Finite Group Databasebeta

← #30600671

Subgroups — #30600671

Order 15616.

450 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462620C211yesmaximal, characteristic
2#21461962C211yesmaximal, characteristic
3#21461328C211yesmaximal, characteristic
4#21461149C211yesmaximal, characteristic
5#21460689C211yesmaximal, characteristic
6#21460664C211yesmaximal, characteristic
7C2×#16840046C211yesmaximal, characteristic
8#16840814—22no—
9#16840812—21no—
10#16840811—21no—
11#16840779C2211yescharacteristic
12#16840765—21no—
13#16840765C2211yescharacteristic
14#16840765C2211yescharacteristic
15C2×#14519838—21no—
16C2×#14519838—21no—
17C4×#11758217—21no—
18C4×#11758217C2211yescharacteristic
19#16840621—22no—
20#16840612—21no—
21#16840612—21no—
22C2×#14519776C2211yescharacteristic
23C2×#14519742C2211yescharacteristic
24#16840046—21no—
25#16840046—21no—
26#16840046—21no—
27#16840046—21no—
28C2×#14519708C411yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519702C411yescharacteristic
31C2×#14519700C411yescharacteristic
32C2×#106×C61C411yescharacteristic
33C2×#11758217—21no—
34C2×#11758217—21no—
35C2×#11758217D411yescharacteristic
36C2×#11758217D411yescharacteristic
37#14519844—22no—
38#14519844—21no—
39#14519844—21no—
40#14519844D412yes—
41C4⋊#92420—22no—
42C4⋊#92420—21no—
43C4⋊#92420—21no—
44#14519838—42no—
45#14519838—42no—
46C22⋊#92420—21no—
47#14519832—22no—
48#14519832—21no—
49C4×#92420—22no—
50C4×#92420—21no—
51C4×#92420—21no—
52C22×Dic122—21no—
53C22×Dic122C2×C411yescharacteristic
54C22×#92418C2×C411yescharacteristic
55#14519776—21no—
56#14519776—21no—
57#14519776—21no—
58#14519776—21no—
59#14519742—21no—
60#14519742—21no—
61#14519742D411yescharacteristic
62#14519742D411yescharacteristic
63#14519742D411yescharacteristic
64#14519742D411yescharacteristic
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61C2311yescharacteristic
70#14519708—21no—
71#14519708—21no—
72#14519706—21no—
73#14519706—21no—
74#14519702—21no—
75#14519702—21no—
76#14519700—21no—
77#14519700—21no—
78C22×C8×C61C2×C411yescharacteristic
79C2×C4⋊C4×C61C2×C411yescharacteristic
80C2×C4⋊C4×C61C2×C411yescharacteristic
81#106×C61—21no—
82#106×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61#4111yescharacteristic
90C2×Dic122—22no—
91C2×Dic122—21no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122—41no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C2×Dic122C22⋊C411yescharacteristic
100C2×Dic122C22⋊C411yescharacteristic
101#11758217—21no—
102#11758217—21no—
103#11758217—21no—
104#11758217—41no—
105#11758217—41no—
106#11758217—41no—
107#11758217—41no—
108#11758217SD1612yes—
109C2×#92420—21no—
110C2×#92420—21no—
111C2×#92420—22no—
112C2×#92420—41no—
113C2×#92420—41no—
114C2×C8×C61—21no—
115C2×C8×C61—41no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61C22⋊C411yescharacteristic
120C4⋊C4×C61C22⋊C411yescharacteristic
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123#11758196—21no—
124#11758196—21no—
125#11758196—21no—
126#11758196—21no—
127#11758196—41no—
128#11758196—41no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61C2×D411yescharacteristic
134C4×Dic61C2×D411yescharacteristic
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61#4111yescharacteristic
137C2×#92418—21no—
138C2×#92418—41no—
139C23×C61C4×D411yescharacteristic
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—81no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#12011yescharacteristic
158C2×Dic61#12111yescharacteristic
159C2×Dic61#12111yescharacteristic
160C2×Dic61#12311yescharacteristic
161C2×Dic61C2×SD1611yescharacteristic
162C2×Dic61#13511yescharacteristic
163C2×Dic61AGL(1,ℤ/8)11yescharacteristic
164C2×Dic61#13711yescharacteristic
165Dic122—21no—
166Dic122—21no—
167Dic122—21no—
168Dic122—42no—
169Dic122—81no—
170Dic122—81no—
171Dic122—81no—
172Dic122—81no—
173Dic122#10112yescomplemented
174#92420—22no—
175#92420—41no—
176#92420—42no—
177#92420—81no—
178#92420—81no—
179C8×C61—41no—
180#92418—41no—
181#9252—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61#38611yescharacteristic
