Finite Group Databasebeta

← #30600799

Subgroups — #30600799

Order 15616.

416 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462716C211yesmaximal, characteristic
2#21461690C211yesmaximal, characteristic
3#21461253C211yesmaximal, characteristic
4#21461129C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic
6#21460674C211yesmaximal, characteristic
7#21455619C211yesmaximal, characteristic
8#16840814—22no—
9#16840813—21no—
10#16840812—21no—
11#16840785—21no—
12#16840784—21no—
13#16840781C2211yescharacteristic
14#16840780C2211yescharacteristic
15D61⋊(C4⋊C8)C2211yescharacteristic
16C2×#14519840—21no—
17#16840706C2211yescharacteristic
18#16840635—21no—
19#16840616—21no—
20#16840616—21no—
21#16840612—22no—
22#16840317C2211yescharacteristic
23C4×Q8×D61C2211yescharacteristic
24#16840072—21no—
25#16840071—21no—
26#16840058C411yescharacteristic, complemented
27#16840057C411yescharacteristic, complemented
28#16840044C411yescharacteristic, complemented
29#16839801—21no—
30#16839784C2211yescharacteristic
31#16839769—21no—
32C61×#475C411yescharacteristic, complemented
33C2×D61⋊C8—21no—
34C2×C4⋊#6923—21no—
35#14519844—22no—
36#14519844—21no—
37#14519844—21no—
38C4⋊#92420—22no—
39C4⋊#92420—21no—
40C4⋊#92420—21no—
41#14519840—42no—
42#14519834—21no—
43#14519834D411yescharacteristic
44#14519834D411yescharacteristic
45#14519832—22no—
46#14519832—22no—
47C4×#92420—21no—
48C4×#92420D412yes—
49(C2×#6923)⋊C4—21no—
50(C2×#6923)⋊C4—21no—
51C2×Q8×D61D411yescharacteristic
52C2×#11758189—21no—
53#14519777C2×C411yescharacteristic
54#14519768—21no—
55#14519757—21no—
56#14519753—21no—
57Q8×Dic61—21no—
58Q8×Dic61D411yescharacteristic
59C4×Dic122—21no—
60C4×Dic122C2×C411yescharacteristic
61#14519742—21no—
62#14519742—21no—
63#14519742D411yescharacteristic
64#14519735—21no—
65C4⋊C4×D61—21no—
66C4⋊C4×D61D411yescharacteristic
67C42×D61—21no—
68C42×D61C2311yescharacteristic
69#14519711—21no—
70#14519710—21no—
71#14519708—21no—
72C4⋊#92418C2×C411yescharacteristic
73#14519706—21no—
74#14519702—21no—
75#14519701—21no—
76#14519700—21no—
77C4⋊Q8×C61C2×C411yescharacteristic
78C4×Q8×C61C2×C411yescharacteristic
79#106×C61—21no—
80C4⋊C8×C61C2×C411yescharacteristic
81#103×C61—21no—
82C22×#6923—41no—
83C2×Q8×C61—21no—
84C2×Q8×C61C22⋊C411yescharacteristic
85Q8×D61—21no—
86Q8×D61—21no—
87Q8×D61—21no—
88Q8×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×D411yescharacteristic
93C2×C4×D61#4111yescharacteristic
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122C22⋊C411yescharacteristic
97C2×#92420—21no—
98C2×#92420—21no—
99C2×#92420—22no—
100C2×#92420—41no—
101C4⋊#6923—41no—
102C4⋊#6923—41no—
103D61⋊C8—41no—
104D61⋊C8—41no—
105C2×C8×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61C22⋊C411yescharacteristic
110C42×C61—21no—
111C42×C61C22×C411yescharacteristic
112#11758198—41no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—41no—
117C4⋊Dic61C22⋊C411yescharacteristic
118#11758196—21no—
119#11758196—21no—
120#11758196—21no—
121#11758196—41no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—41no—
126C4×Dic61C2×D411yescharacteristic
127C4×Dic61C2×D411yescharacteristic
128C4×Dic61#4111yescharacteristic
129C2×#92418—21no—
130#11758189—41no—
131#11758189—41no—
132C22×D61#12111yescharacteristic
133C2×#6923—81no—
134C2×#6923—81no—
135C2×#6923—81no—
136Q8×C61—21no—
137Q8×C61—21no—
138Q8×C61—81no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61#12011yescharacteristic
149C2×Dic61#12111yescharacteristic
150C2×Dic61#12311yescharacteristic
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—81no—
156C4×D61AGL(1,ℤ/8)11yescharacteristic
157C4×D61#13711yescharacteristic
158C4×D61#13711yescharacteristic
159C4×D61#13711yescharacteristic
160Dic122—21no—
161Dic122—21no—
162Dic122—41no—
163Dic122—41no—
164Dic122—42no—
165#92420—41no—
166#92420—41no—
167#92420—42no—
168#92420—81no—
169C8×C61—41no—
170#92418—41no—
171#9308—611nomaximal, Sylow
