Finite Group Databasebeta

← #11798100

Subgroups — #11798100

Order 1152.

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

normal subgroups only

This group has 481 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, complemented
2C2×C3×#800C211yesmaximal, characteristic, complemented
3#10590831C211yesmaximal, characteristic
4C2×#63548C211yesmaximal, characteristic, complemented
5#10589369C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
7#10589118C211yesmaximal, characteristic, complemented
8#71483—31nomaximal
9#69112—31nomaximal
10C2×D3×Dic6—21no—
11C2×#3746C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15#63908—21no—
16C2×#3719—21no—
17D3×Dic12—22no—
18D3×Dic12—22no—
19C2×C32×C16C2211yescharacteristic
20#63645C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C3×#800—22no—
23#63563—21no—
24#63548—22no—
25C2×D3×Q16—31no—
26C22×Dic12—31no—
27C2×C3×SD32—31no—
28#5157—31no—
29C2×#827—31no—
30#5115—31no—
31C2×#800—31no—
32C2×#800D311yescharacteristic, complemented
33C3×C22⋊C16—31no—
34#4564—31no—
35(C2×D3)⋊C16D311yescharacteristic, complemented
36#4503—31no—
37#4503—31no—
38#4503—31no—
39#4503—61no—
40C2×#634—21no—
41C2×C3×D12—21no—
42C2×C3×C4×D3D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×#627—41no—
45C2×#625—41no—
46C2×D3×Dic3—41no—
47D3×Dic6—24no—
48D3×Dic6—42no—
49C2×C32×C8C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51#3746—21no—
52#3746D412yescomplemented
53C2×C3×C3⋊C8D411yescharacteristic
54C3×Dic12—21no—
55C3×Dic12D412yescomplemented
56C3×D24—21no—
57C3×D24—21no—
58C3×D3×C8—21no—
59C3×D3×C8—21no—
60(C2×D3)⋊Dic3—41no—
61#3719—24no—
62C32×C16—21no—
63C3×C3⋊C16—21no—
64#2185—91noSylow
65C2×D3×Q8—61no—
66C22×Dic6—61no—
67C2×C3×Q16—31no—
68C2×C3×D8—31no—
69C22×C3×C8—31no—
70C2×#216—61no—
71#938—61no—
72#930—61no—
73D3×Q16—62no—
74D3×Q16—62no—
75C2×Dic12—31no—
76C2×Dic12—31no—
77C2×Dic12—61no—
78C2×Dic12—62no—
79C2×Dic12—61no—
80C2×Dic12—62no—
81C2×Dic12C2×D311yescharacteristic
82C2×D24C2×D311yescharacteristic
83C2×D3×C8C2×D311yescharacteristic
84C3×SD32—62no—
85C2×C3×C16—21no—
86C2×C3×C16—31no—
87C2×C3×C16C2×D311yescharacteristic
88C2×C3×C16C2×D311yescharacteristic
89#832—61no—
90#827—62no—
91#821—61no—
92#818—31no—
93#818—31no—
94#818—61no—
95C2×C3⋊C16C2×D311yescharacteristic
96#800—22no—
97#800—62no—
98C22×C3×D3—41no—
99C22×C3×D3D811yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103#634—22no—
104#634—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3D811yescharacteristic
107C3×D12—41no—
108C3×D12—41no—
109C3×C4×D3—21no—
110C3×C4×D3—21no—
111C3×Dic6—22no—
112C3×Dic6—41no—
113#627—44no—
114#625—82no—
115D3×Dic3—44no—
116C32×C8C2×D411yescharacteristic
117C32×C8C2×D411yescharacteristic
118C3×C3⋊C8—21no—
119C22×Q16—91no—
120C2×SD32—31no—
121C2×SD32—91no—
122#466—91no—
123#358—91no—
124#358—91no—
125C22⋊C16—31no—
126C2×C3×Q8—61no—
127C2×C3×D4—61no—
128C22×C3×C4—31no—
129C2×#67—121no—
130C2×#67—121no—
131C22×Dic3—121no—
132D3×Q8—64no—
133D3×Q8—122no—
134C2×D12—21no—
135C2×C4×D3—121no—
136C2×C4×D3D1211yescharacteristic
137C2×Dic6—21no—
138C2×Dic6—64no—
139C2×Dic6—61no—
140C2×Dic6—61no—
141C2×Dic6—121no—
142C2×Dic6—122no—
143C2×Dic6—121no—
144C2×Dic6—121no—
145C3×Q16—32no—
146C3×Q16—61no—
147C3×D8—61no—
148C3×D8—61no—
149C2×C3×C8—21no—
150C2×C3×C8—31no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C2×C3×C8C22×D311yescharacteristic
154C2×C3×C8C22×D311yescharacteristic
155#217—121no—
156#216—64no—
157(C2×D3)⋊C4—121no—
158C4⋊Dic3—61no—
159C4⋊Dic3—61no—
160C4⋊Dic3—121no—
161C2×C3⋊C8D1211yescharacteristic
162Dic12—21no—
163Dic12—32no—
164Dic12—32no—
165Dic12—62no—
166Dic12—64no—
167Dic12—61no—
168Dic12—61no—
169Dic12—121no—
170Dic12#6712yescomplemented
171D24—21no—
172D24—21no—
173D3×C8—21no—
174D3×C8—21no—
175C3×C16—21no—
176C3×C16—21no—
177C3×C16—41no—
178C3×C16—61no—
179C3⋊C16—21no—
180C22×C32C2×D811yescharacteristic
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C2×C3×D3SD3212yescomplemented
