Finite Group Databasebeta

← #11787152

Subgroups — #11787152

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C22×#3710C211yesmaximal, characteristic, complemented
3C2×C3×#830C212yesmaximal, complemented
4C2×#63557C211yesmaximal, characteristic, complemented
5#10589156C212yesmaximal, complemented
6#69957—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C411yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×#3757C411yescharacteristic
11C4×#638—22no—
12C4×#638—22no—
13C2×#3752C411yescharacteristic
14C2×#3750C411yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3710—22no—
19C2×#3710—24no—
20C3×#830—24no—
21#63557—22no—
22C2×C4×#67—32no—
23C2×C4×#67—61no—
24C22×D3×C8—32no—
25C2×C3×C22⋊C8—32no—
26C2×#830D312yescomplemented
27C2×(C2×D3)⋊C8—32no—
28#4550—32no—
29#4550—32no—
30C24×C32C2×C411yescharacteristic
31C23×C3⋊D3C2×C411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4—21no—
34C22×C32×C4—22no—
35C22×C32×C4—22no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C2×#638—22no—
39C2×#638—22no—
40C2×#638C814yescomplemented
41C22×C3⋊Dic3C2×C411yescharacteristic
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C411yescharacteristic
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3D412yes—
47C2×C4×C3⋊D3D412yes—
48#3757—22no—
49#3752—22no—
50#3750—22no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8D414yescomplemented
59#3710—28no—
60#1869—91noSylow
61C23×C3×C4—21no—
62C23×C3×C4C2×D312yes—
63C22×#67—32no—
64C22×#67—61no—
65C22×C4×D3—32no—
66C22×C4×D3—61no—
67C22×C3×C8—32no—
68C22×C3×C8—32no—
69C2×#217—32no—
70C2×#217—61no—
71C4×#67—64no—
72C4×#67—64no—
73C4×#67—64no—
74C4×#67—64no—
75C2×(C2×D3)⋊C4—32no—
76C2×(C2×D3)⋊C4—61no—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—61no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C22×C3⋊C8C2×D312yes—
82C22×C3⋊C8C2×D312yes—
83C2×D3×C8—64no—
84C2×D3×C8—64no—
85C2×D3×C8—64no—
86C3×C22⋊C8—64no—
87#830—24no—
88(C2×D3)⋊C8—64no—
89C23×C32—21no—
90C23×C32—21no—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32C2×C812yescomplemented
94C23×C32C22×C411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3C22⋊C412yes—
98C22×C3⋊D3C2×C812yes—
99C22×C3⋊D3M1612yes—
100C2×C32×C4—21no—
101C2×C32×C4—22no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4—41no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D412yes—
108C2×C32×C4#4112yes—
109#638—28no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3C22⋊C412yes—
116C2×C3⋊Dic3C2×C812yescomplemented
117C4×C3⋊D3—22no—
118C4×C3⋊D3—24no—
119C4×C3⋊D3—22no—
120C3×C3⋊C8—24no—
121C3×C3⋊C8—42no—
122C23×C8—91no—
123C2×C4×D4—91no—
124C2×C22⋊C8—32no—
125C2×C22⋊C8—91no—
126#336—92no—
127C24×C3—21no—
128C24×C3C4×D312yes—
129C23×D3—32no—
130C23×D3—61no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—42no—
142C22×C3×C4—42no—
143C22×C3×C4C4×D312yes—
144C22×C3×C4C22×D312yes—
145C2×#67—38no—
146C2×#67—64no—
147C2×#67—64no—
148C2×#67—64no—
149C2×#67—64no—
150C2×#67—64no—
151C22×Dic3—32no—
152C22×Dic3—32no—
153C22×Dic3—32no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C2×C4×D3—34no—
158C2×C4×D3—34no—
159C2×C4×D3—62no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×C4×D3—62no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×C4×D3—122no—
166C2×C4×D3—122no—
