Finite Group Databasebeta

← #30600712

Subgroups — #30600712

Order 15616.

412 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 88 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#21462616C211yesmaximal, characteristic
2#21462012C211yesmaximal, characteristic
3#21461337C211yesmaximal, characteristic
4C2×#16840621C211yesmaximal, characteristic
5#21460710C211yesmaximal, characteristic
6#21460663C211yesmaximal, characteristic
7#21456968C211yesmaximal, characteristic
8#16840814—21no—
9#16840814—21no—
10#16840813—21no—
11#16840811—21no—
12#16840768—21no—
13#16840765C2211yescharacteristic
14C2×#14519844C2211yescharacteristic
15C2×#14519844C2211yescharacteristic
16#16840726—21no—
17C4×#11758217C2211yescharacteristic
18#16840642—21no—
19#16840642—21no—
20#16840622—21no—
21#16840621—21no—
22#16840621—21no—
23#16840621—21no—
24#16840314C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26#16840166—21no—
27#16840111—21no—
28#16840098C411yescharacteristic
29#16840097C411yescharacteristic
30#16840095C411yescharacteristic
31#16840056—21no—
32#16840055—21no—
33#16839812C2211yescharacteristic
34C61×#484C411yescharacteristic
35C2×#11758217—21no—
36C2×#11758217D411yescharacteristic
37C2×#11758217D411yescharacteristic
38C22×#92420—21no—
39C22×#92420—21no—
40#14519844—21no—
41#14519844—21no—
42#14519844—21no—
43#14519844—21no—
44#14519844—21no—
45#14519844—21no—
46#14519844D411yescharacteristic
47#14519844D411yescharacteristic
48C4⋊#92420—21no—
49C4⋊#92420—21no—
50C4⋊#92420—21no—
51#14519832—21no—
52#14519832—21no—
53#14519832—21no—
54C4×#92420—21no—
55C4×#92420—21no—
56C4×#92420—21no—
57C22×Dic122—21no—
58#14519776—21no—
59#14519776—21no—
60#14519776—21no—
61#14519776—21no—
62#14519776D411yescharacteristic
63#14519775D411yescharacteristic
64#14519767—21no—
65#14519756C2×C411yescharacteristic
66#14519754—21no—
67Q8×Dic61D411yescharacteristic
68#14519742—21no—
69#14519742D411yescharacteristic
70#14519733—21no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×#11758196—21no—
73C2×C4×Dic61C2311yescharacteristic
74#14519711—21no—
75#14519710—21no—
76#14519710—21no—
77#14519706—21no—
78#14519702—21no—
79#14519701—21no—
80#14519700—21no—
81C22⋊#92418C2×C411yescharacteristic
82C8×Dic61—21no—
83C22⋊Q8×C61C2×C411yescharacteristic
84C2×C4⋊C4×C61C2×C411yescharacteristic
85#107×C61—21no—
86#103×C61—21no—
87C22⋊C8×C61C2×C411yescharacteristic
88C2×Q8×C61C22⋊C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C22×Dic61—21no—
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61#4111yescharacteristic
94C2×Dic122—21no—
95C2×Dic122—41no—
96C2×Dic122—41no—
97C2×Dic122—81no—
98C2×Dic122—81no—
99C2×Dic122C22⋊C411yescharacteristic
100#11758217—21no—
101#11758217—21no—
102#11758217—21no—
103#11758217—41no—
104#11758217—41no—
105#11758217Q1612yes—
106C2×#92420—21no—
107C2×#92420—21no—
108C2×#92420—21no—
109C2×#92420—21no—
110C2×#92420—41no—
111C2×#92420—41no—
112C2×#92420—41no—
113C2×#92420—41no—
114C2×#92420—81no—
115C2×C8×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61C22⋊C411yescharacteristic
120C22⋊C4×C61—21no—
121C22⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61C22⋊C411yescharacteristic
126#11758196—21no—
127#11758196—21no—
128#11758196—21no—
129#11758196—21no—
130#11758196—21no—
131#11758196—41no—
132#11758196—41no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61C2×D411yescharacteristic
137C4×Dic61C2×D411yescharacteristic
138C4×Dic61#4111yescharacteristic
139C2×#92418—21no—
140C23×C61C4×D411yescharacteristic
141Q8×C61—41no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—81no—
155C2×Dic61#12011yescharacteristic
156C2×Dic61#12111yescharacteristic
157C2×Dic61#12111yescharacteristic
158C2×Dic61#12311yescharacteristic
159C2×Dic61C2×Q1611yescharacteristic
160C2×Dic61#13511yescharacteristic
161C2×Dic61#13711yescharacteristic
162C2×Dic61#13711yescharacteristic
163Dic122—41no—
164Dic122—41no—
165Dic122—41no—
166Dic122—82no—
167Dic122—81no—
168Dic122—81no—
169#92420—22no—
170#92420—41no—
171#92420—41no—
172#92420—41no—
173#92420—81no—
174#92420—81no—
