Finite Group Databasebeta

← #11798090

Subgroups — #11798090

Order 1152.

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

normal subgroups only

This group has 497 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×#63654C211yesmaximal, characteristic, complemented
3C3×#5157C211yesmaximal, characteristic
4C2×C3×#827C211yesmaximal, characteristic, complemented
5#10589119C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
8#71483—31nomaximal
9#71077—31nomaximal
10C2×D3×Dic6—21no—
11C2×C32×D8C2211yescharacteristic
12C2×#3746C2211yescharacteristic
13C3×#938—21no—
14C2×C3×Dic12C2211yescharacteristic
15C2×C3×D3×C8C2211yescharacteristic
16C2×#3719—21no—
17D3×Dic12—22no—
18D3×Dic12—22no—
19#63654—22no—
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C3×#832—21no—
22C3×#827—22no—
23C3×#818C2211yescharacteristic
24C2×C3×C3⋊C16C2211yescharacteristic
25C2×D3×Q16—31no—
26C22×Dic12—31no—
27C2×C3×SD32—31no—
28C3×#466—31no—
29#5157D311yescharacteristic
30C2×#827—31no—
31C2×#827—31no—
32C2×#827—61no—
33C2×#827D311yescharacteristic, complemented
34#4564—31no—
35#4549—31no—
36(C2×D3)⋊C16—31no—
37#4503—31no—
38#4492—31no—
39#4492—31no—
40C2×C32×D4—21no—
41C2×#634—21no—
42C2×C3×#67—41no—
43C2×C3×C4×D3D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×#627—41no—
46C2×D3×Dic3—41no—
47D3×Dic6—24no—
48D3×Dic6—42no—
49C32×D8—21no—
50C32×D8—21no—
51C2×C32×C8C2311yescharacteristic
52#3746—21no—
53#3746D412yescomplemented
54C3×#217—41no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C3×Dic12—21no—
58C3×Dic12D412yescomplemented
59C3×D3×C8—21no—
60C3×D3×C8—21no—
61#3719—24no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2185—91noSylow
65C2×D3×Q8—61no—
66C22×Dic6—61no—
67C2×C3×Q16—31no—
68C2×C3×D8—21no—
69C2×C3×D8C2×D311yescharacteristic
70C2×C3×D8C2×D311yescharacteristic
71C22×C3×C8—31no—
72C3×#121—61no—
73C2×#216—61no—
74#938—21no—
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×SD32—62no—
86C2×C3×C16—31no—
87C3×#107—31no—
88C3×#102—61no—
89#832—21no—
90#827—22no—
91#827—62no—
92#827—62no—
93#827—64no—
94#818C2×D311yescharacteristic
95C2×C3⋊C16—31no—
96C2×C3⋊C16—31no—
97C2×C3⋊C16—61no—
98C2×C3⋊C16C2×D311yescharacteristic
99C23×C32—41no—
100C22×C3×D3D811yescharacteristic
101C32×D4—41no—
102C32×D4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C3⋊Dic3—41no—
105#634—22no—
106#634—41no—
107C3×#67—82no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3D811yescharacteristic
111C3×C4×D3—21no—
112C3×C4×D3—21no—
113C3×Dic6—22no—
114C3×Dic6—41no—
115#627—44no—
116D3×Dic3—44no—
117C32×C8C2×D411yescharacteristic
118C32×C8C2×D411yescharacteristic
119C3×C3⋊C8—21no—
120C22×Q16—91no—
121C2×SD32—31no—
122C2×SD32—91no—
123#466—31no—
124#358—91no—
125#358—91no—
126C22⋊C16—91no—
127C2×C3×Q8—61no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—41no—
131C2×C3×D4—121no—
132C22×C3×C4—31no—
133C2×#67—41no—
134C22×Dic3—121no—
135D3×Q8—64no—
136D3×Q8—122no—
137C2×C4×D3—121no—
138C2×C4×D3#6711yescharacteristic
139C2×Dic6—21no—
140C2×Dic6—64no—
141C2×Dic6—61no—
142C2×Dic6—61no—
143C2×Dic6—121no—
144C2×Dic6—122no—
145C2×Dic6—121no—
146C2×Dic6—121no—
147C3×Q16—32no—
148C3×Q16—61no—
149C3×D8—22no—
150C3×D8—21no—
151C3×D8—21no—
152C3×D8—21no—
153C3×D8—21no—
154C3×D8—41no—
155C2×C3×C8—21no—
156C2×C3×C8—31no—
157C2×C3×C8—61no—
158C2×C3×C8—61no—
159C2×C3×C8C22×D311yescharacteristic
160C2×C3×C8C22×D311yescharacteristic
161C3×C4⋊C4—61no—
162C3×C22⋊C4—121no—
163#217—41no—
164#216—64no—
165C4⋊Dic3—21no—
166C2×C3⋊C8#6711yescharacteristic
167Dic12—21no—
168Dic12—32no—
169Dic12—32no—
170Dic12—62no—
171Dic12—64no—
172Dic12—61no—
173Dic12—61no—
174Dic12—121no—
175Dic12#6712yescomplemented
176D3×C8—21no—
177D3×C8—21no—
178C3×C16—61no—
179C3⋊C16—21no—
180C3⋊C16—62no—
181C3⋊C16—61no—
182C3⋊C16—61no—
183C22×C32—81no—
184C22×C32—81no—
185C22×C32—81no—
186C22×C32C2×D811yescharacteristic
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3SD3212yescomplemented
190C32×C4#12011yescharacteristic
191C32×C4AGL(1,ℤ/8)11yescharacteristic
192C3⋊Dic3—42no—
193C3×Dic3—21no—
194C3×Dic3—42no—
195C3×Dic3—81no—
196C22×Q8—181no—
197C2×Q16—31no—
198C2×Q16—91no—
199C2×Q16—181no—
200C2×Q16—182no—
