Finite Group Databasebeta

← #11798202

Subgroups — #11798202

Order 1152.

461 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 461 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×C3×D3×Q16C211yesmaximal, characteristic
2C2×C3×#829C211yesmaximal, characteristic, complemented
3#10590851C211yesmaximal, characteristic
4C2×#63550C211yesmaximal, characteristic, complemented
5#10589430C211yesmaximal, characteristic, complemented
6#10589118C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic
8#72064—31nomaximal
9#71502—31nomaximal
10C2×C3×D3×Q8—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×C3×#216—21no—
13C3×D3×Q16—22no—
14C3×D3×Q16—22no—
15C2×C3×Dic12C2211yescharacteristic
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18#63856—21no—
19#63645C2211yescharacteristic
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C3×#829—22no—
22C2×C3×C3⋊C16C2211yescharacteristic
23#63566—21no—
24#63550—22no—
25C22×C3×Q16—31no—
26C2×D3×Q16D311yescharacteristic
27C2×C3×Q32—31no—
28#5188—31no—
29C2×#829—31no—
30C2×#829—31no—
31C2×#829D311yescharacteristic, complemented
32#5116—31no—
33#4564—31no—
34#4564—31no—
35#4564—31no—
36#4564—61no—
37#4549—31no—
38(C2×D3)⋊C16—31no—
39#4503—31no—
40C2×C32×Q8—21no—
41C3×D3×Q8—24no—
42C3×D3×Q8—42no—
43C2×C3×C4×D3—41no—
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—41no—
48C32×Q16—21no—
49C32×Q16D412yes—
50C2×C32×C8C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C3×#216—24no—
53C2×C3×C3⋊C8D411yescharacteristic
54C3×Dic12—21no—
55C3×Dic12—21no—
56C3×Dic12—21no—
57C3×Dic12D412yes—
58C3×D3×C8—21no—
59C3×D3×C8—21no—
60#3724—41no—
61(C2×D3)⋊Dic3—41no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2188—91noSylow
65C22×C3×Q8—61no—
66C2×D3×Q8—21no—
67C2×C3×Q16—21no—
68C2×C3×Q16—31no—
69C2×C3×Q16—31no—
70C2×C3×Q16—61no—
71C2×C3×Q16—62no—
72C2×C3×Q16—62no—
73C2×C3×Q16C2×D311yescharacteristic
74C2×C3×Q16C2×D311yescharacteristic
75C22×C3×C8—31no—
76#946—61no—
77C2×#216—21no—
78#924—61no—
79D3×Q16—22no—
80D3×Q16—22no—
81C2×Dic12C2×D311yescharacteristic
82C2×Dic12C2×D311yescharacteristic
83C2×D3×C8C2×D311yescharacteristic
84C3×Q32—62no—
85C2×C3×C16—31no—
86#835—61no—
87#829—22no—
88#829—62no—
89#829—62no—
90#818—31no—
91#818—31no—
92#818—61no—
93#816—61no—
94C2×C3⋊C16—31no—
95C2×C3⋊C16—31no—
96C2×C3⋊C16—61no—
97C2×C3⋊C16C2×D311yescharacteristic
98C22×C3×D3D811yescharacteristic
99C32×Q8—22no—
100C32×Q8—41no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C3⋊Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3D811yescharacteristic
107C3×C4×D3—21no—
108C3×C4×D3—21no—
109C3×C4×D3—44no—
110C3×Dic6—22no—
111C3×Dic6—44no—
112C3×Dic6—41no—
113C3×Dic6—41no—
114C3×Dic6—41no—
115C32×C8C2×D411yescharacteristic
116C32×C8C2×D411yescharacteristic
117C3×C3⋊C8—21no—
118C22×Q16—31no—
119C2×Q32—31no—
120C2×Q32—91no—
121#467—91no—
122#358—91no—
123#358—91no—
124C22⋊C16—91no—
125C2×C3×Q8—21no—
126C2×C3×Q8—21no—
127C2×C3×Q8—41no—
128C2×C3×Q8—64no—
129C2×C3×Q8—61no—
130C2×C3×Q8—61no—
131C2×C3×Q8—121no—
132C2×C3×Q8—122no—
133C22×C3×C4—31no—
134C22×C3×C4—121no—
135D3×Q8—24no—
136D3×Q8—42no—
137C2×C4×D3—41no—
138C2×C4×D3#6711yescharacteristic
139C2×Dic6—21no—
140C2×Dic6—21no—
141C2×Dic6—41no—
142C3×Q16—21no—
143C3×Q16—21no—
144C3×Q16—22no—
145C3×Q16—32no—
146C3×Q16—41no—
147C3×Q16—64no—
148C3×Q16—61no—
149C3×Q16—61no—
150C3×Q16—61no—
151C3×Q16#6712yes—
152C3×Q16#6712yes—
153C2×C3×C8—21no—
154C2×C3×C8—31no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8C22×D311yescharacteristic
158C2×C3×C8C22×D311yescharacteristic
159#217—121no—
160#216—24no—
161(C2×D3)⋊C4—121no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—121no—
165Dic3⋊C4—121no—
166Dic3⋊C4—121no—
167C2×C3⋊C8#6711yescharacteristic
168Dic12—21no—
169Dic12—21no—
170Dic12—21no—
171Dic12#6712yes—
172D3×C8—21no—
173D3×C8—21no—
174C3×C16—61no—
175C3⋊C16—21no—
176C3⋊C16—61no—
177C3⋊C16—61no—
178C3⋊C16—121no—
179C22×C32C2×D811yescharacteristic
180C2×C3×D3—21no—
