Finite Group Databasebeta

← #11875029

Subgroups — #11875029

Order 1152.

881 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 881 conjugacy classes of subgroups — too many to draw. Only its 188 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
1C3⋊D3×#125C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C3×#5064C212yesmaximal, complemented
4#10590575C212yesmaximal
5#10590573C212yesmaximal
6#10590564C212yesmaximal, complemented
7#10590563C212yesmaximal, complemented
8#10590322C211yesmaximal, characteristic
9#10590305C212yesmaximal, complemented
10D3×#501—32nomaximal
11C2×#3797—21no—
12C32×#125C2211yescharacteristic
13C4⋊C4×C3⋊D3—21no—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17#64099C2211yescharacteristic
18#64099C2211yescharacteristic
19#64098—21no—
20#64098—21no—
21C42×C3⋊D3C2211yescharacteristic
22#64079C2211yescharacteristic
23C3×#869C2212yes—
24#63919—21no—
25#63919C2212yes—
26#63900—21no—
27#63900C2212yes—
28#63873—21no—
29C2×#3710C2212yes—
30C3×#808C2214yes—
31C3×#807C2214yes—
32C3×#803C2212yes—
33#63575C2214yes—
34#63573C2214yes—
35#63555C2212yes—
36D3×C4⋊Q8—32no—
37D3×#125—32no—
38D3×#125—61no—
39C3×#501—32no—
40#5081—32no—
41#5064D312yescomplemented
42D3×#107—34no—
43#4876—34no—
44D3×#106—34no—
45#4856—34no—
46D3×#97—32no—
47#4702—32no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×C3×Dic6—22no—
54C2×#627—22no—
55C2×#624—22no—
56#3797—44no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4C2311yescharacteristic
60C32×C4⋊C4C2311yescharacteristic
61C32×C42C2311yescharacteristic
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2311yescharacteristic
65C4⋊(C3⋊Dic3)C2311yescharacteristic
66#3750—21no—
67#3750—21no—
68#3750—21no—
69#3750—21no—
70#3750—21no—
71#3750—21no—
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3C2314yes—
77C2×C3×C3⋊C8C2314yes—
78#3724—22no—
79#3724—22no—
80#3710Q818yescomplemented
81C2×#501—91noSylow
82C2×D3×Q8—62no—
83C3×C4⋊Q8—32no—
84C3×#125—21no—
85C3×#125C2×D312yes—
86#944—62no—
87C2×D3×C8—34no—
88D3×C4⋊C4—32no—
89D3×C4⋊C4—32no—
90D3×C4⋊C4—34no—
91D3×C4⋊C4—61no—
92D3×C4⋊C4—61no—
93D3×C4⋊C4—62no—
94D3×C4⋊C4—62no—
95D3×C4⋊C4—62no—
96D3×C4⋊C4—62no—
97D3×C4⋊C4—62no—
98#890—32no—
99#890—32no—
100#890—61no—
101#890—61no—
102#889—62no—
103#889—62no—
104#889—62no—
105#889—62no—
106#888—34no—
107#888—62no—
108C42×D3—32no—
109C42×D3—61no—
110#870—32no—
111#870—61no—
112#869C2×D312yes—
113C3×#107—34no—
114C3×#106—34no—
115C3×#97—32no—
116#818—34no—
117#817—34no—
118#815—34no—
119#808—34no—
120#808C2×D314yes—
121#807—34no—
122#807C2×D314yes—
123#803C2×D312yes—
124C22×C3⋊D3C2×D411yescharacteristic
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—42no—
138C4×C3⋊D3—42no—
139C4×C3⋊D3C2×Q814yes—
140C2×C3×Dic3—24no—
141C3×Dic6—44no—
142#627—44no—
143#624—44no—
144C3×C3⋊C8C2×Q818yescomplemented
145C2×C4⋊Q8—91no—
146C2×#125—91no—
147#501—32no—
148#501—92no—
149#501—92no—
150#501—92no—
151C2×#107—92no—
152C2×#106—92no—
153C2×#97—91no—
154C2×C3×Q8—62no—
155D3×Q8—128no—
156C2×C4×D3—32no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—64no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×Dic6—22no—
168C2×Dic6—64no—
169C2×C3×C8—34no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—34no—
177C3×C4⋊C4—62no—
178C3×C4⋊C4C22×D312yes—
179C3×C4⋊C4C22×D312yes—
180C3×C42—21no—
181C3×C42C22×D312yes—
182C4⋊Dic3—22no—
183C4⋊Dic3—32no—
184C4⋊Dic3—32no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—62no—
190C4⋊Dic3—62no—
191C4⋊Dic3C22×D314yes—
192Dic3⋊C4—64no—
193Dic3⋊C4—64no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200Dic3⋊C4—62no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203Dic3⋊C4—62no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—32no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C2×C3⋊C8C22×D314yes—