185C22×C61C4×SD1611yescharacteristic
186C22×C61#44011yescharacteristic
187C4×C61—21no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61—81no—
191C4×C61C2×#10111yescharacteristic
192C4×C61#41311yescharacteristic
193Dic61—22no—
194Dic61—21no—
195Dic61—21no—
196Dic61—41no—
197Dic61—81no—
198Dic61#44811yescharacteristic
199Dic61#44911yescharacteristic
200Dic61#46011yescharacteristic
201Dic61#46411yescharacteristic
202C2×#475—611no—
203Q8×M16—611no—
204#1966—611no—
205#1546—611no—
206#1487—611no—
207#1292—611no—
208#1283—611no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61#188011yescharacteristic
212C2×C61#190111yescharacteristic
213C2×C61#190211yescharacteristic
214C2×C4⋊Q8—611no—
215C2×C4×Q8—611no—
216#475—1221no—
217#475—1221no—
218#475—1221no—
219#475—1221no—
220#446—1222no—
221#446—1221no—
222C8×Q8—1221no—
223#431—611no—
224C2×#106—611no—
225C2×#106#692311yescharacteristic
226#423—611no—
227#423—611no—
228#423—1221no—
229C2×C4⋊C8—611no—
230C2×#103—611no—
231C2×#103—611no—
232C2×#101—1221no—
233C2×#101—1221no—
234C4×M16—611no—
235C4×M16—1221no—
236#332—1222no—
237Q8⋊C8—1221no—
238Q8⋊C8—1221no—
239C61#925211yescharacteristic, complemented, Sylow
240C22×Q8—611no—
241C22×Q8—1221no—
242C2×M16—611no—
243C2×M16—611no—
244C2×M16—1221no—
245C2×M16—1221no—
246C22×C8—611no—
247C22×C8C2×#692311yescharacteristic
248C4⋊Q8—1221no—
249C4⋊Q8—1221no—
250C4⋊Q8—1221no—
251C4⋊Q8—1221no—
252C4×Q8—611no—
253C4×Q8—611no—
254C4×Q8—611no—
255C4×Q8—611no—
256C4×Q8—1221no—
257C4×Q8—1221no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4C2×#692311yescharacteristic
262C2×C4⋊C4C2×#692311yescharacteristic
263C2×C42—611no—
264C2×C42—1221no—
265#106—21no—
266#106—21no—
267#106—1221no—
268#106—1221no—
269C4⋊C8—612no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8—1222no—
277C4⋊C8—1222no—
278#103—1221no—
279#103—1221no—
280#103—1221no—
281#103—1221no—
282#101—2442no—
283#101—2442no—
284C22⋊C8—1221no—
285#97—1221no—
286#97—1222no—
287C4×C8—1221no—
288C4×C8—1221no—
289C4×C8—1222no—
290C2×Q8—611no—
291C2×Q8—611no—
292C2×Q8—1222no—
293C2×Q8—1221no—
294C2×Q8—2441no—
295C2×Q8—2441no—
296C2×Q8—2441no—
297C2×Q8—2441no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8—2441no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4C22×#692311yescharacteristic
308M16—612no—
309M16—1221no—
310M16—1221no—
311M16—1221no—
312M16—2441no—
313M16—2441no—
314M16—2441no—
315M16—2441no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—1221no—
319C2×C8—1222no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4C22⋊#692311yescharacteristic
337C4⋊C4C22⋊#692311yescharacteristic
338C42—611no—
339C42—611no—
340C42—611no—
341C42—611no—
342C42—1221no—
343C42—1221no—
344C42—1221no—
345C42—1221no—
346C23D4×#692311yescharacteristic
347Q8—612no—
348Q8—1221no—
349Q8—1221no—
350Q8—1221no—
351Q8—4881no—
352Q8—4881no—
353Q8—4881no—
354Q8—4881no—
355Q8—2442no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—2441no—
375C2×C4—2442no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4C2×C22⋊#692311yescharacteristic
380C2×C4D4×#692311yescharacteristic
381C8—41no—
382C8—1222no—
383C8—4881no—
384C8—4881no—
385C8—2441no—
386C8—2442no—
387C8—2441no—
388C22—21no—
389C22—21no—
390C22#1684071011yescharacteristic
391C22SD16×#692311yescharacteristic
392C22#1684080111yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—611no—
398C4—611no—
399C4—611no—
400C4—611no—
401C4—1222no—
402C4—1221no—
403C4—1221no—
404C4—4881no—
405C4—2441no—
406C4D61⋊#10111yescharacteristic
407C4#1684074811yescharacteristic
408C2—21no—
409C2—21no—
410C2#2146181511yescharacteristic
411C2#2146184711yescharacteristic
412C2#2146184811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#106×C61C4
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC2×#106#6923
hypocenterC61#9252
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
173. Dic122#101semidirect
239. C61#9252semidirect

Maximal subgroups

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

subgroupindex
#214626202
#214619622
#214613282
#214611492
#214606892
#214606642
C2×#168400462
#925261