C2×SD16—2441no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—2441no—
236C22⋊Q8—2441no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—2441no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4C22⋊D6111yescharacteristic
249C2×C22⋊C4C22×D6111yescharacteristic
250#103—2441no—
251#102—2441no—
252C22⋊C8—1221no—
253C22⋊C8—1221no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—2441no—
260#95C22⋊D6111yescharacteristic
261#95C22⋊D6111yescharacteristic
262C24—21no—
263C24C2×C22⋊D6111yescharacteristic
264C2×Q8—41no—
265C2×Q8—81no—
266C2×Q8—1221no—
267C2×Q8—1221no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—81no—
272C2×D4—81no—
273C2×D4—81no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—81no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4C2×C22⋊D6111yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286Q16—4882no—
287SD16—4882no—
288C2×C8—2441no—
289C2×C8—2441no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—4882no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—41no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—1222no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#1451974611yescharacteristic
322C23#1451979711yescharacteristic
323C23#1451980711yescharacteristic
324Q8—42no—
325Q8—81no—
326Q8—4881no—
327Q8—4881no—
328D4—42no—
329D4—81no—
330D4—82no—
331D4—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
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—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C8—4881no—
361C8—4881no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1683992411yescharacteristic
379C22#1683994511yescharacteristic
380C22#1683994911yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—4882no—
389C4—4881no—
390C4—4881no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2#2144478211yescharacteristic
397C2#2144782011yescharacteristic
398C2#2144782611yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2824C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#392C22
hypercenter#2824D61
hypocenterC61#12230
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2824

Complements

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

NH ≅ G/Ntype
1. #21447172C2semidirect
2. #21444775C2semidirect
4. #21443840C2semidirect
6. #21443767C2semidirect
226. C61#12230semidirect

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×#28242
#1223061