Finite Group Databasebeta

← #29569260

Subgroups — #29569260

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#21447296C211yesmaximal, characteristic, complemented
3#21447228C211yesmaximal, characteristic, complemented
4#21443644C211yesmaximal, characteristic, complemented
5#21443643C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic
7C61×#2093C211yesmaximal, characteristic
8C2×#14519708—21no—
9C2×#14519700—21no—
10#16839687—21no—
11#16839676—21no—
12#16839674—21no—
13#16839668C2211yescharacteristic
14#16839660C2211yescharacteristic
15#16839655—21no—
16#16839655—21no—
17#16839643—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#107×C61—21no—
23C2×#102×C61—21no—
24C61×#390C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39#14519708—42no—
40#14519700—42no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×D4×C61D411yescharacteristic
48C22×C8×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C42×C61C2311yescharacteristic
56#107×C61—42no—
57#102×C61—42no—
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×C61—41no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C42×C61—41no—
91C22⋊Dic61—81no—
92C22⋊Dic61—81no—
93C22⋊Dic61—81no—
94C22⋊Dic61—81no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—81no—
102C2×#92418—22no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
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×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61#13511yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61#13711yescharacteristic
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—41no—
147C2×Dic61—41no—
148Dic122—42no—
149Dic122—81no—
150C8×C61—42no—
151#92418—42no—
152#92418—81no—
153#7820—611nomaximal, Sylow
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61#44911yescharacteristic
162C22×C61#44911yescharacteristic
163C22×C61#45211yescharacteristic
164C22×C61#45311yescharacteristic
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—
175C4×C61—161no—
176Dic61—81no—
177Dic61—81no—
178Dic61—81no—
179Dic61—81no—
180#2808—611no—
181#2093D6111yescharacteristic
182#2084—611no—
183#2072—611no—
184#1272—611no—
185#1271—611no—
186#1270—611no—
187C2×C61—161no—
188C2×C61#160911yescharacteristic
189C2×C61#161211yescharacteristic
190C2×C61#161811yescharacteristic
191C2×C61#162011yescharacteristic
192C2×C61#164611yescharacteristic
193C2×C61#165211yescharacteristic
194C2×C61#166111yescharacteristic
195C2×#107—21no—
196C2×#106—1221no—
197C2×#103—1221no—
198C2×#102—21no—
199#397—1221no—
200#394—1221no—
201#393—1221no—
202#391—611no—
203#390C2×D6111yescharacteristic
204#389—611no—
205#388—1221no—
206#388—1221no—
207#387—1221no—
208#384C2×D6111yescharacteristic
209#340—1221no—
210#340—1221no—
211#336—611no—
212#336—611no—
213#336C2×D6111yescharacteristic
214C61#782011yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C22×D4C22⋊D6111yescharacteristic
217C22×C8—21no—
218C22×C8—1221no—
219C22×C8—1221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4C22⋊D6111yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C42—1221no—
235C2×C42C22×D6111yescharacteristic
236#107—42no—
237#106—2442no—
238#103—2442no—
239#102—42no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—21no—
247C2×Q8—1221no—
248C2×Q8—1221no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4D4×D6111yescharacteristic
262C22×C4D4×D6111yescharacteristic
263C22×C4C2×C22⋊D6111yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—1222no—
268C2×C8—2441no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8—2441no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—4881no—
291C22⋊C4—4881no—
292C22⋊C4—4881no—
293C22⋊C4—4881no—
294C42—41no—
295C42—4881no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23#1451974511yescharacteristic
304Q8—4881no—
305Q8—2442no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
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×C4#1451979611yescharacteristic
333C2×C4#1451979611yescharacteristic
334C2×C4#1451979711yescharacteristic
335C2×C4#1451980111yescharacteristic
336C2×C4#1451980111yescharacteristic
337C2×C4#1451980811yescharacteristic
338C8—42no—
339C8—4881no—
340C8—2442no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1683990411yescharacteristic
349C22#1683990411yescharacteristic
350C22#1683992211yescharacteristic
351C22#1683992911yescharacteristic
352C22#1683993811yescharacteristic
353C22#1683994311yescharacteristic
354C22#1683995111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—161no—
363C4—4881no—
364C4—4881no—
365C4—4881no—
366C4—4881no—
367C2—161no—
368C2#2144481311yescharacteristic
369C2#2144483011yescharacteristic
370C2#2144486511yescharacteristic
371C2#2144487611yescharacteristic
372C2#2144504611yescharacteristic
373C2#2144508811yescharacteristic
374C2#2144513311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2093C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#2093D61
hypocenterC61#7820
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #21447296C2semidirect
3. #21447228C2semidirect
4. #21443644C2semidirect
5. #21443643C2semidirect
214. C61#7820semidirect

Maximal subgroups

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

subgroupindex
#214537992
#214472962
#214472282
#214436442
#214436432
#214436402
C61×#20932
#782061