Finite Group Databasebeta

← #11780630

Subgroups — #11780630

Order 1152.

624 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C32×#562C211yesmaximal, characteristic
2#10592763C211yesmaximal, characteristic, complemented
3#10592759C211yesmaximal, characteristic, complemented
4#10592754C211yesmaximal, characteristic, complemented
5#10589409C211yesmaximal, characteristic, complemented
6#10589406C211yesmaximal, characteristic, complemented
7#10589406C211yesmaximal, characteristic, complemented
8#71953—34nomaximal
9C32×#125C2211yescharacteristic
10C32×#124C2211yescharacteristic
11C32×#124C2211yescharacteristic
12C32×#123—21no—
13C32×#123—21no—
14C32×C22⋊Q8—21no—
15C32×C22⋊Q8—21no—
16C32×#121—21no—
17C32×#121—21no—
18C2×#3756—21no—
19C2×#3754—21no—
20#64078C2211yescharacteristic
21#63662—21no—
22#63659—21no—
23#63635—21no—
24#63634—21no—
25#63630C2211yescharacteristic
26#63630C2211yescharacteristic
27#63630C2211yescharacteristic
28C3×#562D314yes—
29#5064—34no—
30#5060—34no—
31#5055—34no—
32#4543—34no—
33#4540—34no—
34#4540—34no—
35C2×C32×Q8D411yescharacteristic
36C2×C32×Q8D411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4D411yescharacteristic
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C2×#634—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C4⋊C4D411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57#3756—42no—
58#3754—42no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#1661—91noSylow
65C3×#125C2×D314yes—
66C3×#124C2×D314yes—
67C3×#124C2×D314yes—
68C3×#123—24no—
69C3×#123—24no—
70C3×C22⋊Q8—24no—
71C3×C22⋊Q8—24no—
72C3×#121—24no—
73C3×#121—24no—
74C2×#216—64no—
75C2×#214—64no—
76#869—34no—
77#835—64no—
78#832—64no—
79#808—64no—
80#807—64no—
81#803—34no—
82#803—34no—
83#803—34no—
84C23×C32—21no—
85C23×C32—21no—
86C32×Q8—41no—
87C32×Q8—41no—
88C32×D4—41no—
89C32×D4—41no—
90C32×D4—81no—
91C32×D4—81no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—81no—
97C2×C32×C4—81no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3⋊Dic3—41no—
102#634—41no—
103#634—41no—
104C3⋊(C3⋊C8)—22no—
105C3⋊(C3⋊C8)—22no—
106C3⋊(C3⋊C8)—41no—
107#562C3⋊D311yescharacteristic
108#501—91no—
109#497—91no—
110#489—91no—
111#330—91no—
112#329—91no—
113#329—91no—
114C2×C3×Q8#6714yes—
115C2×C3×Q8#6714yes—
116C2×C3×D4—24no—
117C2×C3×D4—24no—
118C2×C3×D4#6714yes—
119C2×C3×D4#6714yes—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C2×Dic6—64no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4—24no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4#6714yes—
128C3×C4⋊C4#6714yes—
129C3×C22⋊C4—24no—
130C3×C22⋊C4—24no—
131C3×C22⋊C4—24no—
132C3×C22⋊C4—24no—
133C3×C22⋊C4—24no—
134C3×C22⋊C4—24no—
135C3×C42C22×D314yes—
136#216—128no—
137#214—128no—
138C4⋊Dic3—64no—
139C4⋊Dic3—64no—
140C2×C3⋊C8—64no—
141C2×C3⋊C8—64no—
142C2×C3⋊C8—64no—
143C22×C32—41no—
144C22×C32—41no—
145C22×C32—41no—
146C22×C32—41no—
147C22×C32—41no—
148C22×C32—41no—
149C22×C32#12011yescharacteristic
150C32×C4—21no—
151C32×C4—21no—
152C32×C4—21no—
153C32×C4—41no—
154C32×C4—41no—
155C32×C4—41no—
156C32×C4—41no—
157C3⋊Dic3—81no—
158C2×Q16—181no—
159C2×SD16—181no—
160C4⋊Q8—91no—
161#125C2×C3⋊D311yescharacteristic
162#124C2×C3⋊D311yescharacteristic
163#124C2×C3⋊D311yescharacteristic
164#123—21no—
165#123—21no—
166C22⋊Q8—21no—
167C22⋊Q8—21no—
168#121—21no—
169#121—21no—
170#107—181no—
171#106—181no—
172#103—181no—
173#102—181no—
174#97—91no—
175#97—91no—
176#97—91no—
177C23×C3—24no—
178C23×C3—24no—
179C3×Q8—44no—
180C3×Q8—44no—
181C3×D4—44no—
182C3×D4—44no—
183C3×D4—84no—
184C3×D4—84no—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—84no—
190C2×C3×C4—84no—
191C2×C3×C4C2×#6714yes—
192C2×C3×C4C2×#6714yes—
193C2×C3×C4C2×#6714yes—
194C2×Dic3—124no—
195Dic6—124no—
196Dic6—124no—
197C3⋊C8—68no—
198C3⋊C8—68no—
199C3⋊C8—124no—
200C2×C32—81no—
201C2×C32—81no—
202C2×C32#45311yescharacteristic
203C2×C32#45511yescharacteristic
204C2×C32#45611yescharacteristic
205C2×Q8—181no—
206C2×Q8#63811yescharacteristic
207C2×Q8#63811yescharacteristic
208C2×D4—21no—
209C2×D4—21no—
210C2×D4#63811yescharacteristic
211C2×D4#63811yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214Q16—362no—
215SD16—362no—
216C2×C8—181no—
217C2×C8—181no—
218C2×C8—181no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4#63811yescharacteristic
226C4⋊C4#63811yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—21no—
233C42C22×C3⋊D311yescharacteristic
234C22×C3—44no—
235C22×C3—44no—
236C22×C3—44no—
237C22×C3—44no—
238C22×C3—44no—
239C22×C3—44no—
240C22×C3#95314yes—
241C3×C4—24no—
242C3×C4—24no—
243C3×C4—24no—
244C3×C4—44no—
245C3×C4—44no—
246C3×C4—44no—
247C3×C4—44no—
248Dic3—244no—
249C32#166111yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252Q8—41no—
253Q8—41no—
254Q8—361no—
255Q8—361no—
256D4—41no—
257D4—41no—
258D4—81no—
259D4—81no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—361no—
267C2×C4C2×#63811yescharacteristic
268C2×C4C2×#63811yescharacteristic
269C2×C4C2×#63811yescharacteristic
270C8—182no—
271C8—182no—
272C8—361no—
273C2×C3—84no—
274C2×C3—84no—
275C2×C3#524114yes—
276C2×C3#524214yes—
277C2×C3#524614yes—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22#6416211yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—721no—
293C3#7195314yescomplemented
294C2—81no—
295C2—81no—
296C2#1059294011yescharacteristic
297C2#1059294111yescharacteristic
298C2#1059294511yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
Fitting, prime radicalC32×#562C2
socleC22×C32#120
hypercenter#562C3⋊D3
hypocenterC32#1661
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
2. #10592763C2semidirect
3. #10592759C2semidirect
4. #10592754C2semidirect
5. #10589409C2semidirect
6. #10589406C2semidirect
7. #10589406C2semidirect
249. C32#1661semidirect
293. C3#71953semidirect

Maximal subgroups

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

subgroupindex
C32×#5622
#105927632
#105927592
#105927542
#105894092
#105894062
#719533