Finite Group Databasebeta

← #30604234

Subgroups — #30604234

Order 15616.

492 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461064C211yesmaximal, characteristic
2C2×#16840605C211yesmaximal, characteristic
3#21460763C212yesmaximal, complemented
4#21460746C212yesmaximal, complemented
5#21450100C211yesmaximal, characteristic
6#16840732—21no—
7C2×C22⋊#92420—21no—
8#16840605—21no—
9#16840605—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C22×C22⋊Dic61C411yescharacteristic
13C22×C22⋊Dic61C2211yescharacteristic
14#16839687—21no—
15#16839687—21no—
16#16839637—21no—
17#16839637C411yescharacteristic
18#16839637C2211yescharacteristic
19#16839623—21no—
20#16839623C411yescharacteristic
21#16839623C2211yescharacteristic
22C61×#379C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C22⋊#92420—41no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—41no—
38C2×C22⋊Dic61—41no—
39C2×C22⋊Dic61—41no—
40C2×C22⋊Dic61—41no—
41C2×C22⋊Dic61C2×C411yescharacteristic
42C2×C22⋊Dic61D411yescharacteristic
43C2×C22⋊Dic61D411yescharacteristic
44C2×C22⋊Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C25×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
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×C61C22×C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—22no—
74C22×Dic61—42no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—81no—
79C22×Dic61—81no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84#11758217—82no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—82no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—42no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C4⋊Dic61—81no—
100C4⋊Dic61—81no—
101C23×C61—22no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—42no—
111C23×C61—42no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—42no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—42no—
118C23×C61—81no—
119C23×C61—81no—
120C23×C61—84no—
121C23×C61—84no—
122C23×C61#9911yescharacteristic
123C23×C61#9911yescharacteristic
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61#13112yes—
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×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—41no—
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—81no—
149C2×Dic61—81no—
150C2×Dic61—82no—
151C2×Dic61—82no—
152#92420—82no—
153#92420—82no—
154#11543—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—22no—
162C22×C61—21no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—84no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—84no—
176C22×C61#35212yes—
177C22×C61#40811yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61#41311yescharacteristic
180C4×C61—81no—
181C4×C61—81no—
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61—81no—
187Dic61—81no—
188#2483—611no—
189#1462—611no—
190C2×#323—611no—
191#1326—612no—
192#1317—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—22no—
196C2×C61—41no—
197C2×C61—42no—
198C2×C61—81no—
199C2×C61#146811yescharacteristic
200C2×C61C2×#35211yescharacteristic
201C2×C61#212111yescharacteristic
202C22×C22⋊C4—611no—
203C22×C22⋊C4—611no—
204#407—1221no—
205C2×C22⋊C8—1221no—
206#397—1221no—
207#397—1221no—
208#385—611no—
209#385—611no—
210#385—1221no—
211#381—611no—
212#381—611no—
213#381—1221no—
214#379#692311yescharacteristic
215#323—612no—
216#323—612no—
217#323—1221no—
218#323—1221no—
219C61#1154311yescharacteristic, complemented, Sylow
220C25C2×#692311yescharacteristic
221C23×C4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4—611no—
225C2×M16—2441no—
226C22×C8—2441no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—2441no—
238C2×C22⋊C4—2441no—
239C2×C22⋊C4—2441no—
240C2×C22⋊C4—2441no—
241C2×C22⋊C4C2×#692311yescharacteristic
242C2×C22⋊C4C2×#692311yescharacteristic
243C22⋊C8—1222no—
244C22⋊C8—1222no—
245C22⋊C8—2441no—
246C22⋊C8—2441no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253C24—21no—
254C24—21no—
255C24—22no—
256C24—41no—
257C24—42no—
258C24—81no—
259C24C22⋊#692311yescharacteristic
260C24C22⋊#692311yescharacteristic
261C24C22×#692311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1222no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—4881no—
276C22×C4—4881no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2442no—
281M16—4882no—
282C2×C8—4882no—
283C2×C8—2442no—
284C2×C8—2442no—
285C4⋊C4—4881no—
286C4⋊C4—4881no—
287C22⋊C4—22no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—81no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—84no—
318C23—84no—
319C23#1451983611yescharacteristic
320C23#1451983611yescharacteristic
321C23C2×C22⋊#692311yescharacteristic
322C23#1451986412yes—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—4882no—
334C2×C4—4882no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C8—4882no—
350C8—4882no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—84no—
372C22#1684066512yes—
373C22#1684073511yescharacteristic
374C22C2×#1451983611yescharacteristic
375C22#1684074911yescharacteristic
376C4—81no—
377C4—81no—
378C4—4881no—
379C4—4881no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4—2441no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2#2146108611yescharacteristic
391C2C2×#1684066511yescharacteristic
392C2#2146207611yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#379C4
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#379#6923
hypocenterC61#11543
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
3. #21460763C2semidirect
4. #21460746C2semidirect
219. C61#11543semidirect

Maximal subgroups

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

subgroupindex
#214610642
C2×#168406052
#214607632
#214607462
#214501002
#1154361