Finite Group Databasebeta

← #29575974

Subgroups — #29575974

Order 15616.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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#21454848C211yesmaximal, characteristic
2#21451736C211yesmaximal, characteristic
3#21444338C212yesmaximal, complemented
4#21443672C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic
6C2×#14519756C2211yescharacteristic
7#16839834—24no—
8#16839819—21no—
9#16839726C2212yes—
10C2×C22⋊#92418—21no—
11#16839692C411yescharacteristic, complemented
12#16839690—21no—
13#16839687C411yescharacteristic, complemented
14#16839682C411yescharacteristic, complemented
15#16839676—21no—
16#16839674C411yescharacteristic, complemented
17#16839646—21no—
18#16839635—21no—
19#16839625C2211yescharacteristic
20#16839498—24no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×#99×C61—21no—
23C4×C22⋊C4×C61C2212yes—
24C61×#342—21no—
25C22×Dic122C2×C411yescharacteristic
26C2×#11758194—22no—
27C22×#92418—22no—
28#14519756—22no—
29#14519756—22no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C4⋊#92418—22no—
39C22⋊#92418—22no—
40C22⋊#92418—22no—
41C22⋊#92418D414yes—
42#14519688—22no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×D4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C4×D4×C61—22no—
54C4×D4×C61—22no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—22no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C42×C61—22no—
60C2×C42×C61D411yescharacteristic
61#99×C61—24no—
62#95×C61—22no—
63C24×C61C22⋊C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—42no—
71C22×C4×C61—81no—
72C22×C4×C61—81no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D412yes—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4112yes—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C2×Dic122—22no—
85C2×Dic122—81no—
86C4⋊C4×C61—22no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—24no—
90C22⋊C4×C61—42no—
91C42×C61—21no—
92C42×C61—21no—
93C42×C61—82no—
94C22⋊Dic61—42no—
95C22⋊Dic61—42no—
96C22⋊Dic61—81no—
97C22⋊Dic61—81no—
98C4⋊Dic61—22no—
99#11758196—42no—
100#11758196—41no—
101#11758196—41no—
102#11758196—81no—
103#11758194—82no—
104C2×#92418—24no—
105C2×#92418—82no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61#10412yes—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61#12112yes—
117D4×C61—44no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—44no—
131C2×C4×C61—81no—
132C2×C4×C61—82no—
133C2×C4×C61—82no—
134C2×C4×C61C4×D412yes—
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149Dic122—82no—
150#92418—44no—
151#9183—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—42no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61#38611yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C22×C61#42111yescharacteristic
167C4×C61—21no—
168C4×C61—22no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—84no—
174Dic61—81no—
175Dic61—81no—
176Dic61—81no—
177Dic61—81no—
178#2973—611no—
179#2638—611no—
180C4×#99D6111yescharacteristic
181#1508—612no—
182#1284—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—42no—
186C2×C61—42no—
187C2×C61#187111yescharacteristic
188C2×C61#190911yescharacteristic
189C2×C61#191311yescharacteristic
190C2×C22⋊Q8—611no—
191C2×C4×D4C2×D6111yescharacteristic
192#435—1224no—
193#432—1221no—
194C2×#99—21no—
195#407—612no—
196C2×C22⋊C8—1221no—
197#398—611no—
198#397—611no—
199#397—1221no—
200#395—611no—
201#394—1221no—
202#393—611no—
203#387—1221no—
204#385—1221no—
205#381—611no—
206C4×C22⋊C4C2×D6112yes—
207#342—21no—
208#328—1224no—
209C61#918311yescharacteristic, complemented, Sylow
210C22×Q8—611no—
211C22×D4C22⋊D6111yescharacteristic
212C23×C4D24411yescharacteristic
213C23×C4C22×D6111yescharacteristic
214C2×M16—1222no—
215C22×C8—1222no—
216C22⋊Q8—1222no—
217C22⋊Q8—1222no—
218C4×D4—22no—
219C4×D4—22no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4C4×D6111yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4C4×D6111yescharacteristic
231C2×C22⋊C4C22⋊D6111yescharacteristic
232C2×C42—22no—
233C2×C42D24411yescharacteristic
234C4⋊C8—1222no—
235#99—24no—
236C22⋊C8—614no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239#97—1222no—
240#95—22no—
241#95—611no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248C24#1175819811yescharacteristic
249C24C2×C22⋊D6111yescharacteristic
250C2×Q8—1222no—
251C2×Q8—4881no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—42no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4C2×D24411yescharacteristic
269C22×C4D4×D6112yes—
270C22×C4#1175822412yes—
271M16—4882no—
272C2×C8—1224no—
273C2×C8—4882no—
274C4⋊C4—22no—
275C4⋊C4—1222no—
276C4⋊C4—4881no—
277C4⋊C4—2442no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—24no—
283C22⋊C4—42no—
284C22⋊C4—4881no—
285C22⋊C4—4881no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C42—21no—
289C42—21no—
290C42—82no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23#1451970512yes—
300C23C2×#1175819811yescharacteristic
301C23#1451974912yes—
302Q8—4882no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451973712yes—
333C2×C4#1451974711yescharacteristic
334C2×C4#1451976111yescharacteristic
335C8—2444no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1683963911yescharacteristic
349C22C2×#1451970511yescharacteristic
350C22#1683978011yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—4881no—
359C4—4881no—
360C4—4881no—
361C4—4881no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—42no—
366C2#2144611911yescharacteristic
367C2#2144633911yescharacteristic
368C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC4×#99×C61C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenterC4×#99D61
hypocenterC61#9183
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #21444338C2semidirect
4. #21443672C2semidirect
11. #16839692C4semidirect
13. #16839687C4semidirect
14. #16839682C4semidirect
16. #16839674C4semidirect
209. C61#9183semidirect

Maximal subgroups

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

subgroupindex
#214548482
#214517362
#214443382
#214436722
C4×#99×C612
#918361