187C32×C4#12011yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C3⋊Dic3—42no—
190C3⋊Dic3—81no—
191C3×Dic3—21no—
192C3×Dic3—42no—
193C22×Q8—181no—
194C2×Q16—31no—
195C2×Q16—91no—
196C2×Q16—181no—
197C2×Q16—182no—
198C2×Q16—182no—
199C2×D8—31no—
200C22×C8—31no—
201#121—181no—
202SD32—62no—
203SD32—182no—
204C2×C16—31no—
205C2×C16D3211yescharacteristic
206#107—91no—
207#102—181no—
208C23×C3—31no—
209C23×C3—121no—
210C22×D3—41no—
211C22×D3D2411yescharacteristic
212C3×Q8—62no—
213C3×Q8—121no—
214C3×D4—121no—
215C3×D4—121no—
216C2×C3×C4—21no—
217C2×C3×C4—31no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—121no—
221C2×C3×C4C2×D1211yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223#67—242no—
224#67—242no—
225C2×Dic3—41no—
226C2×Dic3—124no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231C2×Dic3—241no—
232C2×Dic3—241no—
233C2×Dic3D2411yescharacteristic
234D12—41no—
235D12—41no—
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×SD3211yescharacteristic
259C2×C32#51011yescharacteristic
260C3×D3—22no—
261C3×D3—161no—
262C2×Q8—61no—
263C2×Q8—184no—
264C2×Q8—181no—
265C2×Q8—361no—
266C2×Q8—362no—
267C2×D4—61no—
268C2×D4—361no—
269C22×C4—31no—
270C22×C4—361no—
271Q16—32no—
272Q16—61no—
273Q16—92no—
274Q16—184no—
275Q16—181no—
276D8—61no—
277D8—61no—
278C2×C8—31no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8C2×D3211yescharacteristic
282C4⋊C4—181no—
283C22⋊C4—361no—
284C16—21no—
285C16—61no—
286C22×C3—21no—
287C22×C3—32no—
288C22×C3—61no—
289C22×C3—61no—
290C22×C3—241no—
291C22×C3—241no—
292C22×C3—241no—
293C22×C3C2×D2411yescharacteristic
294C22×C3D3×D811yescharacteristic
295C2×D3—21no—
296C2×D3—21no—
297C2×D3—81no—
298C2×D3—81no—
299C2×D3—81no—
300C2×D3#80012yescomplemented
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—61no—
304C3×C4—122no—
305C3×C4#88211yescharacteristic
306C3×C4#90811yescharacteristic
307C3×C4#91111yescharacteristic
308C3×C4#93711yescharacteristic
309Dic3—21no—
310Dic3—42no—
311Dic3—122no—
312Dic3—122no—
313Dic3—242no—
314Dic3—241no—
315Dic3—241no—
316Dic3—481no—
317C32#218511yescharacteristic, complemented, Sylow
318C23—31no—
319C23—121no—
320Q8—62no—
321Q8—121no—
322Q8—182no—
323Q8—364no—
324Q8—361no—
325D4—121no—
326D4—121no—
327D4—722no—
328C2×C4—31no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—121no—
332C2×C4—364no—
333C2×C4—361no—
334C2×C4—361no—
335C2×C4D3×D1211yescharacteristic
336C8—61no—
337C8#380211yescharacteristic
338C8D3×#6711yescharacteristic
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—62no—
343C2×C3—481no—
344C2×C3#473211yescharacteristic
345C2×C3C2×#80011yescharacteristic
346C2×C3#490911yescharacteristic
347C2×C3D3×SD3211yescharacteristic
348C2×C3#491511yescharacteristic
349C2×C3#515611yescharacteristic
350D3—22no—
351D3—161no—
352C22—32no—
353C22—61no—
354C22—61no—
355C22—241no—
356C22—241no—
357C22—241no—
358C22D3×D2411yescharacteristic
359C4—61no—
360C4—122no—
361C4—362no—
362C4—721no—
363C4#6379511yescharacteristic
364C4#6392211yescharacteristic
365C3—21no—
366C3#6911211yescharacteristic, complemented
367C3#7148311yescharacteristic, complemented
368C2—62no—
369C2—481no—
370C2D3×#80011yescharacteristic
371C2#1059023911yescharacteristic
372C2#1059094411yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radical#10590831C2
hypercenterC2×C16D32
hypocenterC32#2185
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
2. C2×C3×#800C2semidirect
4. C2×#63548C2semidirect
5. #10589369C2semidirect
6. C3×(C2×D3)⋊C16C2semidirect
7. #10589118C2semidirect
32. C2×#800D3semidirect
35. (C2×D3)⋊C16D3semidirect
52. #3746D4semidirect
55. C3×Dic12D4semidirect
170. Dic12#67semidirect
186. C2×C3×D3SD32semidirect
300. C2×D3#800semidirect
317. C32#2185semidirect
366. C3#69112semidirect
367. C3#71483semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×C3×#8002
#105908312
C2×#635482
#105893692
C3×(C2×D3)⋊C162
#105891182
#714833
#691123