Finite Group Databasebeta

← #29736759

Subgroups — #29736759

Order 15616.

1194 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 191 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#21459622C211yesmaximal, characteristic, complemented
2#21456193C212yesmaximal, complemented
3#21446975C214yesmaximal, complemented
4#21446762C212yesmaximal, complemented
5#21446218C214yesmaximal, complemented
6C4×#14519694C211yesmaximal, characteristic, complemented
7C61×#2541C211yesmaximal, characteristic
8#16840471—24no—
9#16840469—22no—
10D4×Dic122—22no—
11#16840393C2212yes—
12#16840388—22no—
13#16840319C2212yes—
14C2×#14519756—22no—
15#16840237C2212yes—
16#16840126—24no—
17#16840108—22no—
18#16840108—22no—
19#16839767C2218yes—
20C2×#14519694C2212yes—
21C4×#11758194C2212yes—
22#16839531C2212yes—
23#16839522C2218yes—
24C2×#127×C61C2211yescharacteristic
25C2×#127×C61C2212yes—
26C2×#121×C61—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#392—22no—
29C61×#390C2212yes—
30C4×C4⋊C4×C61C2211yescharacteristic
31C22×Dic122—22no—
32C2×#11758194C2314yes—
33#14519777D412yescomplemented
34#14519777D412yescomplemented
35#14519776—24no—
36#14519769D414yescomplemented
37#14519768—24no—
38#14519756—24no—
39#14519756—24no—
40#14519756—22no—
41#14519756—24no—
42#14519756—22no—
43#14519754—28no—
44#14519754—28no—
45C4×Dic122—22no—
46C4×Dic122—22no—
47D4×Dic61—24no—
48D4×Dic61—24no—
49#14519736C2314yes—
50C2×C4⋊Dic61—22no—
51C2×#11758196—24no—
52C2×C22⋊Dic61—24no—
53#14519698—28no—
54#14519698—28no—
55#14519694—24no—
56#14519688—22no—
57C4×#92418—22no—
58C22×D4×C61—24no—
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61C2312yes—
62C22×D4×C61C2311yescharacteristic
63C23×C4×C61D412yes—
64#127×C61—28no—
65#127×C61—22no—
66#127×C61—22no—
67#121×C61—48no—
68C4×D4×C61—22no—
69C4×D4×C61—22no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2311yescharacteristic
72C2×C22⋊C4×C61—24no—
73C2×C22⋊C4×C61D412yes—
74C2×C42×C61C2312yes—
75C2×C42×C61C2311yescharacteristic
76#95×C61—21no—
77C24×C61—22no—
78C24×C61C2×D412yes—
79C2×D4×C61—22no—
80C2×D4×C61—24no—
81C2×D4×C61—24no—
82C2×D4×C61—22no—
83C2×D4×C61—24no—
84C2×D4×C61—44no—
85C2×D4×C61—48no—
86C2×D4×C61—48no—
87C2×D4×C61—41no—
88C2×D4×C61—42no—
89C2×D4×C61—41no—
90C2×D4×C61—82no—
91C2×D4×C61—84no—
92C2×D4×C61#4114yes—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—44no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D412yes—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2411yescharacteristic
101C22×Dic61—24no—
102C22×Dic61—24no—
103C2×Dic122—22no—
104C2×Dic122—24no—
105C2×Dic122—22no—
106C2×Dic122—84no—
107C4⋊C4×C61—24no—
108C4⋊C4×C61—22no—
109C22⋊C4×C61—24no—
110C22⋊C4×C61—48no—
111C42×C61—24no—
112C42×C61C2×D412yes—
113C42×C61C2×D412yes—
114C22⋊Dic61—28no—
115C22⋊Dic61—24no—
116C4⋊Dic61—24no—
117C4⋊Dic61—22no—
118C4⋊Dic61—22no—
119C4⋊Dic61C2×D414yes—
120C4⋊Dic61C2×D414yes—
