Finite Group Databasebeta

← #11788155

Subgroups — #11788155

Order 1152.

1326 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 195 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
1#10596299C211yesmaximal, characteristic
2C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#104C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#70382—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14#64155C412yescomplemented
15#64147C412yescomplemented
16#64146—21no—
17#64144—21no—
18C4×#638—22no—
19#64135C2211yescharacteristic
20C2×C4×C3⋊Dic3—21no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×#3748C2211yescharacteristic
23C42×C3⋊D3—22no—
24C42×C3⋊D3—22no—
25C32×#104—22no—
26#63664—22no—
27#63647—22no—
28#5828—34no—
29C2×C42×D3—34no—
30C2×C3×#104D314yescomplemented
31C2×#837—34no—
32#5126—34no—
33#4555—34no—
34#4523—34no—
35C23×C3⋊D3D411yescharacteristic
36C32×#41—21no—
37C32×#41—21no—
38C32×#41—21no—
39C32×#41—21no—
40C2×C32×Q8C2×C411yescharacteristic, complemented
41C2×C32×D4—21no—
42C2×C32×D4C2×C411yescharacteristic, complemented
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—22no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—28no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3D412yes—
57C32×M16—21no—
58C32×M16—21no—
59C2×C32×C8—21no—
60C32×C42—21no—
61C32×C42D412yescomplemented
62#3757—21no—
63#3757—22no—
64#3752—22no—
65C4⋊(C3⋊Dic3)C2×C412yescomplemented
66#3750—22no—
67C4×C3⋊Dic3—24no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3D412yescomplemented
71#3748—21no—
72#3748—21no—
73C2×C3⋊(C3⋊C8)—21no—
74#1896—91noSylow
75C2×C3×#41C2×D314yes—
76C22×C4×D3—34no—
77C22×C4×D3—64no—
78C2×C3×M16C2×D314yes—
79C2×C3×C42C2×D314yes—
80#946—38no—
81#938—38no—
82#937—64no—
83#935—64no—
84C4×#67—68no—
85#926—34no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—64no—
88C2×#208—34no—
89C42×D3—68no—
90C42×D3—68no—
91C3×#104—28no—
92#837—68no—
93(C2×D3)⋊C8—68no—
94C23×C32—21no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3—21no—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—24no—
99C22×C3⋊D3C22⋊C412yes—
100C32×Q8—21no—
101C32×Q8—21no—
102C32×D4—21no—
103C32×D4—21no—
104C32×D4—41no—
105C32×D4—41no—
106C2×C32×C4—24no—
107C2×C32×C4—22no—
108C2×C32×C4—21no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117#638—44no—
118C2×C3⋊Dic3—24no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C22⋊C412yes—
124C4×C3⋊D3—216no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—22no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—41no—
131#525—91no—
132C22×C42—91no—
133C2×#104—91no—
134C2×#104C3⋊D311yescharacteristic, complemented
135#407—91no—
136#339—91no—
137#339—91no—
138C23×D3—34no—
139C3×#41—24no—
140C3×#41—24no—
141C3×#41—24no—
142C3×#41—24no—
143C2×C3×Q8C4×D314yescomplemented
144C2×C3×D4—24no—
145C2×C3×D4C4×D314yescomplemented
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4C22×D314yes—
149C2×#67—68no—
150C22×Dic3—34no—
151C22×Dic3—64no—
152C2×C4×D3—38no—
153C2×C4×D3—38no—
154C2×C4×D3—616no—
155C2×C4×D3—632no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C3×M16—24no—
161C3×M16—24no—
162C2×C3×C8—24no—
163C3×C42—24no—
164C3×C42#6718yescomplemented
165#217—68no—
166#217—64no—
167(C2×D3)⋊C4—68no—
168C4⋊Dic3—38no—
169Dic3⋊C4—68no—
170C4×Dic3—38no—
171C4×Dic3—616no—
172C4×Dic3—64no—
173C4×Dic3—64no—
174#208—64no—
175#208—64no—
176C2×C3⋊C8—64no—
177C22×C32—22no—
178C22×C32—41no—
179C22×C32—42no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32#12011yescharacteristic
182C22×C32#12311yescharacteristic
183C2×C3⋊D3—24no—
184C2×C3⋊D3—24no—
185C2×C3⋊D3—22no—
186C2×C3⋊D3—22no—
187C2×C3⋊D3#10414yescomplemented
188C32×C4—24no—
189C32×C4—41no—
190C32×C4C4×D411yescharacteristic
191C32×C4C4×D411yescharacteristic
192C32×C4#12111yescharacteristic
193C32×C4#12111yescharacteristic
194C3⋊Dic3—24no—
195C3⋊Dic3—22no—
196C3⋊Dic3—42no—
197C2×#41C2×C3⋊D311yescharacteristic
198C23×C4—91no—
199C23×C4—181no—
200C2×M16—91no—
201C2×M16C2×C3⋊D311yescharacteristic
202#123—181no—
203C22⋊Q8—92no—
204#121—92no—
205#120—181no—
206C4×D4—182no—
207#117—91no—
208C2×C42—91no—
