Finite Group Databasebeta

← #29569050

Subgroups — #29569050

Order 15616.

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

normal subgroups only

This group has 418 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#21452749C211yesmaximal, characteristic
2#21447378C211yesmaximal, characteristic, complemented
3#21447292C211yesmaximal, characteristic, complemented
4#21447222C211yesmaximal, characteristic
5#21443641C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic
8C2×#14519758—21no—
9C2×#14519711—21no—
10C2×#14519698—21no—
11#16839692—21no—
12#16839687—21no—
13#16839687—21no—
14#16839660C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839637—21no—
17#16839637—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C23×Dic61—21no—
28C22×#92418—21no—
29#14519758—42no—
30#14519758—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44#14519711—42no—
45#14519698—42no—
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—41no—
61C2×D4×C61—41no—
62C2×D4×C61D812yes—
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—42no—
72C22×Dic61—41no—
73C22×Dic61—81no—
74C22×Dic61—81no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61—41no—
87C22⋊Dic61—42no—
88C22⋊Dic61—42no—
89C22⋊Dic61—42no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—42no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—81no—
102#11758196—41no—
103#11758196—41no—
104#11758196—41no—
105#11758196—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61—22no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61#12011yescharacteristic
117D4×C61—42no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61C2×D811yescharacteristic
129C2×C4×C61#13511yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
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—41no—
146C2×Dic61—84no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C8×C61—42no—
151C8×C61—81no—
152#92418—81no—
153#7788—611nomaximal, Sylow
154C22×C61—42no—
155C22×C61—42no—
156C22×C61—42no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61#44711yescharacteristic
162C22×C61#44911yescharacteristic
163C22×C61#45211yescharacteristic
164C22×C61#45411yescharacteristic
165C22×C61#45511yescharacteristic
166C22×C61#45611yescharacteristic
167C22×C61#45811yescharacteristic
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—81no—
175Dic61—81no—
176Dic61—81no—
177Dic61—81no—
178Dic61—81no—
179Dic61—161no—
180#2724—611no—
181#2099—611no—
182#2083—611no—
183#2071—611no—
184#1271—611no—
185#1271—611no—
186#1270D6111yescharacteristic
187C2×C61—82no—
188C2×C61#160711yescharacteristic
189C2×C61#160911yescharacteristic
190C2×C61#161511yescharacteristic
191C2×C61#162511yescharacteristic
192C2×C61#164011yescharacteristic
193C2×C61#164711yescharacteristic
194C2×C61#166411yescharacteristic
195C2×#123—1221no—
196C2×#107—1221no—
197C2×#102—1221no—
198#398—1221no—
199#397—1221no—
200#397—1221no—
201#390C2×D6111yescharacteristic
202#389—611no—
203#389—611no—
204#385—1221no—
205#385—1221no—
206#384—611no—
207#340—1221no—
208#340—1221no—
209#340—1221no—
210#340—1221no—
211#336—611no—
212#336C2×D6111yescharacteristic
213#336C2×D6111yescharacteristic
214C61#778811yescharacteristic, complemented, Sylow
215C22×D4D24411yescharacteristic
216C23×C4—1221no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—1221no—
220#123—2442no—
221#123—2442no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4D24411yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C42C22×D6111yescharacteristic
239#107—2442no—
240#102—2442no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—21no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4D48812yes—
251C22×C4—21no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—4881no—
257C22×C4—4881no—
258C22×C4—2441no—
259C22×C4—2442no—
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—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C4⋊C4—41no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—4881no—
278C4⋊C4—2442no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C42—41no—
297C23—22no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#1451974711yescharacteristic
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4884no—
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—2441no—
331C2×C4—2441no—
332C2×C4C2×D48811yescharacteristic
333C2×C4#1451979611yescharacteristic
334C2×C4#1451979811yescharacteristic
335C2×C4#1451980111yescharacteristic
336C2×C4#1451980511yescharacteristic
337C2×C4#1451980611yescharacteristic
338C8—42no—
339C8—81no—
340C8—4881no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1683989811yescharacteristic
349C22#1683990811yescharacteristic
350C22#1683992511yescharacteristic
351C22#1683993611yescharacteristic
352C22#1683994211yescharacteristic
353C22#1683994611yescharacteristic
354C22#1683995311yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—9761no—
363C4—4881no—
364C4—4881no—
365C4—4881no—
366C4—4881no—
367C2—82no—
368C2#2144480711yescharacteristic
369C2#2144481711yescharacteristic
370C2#2144485111yescharacteristic
371C2#2144491011yescharacteristic
372C2#2144500611yescharacteristic
373C2#2144505611yescharacteristic
374C2#2144515611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7788
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. #21447378C2semidirect
3. #21447292C2semidirect
5. #21443641C2semidirect
6. #21443641C2semidirect
214. C61#7788semidirect

Maximal subgroups

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

subgroupindex
#214527492
#214473782
#214472922
#214472222
#214436412
C61×#12702
#778861