Finite Group Databasebeta

← #29569338

Subgroups — #29569338

Order 15616.

396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453799C211yesmaximal, characteristic
2#21447383C211yesmaximal, characteristic, complemented
3#21447356C211yesmaximal, characteristic, complemented
4#21447352C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic
8C2×#14519711—21no—
9C2×#14519708—21no—
10C2×#14519702—21no—
11C2×#14519698—21no—
12#16839687—21no—
13#16839676—21no—
14#16839674—21no—
15#16839668C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839655—21no—
18#16839655—21no—
19#16839643—21no—
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839525—21no—
23#16839517C2211yescharacteristic
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×#92418—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—21no—
41#14519711—42no—
42#14519708—42no—
43#14519702—42no—
44#14519698—42no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61D411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C24×C61—21no—
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—41no—
88C22⋊Dic61—81no—
89C22⋊Dic61—81no—
90C22⋊Dic61—81no—
91C22⋊Dic61—81no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—42no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—81no—
104C2×#92418—22no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61#12011yescharacteristic
115D4×C61—42no—
116D4×C61—81no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61#13511yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147Dic122—42no—
148Dic122—81no—
149C8×C61—42no—
150C8×C61—81no—
151#92418—42no—
152#7834—611nomaximal, Sylow
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61#45211yescharacteristic
161C22×C61#45211yescharacteristic
162C22×C61#45211yescharacteristic
163C22×C61#45311yescharacteristic
164C22×C61#45311yescharacteristic
165C22×C61#45411yescharacteristic
166C22×C61#45811yescharacteristic
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—81no—
174Dic61—81no—
175Dic61—81no—
176Dic61—81no—
177Dic61—81no—
178Dic61—161no—
179#2808—611no—
180#2100—611no—
181#2095—611no—
182#2094—611no—
183#1272—611no—
184#1271—611no—
185#1270D6111yescharacteristic
186C2×C61—161no—
187C2×C61#161511yescharacteristic
188C2×C61#161811yescharacteristic
189C2×C61#161811yescharacteristic
190C2×C61#163011yescharacteristic
191C2×C61#163411yescharacteristic
192C2×C61#163811yescharacteristic
193C2×C61#165611yescharacteristic
194C2×#107—1221no—
195C2×#106—1221no—
196C2×#103—1221no—
197C2×#102—1221no—
198#397—1221no—
199#394—1221no—
200#393—1221no—
201#391—611no—
202#390C2×D6111yescharacteristic
203#389—611no—
204#388—1221no—
205#388—1221no—
206#387—1221no—
207#384—611no—
208#340—1221no—
209#340—1221no—
210#336—611no—
211#336C2×D6111yescharacteristic
212#336C2×D6111yescharacteristic
213C61#783411yescharacteristic, complemented, Sylow
214C22×Q8—611no—
215C22×D4D24411yescharacteristic
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—1221no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4D24411yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C42—1221no—
234C2×C42C22×D6111yescharacteristic
235#107—2442no—
236#106—2442no—
237#103—2442no—
238#102—2442no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245C24—21no—
246C2×Q8—1221no—
247C2×Q8—1221no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—2441no—
260C22×C4C2×D24411yescharacteristic
261C22×C4D4×D6111yescharacteristic
262C22×C4D4×D6111yescharacteristic
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—1222no—
270C2×C8—2441no—
271C2×C8—2441no—
272C4⋊C4—41no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—4881no—
289C22⋊C4—4881no—
290C22⋊C4—4881no—
291C22⋊C4—4881no—
292C42—41no—
293C42—4881no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#1451974711yescharacteristic
302Q8—4881no—
303Q8—2442no—
304D4—42no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4#1451979611yescharacteristic
331C2×C4#1451979611yescharacteristic
332C2×C4#1451979911yescharacteristic
333C2×C4#1451980611yescharacteristic
334C2×C4#1451980611yescharacteristic
335C2×C4#1451981011yescharacteristic
336C8—42no—
337C8—81no—
338C8—2442no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1683992511yescharacteristic
347C22#1683992511yescharacteristic
348C22#1683992611yescharacteristic
349C22#1683993111yescharacteristic
350C22#1683993211yescharacteristic
351C22#1683993611yescharacteristic
352C22#1683995311yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—9761no—
361C4—4881no—
362C4—4881no—
363C4—4881no—
364C4—4881no—
365C2—161no—
366C2#2144485111yescharacteristic
367C2#2144486811yescharacteristic
368C2#2144486911yescharacteristic
369C2#2144494111yescharacteristic
370C2#2144496611yescharacteristic
371C2#2144499311yescharacteristic
372C2#2144511311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7834
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21447383C2semidirect
3. #21447356C2semidirect
5. #21443644C2semidirect
6. #21443641C2semidirect
213. C61#7834semidirect

Maximal subgroups

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

subgroupindex
#214537992
#214473832
#214473562
#214473522
#214436442
#214436412
C61×#12702
#783461