Finite Group Databasebeta

← #11788189

Subgroups — #11788189

Order 1152.

1074 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64081C211yesmaximal, characteristic, complemented
3C2×C32×#104C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#70383—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64155C412yescomplemented
14#64147C412yescomplemented
15#64146—21no—
16#64144—21no—
17C4×#638—22no—
18C2×#3752—21no—
19#64135C2211yescharacteristic
20C2×#3750—21no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×#3748C2211yescharacteristic
23#64081—22no—
24#64081—22no—
25C32×#104—22no—
26#63664—22no—
27#63647—22no—
28#5828—34no—
29C2×#872—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
41C2×C32×D4—21no—
42C2×C32×D4C2×C411yescharacteristic
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—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3C2×C412yes—
54C2×C4×C3⋊D3D412yes—
55C32×M16—21no—
56C32×M16—21no—
57C2×C32×C8—21no—
58C32×C42—21no—
59C32×C42D412yescomplemented
60#3757—21no—
61#3757—22no—
62#3752—24no—
63#3752—22no—
64C4⋊(C3⋊Dic3)C2×C412yes—
65#3750—24no—
66#3750—22no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3D412yescomplemented
70#3748—21no—
71#3748—21no—
72C2×C3⋊(C3⋊C8)—21no—
73#1897—91noSylow
74C2×C3×#41C2×D314yes—
75C22×C4×D3—34no—
76C2×C3×M16C2×D314yes—
77C2×C3×C42C2×D314yes—
78#946—38no—
79#938—38no—
80#937—64no—
81#935—64no—
82C4×#67—68no—
83C2×(C2×D3)⋊C4—64no—
84#926—34no—
85C2×Dic3⋊C4—64no—
86C2×C4×Dic3—34no—
87C2×#208—34no—
88#872—68no—
89#872—68no—
90C3×#104—28no—
91#837—68no—
92(C2×D3)⋊C8—68no—
93C23×C32—21no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—42no—
98C22×C3⋊D3C22⋊C412yes—
99C32×Q8—21no—
100C32×Q8—21no—
101C32×D4—21no—
102C32×D4—21no—
103C32×D4—41no—
104C32×D4—41no—
105C2×C32×C4—21no—
106C2×C32×C4—22no—
107C2×C32×C4—42no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116#638—44no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—42no—
122C2×C3⋊Dic3C22⋊C412yes—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C32×C8—41no—
128C3⋊(C3⋊C8)—41no—
129#525—91no—
130C2×#117—91no—
131C2×#104—91no—
132C2×#104C3⋊D311yescharacteristic, complemented
133#407—91no—
134#339—91no—
135#339—91no—
136C23×D3—34no—
137C3×#41—24no—
138C3×#41—24no—
139C3×#41—24no—
140C3×#41—24no—
141C2×C3×Q8C4×D314yes—
142C2×C3×D4—24no—
143C2×C3×D4C4×D314yes—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4C22×D314yes—
147C2×#67—68no—
148C22×Dic3—34no—
149C22×Dic3—64no—
150C2×C4×D3—38no—
151C2×C4×D3—38no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×C4×D3—64no—
156C3×M16—24no—
157C3×M16—24no—
158C2×C3×C8—24no—
159C3×C42—24no—
160C3×C42#6718yescomplemented
161#217—68no—
162#217—64no—
163(C2×D3)⋊C4—68no—
164(C2×D3)⋊C4—616no—
165C4⋊Dic3—38no—
166Dic3⋊C4—68no—
167Dic3⋊C4—616no—
168C4×Dic3—38no—
169C4×Dic3—64no—
170C4×Dic3—64no—
171#208—64no—
172#208—64no—
173C2×C3⋊C8—64no—
174C22×C32—22no—
175C22×C32—41no—
176C22×C32—42no—
177C22×C32C2×C22⋊C411yescharacteristic
178C22×C32#12011yescharacteristic
179C22×C32#12311yescharacteristic
180C2×C3⋊D3—22no—
181C2×C3⋊D3—22no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C32×C4—42no—
186C32×C4—41no—
187C32×C4C4×D411yescharacteristic
188C32×C4C4×D411yescharacteristic
189C32×C4#12111yescharacteristic
190C32×C4#12111yescharacteristic
191C3⋊Dic3—22no—
192C3⋊Dic3—42no—
193C3⋊Dic3—42no—
194C2×#41C2×C3⋊D311yescharacteristic
195C23×C4—91no—
196C2×M16—91no—
197C2×M16C2×C3⋊D311yescharacteristic
198#123—181no—
199C22⋊Q8—92no—
200#121—92no—
201#120—181no—
202C4×D4—182no—
203#117—91no—
204#117—182no—
205#117—182no—
206C2×C4⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—91no—
209C2×C42C2×C3⋊D311yescharacteristic