121#11758196—28no—
122#11758196—24no—
123#11758196—24no—
124C4×Dic61—24no—
125#11758194—24no—
126#11758194—24no—
127C2×#92418—24no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61—42no—
131C23×C61—42no—
132C23×C61—44no—
133C23×C61—44no—
134C23×C61—42no—
135C23×C61—42no—
136C23×C61—42no—
137C23×C61#12414yes—
138C23×C61C22×D411yescharacteristic
139D4×C61—28no—
140D4×C61—48no—
141D4×C61—82no—
142D4×C61—84no—
143D4×C61—816no—
144D4×C61—82no—
145C2×C4×C61—22no—
146C2×C4×C61—24no—
147C2×C4×C61—22no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—44no—
152C2×C4×C61—42no—
153C2×C4×C61—82no—
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12012yes—
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61C22×D412yes—
158C2×C4×C61C2×#4112yes—
159C2×C4×C612−1+412yes—
160C2×Dic61—24no—
161C2×Dic61—24no—
162C2×Dic61—84no—
163C2×Dic61—84no—
164Dic122—44no—
165Dic122—82no—
166Dic122—84no—
167#92418—44no—
168#25918—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—24no—
172C22×C61—44no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—82no—
176C22×C61—84no—
177C22×C61—84no—
178C22×C61—82no—
179C22×C61—82no—
180C22×C61—82no—
181C22×C61C2×#12011yescharacteristic
182C22×C61C2×#12411yescharacteristic
183C22×C61#53611yescharacteristic
184C4×C61—21no—
185C4×C61—22no—
186C4×C61—44no—
187C4×C61—42no—
188C4×C61#45312yes—
189C4×C61#54814yes—
190Dic61—44no—
191Dic61—44no—
192#3501—611no—
193#3138—612no—
194#2541D6111yescharacteristic
195#2027—614no—
196#1986—612no—
197#1887—614no—
198C4×#100—611no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—44no—
202C2×C61—162no—
203C2×C61#243611yescharacteristic
204C2×C61C2×#45311yescharacteristic
205C2×C61#302111yescharacteristic
206#554—1224no—
207#554—1222no—
208D4×Q8—1222no—
209#544—612no—
210#543—1222no—
211#533—612no—
212C2×#127C2×D6112yes—
213C2×#127C2×D6111yescharacteristic
214C2×C22⋊Q8—1222no—
215C2×#121—22no—
216#518—612no—
217C2×C4×D4C2×D6111yescharacteristic
218#490—1224no—
219#486—1222no—
220#486—1222no—
221#418—618no—
222C2×#100—612no—
223C4×M16—612no—
224#392—22no—
225#390C2×D6112yes—
226C4×C4⋊C4C2×D6111yescharacteristic
227#343—612no—
228#339—618no—
229C61#2591811yescharacteristic, complemented, Sylow
230C22×Q8—1222no—
231C22×D4—24no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4C22×D6112yes—
235C22×D4C22×D6111yescharacteristic
236C23×C4C22⋊D6112yes—
237C2×M16—614no—
238C4⋊Q8—612no—
239C4⋊Q8—612no—
240C4⋊Q8—1224no—
241#127—28no—
242#127—22no—
243#127—22no—
244#125—614no—
245#125—1224no—
246C22⋊Q8—1228no—
247C22⋊Q8—1228no—
248C22⋊Q8—1224no—
249C22⋊Q8—1224no—
250C22⋊Q8—1222no—
251C22⋊Q8—1224no—
252C22⋊Q8—1222no—
253#121—48no—
254C4×Q8—1222no—
255C4×Q8—1222no—
256C4×D4—22no—
257C4×D4—22no—
258C4×D4—1224no—
259C4×D4—1224no—
260#117—614no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—1224no—
263C2×C4⋊C4—1222no—
264C2×C4⋊C4C22×D6111yescharacteristic
