Finite Group Databasebeta

← #29592238

Subgroups — #29592238

Order 15616.

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

normal subgroups only

This group has 440 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#21454076C211yesmaximal, characteristic, complemented
2#21444839C211yesmaximal, characteristic
3#21444771C211yesmaximal, characteristic
4#21443842C211yesmaximal, characteristic, complemented
5#21443839C211yesmaximal, characteristic, complemented
6#21443749C211yesmaximal, characteristic, complemented
7C61×#2022C211yesmaximal, characteristic
8#16840078—21no—
9#16839900—21no—
10#16839704—21no—
11#16839698C2211yescharacteristic
12#16839696—21no—
13#16839694—21no—
14#16839685—21no—
15#16839683—21no—
16#16839674C2211yescharacteristic
17#16839622—21no—
18#16839496—21no—
19#16839496—21no—
20#16839486C2211yescharacteristic
21#16839486C2211yescharacteristic
22C61×#534C2211yescharacteristic
23C2×#123×C61—21no—
24C2×#99×C61—21no—
25C61×#381C2211yescharacteristic
26C61×#342C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758200—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38#14519708—41no—
39#14519700—41no—
40#14519698—41no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C22×D4×C61—21no—
50C23×C4×C61D411yescharacteristic
51#123×C61—42no—
52#123×C61—41no—
53#123×C61—42no—
54#121×C61—21no—
55#121×C61—21no—
56#120×C61—41no—
57C2×C4⋊C4×C61—41no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—41no—
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C22⋊C4×C61C2311yescharacteristic
62#99×C61—42no—
63#95×C61—21no—
64#95×C61—21no—
65C24×C61—21no—
66C24×C61C2×D411yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61SD1612yescomplemented
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C2×Dic122—41no—
90C2×Dic122—81no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—44no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—44no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊Dic61—81no—
102C22⋊Dic61—81no—
103#11758200—82no—
104C4⋊Dic61—41no—
105C4⋊Dic61—81no—
106C4⋊Dic61—81no—
107C4⋊Dic61—81no—
108#11758196—81no—
109#11758196—81no—
110#11758196—81no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—81no—
121C23×C61—81no—
122C23×C61#12011yescharacteristic
123C23×C61C2×SD1611yescharacteristic
124C23×C61#13711yescharacteristic
125D4×C61—81no—
126D4×C61—81no—
127D4×C61—81no—
128D4×C61—81no—
129D4×C61—81no—
130D4×C61—81no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—42no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
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—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161Dic122—42no—
162Dic122—81no—
163#92418—81no—
164#92418—81no—
165#12125—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×C61—82no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—161no—
180C22×C61#44811yescharacteristic
181C22×C61#45311yescharacteristic
182C22×C61B(4,𝔽2)11yescharacteristic
183C4×C61—42no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—81no—
187C4×C61—82no—
188C4×C61—81no—
189Dic61—81no—
190Dic61—81no—
191Dic61—81no—
192Dic61—81no—
193#2841—611no—
194#2022D6111yescharacteristic
195#1613—611no—
196#1601—611no—
197#1352—611no—
198#1351—611no—
199#1317—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—41no—
203C2×C61—41no—
204C2×C61—161no—
205C2×C61#159611yescharacteristic
206C2×C61#220011yescharacteristic
207C2×C61#220111yescharacteristic
208#534C2×D6111yescharacteristic
209C2×#123—21no—
210#481—1221no—
211#448—1221no—
212C2×#99—21no—
213#400—1221no—
214#399—611no—
215#398—1221no—
216#398—1221no—
217#396—1221no—
218#395—1221no—
219#393—611no—
220#381C2×D6111yescharacteristic
221#380—1221no—
222#342C2×D6111yescharacteristic
223#327—1221no—
224#327—1221no—
225#323—611no—
226#323—611no—
227C61#1212511yescharacteristic, complemented, Sylow
228C22×Q8—611no—
229C22×D4—21no—
230C23×C4C22⋊D6111yescharacteristic
231C2×SD16—2441no—
232#123—42no—
233#123—41no—
234#123—42no—
235#121—21no—
236#121—21no—
237#120—41no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—41no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4C22⋊D6111yescharacteristic
251C2×C22⋊C4C22×D6111yescharacteristic
252#106—2441no—
253#103—2441no—
254#102—2441no—
255#99—42no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258#95—21no—
259#95—21no—
260#95—611no—
261#95—611no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266C24—21no—
267C24C2×C22⋊D6111yescharacteristic
268C2×Q8—4881no—
269C2×Q8—2441no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4#1175820012yescomplemented
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292SD16—4882no—
293C2×C8—2441no—
294C2×C8—2441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—44no—
298C4⋊C4—4881no—
299C4⋊C4—4881no—
300C4⋊C4—4881no—
301C4⋊C4—4881no—
302C4⋊C4—4881no—
303C4⋊C4—4881no—
304C4⋊C4—2441no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—44no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—4881no—
313C22⋊C4—4881no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—81no—
322C23—81no—
323C23#1451974511yescharacteristic
324C23C2×#1175820011yescharacteristic
325C23#1451980711yescharacteristic
326Q8—4881no—
327Q8—2442no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C8—4881no—
365C8—4881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—82no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—161no—
380C22#1683990011yescharacteristic
381C22#1683992911yescharacteristic
382C22#1683994811yescharacteristic
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—4881no—
390C4—4881no—
391C4—4881no—
392C4—4881no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—161no—
398C2#2144474111yescharacteristic
399C2#2144782311yescharacteristic
400C2#2144783011yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2022C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#534C22
hypercenter#2022D61
hypocenterC61#12125
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #21454076C2semidirect
4. #21443842C2semidirect
5. #21443839C2semidirect
6. #21443749C2semidirect
82. C22×C4×C61SD16semidirect
227. C61#12125semidirect
289. C22×C4#11758200semidirect

Maximal subgroups

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

subgroupindex
#214540762
#214448392
#214447712
#214438422
#214438392
#214437492
C61×#20222
#1212561