Finite Group Databasebeta

← #29577360

Subgroups — #29577360

Order 15616.

446 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454455C211yesmaximal, characteristic
2#21451519C211yesmaximal, characteristic
3#21444421C211yesmaximal, characteristic, complemented
4#21444151C211yesmaximal, characteristic
5#21443713C211yesmaximal, characteristic, complemented
6#21443711C211yesmaximal, characteristic, complemented
7C61×#1528C211yesmaximal, characteristic, complemented
8C2×#14519734C2211yescharacteristic
9#16839824—22no—
10#16839821—22no—
11#16839819C2211yescharacteristic
12#16839785—21no—
13#16839725—21no—
14C4×#11758194C2211yescharacteristic
15#16839700C411yescharacteristic
16#16839697C411yescharacteristic
17#16839693C411yescharacteristic
18#16839688C411yescharacteristic
19#16839657—21no—
20#16839652—21no—
21#16839643—21no—
22#16839633—21no—
23#16839608C2211yescharacteristic
24#16839504—22no—
25#16839487—21no—
26#16839485—21no—
27C2×#125×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#330—22no—
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33#14519734—21no—
34#14519734—21no—
35#14519734—21no—
36#14519734—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47C4⋊#92418—21no—
48#14519706—24no—
49C22⋊#92418—21no—
50#14519689—24no—
51#14519688—21no—
52#14519688D412yes—
53C4×#92418—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684C2×C411yescharacteristic
60#14519684C2×C411yescharacteristic
61C2×M16×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65#125×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61D412yes—
75C4×C8×C61—21no—
76C23×D61C22⋊C411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91M16×C61—41no—
92M16×C61—41no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—42no—
112#11758198—42no—
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117#11758196—42no—
118#11758196—42no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—42no—
122#11758194—41no—
123#11758194—41no—
124C2×#92418—22no—
125C2×#92418—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—41no—
131C22×D61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
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×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×Dic61—22no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C4×D61—42no—
162C4×D61—42no—
163C8×C61—42no—
164C8×C61—81no—
165#92418—42no—
166#92418—81no—
167#9390—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61#38611yescharacteristic
171C22×C61#42111yescharacteristic
172C22×C61#42111yescharacteristic
173C2×D61—42no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—42no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191#2921—611no—
192#2611—611no—
193#1528—611no—
194#1528D6111yescharacteristic, complemented
195#1464—611no—
196#1300—611no—
197#1300—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#188411yescharacteristic
201C2×C61#189711yescharacteristic
202C2×C61#191511yescharacteristic
203D61—81no—
204C2×#125C2×D6111yescharacteristic
205C2×#117—611no—
206#433—1222no—
207#433—1222no—
208#432—611no—
209#432C2×D6111yescharacteristic
210#423—1221no—
211#407—1221no—
212C4×M16—611no—
213C4×M16C2×D6111yescharacteristic
214#400—611no—
215#399—611no—
216#398—611no—
217#397—611no—
218#389—1221no—
219#388—1221no—
220#387—1221no—
221#385—1221no—
222#376—611no—
223#330—22no—
224#330—1222no—
225#324—1221no—
226#323—1221no—
227C61#939011yescharacteristic, complemented, Sylow
228C23×C4—611no—
229C2×M16—21no—
230C2×M16—1221no—
231#125—21no—
232#125—21no—
233#125—21no—
234#125—21no—
235#117—1221no—
236#117—1221no—
237#117—1221no—
238#117—1221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4C4×D6111yescharacteristic
246C2×C4⋊C4C4×D6111yescharacteristic
247C2×C22⋊C4—611no—
248C2×C22⋊C4—611no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42—611no—
252C2×C42—1221no—
253C2×C42C22×D6111yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—1224no—
256C4⋊C8—1221no—
257C22⋊C8—21no—
258C22⋊C8—1224no—
259C22⋊C8—1221no—
260#97—21no—
261#97—612no—
262#97—1221no—
263#97C22⋊D6112yes—
264C4×C8—21no—
265C4×C8—1221no—
266#95—611no—
267#95—611no—
268#95—1221no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273C24—611no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4C2×C4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288M16—41no—
289M16—41no—
290M16—2441no—
291M16—2441no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—1222no—
295C2×C8—2441no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—2442no—
309C4⋊C4—2442no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—2442no—
315C22⋊C4—2442no—
316C42—1221no—
317C42—1221no—
318C42—2442no—
319C42#1175822211yescharacteristic
320C42D4×D6111yescharacteristic
321C42#1175822411yescharacteristic
322C42C2×C22⋊D6111yescharacteristic
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—2441no—
327C23—2441no—
328C23C22⋊C4×D6111yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—1222no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4#1451973711yescharacteristic
355C2×C4C4×C22⋊D6111yescharacteristic
356C2×C4#1451974511yescharacteristic
357C2×C4#1451974811yescharacteristic
358C2×C4#1451975011yescharacteristic
359C2×C4#1451975911yescharacteristic
360C8—42no—
361C8—81no—
362C8—4881no—
363C8—2442no—
364C22—21no—
365C22—21no—
366C22—4881no—
367C22—2442no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22#1683963811yescharacteristic
372C22#1683977711yescharacteristic
373C22#1683977711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—81no—
381C4—81no—
382C4—4881no—
383C4—2442no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C2—21no—
388C2—21no—
389C2—4881no—
390C2#2144619911yescharacteristic
391C2#2144626411yescharacteristic
392C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1528C2
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1528D61
hypocenterC61#9390
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
3. #21444421C2semidirect
5. #21443713C2semidirect
6. #21443711C2semidirect
7. C61×#1528C2semidirect
194. #1528D61semidirect
227. C61#9390semidirect

Maximal subgroups

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

subgroupindex
#214544552
#214515192
#214444212
#214441512
#214437132
#214437112
C61×#15282
#939061