Finite Group Databasebeta

← #29569310

Subgroups — #29569310

Order 15616.

404 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452778C211yesmaximal, characteristic
2#21447383C211yesmaximal, characteristic, complemented
3#21447383C211yesmaximal, characteristic, complemented
4#21447352C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic
8C2×#14519770—21no—
9C2×#14519708—21no—
10C2×#14519698—21no—
11#16839698—21no—
12#16839685—21no—
13#16839676—21no—
14#16839660C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839657—21no—
17#16839655—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839525—21no—
22#16839525—21no—
23#16839517C2211yescharacteristic
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28#14519770—42no—
29#14519770—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C4×Dic61—21no—
46#14519708—42no—
47#14519698—42no—
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×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C4⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—41no—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C22⋊Dic61—81no—
87C22⋊Dic61—81no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—42no—
96C4⋊Dic61—42no—
97C4⋊Dic61SD1612yes—
98#11758196—42no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—41no—
103#11758196—81no—
104C4×Dic61—42no—
105C2×#92418—22no—
106C2×#92418—41no—
107C2×#92418—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61#12011yescharacteristic
116D4×C61—42no—
117D4×C61—81no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61C2×SD1611yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61#13511yescharacteristic
130C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C2×Dic61—22no—
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—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C8×C61—81no—
149C8×C61—81no—
150#92418—42no—
151#7828—611nomaximal, Sylow
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61#45011yescharacteristic
160C22×C61#45211yescharacteristic
161C22×C61#45211yescharacteristic
162C22×C61#45311yescharacteristic
163C22×C61#45411yescharacteristic
164C22×C61#45411yescharacteristic
165C22×C61#45811yescharacteristic
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—81no—
173Dic61—42no—
174Dic61—81no—
175Dic61—81no—
176Dic61—81no—
177Dic61—161no—
178#2727—611no—
179#2100—611no—
180#2100—611no—
181#2094—611no—
182#1271—611no—
183#1271—611no—
184#1270D6111yescharacteristic
185C2×C61—161no—
186C2×C61#161511yescharacteristic
187C2×C61#161611yescharacteristic
188C2×C61#161811yescharacteristic
189C2×C61#163111yescharacteristic
190C2×C61#163511yescharacteristic
191C2×C61#163811yescharacteristic
192C2×C61#165711yescharacteristic
193C2×#126—1221no—
194C2×#106—1221no—
195C2×#102—1221no—
196#399—1221no—
197#396—1221no—
198#394—1221no—
199#390C2×D6111yescharacteristic
200#389—611no—
201#389—611no—
202#389—1221no—
203#388—1221no—
204#384—611no—
205#340—1221no—
206#340—1221no—
207#340—1221no—
208#340—1221no—
209#336—611no—
210#336C2×D6111yescharacteristic
211#336C2×D6111yescharacteristic
212C61#782811yescharacteristic, complemented, Sylow
213C22×D4D24411yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—1221no—
217#126—2442no—
218#126—2442no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4D24411yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C42—1221no—
238C2×C42C22×D6111yescharacteristic
239#106—2442no—
240#102—2442no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244C24—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—2441no—
255C22×C4C2×D24411yescharacteristic
256C22×C4D4×D6111yescharacteristic
257C22×C4D4×D6111yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—1222no—
265C2×C8—2441no—
266C2×C8—2441no—
267C4⋊C4—41no—
268C4⋊C4—612no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—4881no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2442no—
276C4⋊C4—2442no—
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—2442no—
291C22⋊C4—2442no—
292C42—41no—
293C42—2442no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#1451974711yescharacteristic
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—1222no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—2441no—
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×C4SD16×D6111yescharacteristic
329C2×C4#1451979611yescharacteristic
330C2×C4#1451979911yescharacteristic
331C2×C4#1451980111yescharacteristic
332C2×C4#1451980611yescharacteristic
333C2×C4#1451981011yescharacteristic
334C8—81no—
335C8—81no—
336C8—2442no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22#1683991411yescharacteristic
345C22#1683992511yescharacteristic
346C22#1683992611yescharacteristic
347C22#1683993211yescharacteristic
348C22#1683993611yescharacteristic
349C22#1683993611yescharacteristic
350C22#1683995311yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—9761no—
359C4—4881no—
360C4—4881no—
361C4—4881no—
362C4—2442no—
363C2—161no—
364C2#2144485111yescharacteristic
365C2#2144485711yescharacteristic
366C2#2144486911yescharacteristic
367C2#2144494711yescharacteristic
368C2#2144497311yescharacteristic
369C2#2144499311yescharacteristic
370C2#2144511811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7828
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. #21447383C2semidirect
5. #21443643C2semidirect
6. #21443641C2semidirect
212. C61#7828semidirect

Maximal subgroups

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

subgroupindex
#214527782
#214473832
#214473522
#214436432
#214436412
C61×#12702
#782861