Finite Group Databasebeta

← #11787266

Subgroups — #11787266

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic
2C2×#64101C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic
6#10589417C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70269—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13#64155—22no—
14#64155C414yescomplemented
15C2×#3752—21no—
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750—21no—
20C2×C4×C3⋊Dic3—21no—
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22#64101—22no—
23#64101—22no—
24C32×#103—22no—
25#63662—22no—
26#63647—22no—
27C2×#946—34no—
28C2×#892—34no—
29C2×C3×#103D314yescomplemented
30C2×#835—34no—
31C2×(C2×D3)⋊C8—34no—
32#4551—34no—
33#4529—34no—
34C23×C3⋊D3D411yescharacteristic
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8C2×C412yes—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3C2×C412yes—
52C2×C4×C3⋊D3D412yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D412yes—
58#3752—24no—
59#3752—24no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)C2×C412yes—
63C4⋊(C3⋊Dic3)D412yes—
64#3750—24no—
65C4×C3⋊Dic3—24no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69#1873—91noSylow
70C22×C3×Q8C2×D314yes—
71C22×C4×D3—34no—
72C22×C3×C8C2×D314yes—
73C2×C3×C4⋊C4C2×D314yes—
74#946—316no—
75#946—68no—
76C2×(C2×D3)⋊C4—64no—
77C2×(C2×D3)⋊C4—64no—
78C2×C4⋊Dic3—34no—
79C2×C4⋊Dic3—34no—
80C2×Dic3⋊C4—64no—
81C2×C4×Dic3—64no—
82C22×C3⋊C8—34no—
83#892—68no—
84#892—68no—
85C3×#103—28no—
86#835—68no—
87(C2×D3)⋊C8—68no—
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—21no—
94C22×C3⋊D3—21no—
95C22×C3⋊D3C22⋊C412yes—
96C32×Q8—22no—
97C32×Q8—22no—
98C32×Q8—41no—
99C32×Q8—41no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3C22⋊C412yes—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125C32×C8—41no—
126C3⋊(C3⋊C8)—41no—
127C2×C22⋊Q8—91no—
128C2×#117—91no—
129C2×#103—91no—
130C2×#103C3⋊D311yescharacteristic, complemented
131C2×C22⋊C8—91no—
132#340—91no—
133#340—91no—
134C23×D3—34no—
135C2×C3×Q8—24no—
136C2×C3×Q8—24no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—24no—
140C2×C3×Q8C4×D318yes—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4C22×D314yes—
144C22×Dic3—34no—
145C22×Dic3—64no—
146C22×Dic3—64no—
147C2×C4×D3—38no—
148C2×C4×D3—38no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C3×C8—24no—
154C2×C3×C8—24no—
155C2×C3×C8—24no—
156C3×C4⋊C4—24no—
157C3×C4⋊C4#6718yes—
158(C2×D3)⋊C4—616no—
159(C2×D3)⋊C4—616no—
160C4⋊Dic3—38no—
161C4⋊Dic3—38no—
162C4⋊Dic3—64no—
163C4⋊Dic3—64no—
164Dic3⋊C4—616no—
165C4×Dic3—616no—
166C2×C3⋊C8—64no—
167C2×C3⋊C8—64no—
168C2×C3⋊C8—64no—
169C22×C32C2×C22⋊C411yescharacteristic
170C22×C32#12011yescharacteristic
171C22×C32#12311yescharacteristic
172C22×C32#13511yescharacteristic
173C22×C32#13511yescharacteristic
174C22×C32#13711yescharacteristic
175C22×C32#13711yescharacteristic
176C2×C3⋊D3—22no—
177C2×C3⋊D3—22no—
178C2×C3⋊D3—22no—
179C2×C3⋊D3—41no—
180C2×C3⋊D3—41no—
181C2×C3⋊D3—41no—
182C2×C3⋊D3—41no—
183C32×C4—42no—
184C32×C4—42no—
185C32×C4C4×D411yescharacteristic
186C32×C4C4×D411yescharacteristic
187C32×C4#12111yescharacteristic
188C32×C4#12111yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—42no—
191C3⋊Dic3—42no—
192C22×Q8C2×C3⋊D311yescharacteristic
193C23×C4—91no—
194C22×C8—91no—
195C22×C8C2×C3⋊D311yescharacteristic
196C22⋊Q8—94no—
197C22⋊Q8—182no—
198#117—182no—
199#117—182no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—181no—
203C2×C4⋊C4C2×C3⋊D311yescharacteristic
204C2×C22⋊C4—181no—
205C2×C22⋊C4—181no—
206C2×C42—181no—
207#103—22no—
208#103—182no—
209C22⋊C8—182no—
210C23×C3D3×D414yes—
211C22×D3—38no—
212C22×D3—64no—
213C22×D3—64no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—64no—