265C2×C22⋊C4—24no—
266C2×C22⋊C4—1224no—
267C2×C22⋊C4C22⋊D6112yes—
268C2×C42C22×D6112yes—
269C2×C42C22×D6111yescharacteristic
270#102—1228no—
271#102—1228no—
272#100—1224no—
273#97—1222no—
274C4×C8—1222no—
275#95—21no—
276C24—22no—
277C24C2×C22⋊D6112yes—
278C2×Q8—1224no—
279C2×Q8—1222no—
280C2×Q8—1222no—
281C2×Q8—4884no—
282C2×D4—22no—
283C2×D4—24no—
284C2×D4—24no—
285C2×D4—22no—
286C2×D4—24no—
287C2×D4—44no—
288C2×D4—48no—
289C2×D4—48no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—82no—
294C2×D4—84no—
295C2×D4#1175822414yes—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—44no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4C2×C22⋊D6111yescharacteristic
303C22×C4C2×C22⋊D6112yes—
304C22×C4C2×C22⋊D6111yescharacteristic
305C22×C4C23×D6111yescharacteristic
306M16—1224no—
307M16—1224no—
308C2×C8—1224no—
309C4⋊C4—24no—
310C4⋊C4—22no—
311C4⋊C4—614no—
312C4⋊C4—614no—
313C4⋊C4—1228no—
314C4⋊C4—1224no—
315C4⋊C4—1224no—
316C4⋊C4—1222no—
317C4⋊C4—1224no—
318C4⋊C4—1222no—
319C22⋊C4—24no—
320C22⋊C4—48no—
321C22⋊C4—1228no—
322C22⋊C4—1224no—
323C42—24no—
324C42—1224no—
325C42D4×D6112yes—
326C42D4×D6112yes—
327C23—22no—
328C23—22no—
329C23—42no—
330C23—42no—
331C23—44no—
332C23—44no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23#1451976414yes—
337C23C22×C22⋊D6111yescharacteristic
338Q8—4882no—
339Q8—4884no—
340Q8—2444no—
341D4—28no—
342D4—48no—
343D4—82no—
344D4—84no—
345D4—816no—
346D4—82no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—82no—
356C2×C4—1224no—
357C2×C4—1224no—
358C2×C4—4884no—
359C2×C4—4884no—
360C2×C4#1451974512yes—
361C2×C4#1451974511yescharacteristic
362C2×C4#1451974511yescharacteristic
363C2×C4C2×D4×D6112yes—
364C2×C4C2×#1175822412yes—
365C2×C4#1451982412yes—
366C8—2444no—
367C22—21no—
368C22—21no—
369C22—24no—
370C22—44no—
371C22—42no—
372C22—42no—
373C22—82no—
374C22—84no—
375C22—84no—
376C22—82no—
377C22—82no—
378C22—82no—
379C22C2×#1451974511yescharacteristic
380C22C2×#1451976411yescharacteristic
381C22#1684033311yescharacteristic
382C4—21no—
383C4—22no—
384C4—44no—
385C4—42no—
386C4—2444no—
387C4—2444no—
388C4#1683992912yes—
389C4#1684041814yes—
390C2—21no—
391C2—21no—
392C2—44no—
393C2—162no—
394C2#2144947811yescharacteristic
395C2C2×#1683992911yescharacteristic
396C2#2145519011yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2541C2
socleC22×C61C2×#120
hypercenter#2541D61
hypocenterC61#25918
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #21459622C2semidirect
2. #21456193C2semidirect
3. #21446975C2semidirect
4. #21446762C2semidirect
5. #21446218C2semidirect
6. C4×#14519694C2semidirect
33. #14519777D4semidirect
34. #14519777D4semidirect
36. #14519769D4semidirect
229. C61#25918semidirect

Maximal subgroups

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

subgroupindex
#214596222
#214561932
#214469752
#214467622
#214462182
C4×#145196942
C61×#25412
#2591861