213D3×C8—316no—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3C4⋊Q812yes—
216C2×C3⋊D3AGL(1,ℤ/8)12yes—
217C2×C3⋊D3#13712yes—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4—41no—
222C32×C4C22×Q812yes—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C3⋊Dic3C4⋊Q812yes—
228C3×Dic3—44no—
229C22×Q8—181no—
230C22×C8—92no—
231C4⋊Q8—32no—
232C4⋊Q8—92no—
233C4⋊Q8—181no—
234C4⋊Q8—181no—
235#125—91no—
236#125—91no—
237#125—91no—
238#125—181no—
239#125—181no—
240#125D3211yescharacteristic
241C2×C4⋊C4—92no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C42—91no—
248#107—34no—
249#107—94no—
250#106—34no—
251#106—94no—
252#97—32no—
253#97—92no—
254C22×D3—32no—
255C22×D3—61no—
256C3×Q8—124no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—64no—
265C2×C3×C4D3×D412yes—
266C2×C3×C4D3×D412yes—
267C2×C3×C4C23×D312yes—
268C2×Dic3—24no—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C4×D3—38no—
280C4×D3—64no—
281C4×D3—64no—
282C4×D3—64no—
283C4×D3—122no—
284C4×D3—122no—
285C4×D3—128no—
286C4×D3—124no—
287C4×D3—124no—
288C4×D3—124no—
289C4×D3—124no—
290Dic6—44no—
291Dic6—128no—
292C3×C8—38no—
293C3⋊C8D3×Q818yescomplemented
294C2×C32C2×C4⋊Q811yescharacteristic
295C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
296C2×C32C2×#13711yescharacteristic
297C3⋊D3#50114yescomplemented
298C2×Q8—62no—
299C2×Q8—182no—
300C2×Q8—364no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—181no—
305C22×C4—181no—
306C22×C4—182no—
307C2×C8—34no—
308C2×C8—98no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—34no—
312C4⋊C4—62no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—182no—
322C4⋊C4—182no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4C2×D3211yescharacteristic
326C4⋊C4C2×D3211yescharacteristic
327C42—91no—
328C42—91no—
329C42—91no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3C2×D3×D412yes—
333C2×D3—34no—
334C2×D3—34no—
335C2×D3—34no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—42no—
347C3×C4—42no—
348C3×C4—124no—
349C3×C4C2×D3×Q814yes—
350Dic3—34no—
351Dic3—44no—
352Dic3—62no—
353Dic3—62no—
354Dic3—62no—
355Dic3—121no—
356Dic3—121no—
357Dic3—122no—
358Dic3—122no—
359Dic3—122no—
360Dic3—122no—
361C32C2×#50111yescharacteristic, complemented, Sylow
362C23—91no—
363Q8—124no—
364Q8—364no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—64no—
368C2×C4—91no—
369C2×C4—94no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—362no—
377C2×C4—362no—
378C2×C4—364no—
379C2×C4#381111yescharacteristic
380C2×C4#381111yescharacteristic
381C2×C4C22×D3211yescharacteristic
382C8—38no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3D3×C4⋊Q812yes—
387C2×C3D3×AGL(1,ℤ/8)12yes—
388C2×C3D3×#13712yes—
389D3—38no—
390D3—64no—
391C22—92no—
392C22—92no—
393C22—92no—
394C22C2×#381111yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—92no—
400C4—124no—
401C4—181no—
402C4—181no—
403C4—361no—
404C4—361no—
405C4D32×Q812yes—
406C3—21no—
407C3D3×#50112yescomplemented
408C2—94no—
409C2#1059536511yescharacteristic
410C2#1059545811yescharacteristic
411C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#125D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C3×#5064C2semidirect
6. #10590564C2semidirect
7. #10590563C2semidirect
9. #10590305C2semidirect
41. #5064D3semidirect
80. #3710Q8semidirect
144. C3×C3⋊C8C2×Q8semidirect
293. C3⋊C8D3×Q8semidirect
297. C3⋊D3#501semidirect
361. C32C2×#501semidirect
407. C3D3×#501semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
#105939092
C3×#50642
#105905752
#105905732
#105905642
#105905632
#105903222
#105903052
D3×#5013