218C3×Q8—28no—
219C3×Q8—28no—
220C3×Q8—44no—
221C3×Q8—44no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—44no—
228C2×C3×C4C2×C4×D314yes—
229C2×C3×C4#23514yes—
230C2×C3×C4D3×D414yes—
231C2×C3×C4D3×D414yes—
232C2×C3×C4#23714yes—
233C2×C3×C4C2×#6714yes—
234C2×Dic3—38no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—68no—
238C2×Dic3—68no—
239C2×Dic3—124no—
240C2×Dic3—124no—
241C2×Dic3—124no—
242C2×Dic3—124no—
243C4×D3—68no—
244C4×D3—68no—
245C4×D3—68no—
246C4×D3—68no—
247C3×C8—44no—
248C3⋊C8—124no—
249C2×C32#38611yescharacteristic
250C2×C32#41611yescharacteristic
251C2×C32#41911yescharacteristic
252C2×C32#45211yescharacteristic
253C2×C32#45211yescharacteristic
254C2×C32#48511yescharacteristic
255C2×C32#48511yescharacteristic
256C3⋊D3—42no—
257C24—91no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8C4×C3⋊D312yes—
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×C4—181no—
275C22×C4C22×C3⋊D311yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—181no—
280C2×C8—181no—
281C2×C8—181no—
282C4⋊C4—21no—
283C4⋊C4—92no—
284C4⋊C4—92no—
285C4⋊C4—184no—
286C4⋊C4—181no—
287C4⋊C4—181no—
288C4⋊C4#63812yes—
289C22⋊C4—184no—
290C22⋊C4—184no—
291C42—184no—
292C22×C3D3×C22⋊C414yes—
293C22×C3#88314yes—
294C22×C3#91514yes—
295C22×C3#91614yes—
296C22×C3#91814yes—
297C22×C3#91914yes—
298C22×C3#93714yes—
299C2×D3—68no—
300C2×D3—68no—
301C2×D3—68no—
302C2×D3—124no—
303C2×D3—124no—
304C2×D3—124no—
305C2×D3—124no—
306C3×C4—48no—
307C3×C4—48no—
308C3×C4#67⋊C414yes—
309C3×C4#88414yes—
310C3×C4C4×#6714yes—
311C3×C4#93814yes—
312Dic3—68no—
313Dic3—128no—
314Dic3—128no—
315C32#187311yescharacteristic, complemented, Sylow
316C23—92no—
317C23—181no—
318C23—181no—
319C23—181no—
320C23—181no—
321C23—181no—
322C23—181no—
323C23D4×C3⋊D311yescharacteristic
324Q8—22no—
325Q8—22no—
326Q8—41no—
327Q8—41no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—92no—
335C2×C4—181no—
336C2×C4—181no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—361no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C4—361no—
347C2×C4C2×C4×C3⋊D311yescharacteristic
348C2×C4#382811yescharacteristic
349C2×C4D4×C3⋊D311yescharacteristic
350C2×C4D4×C3⋊D311yescharacteristic
351C2×C4#383011yescharacteristic
352C2×C4C2×#63811yescharacteristic
353C8—41no—
354C8—361no—
355C2×C3#480214yes—
356C2×C3#480414yes—
357C2×C3#481414yes—
358C2×C3#481514yes—
359C2×C3#495614yes—
360C2×C3#517314yes—
361C2×C3#518714yes—
362D3—128no—
363C22—182no—
364C22—182no—
365C22—182no—
366C22—361no—
367C22—361no—
368C22—361no—
369C22—361no—
370C22C22⋊C4×C3⋊D311yescharacteristic
371C22#6409211yescharacteristic
372C22#6412411yescharacteristic
373C22#6412511yescharacteristic
374C22#6412711yescharacteristic
375C22#6412811yescharacteristic
376C22#6414611yescharacteristic
377C4—42no—
378C4—42no—
379C4—182no—
380C4—362no—
381C4—362no—
382C4#6409011yescharacteristic
383C4#6409311yescharacteristic
384C4C4×#63811yescharacteristic
385C4#6414711yescharacteristic
386C3#7026914yescomplemented
387C2—362no—
388C2#1059250111yescharacteristic
389C2#1059250311yescharacteristic
390C2#1059251311yescharacteristic
391C2#1059251411yescharacteristic
392C2#1059265511yescharacteristic
393C2#1059287211yescharacteristic
394C2#1059288611yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1873
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×C32×#103C2semidirect
4. C2×#63662C2semidirect
6. #10589417C2semidirect
7. #10589395C2semidirect
14. #64155C4semidirect
29. C2×C3×#103D3semidirect
130. C2×#103C3⋊D3semidirect
315. C32#1873semidirect
386. C3#70269semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C2×#641012
C2×C32×#1032
C2×#636622
C2×#636472
#105894172
#105893952
#702693