Finite Group Databasebeta

← #29591130

Subgroups — #29591130

Order 15616.

452 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 77 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#21451172C211yesmaximal, characteristic
2#21445806C211yesmaximal, characteristic
3#21444134C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443840C211yesmaximal, characteristic, complemented
7C61×#1351C211yesmaximal, characteristic, complemented
8C2×Q8×Dic61C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10C2×#14519691—21no—
11C22⋊C8×D61—21no—
12#16839699C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839673C411yescharacteristic, complemented
15#16839662—21no—
16#16839659—21no—
17#16839637—21no—
18#16839636—21no—
19#16839626C411yescharacteristic, complemented
20#16839620—21no—
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#393C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×C8×D61—41no—
31Q8×Dic61—41no—
32Q8×Dic61—41no—
33#14519737—41no—
34#14519737—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—41no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49#14519691—42no—
50C22⋊#92418—21no—
51#14519689—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—42no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61SD1612yes—
75C2×C22⋊D61Q1612yes—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—41no—
81C22×Dic61—81no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—81no—
88C2×C8×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—81no—
96#11758198—41no—
97#11758198—42no—
98#11758198—81no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—81no—
103#11758196—41no—
104#11758196—42no—
105#11758196—81no—
106#11758196—82no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—42no—
110C2×#92418—41no—
111C8×D61—82no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61C2×SD1611yescharacteristic
118C23×C61C2×Q1611yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61#10312yes—
124Q8×C61—42no—
125Q8×C61—42no—
126C2×C4×C61—22no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
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×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61—81no—
156C2×Dic61—81no—
157C2×Dic61#9911yescharacteristic
158C2×Dic61#9911yescharacteristic
159C2×Dic61#10312yes—
160C4×D61—42no—
161C4×D61—81no—
162C8×C61—81no—
163#92418—81no—
164#11897—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—81no—
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10311yescharacteristic
176C22×C61#42111yescharacteristic
177C2×D61—22no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—42no—
181C2×D61—81no—
182C4×C61—42no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186C4×C61—161no—
187Dic61—21no—
188Dic61—21no—
189Dic61—22no—
190Dic61—41no—
191Dic61—81no—
192Dic61—81no—
193Dic61—161no—
194#2580—611no—
195#1799—611no—
196#1459—611no—
197#1352—611no—
198#1352—611no—
199#1351—611no—
200#1351D6111yescharacteristic, complemented
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—41no—
204C2×C61—41no—
205C2×C61#152011yescharacteristic
206C2×C61#212011yescharacteristic
207C2×C61#212711yescharacteristic
208D61—42no—
209C2×C4×Q8—611no—
210C2×C4×D4—611no—
211C2×#99—1221no—
212C2×C22⋊C8—1221no—
213#399—611no—
214#399—611no—
215#393—611no—
216#393C2×D6111yescharacteristic
217#390—1221no—
218#389—1221no—
219#385—1221no—
220#385—1221no—
221#382—611no—
222#380—1221no—
223#342—611no—
224#342C2×D6111yescharacteristic
225#324—1221no—
226#323—611no—
227#323C2×D6111yescharacteristic
228C61#1189711yescharacteristic, complemented, Sylow
229C22×Q8C4×D6111yescharacteristic
230C22×D4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C22×C8—2441no—
234C4×Q8—2441no—
235C4×Q8—2441no—
236C4×D4—2441no—
237C4×D4—2441no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—2441no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4C22×D6111yescharacteristic
253C2×C42—611no—
254C2×C42—1221no—
255#99—2442no—
256C22⋊C8—21no—
257C22⋊C8—1221no—
258C22⋊C8—2441no—
259#95—21no—
260#95—611no—
261#95—1221no—
262#95—1221no—
263#95—2441no—
264#95C4×D6111yescharacteristic
265C24—611no—
266C24D4×D6111yescharacteristic
267C2×Q8—42no—
268C2×Q8—41no—
269C2×D4—612no—
270C2×D4—612no—
271C2×D4—2441no—
272C2×D4—2441no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—4881no—
286C22×C4—4881no—
287C22×C4—2441no—
288C22×C4C2×C4×D6111yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C2×C8—41no—
291C2×C8—4882no—
292C2×C8—2441no—
293C4⋊C4—4881no—
294C4⋊C4—4881no—
295C4⋊C4—4882no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2442no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—4881no—
306C22⋊C4—4881no—
307C22⋊C4—2441no—
308C22⋊C4—2442no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C42—1221no—
312C42—1221no—
313C42—2442no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—612no—
319C23—1221no—
320C23—1221no—
321C23—2441no—
322C23—2441no—
323C23C22⋊C4×D6111yescharacteristic
324C23SD16×D6111yescharacteristic
325C23Q16×D6111yescharacteristic
326Q8—42no—
327Q8—42no—
328D4—2442no—
329D4—2442no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—612no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C8—81no—
365C8—4881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—1222no—
376C22—4881no—
377C22—2442no—
378C22—2441no—
379C22—2441no—
380C22#99×D6111yescharacteristic
381C22#103×D6111yescharacteristic
382C22#1683977711yescharacteristic
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—161no—
388C4—1222no—
389C4—1221no—
390C4—1221no—
391C4—9761no—
392C4—4881no—
393C4—4881no—
394C4—2441no—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—2442no—
400C2#2144438911yescharacteristic
401C2#2144745711yescharacteristic
402C2#2144748711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1351C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1351D61
hypocenterC61#11897
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #21443844C2semidirect
5. #21443842C2semidirect
6. #21443840C2semidirect
7. C61×#1351C2semidirect
8. C2×Q8×Dic61C4semidirect
12. #16839699C4semidirect
14. #16839673C4semidirect
19. #16839626C4semidirect
200. #1351D61semidirect
228. C61#11897semidirect

Maximal subgroups

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

subgroupindex
#214511722
#214458062
#214441342
#214438442
#214438422
#214438402
C61×#13512
#1189761