Finite Group Databasebeta

← #11875033

Subgroups — #11875033

Order 1152.

841 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 841 conjugacy classes of subgroups — too many to draw. Only its 192 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#10593948C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C3⋊D3×#97C211yesmaximal, characteristic
4C3×#4702C212yesmaximal, complemented
5#10590903C214yesmaximal, complemented
6#10590687C212yesmaximal
7#10590685C212yesmaximal
8#10590315C212yesmaximal, complemented
9D3×#501—32nomaximal
10C2×#3797—21no—
11C2×C8×C3⋊D3C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×#870C2212yes—
14C3×#869C2212yes—
15#63919—21no—
16#63919C2212yes—
17#63900—21no—
18#63900C2212yes—
19#63900C2211yescharacteristic
20#63900C2211yescharacteristic
21#63883—21no—
22#63883—21no—
23#63873—21no—
24#63872C2212yes—
25#63870—21no—
26#63870—21no—
27C32×#97C2211yescharacteristic
28#63642C2212yes—
29#63630C2211yescharacteristic
30C3×#818C2214yes—
31C3×#817C2214yes—
32#63576C2214yes—
33#63574C2214yes—
34D3×C4⋊Q8—32no—
35D3×#125—32no—
36C3×#501—32no—
37#5081—32no—
38#5064—32no—
39D3×#107—34no—
40#4876—34no—
41D3×#106—34no—
42#4856—34no—
43D3×#97—32no—
44D3×#97—61no—
45#4702D312yescomplemented
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×C3×Dic6—22no—
50C2×#627—22no—
51C2×#624—22no—
52C2×#624—21no—
53C2×#624—21no—
54#3797—44no—
55C2×C32×C8C2312yes—
56C32×C42C2311yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3C2311yescharacteristic
60C2×C3⋊(C3⋊C8)C2312yes—
61C8×C3⋊D3Q818yescomplemented
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3C2312yes—
64C3×C4⋊Dic3C2314yes—
65C3×C4⋊Dic3C2312yes—
66C3×Dic3⋊C4—22no—
67C3×Dic3⋊C4—22no—
68#3724—21no—
69#3724—21no—
70#3724—22no—
71#3724—22no—
72Dic3⋊Dic3—22no—
73Dic3⋊Dic3—22no—
74C2×#501—91noSylow
75C2×D3×Q8—62no—
76C3×C4⋊Q8—32no—
77C3×#125—32no—
78#944—62no—
79C2×D3×C8—34no—
80C2×D3×C8—62no—
81D3×C4⋊C4—32no—
82D3×C4⋊C4—34no—
83D3×C4⋊C4—32no—
84D3×C4⋊C4—62no—
85D3×C4⋊C4—62no—
86D3×C4⋊C4—62no—
87#890—32no—
88#890—32no—
89#889—62no—
90#889—62no—
91#888—34no—
92#888—62no—
93C42×D3—32no—
94C42×D3—61no—
95#870C2×D312yes—
96#869C2×D312yes—
97C3×#107—34no—
98C3×#106—34no—
99C3×#97—21no—
100C3×#97C2×D312yes—
101#818C2×D314yes—
102#817C2×D314yes—
103#815—34no—
104#815—62no—
105#808—34no—
106#808—34no—
107#807—34no—
108#807—34no—
109#803—32no—
110#803—61no—
111C22×C3⋊D3C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2×D411yescharacteristic
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3C2×Q814yes—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—24no—
124C3×Dic6—44no—
125#627—44no—
126#624—44no—
127#624—42no—
128#624—42no—
129C32×C8C2×Q814yescomplemented
130C3⋊(C3⋊C8)C2×Q814yescomplemented
131C2×C4⋊Q8—91no—
132C2×#125—91no—
133#501—32no—
134#501—94no—
135#501—92no—
136C2×#107—92no—
137C2×#106—92no—
138C2×#97—91no—
139C2×C3×Q8—62no—
140D3×Q8—128no—
141C2×C4×D3—32no—
142C2×C4×D3—32no—
143C2×C4×D3—32no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—64no—
150C2×Dic6—22no—
151C2×Dic6—64no—
152C2×C3×C8—22no—
153C2×C3×C8C22×D314yes—
154C3×C4⋊C4—32no—
155C3×C4⋊C4—34no—
156C3×C4⋊C4—32no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—62no—
160C3×C42—21no—
161C3×C42C22×D312yes—
162C4⋊Dic3—22no—
163C4⋊Dic3—62no—
164C4⋊Dic3—62no—
165C4⋊Dic3C22×D312yes—
166C4⋊Dic3C22×D314yes—
167C4⋊Dic3C22×D312yes—
168Dic3⋊C4—22no—
169Dic3⋊C4—22no—
170Dic3⋊C4—64no—
171Dic3⋊C4—64no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176C4×Dic3—32no—
177C4×Dic3—32no—
178C4×Dic3—32no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C2×C3⋊C8—34no—
183C2×C3⋊C8—62no—
184D3×C8—316no—
185D3×C8—68no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3C4⋊Q812yes—
