Finite Group Databasebeta

← #29590902

Subgroups — #29590902

Order 15616.

506 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 83 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#21450977C211yesmaximal, characteristic
2#21445893C211yesmaximal, characteristic
3#21443841C212yesmaximal, complemented
4#21443820C212yesmaximal, complemented
5C2×C61×#323C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic, complemented
7#16839687C411yescharacteristic, complemented
8#16839687C2211yescharacteristic
9#16839674C411yescharacteristic, complemented
10#16839674C2211yescharacteristic
11#16839656—21no—
12#16839656—21no—
13#16839625—21no—
14#16839618—21no—
15#16839618—21no—
16C4×C22⋊Dic61C411yescharacteristic, complemented
17#16839529—21no—
18#16839529C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#323—21no—
22C61×#323C2212yes—
23C22×Dic122C2×C411yescharacteristic
24#14519756—41no—
25#14519756—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—21no—
28C2×C22⋊Dic61—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—22no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—41no—
36C2×C22⋊Dic61—41no—
37C2×C4×Dic61—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C25×C61D411yescharacteristic
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—41no—
48C2×C22⋊C4×C61—41no—
49C2×C22⋊C4×C61—41no—
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C22⋊C8×C61—22no—
55C22⋊C8×C61—41no—
56C24×C61—21no—
57C24×C61—21no—
58C24×C61—22no—
59C24×C61—41no—
60C24×C61—42no—
61C24×C61—81no—
62C24×C61C22⋊C411yescharacteristic
63C24×C61C22⋊C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—42no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—42no—
80C2×Dic122—41no—
81C2×Dic122—81no—
82C2×C8×C61—42no—
83C2×C8×C61—82no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊Dic61—42no—
89C22⋊Dic61—42no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C22⋊Dic61—81no—
96C22⋊Dic61—81no—
97C22⋊Dic61—82no—
98C22⋊Dic61—82no—
99C4⋊Dic61—41no—
100#11758196—42no—
101C4×Dic61—81no—
102C23×C61—22no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61—42no—
112C23×C61—42no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—42no—
118C23×C61—42no—
119C23×C61—81no—
120C23×C61—81no—
121C23×C61—84no—
122C23×C61—84no—
123C23×C61#9911yescharacteristic
124C23×C61#9911yescharacteristic
125C23×C61C2×C22⋊C411yescharacteristic
126C23×C61#13512yes—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
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—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—82no—
152C2×Dic61—82no—
153C2×Dic61—82no—
154Dic122—82no—
155C8×C61—82no—
156#11845—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—22no—
164C22×C61—21no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—81no—
175C22×C61—84no—
176C22×C61—81no—
177C22×C61—84no—
178C22×C61#35412yes—
179C22×C61C2×#9911yescharacteristic
180C22×C61#41611yescharacteristic
181C22×C61#42111yescharacteristic
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186Dic61—81no—
187Dic61—81no—
188Dic61—81no—
189Dic61—81no—
190Dic61—162no—
191#2561—611no—
192#1819—611no—
193C2×#323D6111yescharacteristic
194#1351—612no—
195#1344—612no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—22no—
199C2×C61—42no—
200C2×C61—41no—
201C2×C61—81no—
202C2×C61#151611yescharacteristic
203C2×C61#212111yescharacteristic
204C2×C61C2×#35411yescharacteristic
205C2×C22⋊Q8—611no—
206C22×C22⋊C4C2×D6111yescharacteristic
207C2×C22⋊C8—21no—
208#397—611no—
209#397—611no—
210#393—611no—
211#393—611no—
212#388—1221no—
213#388—1221no—
214#381—1221no—
215#379—1221no—
216#379—1221no—
217C4×C22⋊C4—611no—
218#342—612no—
219#342—1221no—
220#323—21no—
221#323C2×D6112yes—
222C61#1184511yescharacteristic, complemented, Sylow
223C25D24411yescharacteristic
224C22×Q8—611no—
225C23×C4C4×D6111yescharacteristic
226C23×C4C22⋊D6111yescharacteristic
227C22×C8—41no—
228C22⋊Q8—2441no—
229C22⋊Q8—2441no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C22⋊C4—41no—
233C2×C22⋊C4—41no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1222no—
241C2×C22⋊C4—2441no—
242C2×C22⋊C4—2441no—
243C2×C22⋊C4C4×D6111yescharacteristic
244C2×C22⋊C4D24411yescharacteristic
245C2×C22⋊C4C22⋊D6111yescharacteristic
246C2×C22⋊C4C22×D6111yescharacteristic
247C2×C42—1221no—
248C22⋊C8—22no—
249C22⋊C8—41no—
250#95—611no—
251#95—611no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256C24—21no—
257C24—21no—
258C24—22no—
259C24—41no—
260C24—42no—
261C24—81no—
262C24#1175819811yescharacteristic
263C24#1175819811yescharacteristic
264C24C2×D24411yescharacteristic
265C2×Q8—4881no—
266C2×Q8—2441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—81no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—2442no—
278C22×C4#1175819811yescharacteristic
279C22×C4#1175819811yescharacteristic
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282C2×C8—42no—
283C2×C8—82no—
284C4⋊C4—2441no—
285C4⋊C4—2442no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—4882no—
291C22⋊C4—4882no—
292C22⋊C4—4881no—
293C22⋊C4—4881no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2442no—
301C42—4881no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—22no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23—84no—
322C23—84no—
323C23#1451969111yescharacteristic
324C23#1451969111yescharacteristic
325C23C2×#1175819811yescharacteristic
326C23#1451979912yes—
327Q8—4882no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—4882no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C8—82no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—84no—
375C22—81no—
376C22—84no—
377C22#1683955612yes—
378C22C2×#1451969111yescharacteristic
379C22#1683975911yescharacteristic
380C22#1683977811yescharacteristic
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—9762no—
386C4—4881no—
387C4—4881no—
388C4—4881no—
389C4—4881no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—42no—
394C2—41no—
395C2—81no—
396C2#2144437611yescharacteristic
397C2#2144746611yescharacteristic
398C2C2×#1683955611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC2×C61×#323C2
socleC22×C61C2×#99
prime radicalC25×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenterC2×#323D61
hypocenterC61#11845
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #21443841C2semidirect
4. #21443820C2semidirect
6. C2×#14519756C4semidirect
7. #16839687C4semidirect
9. #16839674C4semidirect
16. C4×C22⋊Dic61C4semidirect
222. C61#11845semidirect

Maximal subgroups

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

subgroupindex
#214509772
#214458932
#214438412
#214438202
C2×C61×#3232
#1184561