Finite Group Databasebeta

← #11798198

Subgroups — #11798198

Order 1152.

473 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 86 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×D3×Dic12C211yesmaximal, characteristic
2C2×#63656C211yesmaximal, characteristic, complemented
3C3×#5188C211yesmaximal, characteristic
4C2×C3×#829C211yesmaximal, characteristic, complemented
5#10589119C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic
8#71502—31nomaximal
9#71087—31nomaximal
10C2×D3×Dic6—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×#3746C2211yescharacteristic
13C3×#946—21no—
14C2×C3×Dic12C2211yescharacteristic
15C2×C3×D3×C8C2211yescharacteristic
16C2×#3719—21no—
17D3×Dic12—22no—
18D3×Dic12—22no—
19#63656—22no—
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C3×#835—21no—
22C3×#829—22no—
23C3×#818C2211yescharacteristic
24C2×C3×C3⋊C16C2211yescharacteristic
25C2×D3×Q16—31no—
26C22×Dic12—31no—
27C2×C3×Q32—31no—
28C3×#467—31no—
29#5188D311yescharacteristic
30C2×#829—31no—
31C2×#829—31no—
32C2×#829—61no—
33C2×#829D311yescharacteristic, complemented
34#4564—31no—
35#4549—31no—
36(C2×D3)⋊C16—31no—
37#4503—31no—
38#4492—31no—
39#4492—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×C4×D3D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×#627—41no—
45C2×D3×Dic3—41no—
46D3×Dic6—24no—
47D3×Dic6—42no—
48C32×Q16—21no—
49C32×Q16—21no—
50C2×C32×C8C2311yescharacteristic
51#3746—21no—
52#3746D412yes—
53C3×(C2×D3)⋊C4—41no—
54C3×C4⋊Dic3—21no—
55C3×Dic3⋊C4—41no—
56C2×C3×C3⋊C8D411yescharacteristic
57C3×Dic12—21no—
58C3×Dic12D412yes—
59C3×D3×C8—21no—
60C3×D3×C8—21no—
61#3719—24no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2188—91noSylow
65C2×D3×Q8—61no—
66C22×Dic6—61no—
67C2×C3×Q16—21no—
68C2×C3×Q16—31no—
69C2×C3×Q16C2×D311yescharacteristic
70C2×C3×Q16C2×D311yescharacteristic
71C22×C3×C8—31no—
72C3×C22⋊Q8—61no—
73#946—21no—
74C2×#216—61no—
75D3×Q16—62no—
76D3×Q16—62no—
77C2×Dic12—31no—
78C2×Dic12—31no—
79C2×Dic12—61no—
80C2×Dic12—62no—
81C2×Dic12—61no—
82C2×Dic12—62no—
83C2×Dic12C2×D311yescharacteristic
84C2×D3×C8C2×D311yescharacteristic
85C3×Q32—62no—
86C2×C3×C16—31no—
87C3×#107—31no—
88C3×#103—61no—
89#835—21no—
90#829—22no—
91#829—62no—
92#829—62no—
93#829—64no—
94#818C2×D311yescharacteristic
95C2×C3⋊C16—31no—
96C2×C3⋊C16—31no—
97C2×C3⋊C16—61no—
98C2×C3⋊C16C2×D311yescharacteristic
99C22×C3×D3D811yescharacteristic
100C32×Q8—41no—
101C32×Q8—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C3⋊Dic3—41no—
105#634—22no—
106#634—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3D811yescharacteristic
110C3×C4×D3—21no—
111C3×C4×D3—21no—
112C3×Dic6—22no—
113C3×Dic6—41no—
114#627—44no—
115D3×Dic3—44no—
116C32×C8C2×D411yescharacteristic
117C32×C8C2×D411yescharacteristic
118C3×C3⋊C8—21no—
119C22×Q16—91no—
120C2×Q32—31no—
121C2×Q32—91no—
122#467—31no—
123#358—91no—
124#358—91no—
125C22⋊C16—91no—
126C2×C3×Q8—21no—
127C2×C3×Q8—21no—
128C2×C3×Q8—41no—
129C2×C3×Q8—61no—
130C22×C3×C4—31no—
131C22×Dic3—121no—
132D3×Q8—64no—
133D3×Q8—122no—
134C2×C4×D3—121no—
135C2×C4×D3#6711yescharacteristic
136C2×Dic6—21no—
137C2×Dic6—64no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—121no—
141C2×Dic6—122no—
142C2×Dic6—121no—
143C2×Dic6—121no—
144C3×Q16—22no—
145C3×Q16—21no—
146C3×Q16—21no—
147C3×Q16—21no—
148C3×Q16—21no—
149C3×Q16—32no—
150C3×Q16—41no—
151C3×Q16—61no—
152C2×C3×C8—21no—
153C2×C3×C8—31no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C2×C3×C8C22×D311yescharacteristic
157C2×C3×C8C22×D311yescharacteristic
158C3×C4⋊C4—61no—
159C3×C4⋊C4—121no—
160C3×C22⋊C4—121no—
161#216—64no—
162(C2×D3)⋊C4—41no—
163C4⋊Dic3—21no—
164Dic3⋊C4—41no—
165C2×C3⋊C8#6711yescharacteristic
166Dic12—21no—
167Dic12—32no—
168Dic12—32no—
169Dic12—62no—
170Dic12—64no—
171Dic12—61no—
172Dic12—61no—
173Dic12—121no—
174Dic12#6712yes—
175D3×C8—21no—
176D3×C8—21no—
177C3×C16—61no—
178C3⋊C16—21no—
179C3⋊C16—62no—
180C3⋊C16—61no—