172C22×C61#38611yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61#46811yescharacteristic
176C2×D61#47011yescharacteristic
177#6923—161no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183C4×C61#41711yescharacteristic
184C4×C61#41911yescharacteristic
185Dic61—21no—
186Dic61—21no—
187Dic61—41no—
188Dic61—41no—
189Dic61—81no—
190Dic61#46811yescharacteristic
191Dic61#47011yescharacteristic
192#3078—611no—
193#2983—611no—
194#1805—611no—
195#1518—611no—
196#1481—611no—
197#1301—611no—
198#1286—611no—
199C2×C61#188111yescharacteristic
200C2×C61#189411yescharacteristic
201C2×C61#190511yescharacteristic
202D61—21no—
203D61—21no—
204#533—611no—
205C2×C4×Q8—611no—
206#479—1221no—
207#479—1221no—
208#477—611no—
209#477—611no—
210#475—611no—
211#475#692311yescharacteristic, complemented
212#446—1222no—
213#446—1221no—
214#446—1221no—
215#432—1221no—
216#432—1221no—
217#431—611no—
218#431—611no—
219#428—1221no—
220#423—611no—
221C2×C4⋊C8—611no—
222#419—1221no—
223C2×#103—1221no—
224#382—611no—
225#340—1221no—
226#328—1221no—
227#328—1221no—
228Q8⋊C8—1222no—
229C61#930811yescharacteristic, complemented, Sylow
230C22×Q8—611no—
231C2×M16—1221no—
232C22×C8—1221no—
233C4⋊Q8—611no—
234C4⋊Q8C2×#692311yescharacteristic
235#125—1221no—
236C22⋊Q8—1221no—
237C22⋊Q8—1221no—
238C4×Q8—611no—
239C4×Q8—611no—
240C4×Q8—611no—
241C4×Q8—1221no—
242C4×Q8—1221no—
243C4×Q8—1221no—
244C4×Q8—1221no—
245C4×Q8C2×#692311yescharacteristic
246#117—1221no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C42—611no—
251C2×C42—1221no—
252#107—1221no—
253#107—1221no—
254#106—21no—
255#106—1221no—
256C4⋊C8—611no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—1222no—
263C4⋊C8—1222no—
264C4⋊C8C2×#692311yescharacteristic
265#103—21no—
266#103—1221no—
267#103—1221no—
268#103—1221no—
269#103—2442no—
270C22⋊C8—611no—
271C22⋊C8—611no—
272C22⋊C8—1221no—
273#97—1222no—
274#97—1222no—
275C4×C8—612no—
276C4×C8—1221no—
277#95—1221no—
278#95—1221no—
279C2×Q8—21no—
280C2×Q8—611no—
281C2×Q8—1221no—
282C2×Q8—1221no—
283C2×Q8—1221no—
284C2×Q8—1221no—
285C2×Q8—1221no—
286C2×Q8—1221no—
287C2×Q8C22⋊#692311yescharacteristic
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—2441no—
294M16—2441no—
295M16—2441no—
296C2×C8—21no—
297C2×C8—1222no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—2441no—
302C2×C8—2441no—
303C2×C8—2441no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4C22⋊#692311yescharacteristic
319C22⋊C4—2441no—
320C42—21no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—1221no—
325C42—1221no—
326C42—1221no—
327C42—2441no—
328C42C22×#692311yescharacteristic
329C23—611no—
330Q8—21no—
331Q8—21no—
332Q8—81no—
333Q8—1221no—
334Q8—1221no—
335Q8—2442no—
336Q8—2441no—
337Q8—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4C2×C22⋊#692311yescharacteristic
360C2×C4D4×#692311yescharacteristic
361C2×C4D4×#692311yescharacteristic
362C8—41no—
363C8—4881no—
364C8—2442no—
365C8—2441no—
366C8—2441no—
367C8—2441no—
368C22—611no—
369C22—611no—
370C22—1221no—
371C22—1221no—
372C22#1684071011yescharacteristic
373C4—21no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—611no—
379C4—611no—
380C4—1221no—
381C4—1221no—
382C4—9761no—
383C4—4881no—
384C4—2441no—
385C4—2441no—
386C4#1684075311yescharacteristic
387C4#1684075511yescharacteristic
388C2—1221no—
389C2—1221no—
390C2#2146181611yescharacteristic
391C2#2146183411yescharacteristic
392C2#2146185511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#475C4
socleC22×C61#386
prime radicalC22×D61#121
cosocleC42×D61C23
hypercenter#475#6923
hypocenterC61#9308
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
26. #16840058C4semidirect
27. #16840057C4semidirect
28. #16840044C4semidirect
32. C61×#475C4semidirect
211. #475#6923semidirect
229. C61#9308semidirect

Maximal subgroups

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

subgroupindex
#214627162
#214616902
#214612532
#214611292
#214607092
#214606742
#214556192
#930861