Finite Group Databasebeta

← #11788894

Subgroups — #11788894

Order 1152.

847 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 847 conjugacy classes of subgroups — too many to draw. Only its 124 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#10595996C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3#10591078C211yesmaximal, characteristic, complemented
4C2×#63559C212yesmaximal, complemented
5C3×#4533C212yesmaximal, complemented
6#69040—32nomaximal
7C2×#3828C2211yescharacteristic
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C32×#117C2211yescharacteristic
10#64104—22no—
11#64091C414yes—
12#64084—21no—
13#64083—21no—
14C2×C3×#208C2212yes—
15C2×C3×#208C2212yes—
16#63818—22no—
17#63817—24no—
18#63561—21no—
19#63559—21no—
20#63559—24no—
21#5745—32no—
22#5525—32no—
23#5525—61no—
24#5132—32no—
25C2×#823—32no—
26C2×#823—32no—
27C3×#344—32no—
28#4533D312yescomplemented
29C23×C3⋊D3C2×C412yes—
30C22×C32×C4C2311yescharacteristic
31C2×#638C2×C412yes—
32#3828—22no—
33#3828—22no—
34C2×C4⋊(C3⋊D3)—21no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)—22no—
38C2×C4⋊(C3⋊D3)—24no—
39C2×C4⋊(C3⋊D3)D411yescharacteristic
40C2×C4×C3⋊D3D412yes—
41C2×#634D411yescharacteristic
42C32×C4⋊C4—21no—
43C32×C22⋊C4C2×C412yes—
44C32×C42—21no—
45#3752—24no—
46C3×#208—22no—
47C3×#208—22no—
48C3×#208—22no—
49C3×#208D414yescomplemented
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52#3712—24no—
53#3710—24no—
54#1914—91noSylow
55C2×#235—32no—
56C2×#235—61no—
57C22×D12—32no—
58C22×D12—61no—
59C2×C3×M16—32no—
60C2×C3×M16—32no—
61C3×#117—21no—
62C3×#117C2×D312yes—
63C2×#208C2×D312yes—
64C2×#208C2×D312yes—
65#907—64no—
66D3×M16—64no—
67#901—64no—
68#895—64no—
69#895—64no—
70#882—38no—
71#882—64no—
72#875—62no—
73#875—62no—
74#874—62no—
75#874—62no—
76#824—62no—
77#823—64no—
78#823—62no—
79#823—64no—
80C23×C32C22×C411yescharacteristic
81C22×C3⋊D3—22no—
82C22×C3⋊D3—24no—
83C22×C3⋊D3—82no—
84C22×C3⋊D3C22⋊C412yes—
85C2×C32×C4—22no—
86C2×C32×C4C2×D412yes—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4#4112yes—
90#638—24no—
91C2×C3⋊Dic3C22⋊C412yes—
92C4⋊(C3⋊D3)—22no—
93C4⋊(C3⋊D3)—41no—
94C4⋊(C3⋊D3)—42no—
95C4⋊(C3⋊D3)—41no—
96C4⋊(C3⋊D3)—84no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—22no—
99#634—22no—
100C3×C3⋊C8—24no—
101C3×C3⋊C8—42no—
102#568—91no—
103#535—91no—
104#413—91no—
105C2×#100—92no—
106#344—32no—
107C23×D3—34no—
108C23×D3—62no—
109C22×C3×C4—21no—
110C22×C3×C4C22×D312yes—
111C2×#67—34no—
112C2×#67—62no—
113#235—62no—
114#235—62no—
115#235—62no—
116#235—62no—
117#235—122no—
118#235—122no—
119C2×D12—32no—
120C2×D12—61no—
121C2×D12—62no—
122C2×D12—62no—
123C2×D12—62no—
124C2×D12—62no—
125C2×D12—62no—
126C2×D12—62no—
127C2×D12—62no—
128C2×D12—62no—
129C2×D12—68no—
130C2×D12—68no—
131C2×D12—122no—
132C2×D12—122no—
133C2×C4×D3—34no—
134C2×C4×D3—62no—
135C2×Dic6—32no—
136C2×Dic6—61no—
137C3×M16—34no—
138C3×M16—62no—
139C3×M16—62no—
140C3×M16—62no—
141C2×C3×C8—62no—
142C2×C3×C8—62no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C22⋊C4—22no—
146C3×C22⋊C4C4×D314yes—
147C3×C42—22no—
148C3×C42—22no—
149(C2×D3)⋊C4—68no—
150(C2×D3)⋊C4—68no—
151#208—22no—
152#208—22no—
153#208—22no—
154#208D1214yescomplemented
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157ΓL(1,𝔽25)—68no—
158D3×C8—68no—
159C22×C32—41no—
160C22×C32C2×C22⋊C411yescharacteristic
161C22×C32C4×D412yes—
162C2×C3⋊D3—22no—
163C2×C3⋊D3—42no—
164C2×C3⋊D3—44no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—84no—
167C32×C4—42no—
168C32×C4#12011yescharacteristic
169C32×C4#12112yes—
170C32×C4#12311yescharacteristic
