Finite Group Databasebeta

← #29575858

Subgroups — #29575858

Order 15616.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#21455950C211yesmaximal, characteristic
2#21454909C211yesmaximal, characteristic
3#21445652C211yesmaximal, characteristic
4#21444435C211yesmaximal, characteristic
5#21444317C211yesmaximal, characteristic
6#21443717C211yesmaximal, characteristic
7C61×#1285C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840093—21no—
11#16840048C411yescharacteristic, complemented
12#16840048C411yescharacteristic, complemented
13#16839973C411yescharacteristic, complemented
14#16839973C411yescharacteristic, complemented
15#16839920—21no—
16#16839890—22no—
17#16839889—21no—
18#16839886—21no—
19#16839870—21no—
20#16839870—21no—
21#16839816—21no—
22#16839815C2211yescharacteristic
23#16839812—21no—
24C2×#14519700—21no—
25C2×#14519688C2211yescharacteristic
26#16839524—21no—
27#16839503—22no—
28#16839498—21no—
29#16839498—21no—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C4×C4⋊C4×C61C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×Dic244—21no—
35C2×Dic244—21no—
36C22×#92418—21no—
37#14519777C2×C411yescharacteristic
38#14519777C2×C411yescharacteristic
39#14519769—21no—
40#14519756—21no—
41#14519756—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×Dic122C2×C411yescharacteristic
47C4×Dic122C2×C411yescharacteristic
48C4×Dic122D411yescharacteristic
49C4×Dic122D411yescharacteristic
50#14519736—21no—
51C2×C4⋊Dic61D411yescharacteristic
52C2×#11758196—21no—
53C2×C4×Dic61—21no—
54#14519709—21no—
55#14519709—21no—
56C4⋊#92418—21no—
57#14519706—22no—
58#14519706—22no—
59#14519702—21no—
60#14519702—21no—
61#14519702—21no—
62#14519702—21no—
63#14519700—24no—
64C22⋊#92418D411yescharacteristic
65C22⋊#92418D411yescharacteristic
66#14519688—21no—
67#14519688—21no—
68#14519687—22no—
69C4×#92418—21no—
70C8×Dic61—22no—
71C2×C4⋊C4×C61—21no—
72C2×C42×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61C2×C411yescharacteristic
76C4⋊C8×C61C2×C411yescharacteristic
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79#97×C61—21no—
80#97×C61D412yes—
81#95×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C2×Dic122—22no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—41no—
93C2×Dic122C22⋊C411yescharacteristic
94C2×Dic122C22⋊C411yescharacteristic
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C42×C61—81no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61C22⋊C411yescharacteristic
112C4⋊Dic61C22⋊C411yescharacteristic
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117#11758196—41no—
118#11758196—41no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—41no—
124C2×#92418—22no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—41no—
128C2×#92418—41no—
129Dic244—42no—
130Dic244—42no—
131C23×C61#12111yescharacteristic
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155Dic122—21no—
156Dic122—21no—
157Dic122—21no—
158Dic122—42no—
159Dic122—41no—
160Dic122—41no—
161Dic122—81no—
162Dic122#10412yes—
163C8×C61—42no—
164C8×C61—41no—
165C8×C61—41no—
166#92418—41no—
167#92418—41no—
168#92418—42no—
169#9166—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61#47111yescharacteristic
174C22×C61#47311yescharacteristic
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—82no—
181C4×C61C2×#10411yescharacteristic
182C4×C61#42111yescharacteristic
183Dic61—22no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—81no—
188Dic61—81no—
189#3113—611no—
190#2984—611no—
191#1763—611no—
192#1531—611no—
193#1503—611no—
194#1302—611no—
195#1285D6111yescharacteristic
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#187111yescharacteristic