175C8×C61—41no—
176#92418—41no—
177#9270—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#38611yescharacteristic
181C22×C61C4×Q1611yescharacteristic
182C22×C61#44111yescharacteristic
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—81no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191Dic61—81no—
192Dic61#45111yescharacteristic
193Dic61#45211yescharacteristic
194Dic61#46211yescharacteristic
195Dic61#46411yescharacteristic
196Dic61#47111yescharacteristic
197Dic61#47211yescharacteristic
198#3230—611no—
199#2962—611no—
200#1997—611no—
201#1550—611no—
202C2×#332—611no—
203#1301—611no—
204#1283—611no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61#187811yescharacteristic
208C2×C61#190711yescharacteristic
209C2×C61#191511yescharacteristic
210#533—611no—
211C2×C4⋊Q8—611no—
212#500—1221no—
213#487—1221no—
214#484—611no—
215#484—611no—
216#484—611no—
217#484#692311yescharacteristic
218#477—1221no—
219#477—1221no—
220#446—1221no—
221#446—1221no—
222#446—1221no—
223C8×Q8—1221no—
224#431—611no—
225#424—1221no—
226#423—611no—
227C2×C4⋊C8—611no—
228C2×C4⋊C8—611no—
229#405—1221no—
230C4×M16—611no—
231#343—1221no—
232#343—1221no—
233#333—1221no—
234#332—1221no—
235#332—1221no—
236#332—1221no—
237C61#927011yescharacteristic, complemented, Sylow
238C22×Q8—1221no—
239C2×M16—611no—
240C2×M16—611no—
241C2×M16—1221no—
242C22×C8—1221no—
243C22×C8—1221no—
244C4⋊Q8—611no—
245C4⋊Q8—611no—
246C4⋊Q8—1221no—
247C4⋊Q8—1221no—
248C4⋊Q8—1221no—
249C4⋊Q8—1221no—
250#125—1221no—
251C22⋊Q8—611no—
252C22⋊Q8—1221no—
253C22⋊Q8C2×#692311yescharacteristic
254C4×Q8—611no—
255C4×Q8—611no—
256C4×Q8—1221no—
257#117—1221no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4C2×#692311yescharacteristic
261C2×C42—611no—
262#107—21no—
263#107—1221no—
264#107—1221no—
265#107—1221no—
266C4⋊C8—611no—
267C4⋊C8—611no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278#103—21no—
279#103—1221no—
280#103—1221no—
281#103—1221no—
282C22⋊C8—611no—
283C22⋊C8C2×#692311yescharacteristic
284#97—1221no—
285#97—1221no—
286#97—1221no—
287C4×C8—1221no—
288C4×C8—1221no—
289C4×C8—1221no—
290C4×C8—1221no—
291C2×Q8—611no—
292C2×Q8—1221no—
293C2×Q8—4881no—
294C2×Q8—4881no—
295C2×Q8—2441no—
296C2×Q8—2441no—
297C2×Q8C22⋊#692311yescharacteristic
298C22×C4—21no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—1221no—
302C22×C4C22×#692311yescharacteristic
303M16—612no—
304M16—1221no—
305M16—1221no—
306M16—1221no—
307M16—2441no—
308M16—2441no—
309C2×C8—21no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1221no—
314C2×C8—1221no—
315C2×C8—4881no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—611no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4C22⋊#692311yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—1221no—
337C42—611no—
338C42—611no—
339C42—611no—
340C42—611no—
341C42—1221no—
342C42—1221no—
343C23D4×#692311yescharacteristic
344Q8—41no—
345Q8—4881no—
346Q8—4881no—
347Q8—4882no—
348Q8—2441no—
349Q8—2441no—
350Q8—2441no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—4881no—
369C2×C4—2441no—
370C2×C4C2×C22⋊#692311yescharacteristic
371C2×C4D4×#692311yescharacteristic
372C8—41no—
373C8—1222no—
374C8—4881no—
375C8—4881no—
376C8—2441no—
377C8—2441no—
378C8—2441no—
379C8—2441no—
380C22—21no—
381C22—21no—
382C22#1684071011yescharacteristic
383C22Q16×#692311yescharacteristic
384C22#1684080211yescharacteristic
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—611no—
391C4—611no—
392C4—611no—
393C4—611no—
394C4—611no—
395C4—611no—
396C4—1221no—
397C4—4881no—
398C4—2441no—
399C4—2441no—
400C2—21no—
401C2—21no—
402C2#2146181311yescharacteristic
403C2#2146185811yescharacteristic
404C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#484C4
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenter#484#6923
hypocenterC61#9270
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
237. C61#9270semidirect

Maximal subgroups

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

subgroupindex
#214626162
#214620122
#214613372
C2×#168406212
#214607102
#214606632
#214569682
#927061