Finite Group Databasebeta

← #30600989

Subgroups — #30600989

Order 15616.

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

normal subgroups only

This group has 548 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#21462673C211yesmaximal, characteristic
2#21461681C211yesmaximal, characteristic
3#21461259C212yesmaximal, complemented
4#21460693C212yesmaximal, complemented
5#21450996C211yesmaximal, characteristic
6#16840794—24no—
7#16840783—21no—
8C2×#14519835—21no—
9#16840732—21no—
10D61⋊(C22⋊C8)C2212yes—
11#16840704C2212yes—
12#16840640—21no—
13#16840616—24no—
14C2×#14519753C2211yescharacteristic
15C2×#14519737C2211yescharacteristic
16#16839702C411yescharacteristic, complemented
17#16839698C411yescharacteristic, complemented
18#16839681C411yescharacteristic, complemented
19#16839644—21no—
20#16839638—21no—
21#16839634—21no—
22#16839621—21no—
23#95×D61C2211yescharacteristic
24C61×#393C411yescharacteristic, complemented
25C2×#11758217—22no—
26C2×D61⋊C8—22no—
27C2×C4⋊#6923—22no—
28C2×C22⋊#6923—22no—
29C4⋊#92420—22no—
30#14519835—42no—
31#14519834D414yes—
32C22⋊#92420—22no—
33C22⋊#92420—22no—
34#14519832—22no—
35(C2×#6923)⋊C4—22no—
36C22×C22⋊D61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61C2311yescharacteristic
40#14519753—22no—
41#14519753—22no—
42#14519737—22no—
43#14519737—22no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×#11758198D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C22×Q8×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2×C411yescharacteristic
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61C22⋊C411yescharacteristic
64C23×D61C2×D411yescharacteristic
65C22×#6923—42no—
66C2×Q8×C61—22no—
67C2×Q8×C61—81no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C2×C22⋊D61—22no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—22no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—81no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×C4×D61—42no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—81no—
88C2×C4×D61—81no—
89C2×C4×D61C2×D412yes—
90C2×C4×D61#4112yes—
91C22⋊#6923—42no—
92C22⋊#6923—42no—
93#11758217—82no—
94C2×#92420—24no—
95C4⋊#6923—82no—
96D61⋊C8—82no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—81no—
99C22⋊Dic61—42no—
100#11758198—22no—
101#11758198—42no—
102C4⋊Dic61—22no—
103#11758196—22no—
104#11758196—42no—
105#11758196—41no—
106#11758196—41no—
107#11758196—81no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—41no—
117C22×D61—41no—
118C22×D61#12112yes—
119C22×D61AGL(1,ℤ/8)11yescharacteristic
120C22×D61#13712yes—
121C22×D61#13711yescharacteristic
122C2×#6923—82no—
123C2×#6923—82no—
124C2×#6923—82no—
125Q8×C61—82no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C4×D412yes—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—22no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61#12011yescharacteristic
153C2×Dic61#12311yescharacteristic
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—82no—
157C4×D61—82no—
158#92420—44no—
159#9385—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—42no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—81no—
167C22×C61#38611yescharacteristic
168C22×C61#41711yescharacteristic
169C22×C61#41911yescharacteristic
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—42no—
175C2×D61#46812yes—
176C2×D61#47012yes—
177#6923—162no—
178C4×C61—22no—
179C4×C61—41no—
180C4×C61—81no—
181C4×C61—81no—
182Dic61—21no—
183Dic61—21no—
184Dic61—42no—
185Dic61—41no—
186Dic61—41no—
187Dic61—81no—
188#2973—611no—
189#2564—611no—
190#1799—611no—
191#1520—612no—
192#1294—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—81no—
196C2×C61#188411yescharacteristic
197C2×C61#189411yescharacteristic
198C2×C61#191311yescharacteristic
199D61—22no—
200D61—22no—
201C2×C22⋊Q8—611no—
202C2×C4×D4—611no—
203#435—1224no—
204#432—1221no—
205C2×#99—1221no—
206#407—1221no—
207C2×C22⋊C8—612no—
208#400—611no—
209#399—611no—
210#395—611no—
211#393#692311yescharacteristic, complemented
212#387—1221no—
213#386—1221no—
214#385—1221no—
215#380—612no—
216#380—1221no—
217C2×#95—611no—
218#342—1221no—
219#328—1224no—
220C61#938511yescharacteristic, complemented, Sylow
221C22×Q8C2×#692311yescharacteristic
222C22×D4—611no—
223C23×C4—611no—
224C23×C4—611no—
225C23×C4—1221no—
226C2×M16—1222no—
227C22×C8—1222no—
228C22⋊Q8—1222no—
229C22⋊Q8—1222no—
230C4×D4—1222no—
231C4×D4—1222no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4C2×#692311yescharacteristic
244C2×C42—611no—
245C4⋊C8—1222no—
246#99—2442no—
247C22⋊C8—614no—
248C22⋊C8—1222no—
249C22⋊C8—1222no—
250#97—1222no—
251#95—21no—
252#95—611no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1222no—
258#95C2×#692311yescharacteristic
259C24—611no—
260C24C22⋊#692311yescharacteristic
261C2×Q8—22no—
262C2×Q8—81no—
263C2×D4—1221no—
264C2×D4—1222no—
265C2×D4—1221no—
266C2×D4—1222no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—4881no—
279C22×C4—4881no—
280C22×C4—4881no—
281C22×C4—2442no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2442no—
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287M16—4882no—
288C2×C8—1224no—
289C2×C8—4882no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—4881no—
293C4⋊C4—4882no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2442no—
297C22⋊C4—22no—
298C22⋊C4—81no—
299C22⋊C4—1222no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C42—1221no—
305C42—1221no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—612no—
312C23—611no—
313C23—611no—
314C23—612no—
315C23—2441no—
316C23—2441no—
317C23C2×C22⋊#692311yescharacteristic
318Q8—82no—
319D4—2442no—
320D4—2442no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1222no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4882no—
338C2×C4—4882no—
339C2×C4—4881no—
340C2×C4—4882no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4D4×#692312yes—
354C8—2444no—
355C22—21no—
356C22—21no—
357C22—42no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—81no—
362C22—612no—
363C22—612no—
364C22—1222no—
365C22—1222no—
366C22—2441no—
367C22—2441no—
368C22—2442no—
369C22#1684071011yescharacteristic
370C22#1684075311yescharacteristic
371C22#1684075511yescharacteristic
372C4—22no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—1221no—
377C4—1221no—
378C4—9762no—
379C4—4881no—
380C4—2442no—
381C4—2441no—
382C4—2441no—
383C2—21no—
384C2—21no—
385C2—81no—
386C2—1222no—
387C2—1222no—
388C2#2146182011yescharacteristic
389C2#2146183411yescharacteristic
390C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#393C4
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC22×C4×D61C23
hypercenter#393#6923
hypocenterC61#9385
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
3. #21461259C2semidirect
4. #21460693C2semidirect
16. #16839702C4semidirect
17. #16839698C4semidirect
18. #16839681C4semidirect
24. C61×#393C4semidirect
211. #393#6923semidirect
220. C61#9385semidirect

Maximal subgroups

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

subgroupindex
#214626732
#214616812
#214612592
#214606932
#214509962
#938561