209C2×C42—182no—
210C2×C42—181no—
211C2×C42—182no—
212C2×C42C2×C3⋊D311yescharacteristic
213#104—22no—
214#104—182no—
215C22⋊C8—182no—
216C23×C3—24no—
217C23×C3D3×D414yes—
218C22×D3—38no—
219C22×D3—616no—
220C22×D3—64no—
221C22×D3—64no—
222C3×Q8—24no—
223C3×Q8—24no—
224C3×D4—24no—
225C3×D4—24no—
226C3×D4—44no—
227C3×D4—44no—
228C2×C3×C4—216no—
229C2×C3×C4—28no—
230C2×C3×C4—24no—
231C2×C3×C4—44no—
232C2×C3×C4—44no—
233C2×C3×C4C2×C4×D314yes—
234C2×C3×C4#23514yes—
235C2×C3×C4D3×D414yes—
236C2×C3×C4D3×D414yes—
237C2×C3×C4#23714yes—
238C2×C3×C4C2×#6714yes—
239#67—1216no—
240C2×Dic3—38no—
241C2×Dic3—616no—
242C2×Dic3—64no—
243C2×Dic3—68no—
244C2×Dic3—64no—
245C2×Dic3—68no—
246C4×D3—664no—
247C4×D3—68no—
248C4×D3—68no—
249C4×D3—68no—
250C4×D3—68no—
251C3×C8—44no—
252C3⋊C8—124no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32—81no—
256C2×C32#38611yescharacteristic
257C2×C32C2×#10412yes—
258C3⋊D3—24no—
259C24—91no—
260#41—21no—
261#41—21no—
262#41—21no—
263#41—21no—
264C2×Q8C4×C3⋊D311yescharacteristic, complemented
265C2×D4—21no—
266C2×D4—182no—
267C2×D4C4×C3⋊D311yescharacteristic, complemented
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—91no—
271C22×C4—92no—
272C22×C4—92no—
273C22×C4—184no—
274C22×C4—188no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4C22×C3⋊D311yescharacteristic
281M16—21no—
282M16—21no—
283M16—181no—
284M16—181no—
285C2×C8—21no—
286C2×C8—181no—
287C4⋊C4—92no—
288C4⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—181no—
292C42—21no—
293C42—92no—
294C42—184no—
295C42—181no—
296C42—181no—
297C42#63812yescomplemented
298C22×C3—28no—
299C22×C3—44no—
300C22×C3—48no—
301C22×C3D3×C22⋊C414yes—
302C22×C3#88314yes—
303C22×C3#93714yes—
304C2×D3—316no—
305C2×D3—616no—
306C2×D3—616no—
307C2×D3—68no—
308C2×D3—68no—
309C3×C4—216no—
310C3×C4—44no—
311C3×C4#67⋊C414yes—
312C3×C4#88414yes—
313C3×C4C4×#6714yes—
314C3×C4#93814yes—
315Dic3—616no—
316Dic3—68no—
317Dic3—128no—
318C32#189611yescharacteristic, complemented, Sylow
319C23—21no—
320C23—92no—
321C23—184no—
322C23—181no—
323C23—181no—
324C23D4×C3⋊D311yescharacteristic
325Q8—21no—
326Q8—21no—
327D4—21no—
328D4—21no—
329D4—41no—
330D4—41no—
331D4—364no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—92no—
338C2×C4—1816no—
339C2×C4—184no—
340C2×C4—181no—
341C2×C4—182no—
342C2×C4—181no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4C2×C4×C3⋊D311yescharacteristic
349C2×C4#382811yescharacteristic
350C2×C4D4×C3⋊D311yescharacteristic
351C2×C4D4×C3⋊D311yescharacteristic
352C2×C4#383011yescharacteristic
353C2×C4C2×#63811yescharacteristic
354C8—41no—
355C8—361no—
356C2×C3—24no—
357C2×C3—24no—
358C2×C3—84no—
359C2×C3D3×#10418yes—
360C2×C3#495614yes—
361D3—616no—
362C22—22no—
363C22—42no—
364C22—41no—
365C22—94no—
366C22—184no—
367C22—184no—
368C22—182no—
369C22—182no—
370C22C22⋊C4×C3⋊D311yescharacteristic
371C22#6409211yescharacteristic
372C22#6414611yescharacteristic
373C4—24no—
374C4—41no—
375C4—184no—
376C4—182no—
377C4—362no—
378C4#6409011yescharacteristic
379C4#6409311yescharacteristic
380C4C4×#63811yescharacteristic
381C4#6414711yescharacteristic
382C3#7038214yescomplemented
383C2—21no—
384C2—21no—
385C2—81no—
386C2—184no—
387C2C3⋊D3×#10412yes—
388C2#1059265511yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radical#10596299C2
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C42×C3⋊D3C2semidirect
3. C2×C32×#104C2semidirect
4. C2×#63664C2semidirect
5. #10592825C2semidirect
6. #10589421C2semidirect
7. #10589389C2semidirect
14. #64155C4semidirect
15. #64147C4semidirect
30. C2×C3×#104D3semidirect
40. C2×C32×Q8C2×C4semidirect
42. C2×C32×D4C2×C4semidirect
61. C32×C42D4semidirect
65. C4⋊(C3⋊Dic3)C2×C4semidirect
70. C4×C3⋊Dic3D4semidirect
134. C2×#104C3⋊D3semidirect
143. C2×C3×Q8C4×D3semidirect
145. C2×C3×D4C4×D3semidirect
164. C3×C42#67semidirect
187. C2×C3⋊D3#104semidirect
264. C2×Q8C4×C3⋊D3semidirect
267. C2×D4C4×C3⋊D3semidirect
297. C42#638semidirect
318. C32#1896semidirect
382. C3#70382semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×C42×C3⋊D32
C2×C32×#1042
C2×#636642
#105928252
#105894212
#105893892
#703823