199C2×C61#190511yescharacteristic
200C2×C61#190811yescharacteristic
201#533—611no—
202C2×C4×Q8—611no—
203#483—1221no—
204#475—611no—
205#475—611no—
206#462—611no—
207#462—611no—
208#451—1221no—
209#446—1221no—
210#446—1222no—
211C8×Q8—1221no—
212#441—1221no—
213#441—1221no—
214#432—1221no—
215#432C2×D6111yescharacteristic
216#432C2×D6111yescharacteristic
217#431—611no—
218#431—1221no—
219C2×#103—1221no—
220C2×#97—611no—
221C4×C4⋊C4C2×D6111yescharacteristic
222#340—1221no—
223#330—1222no—
224#328—1221no—
225#328—1221no—
226C61#916611yescharacteristic, complemented, Sylow
227C22×Q8—611no—
228C2×Q16—1221no—
229C2×Q16—1221no—
230C22×C8—1221no—
231C4⋊Q8—611no—
232C4⋊Q8—611no—
233#125—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236C4×Q8—611no—
237C4×Q8—611no—
238C4×Q8—611no—
239C4×Q8—611no—
240C4×Q8—1221no—
241C4×Q8—1221no—
242C4×Q8—1221no—
243C4×Q8—1221no—
244#117—1221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C42—21no—
249C2×C42—1221no—
250C2×C42C22×D6111yescharacteristic
251#106—1221no—
252#106—1221no—
253C4⋊C8—21no—
254C4⋊C8—1222no—
255C4⋊C8—1222no—
256C4⋊C8—1221no—
257C4⋊C8C4×D6111yescharacteristic
258C4⋊C8C4×D6111yescharacteristic
259#103—1224no—
260#103—1221no—
261#103—1221no—
262#103—1221no—
263#103—1221no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—611no—
267C22⋊C8—611no—
268#97—21no—
269#97—1222no—
270#97—1221no—
271#97—1221no—
272#97D24412yes—
273C4×C8—1222no—
274C4×C8—1221no—
275#95—21no—
276C2×Q8—611no—
277C2×Q8—611no—
278C2×Q8—1222no—
279C2×Q8—1221no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×Q8—2441no—
283C22×C4—41no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4#1175822211yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289Q16—2442no—
290Q16—2442no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—1222no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—2441no—
298C2×C8—2441no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—611no—
302C4⋊C4—611no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—2441no—
315C42—81no—
316C42—1221no—
317C42—1221no—
318C42—1221no—
319C42—1221no—
320C42—2441no—
321C42C2×C4×D6111yescharacteristic
322C42C2×D24411yescharacteristic
323C42D4×D6111yescharacteristic
324C42#1175822611yescharacteristic
325C23#1451975011yescharacteristic
326Q8—612no—
327Q8—1221no—
328Q8—1221no—
329Q8—1221no—
330Q8—4881no—
331Q8—2442no—
332Q8—2441no—
333Q8—2441no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4C22⋊C4×D6111yescharacteristic
352C2×C4#1451973911yescharacteristic
353C2×C4C4×D24411yescharacteristic
354C2×C4#1451974711yescharacteristic
355C2×C4#1451975211yescharacteristic
356C2×C4#1451976211yescharacteristic
357C8—42no—
358C8—41no—
359C8—41no—
360C8—2441no—
361C8—2441no—
362C8—2442no—
363C22—21no—
364C22—21no—
365C22#1683964011yescharacteristic
366C22#1684002411yescharacteristic
367C22#1684003611yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—1222no—
375C4—4881no—
376C4—4881no—
377C4—2441no—
378C4—2441no—
379C4—2441no—
380C4#104×D6111yescharacteristic
381C4#1683977711yescharacteristic
382C2—21no—
383C2—21no—
384C2#2144612011yescharacteristic
385C2#2144631411yescharacteristic
386C2#2144633511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radicalC23×C61#121
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9166
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
11. #16840048C4semidirect
12. #16840048C4semidirect
13. #16839973C4semidirect
14. #16839973C4semidirect
226. C61#9166semidirect

Maximal subgroups

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

subgroupindex
#214559502
#214549092
#214456522
#214444352
#214443172
#214437172
C61×#12852
#916661