181C2×C3×D3—21no—
182C2×C3×D3Q3212yescomplemented
183C32×C4—42no—
184C32×C4#12011yescharacteristic
185C32×C4AGL(1,ℤ/8)11yescharacteristic
186C3⋊Dic3—81no—
187C3×Dic3—21no—
188C3×Dic3—42no—
189C3×Dic3—81no—
190C22×Q8—61no—
191C2×Q16—31no—
192C2×Q16—31no—
193C2×Q16—61no—
194C2×Q16—62no—
195C2×Q16—62no—
196C2×Q16D3211yescharacteristic
197C22×C8—31no—
198C22⋊Q8—181no—
199Q32—62no—
200Q32—182no—
201C2×C16—31no—
202C2×C16—91no—
203#107—91no—
204#103—181no—
205C23×C3—31no—
206C22×D3#21311yescharacteristic
207C3×Q8—22no—
208C3×Q8—22no—
209C3×Q8—42no—
210C3×Q8—41no—
211C3×Q8—41no—
212C3×Q8—62no—
213C3×Q8—81no—
214C3×Q8—124no—
215C3×Q8—121no—
216C3×Q8—121no—
217C3×Q8—121no—
218C2×C3×C4—21no—
219C2×C3×C4—31no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—81no—
225C2×C3×C4—124no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—41no—
231C2×Dic3—41no—
232C2×Dic3—121no—
233C2×Dic3—121no—
234C2×Dic3—241no—
235C2×Dic3#21311yescharacteristic
236C4×D3—21no—
237C4×D3—21no—
238C4×D3—44no—
239Dic6—22no—
240Dic6—44no—
241Dic6—41no—
242Dic6—41no—
243Dic6—41no—
244C3×C8—21no—
245C3×C8—21no—
246C3×C8—61no—
247C3×C8D3×D411yescharacteristic
248C3×C8C2×#6711yescharacteristic
249C3×C8C2×#6711yescharacteristic
250C3×C8C2×#6711yescharacteristic
251C3⋊C8—21no—
252C2×C32#44711yescharacteristic
253C2×C32C2×Q3211yescharacteristic
254C2×C32#51011yescharacteristic
255C3×D3—22no—
256C2×Q8—21no—
257C2×Q8—64no—
258C2×Q8—61no—
259C2×Q8—61no—
260C2×Q8—121no—
261C2×Q8—122no—
262C22×C4—31no—
263C22×C4—121no—
264Q16—21no—
265Q16—32no—
266Q16—64no—
267Q16—61no—
268Q16—61no—
269Q16—61no—
270Q16#62512yes—
271C2×C8—31no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8C2×D3211yescharacteristic
275C4⋊C4—181no—
276C4⋊C4—361no—
277C22⋊C4—361no—
278C16—61no—
279C16—181no—
280C22×C3—21no—
281C22×C3—32no—
282C22×C3—61no—
283C22×C3—61no—
284C22×C3D3×D811yescharacteristic
285C22×C3C2×#21311yescharacteristic
286C2×D3—21no—
287C2×D3—21no—
288C2×D3#82912yescomplemented
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—42no—
292C3×C4—42no—
293C3×C4—61no—
294C3×C4—82no—
295C3×C4—122no—
296C3×C4—241no—
297C3×C4#91111yescharacteristic
298C3×C4#93211yescharacteristic
299C3×C4#93711yescharacteristic
300C3×C4#95311yescharacteristic
301Dic3—21no—
302Dic3—42no—
303Dic3—81no—
304Dic3—241no—
305Dic3—241no—
306Dic3—481no—
307C32#218811yescharacteristic, complemented, Sylow
308C23—31no—
309Q8—22no—
310Q8—41no—
311Q8—62no—
312Q8—124no—
313Q8—121no—
314Q8—121no—
315Q8—121no—
316C2×C4—31no—
317C2×C4—41no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—124no—
321C2×C4—121no—
322C2×C4—121no—
323C2×C4—361no—
324C2×C4D3×#6711yescharacteristic
325C8—61no—
326C8C2×#62511yescharacteristic
327C8D3×#6711yescharacteristic
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—62no—
332C2×C3D3×Q3211yescharacteristic
333C2×C3#491811yescharacteristic
334C2×C3#515611yescharacteristic
335C2×C3#517911yescharacteristic
336C2×C3C2×#82911yescharacteristic
337C2×C3#521711yescharacteristic
338D3—22no—
339C22—32no—
340C22—61no—
341C22—61no—
342C22D3×#21311yescharacteristic
343C4—42no—
344C4—61no—
345C4—122no—
346C4—241no—
347C4—721no—
348C4#6393211yescharacteristic
349C4#6397611yescharacteristic
350C3—21no—
351C3#7150211yescharacteristic, complemented
352C3#7206411yescharacteristic, complemented
353C2—62no—
354C2D3×#82911yescharacteristic
355C2#1059104711yescharacteristic
356C2#1059144711yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC22×C3×D3D8
hypercenterC2×Q16D32
hypocenterC32#2188
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#829C2semidirect
4. C2×#63550C2semidirect
5. #10589430C2semidirect
6. #10589118C2semidirect
31. C2×#829D3semidirect
182. C2×C3×D3Q32semidirect
288. C2×D3#829semidirect
307. C32#2188semidirect
351. C3#71502semidirect
352. C3#72064semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
C2×C3×#8292
#105908512
C2×#635502
#105894302
#105891182
(C2×D3)⋊(C3⋊C16)2
#720643
#715023