188C2×C3⋊D3AGL(1,ℤ/8)12yes—
189C2×C3⋊D3#13712yes—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4C22×Q812yes—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3C4⋊Q812yes—
196C3×Dic3—44no—
197C3×Dic3—42no—
198C3×Dic3—42no—
199C22×Q8—181no—
200C22×C8—92no—
201C4⋊Q8—32no—
202C4⋊Q8—92no—
203C4⋊Q8—181no—
204C4⋊Q8—181no—
205#125—32no—
206#125—92no—
207#125—181no—
208#125—181no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—92no—
212C2×C4⋊C4—181no—
213C2×C4⋊C4—181no—
214C2×C4⋊C4—181no—
215C2×C42—91no—
216#107—34no—
217#107—94no—
218#106—34no—
219#106—94no—
220#97—92no—
221#97—91no—
222#97D3211yescharacteristic
223C22×D3—32no—
224C22×D3—61no—
225C3×Q8—124no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—64no—
232C2×C3×C4D3×D412yes—
233C2×C3×C4D3×D412yes—
234C2×C3×C4C23×D312yes—
235C2×Dic3—22no—
236C2×Dic3—22no—
237C2×Dic3—24no—
238C2×Dic3—32no—
239C2×Dic3—32no—
240C2×Dic3—32no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C4×D3—38no—
245C4×D3—64no—
246C4×D3—64no—
247C4×D3—64no—
248C4×D3—122no—
249C4×D3—122no—
250C4×D3—124no—
251C4×D3—124no—
252C4×D3—128no—
253Dic6—44no—
254Dic6—128no—
255C3×C8—24no—
256C3×C8D3×Q818yescomplemented
257C3⋊C8—38no—
258C3⋊C8—64no—
259C2×C32C2×C4⋊Q811yescharacteristic
260C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
261C2×C32C2×#13711yescharacteristic
262C3⋊D3#50114yescomplemented
263C2×Q8—62no—
264C2×Q8—182no—
265C2×Q8—364no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4—182no—
272C2×C8—92no—
273C2×C8—98no—
274C2×C8C2×D3212yes—
275C4⋊C4—32no—
276C4⋊C4—34no—
277C4⋊C4—32no—
278C4⋊C4—62no—
279C4⋊C4—62no—
280C4⋊C4—62no—
281C4⋊C4—181no—
282C4⋊C4—181no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4—182no—
286C4⋊C4—182no—
287C42—91no—
288C42—91no—
289C42—91no—
290C42C2×D3211yescharacteristic
291C22×C3—21no—
292C22×C3C2×D3×D412yes—
293C2×D3—34no—
294C2×D3—34no—
295C2×D3—34no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C3×C4—22no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—124no—
305C3×C4—122no—
306C3×C4—122no—
307C3×C4C2×D3×Q814yes—
308Dic3—34no—
309Dic3—44no—
310Dic3—42no—
311Dic3—42no—
312Dic3—62no—
313Dic3—62no—
314Dic3—62no—
315Dic3—121no—
316Dic3—121no—
317C32C2×#50111yescharacteristic, complemented, Sylow
318C23—91no—
319Q8—124no—
320Q8—364no—
321C2×C4—62no—
322C2×C4—62no—
323C2×C4—64no—
324C2×C4—91no—
325C2×C4—94no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—364no—
331C2×C4—362no—
332C2×C4—362no—
333C2×C4#380211yescharacteristic
334C2×C4#380211yescharacteristic
335C2×C4C22×D3211yescharacteristic
336C8—94no—
337C8#379714yescomplemented
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3D3×C4⋊Q812yes—
342C2×C3D3×AGL(1,ℤ/8)12yes—
343C2×C3D3×#13712yes—
344D3—38no—
345D3—64no—
346C22—92no—
347C22—92no—
348C22—92no—
349C22C2×#380211yescharacteristic
350C4—21no—
351C4—21no—
352C4—92no—
353C4—124no—
354C4—122no—
355C4—122no—
356C4—181no—
357C4—181no—
358C4C2×#379712yes—
359C3—21no—
360C3D3×#50112yescomplemented
361C2—94no—
362C2#1059390911yescharacteristic
363C2#1059471611yescharacteristic
364C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#97D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C3×#4702C2semidirect
5. #10590903C2semidirect
8. #10590315C2semidirect
45. #4702D3semidirect
61. C8×C3⋊D3Q8semidirect
129. C32×C8C2×Q8semidirect
130. C3⋊(C3⋊C8)C2×Q8semidirect
256. C3×C8D3×Q8semidirect
262. C3⋊D3#501semidirect
317. C32C2×#501semidirect
337. C8#3797semidirect
360. C3D3×#501semidirect

Maximal subgroups

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

subgroupindex
#105939482
#105939092
C3⋊D3×#972
C3×#47022
#105909032
#105906872
#105906852
#105903152
D3×#5013