Finite Group Databasebeta

← #30604169

Subgroups — #30604169

Order 15616.

530 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461079C211yesmaximal, characteristic, complemented
2#21461075C211yesmaximal, characteristic, complemented
3#21460763C212yesmaximal, complemented
4#21460743C212yesmaximal, complemented
5#21448480C211yesmaximal, characteristic
6#16840782—21no—
7#16840732—21no—
8#16840607—21no—
9#16840605—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×D4×Dic61C2211yescharacteristic
13C22×C22⋊Dic61C411yescharacteristic
14#16839665—21no—
15#16839655—21no—
16#16839655—21no—
17#16839642—21no—
18#16839642C411yescharacteristic
19#16839637C2211yescharacteristic
20#16839618C2211yescharacteristic
21C22⋊C4×Dic61C411yescharacteristic
22C2×#120×C61C411yescharacteristic
23C2×#11758217—41no—
24#14519844—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28#14519832—41no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32D4×Dic61—41no—
33D4×Dic61—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—41no—
42C2×C22⋊Dic61—41no—
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61C2311yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C25×C61C2×C411yescharacteristic
52C22×D4×C61—21no—
53C22×D4×C61C2×C411yescharacteristic
54#120×C61—22no—
55#120×C61—22no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58C24×C61—21no—
59C24×C61—21no—
60C24×C61—41no—
61C24×C61—41no—
62C24×C61—81no—
63C24×C61—81no—
64C24×C61C22⋊C411yescharacteristic
65C24×C61M1612yescomplemented
66C24×C61C22×C411yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—24no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—81no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—41no—
83C22×Dic61—81no—
84C22×Dic61—81no—
85C22×Dic61—81no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90#11758217—82no—
91C2×#92420—42no—
92C2×#92420—42no—
93C22⋊C4×C61—24no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61M1612yescomplemented
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—81no—
103C22⋊Dic61—81no—
104C22⋊Dic61—81no—
105C4⋊Dic61—41no—
106C4⋊Dic61—81no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—81no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—22no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—42no—
125C23×C61—42no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—82no—
129C23×C61—82no—
130C23×C61—84no—
131C23×C61—82no—
132C23×C61—82no—
133C23×C61C2×C22⋊C411yescharacteristic
134C23×C61C2×M1611yescharacteristic
135C23×C61C2×M1611yescharacteristic
136D4×C61—42no—
137D4×C61—42no—
138D4×C61—84no—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162C2×Dic61—82no—
163C2×Dic61#9911yescharacteristic
164C2×Dic61#9911yescharacteristic
165#92420—82no—
166#92420—82no—
167#11527—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—42no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—84no—
188C22×C61—84no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61#40711yescharacteristic
192C22×C61C2×#9911yescharacteristic
193C22×C61#41311yescharacteristic
194C4×C61—42no—
195C4×C61—41no—
196Dic61—21no—
197Dic61—21no—
198Dic61—41no—
199Dic61—41no—
200Dic61—41no—
201Dic61—81no—
202Dic61—81no—
203#2321—611no—
204#1466—611no—
205#1465—611no—
206#1326—612no—
207#1316—612no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—41no—
211C2×C61—41no—
212C2×C61—81no—
213C2×C61—82no—
214C2×C61#146511yescharacteristic
215C2×C61#212111yescharacteristic
216C2×C61#212211yescharacteristic
217C2×#120#692311yescharacteristic
218C2×C4×D4—611no—
219C22×C22⋊C4—611no—
220#432—1221no—
221#407—1221no—
222#390—1221no—
223#388—1221no—
224#388—1221no—
225#386—611no—
226#386—1221no—
227#385—611no—
228#379—611no—
229C4×C22⋊C4—611no—
230#324—1221no—
231#323—612no—
232#323—612no—
233#323—1221no—
234C61#1152711yescharacteristic, complemented, Sylow
235C25C2×#692311yescharacteristic
236C22×D4—21no—
237C22×D4C2×#692311yescharacteristic
238C23×C4—611no—
239C23×C4—611no—
240C23×C4—611no—
241C2×M16—2441no—
242#120—22no—
243#120—22no—
244C4×D4—2441no—
245C4×D4—2441no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—611no—
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—2441no—
258C2×C22⋊C4—2441no—
259C2×C22⋊C4C2×#692311yescharacteristic
260C2×C42—611no—
261C2×C42—1221no—
262C4⋊C8—2441no—
263C22⋊C8—1222no—
264C22⋊C8—1222no—
265C22⋊C8—2441no—
266#97—2441no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—21no—
271C24—21no—
272C24—41no—
273C24—41no—
274C24—81no—
275C24—81no—
276C24#1175821712yescomplemented
277C24C22⋊#692311yescharacteristic
278C24C22×#692311yescharacteristic
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—24no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—81no—
285C2×D4—81no—
286C22×C4—21no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—4881no—
298C22×C4—4881no—
299C22×C4—4881no—
300C22×C4—2441no—
301C22×C4C22⋊#692311yescharacteristic
302M16—4882no—
303C2×C8—2442no—
304C2×C8—2442no—
305C4⋊C4—4881no—
306C4⋊C4—2441no—
307C22⋊C4—24no—
308C22⋊C4—21no—
309C22⋊C4—4881no—
310C22⋊C4—4881no—
311C22⋊C4—4881no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2442no—
317C22⋊C4—2441no—
318C22⋊C4#1175821712yescomplemented
319C42—1221no—
320C42—1221no—
321C42—4881no—
322C23—21no—
323C23—21no—
324C23—22no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—82no—
341C23—82no—
342C23—82no—
343C23—82no—
344C23—84no—
345C23C2×C22⋊#692311yescharacteristic
346C23C2×#1175821711yescharacteristic
347C23C2×#1175821711yescharacteristic
348D4—42no—
349D4—42no—
350D4—84no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—4882no—
366C2×C4—2441no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C8—4882no—
378C8—4882no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—84no—
399C22—84no—
400C22—81no—
401C22—81no—
402C22#1684073211yescharacteristic
403C22D61⋊#9911yescharacteristic
404C22#1684074911yescharacteristic
405C4—42no—
406C4—41no—
407C4—1221no—
408C4—1221no—
409C4—4881no—
410C4—4881no—
411C4—2441no—
412C4—2441no—
413C4—2441no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2—81no—
419C2—82no—
420C2#2146107511yescharacteristic
421C2#2146207511yescharacteristic
422C2#2146207911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
Fitting, prime radicalC2×#120×C61C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenterC2×#120#6923
hypocenterC61#11527
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #21461079C2semidirect
2. #21461075C2semidirect
3. #21460763C2semidirect
4. #21460743C2semidirect
65. C24×C61M16semidirect
95. C22⋊C4×C61M16semidirect
234. C61#11527semidirect
276. C24#11758217semidirect
318. C22⋊C4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214610792
#214610752
#214607632
#214607432
#214484802
#1152761