171C3⋊Dic3—22no—
172C2×#41—91no—
173C22×D4—91no—
174#131—184no—
175C2×M16—32no—
176C2×M16—32no—
177C2×M16—182no—
178#127—181no—
179#124—181no—
180#121—182no—
181#120—94no—
182#117D3211yescharacteristic
183#101—181no—
184#100—184no—
185#100—181no—
186C23×C3—21no—
187C23×C3C2×C4×D312yes—
188C22×D3—34no—
189C22×D3—62no—
190C22×D3—64no—
191C22×D3—64no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—124no—
195C22×D3—244no—
196C22×D3—244no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4C2×D1212yes—
204C2×C3×C4#23512yes—
205C2×C3×C4D3×D412yes—
206C2×C3×C4D3×D412yes—
207C2×C3×C4D3×D412yes—
208C2×C3×C4#23912yes—
209#67—64no—
210#67—64no—
211#67—124no—
212C2×Dic3—34no—
213C2×Dic3—62no—
214D12—62no—
215D12—62no—
216D12—122no—
217D12—122no—
218D12—124no—
219D12—122no—
220D12—122no—
221D12—122no—
222D12—122no—
223D12—122no—
224D12—248no—
225D12—248no—
226C4×D3—64no—
227C4×D3—64no—
228C4×D3—122no—
229C4×D3—122no—
230Dic6—62no—
231Dic6—62no—
232Dic6—122no—
233C3×C8—64no—
234C3×C8—122no—
235C3⋊C8—24no—
236C3⋊C8—42no—
237C2×C32—21no—
238C2×C32—22no—
239C2×C32#38611yescharacteristic
240C3⋊D3—42no—
241C3⋊D3—82no—
242C24—92no—
243#41—182no—
244#41—182no—
245C2×Q8—91no—
246C2×D4—92no—
247C2×D4—91no—
248C2×D4—184no—
249C2×D4—182no—
250C2×D4—182no—
251C2×D4—181no—
252C2×D4—181no—
253C22×C4—92no—
254C22×C4C2×D3211yescharacteristic
255M16—34no—
256M16—62no—
257M16—62no—
258M16—62no—
259M16—184no—
260C2×C8—62no—
261C2×C8—62no—
262C2×C8—184no—
263C4⋊C4—21no—
264C22⋊C4—184no—
265C22⋊C4#62412yes—
266C42—21no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3—42no—
270C22×C3—42no—
271C22×C3C4×D1212yes—
272C22×C3D3×C22⋊C412yes—
273C22×C3#89312yes—
274C2×D3—64no—
275C2×D3—122no—
276C2×D3—124no—
277C2×D3—124no—
278C2×D3—124no—
279C2×D3—128no—
280C2×D3—128no—
281C2×D3—124no—
282C2×D3—248no—
283C2×D3—244no—
284C2×D3—244no—
285C3×C4—21no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—44no—
289C3×C4—44no—
290C3×C4#88212yes—
291C3×C4#88412yes—
292C3×C4#89412yes—
293C3×C4#89512yes—
294Dic3—64no—
295Dic3—122no—
296C32#191411yescharacteristic, complemented, Sylow
297C23—92no—
298C23—182no—
299C23—184no—
300C23—722no—
301C23C2×#62411yescharacteristic
302Q8—182no—
303D4—184no—
304D4—182no—
305D4—361no—
306D4—362no—
307D4—361no—
308D4—724no—
309C2×C4—22no—
310C2×C4—92no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4#379912yes—
314C2×C4D3×D1212yes—
315C2×C4#381111yescharacteristic
316C2×C4#381111yescharacteristic
317C8—64no—
318C8—122no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—22no—
323C2×C3—21no—
324C2×C3—42no—
325C2×C3#466512yes—
326D3—124no—
327D3—242no—
328D3—244no—
329D3—244no—
330C22—41no—
331C22—182no—
332C22—362no—
333C22—364no—
334C22—362no—
335C22—724no—
336C22#6389412yes—
337C22#6397411yescharacteristic
338C4—42no—
339C4—182no—
340C4#6389711yescharacteristic
341C4#6391012yes—
342C4#6392311yescharacteristic
343C3—21no—
344C3#6904012yescomplemented
345C2—21no—
346C2—22no—
347C2—362no—
348C2—722no—
349C2#1059138011yescharacteristic
subgroupG/H
centerC2#10591380
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595996C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1914
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. #10591078C2semidirect
4. C2×#63559C2semidirect
5. C3×#4533C2semidirect
28. #4533D3semidirect
49. C3×#208D4semidirect
154. #208D12semidirect
296. C32#1914semidirect
344. C3#69040semidirect

Maximal subgroups

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

subgroupindex
#105959962
#105947802
#105910782
C2×#635592
C3×#45332
#690403