201C2×Q16—182no—
202C2×D8D3211yescharacteristic
203C22×C8—31no—
204#121—61no—
205SD32—62no—
206SD32—182no—
207C2×C16—31no—
208C2×C16—91no—
209#107—31no—
210#102—61no—
211C23×C3—31no—
212C23×C3—41no—
213C23×C3—41no—
214C23×C3—81no—
215C22×D3#21311yescharacteristic
216C3×Q8—62no—
217C3×Q8—121no—
218C3×D4—42no—
219C3×D4—41no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—81no—
224C3×D4—242no—
225C2×C3×C4—21no—
226C2×C3×C4—31no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—121no—
230C2×C3×C4—121no—
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233#67—82no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3—124no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239C2×Dic3—241no—
240C2×Dic3#21311yescharacteristic
241C4×D3—21no—
242C4×D3—21no—
243C4×D3—124no—
244Dic6—22no—
245Dic6—41no—
246Dic6—62no—
247Dic6—62no—
248Dic6—122no—
249Dic6—124no—
250Dic6—124no—
251Dic6—121no—
252Dic6—121no—
253Dic6—241no—
254C3×C8—21no—
255C3×C8—21no—
256C3×C8—61no—
257C3×C8D3×D411yescharacteristic
258C3×C8D3×D411yescharacteristic
259C3×C8D3×D411yescharacteristic
260C3×C8C2×#6711yescharacteristic
261C3⋊C8—21no—
262C2×C32—161no—
263C2×C32#44711yescharacteristic
264C2×C32C2×SD3211yescharacteristic
265C2×C32#51011yescharacteristic
266C3×D3—22no—
267C2×Q8—61no—
268C2×Q8—184no—
269C2×Q8—181no—
270C2×Q8—361no—
271C2×Q8—362no—
272C2×D4—21no—
273C2×D4—121no—
274C22×C4—31no—
275C22×C4—361no—
276Q16—32no—
277Q16—61no—
278Q16—92no—
279Q16—184no—
280Q16—181no—
281D8—21no—
282D8—21no—
283C2×C8—31no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8C2×D3211yescharacteristic
287C4⋊C4—61no—
288C22⋊C4—121no—
289C16—61no—
290C16—181no—
291C22×C3—21no—
292C22×C3—32no—
293C22×C3—61no—
294C22×C3—61no—
295C22×C3—82no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3—81no—
299C22×C3—81no—
300C22×C3—81no—
301C22×C3—81no—
302C22×C3—161no—
303C22×C3—161no—
304C22×C3D3×D811yescharacteristic
305C22×C3C2×#21311yescharacteristic
306C2×D3—21no—
307C2×D3—21no—
308C2×D3#82712yescomplemented
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—61no—
312C3×C4—122no—
313C3×C4—241no—
314C3×C4#91111yescharacteristic
315C3×C4#93711yescharacteristic
316C3×C4#93711yescharacteristic
317C3×C4#94911yescharacteristic
318Dic3—21no—
319Dic3—42no—
320Dic3—81no—
321Dic3—122no—
322Dic3—122no—
323Dic3—242no—
324C32#218511yescharacteristic, complemented, Sylow
325C23—31no—
326C23—41no—
327Q8—62no—
328Q8—121no—
329Q8—182no—
330Q8—364no—
331Q8—361no—
332D4—41no—
333D4—41no—
334D4—242no—
335C2×C4—31no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—121no—
339C2×C4—121no—
340C2×C4—364no—
341C2×C4—361no—
342C2×C4D3×#6711yescharacteristic
343C8—61no—
344C8D3×#6711yescharacteristic
345C8#381111yescharacteristic
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—62no—
350C2×C3—162no—
351C2×C3—161no—
352C2×C3—161no—
353C2×C3D3×SD3211yescharacteristic
354C2×C3#491511yescharacteristic
355C2×C3#503611yescharacteristic
356C2×C3C2×#82711yescharacteristic
357C2×C3#515611yescharacteristic
358C2×C3#519511yescharacteristic
359D3—22no—
360C22—32no—
361C22—61no—
362C22—61no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22D3×#21311yescharacteristic
367C4—61no—
368C4—122no—
369C4—241no—
370C4—362no—
371C4#6392511yescharacteristic
372C4#6398311yescharacteristic
373C3—21no—
374C3#7107711yescharacteristic, complemented
375C3#7148311yescharacteristic, complemented
376C2—62no—
377C2—161no—
378C2D3×#82711yescharacteristic
379C2#1059102811yescharacteristic
380C2#1059151511yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
prime radicalC3×#5157C2
hypercenterC2×D8D32
hypocenterC32#2185
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
2. C2×#63654C2semidirect
4. C2×C3×#827C2semidirect
5. #10589119C2semidirect
6. #10589117C2semidirect
7. (C2×D3)⋊(C3⋊C16)C2semidirect
33. C2×#827D3semidirect
53. #3746D4semidirect
58. C3×Dic12D4semidirect
175. Dic12#67semidirect
189. C2×C3×D3SD32semidirect
308. C2×D3#827semidirect
324. C32#2185semidirect
374. C3#71077semidirect
375. 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×#636542
C3×#51572
C2×C3×#8272
#105891192
#105891172
(C2×D3)⋊(C3⋊C16)2
#714833
#710773