210#104—22no—
211#104—182no—
212C22⋊C8—182no—
213C23×C3—24no—
214C23×C3D3×D414yes—
215C22×D3—38no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—128no—
219C3×Q8—24no—
220C3×Q8—24no—
221C3×D4—24no—
222C3×D4—24no—
223C3×D4—44no—
224C3×D4—44no—
225C2×C3×C4—24no—
226C2×C3×C4—28no—
227C2×C3×C4—48no—
228C2×C3×C4—44no—
229C2×C3×C4—44no—
230C2×C3×C4C2×C4×D314yes—
231C2×C3×C4#23514yes—
232C2×C3×C4D3×D414yes—
233C2×C3×C4D3×D414yes—
234C2×C3×C4#23714yes—
235C2×C3×C4C2×#6714yes—
236#67—1216no—
237C2×Dic3—38no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—68no—
241C2×Dic3—68no—
242C2×Dic3—128no—
243C4×D3—68no—
244C4×D3—68no—
245C4×D3—68no—
246C4×D3—68no—
247C3×C8—44no—
248C3⋊C8—124no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—81no—
252C2×C32#38611yescharacteristic
253C2×C32#42112yes—
254C3⋊D3—42no—
255C24—91no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—21no—
260C2×Q8C4×C3⋊D311yescharacteristic
261C2×D4—21no—
262C2×D4—182no—
263C2×D4C4×C3⋊D311yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—91no—
267C22×C4—92no—
268C22×C4—92no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4—181no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4C22×C3⋊D311yescharacteristic
275M16—21no—
276M16—21no—
277M16—181no—
278M16—181no—
279C2×C8—21no—
280C2×C8—181no—
281C4⋊C4—92no—
282C4⋊C4—182no—
283C4⋊C4—184no—
284C22⋊C4—182no—
285C22⋊C4—184no—
286C22⋊C4—182no—
287C22⋊C4—181no—
288C42—21no—
289C42—92no—
290C42—181no—
291C42—181no—
292C42#63812yescomplemented
293C22×C3—28no—
294C22×C3—44no—
295C22×C3—48no—
296C22×C3D3×C22⋊C414yes—
297C22×C3#88314yes—
298C22×C3#93714yes—
299C2×D3—68no—
300C2×D3—68no—
301C2×D3—68no—
302C2×D3—128no—
303C2×D3—128no—
304C3×C4—48no—
305C3×C4—44no—
306C3×C4#67⋊C414yes—
307C3×C4#88414yes—
308C3×C4C4×#6714yes—
309C3×C4#93814yes—
310Dic3—68no—
311Dic3—128no—
312Dic3—128no—
313C32#189711yescharacteristic, complemented, Sylow
314C23—21no—
315C23—92no—
316C23—181no—
317C23—181no—
318C23—362no—
319C23D4×C3⋊D311yescharacteristic
320Q8—21no—
321Q8—21no—
322D4—21no—
323D4—21no—
324D4—41no—
325D4—41no—
326D4—364no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—92no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—362no—
342C2×C4C2×C4×C3⋊D311yescharacteristic
343C2×C4#382811yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4D4×C3⋊D311yescharacteristic
346C2×C4#383011yescharacteristic
347C2×C4C2×#63811yescharacteristic
348C8—41no—
349C8—361no—
350C2×C3—24no—
351C2×C3—24no—
352C2×C3—84no—
353C2×C3#482118yes—
354C2×C3#495614yes—
355D3—128no—
356C22—22no—
357C22—42no—
358C22—41no—
359C22—182no—
360C22—182no—
361C22—182no—
362C22—362no—
363C22—362no—
364C22C22⋊C4×C3⋊D311yescharacteristic
365C22#6409211yescharacteristic
366C22#6414611yescharacteristic
367C4—42no—
368C4—41no—
369C4—182no—
370C4—362no—
371C4—362no—
372C4#6409011yescharacteristic
373C4#6409311yescharacteristic
374C4C4×#63811yescharacteristic
375C4#6414711yescharacteristic
376C3#7038314yescomplemented
377C2—21no—
378C2—21no—
379C2—81no—
380C2—362no—
381C2#1059252012yes—
382C2#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#1897
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×#64081C2semidirect
3. C2×C32×#104C2semidirect
4. C2×#63664C2semidirect
5. #10592825C2semidirect
6. #10589421C2semidirect
7. #10589389C2semidirect
13. #64155C4semidirect
14. #64147C4semidirect
30. C2×C3×#104D3semidirect
59. C32×C42D4semidirect
69. C4×C3⋊Dic3D4semidirect
132. C2×#104C3⋊D3semidirect
160. C3×C42#67semidirect
292. C42#638semidirect
313. C32#1897semidirect
376. C3#70383semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×#640812
C2×C32×#1042
C2×#636642
#105928252
#105894212
#105893892
#703833