Finite Group Databasebeta

← #29568421

Subgroups — #29568421

Order 15616.

468 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454128C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic
3#21445576C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519768C411yescharacteristic
9C2×C42×D61C2211yescharacteristic
10C2×#14519689—21no—
11C2×#14519689—21no—
12C2×C8×Dic61—21no—
13#16839660C2211yescharacteristic
14#16839648—21no—
15#16839644—21no—
16#16839636—21no—
17#16839633—21no—
18#16839627C411yescharacteristic
19#16839619C411yescharacteristic
20#16839619C411yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32#14519768—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C42×D61—42no—
44#14519689—24no—
45#14519689—42no—
46C8×Dic61—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#95×C61—21no—
59C23×D61C22⋊C411yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C2×C4×D61—22no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C8×C61—22no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C42×C61—41no—
94#11758198—42no—
95#11758198—42no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—42no—
99C4⋊Dic61—41no—
100#11758196—42no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C2×#92418—22no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61#10412yes—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61#13111yescharacteristic
133C2×C4×C61#13111yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61#9912yes—
152C2×Dic61#10112yes—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159C8×C61—42no—
160C8×C61—81no—
161#92418—42no—
162#92418—81no—
163#7671—611nomaximal, Sylow
164C22×C61#40811yescharacteristic
165C22×C61C2×#9911yescharacteristic
166C22×C61C2×#10111yescharacteristic
167C22×C61#41611yescharacteristic
168C22×C61#41611yescharacteristic
169C22×C61C2×#10411yescharacteristic
170C22×C61#42111yescharacteristic
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—22no—
187Dic61—22no—
188Dic61—41no—
189Dic61—81no—
190Dic61—81no—
191#2851—611no—
192#1817—611no—
193C4×C22⋊C8—611no—
194#1271—611no—
195#1271—611no—
196#1271—611no—
197#1271D6111yescharacteristic, complemented
198C2×C61#147211yescharacteristic
199C2×C61#148211yescharacteristic
200C2×C61#149411yescharacteristic
201C2×C61#150111yescharacteristic
202C2×C61#151611yescharacteristic
203C2×C61#152811yescharacteristic
204C2×C61#154411yescharacteristic
205D61—42no—
206C2×#125—611no—
207C22×C42—611no—
208C2×C22⋊C8—1221no—
209C2×C22⋊C8—1221no—
210C2×C4×C8—1221no—
211#389—611no—
212#389C2×D6111yescharacteristic
213#387—1221no—
214#387—1221no—
215#385—1221no—
216#385—1221no—
217#382—611no—
218#380—611no—
219#380—611no—
220#336—611no—
221#336—611no—
222#336—1221no—
223#336C2×D6111yescharacteristic
224#336C2×D6111yescharacteristic
225C61#767111yescharacteristic, complemented, Sylow
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—1221no—
232C22×C8—1221no—
233#125—2442no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C4⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—2442no—
248C2×C42C22×D6111yescharacteristic
249C22⋊C8—1224no—
250C22⋊C8—2442no—
251C4×C8—2442no—
252#95—21no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258C24—611no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—1222no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4C2×C4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—1222no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8—2441no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—2441no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C42—41no—
308C42—1222no—
309C42—1222no—
310C42—2441no—
311C23—612no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23C22⋊C4×D6111yescharacteristic
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4#1451978311yescharacteristic
353C2×C4#1451978511yescharacteristic
354C2×C4#1451979611yescharacteristic
355C2×C4#1451979811yescharacteristic
356C2×C4#1451979811yescharacteristic
357C2×C4#1451980011yescharacteristic
358C8—42no—
359C8—81no—
360C8—4881no—
361C8—2442no—
362C22—1222no—
363C22—1222no—
364C22—1222no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22#1683972711yescharacteristic
370C22#99×D6111yescharacteristic
371C22#101×D6111yescharacteristic
372C22#1683975511yescharacteristic
373C22#1683975711yescharacteristic
374C22#104×D6111yescharacteristic
375C22#1683977711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—1222no—
385C4—1222no—
386C4—4881no—
387C4—4881no—
388C4—2441no—
389C2—2442no—
390C2#2144418111yescharacteristic
391C2#2144422411yescharacteristic
392C2#2144427811yescharacteristic
393C2#2144430711yescharacteristic
394C2#2144437411yescharacteristic
395C2#2144441911yescharacteristic
396C2#2144448211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7671
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #21443643C2semidirect
5. #21443642C2semidirect
6. #21443641C2semidirect
7. C61×#1271C2semidirect
197. #1271D61semidirect
225. C61#7671semidirect

Maximal subgroups

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

subgroupindex
#214541282
#214458862
#214455762
#214436432
#214436422
#214436412
C61×#12712
#767161