Finite Group Databasebeta

← #30605395

Subgroups — #30605395

Order 15616.

522 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461679C211yesmaximal, characteristic, complemented
2#21461058C211yesmaximal, characteristic, complemented
3#21460800C212yesmaximal, complemented
4#21460798C212yesmaximal, complemented
5#21450779C211yesmaximal, characteristic
6#16840779—21no—
7C2×#14519835—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840606C2212yes—
11#16840605—21no—
12C2×#14519751—21no—
13C2×#14519751C411yescharacteristic, complemented
14C2×C4×C22⋊D61C2211yescharacteristic
15#16839694C411yescharacteristic, complemented
16#16839689C2211yescharacteristic
17#16839680C411yescharacteristic, complemented
18#16839672C2211yescharacteristic
19#16839654—21no—
20#16839641—21no—
21#16839640—21no—
22C2×#95×C61C411yescharacteristic, complemented
23C2×C4⋊#6923—41no—
24C2×C22⋊#6923—22no—
25#14519844—41no—
26#14519835—42no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×D244—21no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35#14519751—42no—
36#14519751—42no—
37#14519751—41no—
38#14519751—41no—
39C4×C22⋊D61—41no—
40C4×C22⋊D61—41no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196C2×C411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198C2311yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52#14519684—21no—
53#14519684—21no—
54C23×C4×C61—21no—
55C23×C4×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61C2×C411yescharacteristic
58#95×C61C2×C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C23×D61—21no—
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61D812yes—
79C2×C22⋊D61SD1612yes—
80C22×Dic61—21no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×D244—42no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—81no—
89C2×D244—81no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—81no—
93C22⋊#6923—42no—
94C22⋊#6923—42no—
95C2×#92420—42no—
96C4⋊#6923—82no—
97C22⋊Dic61—41no—
98#11758198—41no—
99#11758198—42no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104#11758198—42no—
105#11758198—81no—
106C4⋊Dic61—42no—
107C4⋊Dic61—41no—
108#11758196—41no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61#10212yes—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61C2×D811yescharacteristic
129C22×D61C2×SD1611yescharacteristic
130C2×#6923—82no—
131C2×#6923—82no—
132C2×#6923—82no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61—84no—
145C2×C4×C61#9911yescharacteristic
146C2×C4×C61#9911yescharacteristic
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—84no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61#10212yes—
160D244—82no—
161D244—82no—
162D244—82no—
163C4×D61—42no—
164C4×D61—81no—
165#92420—82no—
166#11876—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—22no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10211yescharacteristic
176C22×C61#42111yescharacteristic
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191#6923—162no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—42no—
195C4×C61—41no—
196C4×C61—81no—
197Dic61—22no—
198Dic61—41no—
199Dic61—41no—
200Dic61—81no—
201#2543—611no—
202#1799—611no—
203#1460—611no—
204#1344—612no—
205#1343—612no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—42no—
209C2×C61#151911yescharacteristic
210C2×C61#212111yescharacteristic
211C2×C61#212611yescharacteristic
212D61—41no—
213D61—41no—
214D61—161no—
215C2×#121—611no—
216C2×#121—1221no—
217C2×C4×D4—611no—
218#431—1221no—
219C2×#99—1221no—
220#398—611no—
221#397—611no—
222#394—611no—
223#392—611no—
224#388—1221no—
225#386—1221no—
226#386—1221no—
227#380—1221no—
228C2×#95#692311yescharacteristic, complemented
229#342—612no—
230#323—612no—
231#323—1221no—
232C61#1187611yescharacteristic, complemented, Sylow
233C22×D4—611no—
234C22×D4—611no—
235C22×D4—1221no—
236C22×D4—1221no—
237C23×C4—21no—
238C23×C4—611no—
239C23×C4C2×#692311yescharacteristic
240#121—2442no—
241#121—2442no—
242#121—2441no—
243#121—2441no—
244C4×D4—2441no—
245C4×D4—2441no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—2441no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1222no—
258C2×C42—611no—
259C4⋊C8—2441no—
260#99—2442no—
261C22⋊C8—1222no—
262C4×C8—2441no—
263#95—21no—
264#95—1221no—
265#95—1221no—
266#95—2441no—
267#95C2×#692311yescharacteristic
268#95C2×#692311yescharacteristic
269C24—611no—
270C24—1221no—
271C24C22⋊#692311yescharacteristic
272C2×D4—612no—
273C2×D4—612no—
274C2×D4—4881no—
275C2×D4—4881no—
276C2×D4—2441no—
277C2×D4—2442no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2442no—
283C2×D4—2442no—
284C2×D4—2442no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—4881no—
300C22×C4—2442no—
301C22×C4C22⋊#692311yescharacteristic
302C22×C4C22×#692311yescharacteristic
303C2×C8—2442no—
304C4⋊C4—4882no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2442no—
308C22⋊C4—4881no—
309C22⋊C4—2441no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2442no—
316C22⋊C4—2442no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C42—1221no—
320C42—1221no—
321C23—21no—
322C23—21no—
323C23—41no—
324C23—41no—
325C23—611no—
326C23—611no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23#1451983912yes—
339C23C2×C22⋊#692311yescharacteristic
340D4—4882no—
341D4—4882no—
342D4—4882no—
343D4—4884no—
344D4—2442no—
345D4—2442no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—84no—
358C2×C4—612no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—4881no—
364C2×C4—4882no—
365C2×C4—4882no—
366C2×C4—4882no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4#1451983611yescharacteristic
374C2×C4#1451983611yescharacteristic
375C8—4882no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—41no—
383C22—1221no—
384C22—1221no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22C2×#1451983611yescharacteristic
398C22C2×#1451983911yescharacteristic
399C22#1684076111yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—41no—
404C4—81no—
405C4—1222no—
406C4—9762no—
407C4—4881no—
408C4—2441no—
409C4—2441no—
410C2—21no—
411C2—21no—
412C2—42no—
413C2—9761no—
414C2—2441no—
415C2—2441no—
416C2#2146125611yescharacteristic
417C2#2146207611yescharacteristic
418C2#2146209211yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC22×C61C2×#99
prime radical#21450779C2
cosocleC2×#11758198C23
hypercenterC2×#95#6923
hypocenterC61#11876
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. #21461679C2semidirect
2. #21461058C2semidirect
3. #21460800C2semidirect
4. #21460798C2semidirect
13. C2×#14519751C4semidirect
15. #16839694C4semidirect
17. #16839680C4semidirect
22. C2×#95×C61C4semidirect
228. C2×#95#6923semidirect
232. C61#11876semidirect

Maximal subgroups

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

subgroupindex
#214616792
#214610582
#214608002
#214607982
#214507792
#1187661