181C3⋊C16—61no—
182C22×C32C2×D811yescharacteristic
183C2×C3×D3—21no—
184C2×C3×D3—21no—
185C2×C3×D3Q3212yescomplemented
186C32×C4—81no—
187C32×C4#12011yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C3⋊Dic3—42no—
190C3×Dic3—21no—
191C3×Dic3—42no—
192C3×Dic3—81no—
193C22×Q8—181no—
194C2×Q16—31no—
195C2×Q16—91no—
196C2×Q16—181no—
197C2×Q16—182no—
198C2×Q16—182no—
199C2×Q16D3211yescharacteristic
200C22×C8—31no—
201C22⋊Q8—61no—
202Q32—62no—
203Q32—182no—
204C2×C16—31no—
205C2×C16—91no—
206#107—31no—
207#103—61no—
208C23×C3—31no—
209C22×D3#21311yescharacteristic
210C3×Q8—42no—
211C3×Q8—41no—
212C3×Q8—41no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—62no—
216C3×Q8—81no—
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—121no—
226C2×C3×C4—121no—
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×Dic3—41no—
230C2×Dic3—41no—
231C2×Dic3—124no—
232C2×Dic3—121no—
233C2×Dic3—121no—
234C2×Dic3—241no—
235C2×Dic3#21311yescharacteristic
236C4×D3—21no—
237C4×D3—21no—
238C4×D3—124no—
239Dic6—22no—
240Dic6—41no—
241Dic6—62no—
242Dic6—62no—
243Dic6—122no—
244Dic6—124no—
245Dic6—124no—
246Dic6—121no—
247Dic6—121no—
248Dic6—241no—
249C3×C8—21no—
250C3×C8—21no—
251C3×C8—61no—
252C3×C8D3×D411yescharacteristic
253C3×C8D3×D411yescharacteristic
254C3×C8D3×D411yescharacteristic
255C3×C8C2×#6711yescharacteristic
256C3⋊C8—21no—
257C2×C32#44711yescharacteristic
258C2×C32C2×Q3211yescharacteristic
259C2×C32#51011yescharacteristic
260C3×D3—22no—
261C2×Q8—21no—
262C2×Q8—61no—
263C2×Q8—184no—
264C2×Q8—181no—
265C2×Q8—361no—
266C2×Q8—362no—
267C22×C4—31no—
268C22×C4—361no—
269Q16—21no—
270Q16—21no—
271Q16—32no—
272Q16—61no—
273Q16—92no—
274Q16—184no—
275Q16—181no—
276C2×C8—31no—
277C2×C8—61no—
278C2×C8—61no—
279C2×C8C2×D3211yescharacteristic
280C4⋊C4—61no—
281C4⋊C4—121no—
282C22⋊C4—121no—
283C16—61no—
284C16—181no—
285C22×C3—21no—
286C22×C3—32no—
287C22×C3—61no—
288C22×C3—61no—
289C22×C3D3×D811yescharacteristic
290C22×C3C2×#21311yescharacteristic
291C2×D3—21no—
292C2×D3—21no—
293C2×D3#82912yescomplemented
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—61no—
297C3×C4—82no—
298C3×C4—81no—
299C3×C4—81no—
300C3×C4—122no—
301C3×C4—241no—
302C3×C4#91111yescharacteristic
303C3×C4#93711yescharacteristic
304C3×C4#93711yescharacteristic
305C3×C4#94911yescharacteristic
306Dic3—21no—
307Dic3—42no—
308Dic3—81no—
309Dic3—122no—
310Dic3—122no—
311Dic3—242no—
312C32#218811yescharacteristic, complemented, Sylow
313C23—31no—
314Q8—41no—
315Q8—41no—
316Q8—62no—
317Q8—121no—
318Q8—182no—
319Q8—364no—
320Q8—361no—
321C2×C4—31no—
322C2×C4—41no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—121no—
326C2×C4—121no—
327C2×C4—364no—
328C2×C4—361no—
329C2×C4D3×#6711yescharacteristic
330C8—61no—
331C8D3×#6711yescharacteristic
332C8#381111yescharacteristic
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—62no—
337C2×C3D3×Q3211yescharacteristic
338C2×C3#491811yescharacteristic
339C2×C3#503611yescharacteristic
340C2×C3#515611yescharacteristic
341C2×C3C2×#82911yescharacteristic
342C2×C3#519511yescharacteristic
343D3—22no—
344C22—32no—
345C22—61no—
346C22—61no—
347C22D3×#21311yescharacteristic
348C4—61no—
349C4—81no—
350C4—122no—
351C4—241no—
352C4—362no—
353C4#6392511yescharacteristic
354C4#6398311yescharacteristic
355C3—21no—
356C3#7108711yescharacteristic, complemented
357C3#7150211yescharacteristic, complemented
358C2—62no—
359C2D3×#82911yescharacteristic
360C2#1059104211yescharacteristic
361C2#1059151511yescharacteristic
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×#63656C2semidirect
4. C2×C3×#829C2semidirect
5. #10589119C2semidirect
6. #10589117C2semidirect
33. C2×#829D3semidirect
185. C2×C3×D3Q32semidirect
293. C2×D3#829semidirect
312. C32#2188semidirect
356. C3#71087semidirect
357. C3#71502semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×#636562
C3×#51882
C2×C3×#8292
#105891192
#105891172
(C2×D3)⋊(C3⋊C16)2
#715023
#710873