167C2×C3×C8—34no—
168C2×C3×C8—62no—
169C2×C3×C8—62no—
170C2×C3×C8—62no—
171C2×C3×C8—62no—
172C2×C3×C8—62no—
173#217—64no—
174#217—64no—
175(C2×D3)⋊C4—64no—
176(C2×D3)⋊C4—64no—
177Dic3⋊C4—64no—
178Dic3⋊C4—64no—
179C4×Dic3—62no—
180C4×Dic3—62no—
181C4×Dic3—62no—
182C4×Dic3—62no—
183C2×C3⋊C8—22no—
184C2×C3⋊C8—22no—
185C2×C3⋊C8—22no—
186C2×C3⋊C8—22no—
187C2×C3⋊C8—22no—
188C2×C3⋊C8#6714yescomplemented
189D3×C8—616no—
190C22×C32—22no—
191C22×C32—24no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32—42no—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32C4×D412yes—
197C22×C32C22×C811yescharacteristic
198C22×C32C2×M1611yescharacteristic
199C22×C32#13112yes—
200C2×C3⋊D3—22no—
201C2×C3⋊D3—22no—
202C2×C3⋊D3—24no—
203C2×C3⋊D3—24no—
204C2×C3⋊D3C22⋊C814yescomplemented
205C32×C4—41no—
206C32×C4#12011yescharacteristic
207C32×C4#12112yes—
208C32×C4#12311yescharacteristic
209C3⋊Dic3—22no—
210C3⋊Dic3—22no—
211C3⋊Dic3—41no—
212C22×D4—91no—
213C23×C4—91no—
214C23×C4D3211yescharacteristic
215C22×C8—32no—
216C22×C8—32no—
217C22×C8—184no—
218C22×C8—182no—
219C4×D4—182no—
220C4×D4—182no—
221C2×C4⋊C4—91no—
222C2×C22⋊C4—91no—
223C2×C22⋊C4—91no—
224C2×C42—91no—
225C22⋊C8—64no—
226C22⋊C8—182no—
227C23×C3—22no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3D3×C814yescomplemented
240C23×C3C2×C4×D312yes—
241C22×D3—34no—
242C22×D3—34no—
243C22×D3—34no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—62no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—122no—
252C22×D3—122no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—42no—
262C2×C3×C4—44no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4#23512yes—
270C2×C3×C4D3×D412yes—
271C2×C3×C4D3×D412yes—
272C2×C3×C4D3×D412yes—
273C2×C3×C4#23712yes—
274C2×C3×C4C2×#6712yes—
275#67—616no—
276#67—616no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C4×D3—64no—
294C4×D3—64no—
295C4×D3—64no—
296C4×D3—64no—
297C4×D3—124no—
298C4×D3—122no—
299C4×D3—122no—
300C3×C8—64no—
301C3×C8—122no—
302C3⋊C8—24no—
303C3⋊C8—42no—
304C2×C32—42no—
305C2×C32#38611yescharacteristic
306C2×C32C2×C22⋊C811yescharacteristic
307C2×C32#40811yescharacteristic
308C2×C32C8×D412yes—
309C2×C32#43512yes—
310C3⋊D3—24no—
311C24—91no—
312C24#62411yescharacteristic
313C2×D4—94no—
314C2×D4—182no—
315C2×D4—182no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—92no—
323C22×C4—92no—
324C22×C4—91no—
325C22×C4—182no—
326C22×C4—182no—
327C22×C4#62411yescharacteristic
328C22×C4C2×D3211yescharacteristic
329C2×C8—34no—
330C2×C8—62no—
331C2×C8—62no—
332C2×C8—62no—
333C2×C8—62no—
334C2×C8—62no—
335C2×C8—188no—
336C4⋊C4—182no—
337C22⋊C4—182no—
338C22⋊C4—182no—
339C42—181no—
340C42—181no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—21no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—44no—
351C22×C3—42no—
352C22×C3—44no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3D3×C22⋊C412yes—
359C22×C3#67⋊C412yes—
360C22×C3C2×D3×C812yes—
361C22×C3#90112yes—
362C22×C3D3×M1612yes—
363C22×C3#90712yes—
364C22×C3C4×#6712yes—
365C2×D3—38no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—64no—
371C2×D3—64no—
372C2×D3—64no—
373C2×D3—122no—
374C2×D3—124no—
375C2×D3—124no—
376C2×D3—122no—
377C3×C4—22no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4#88312yes—
383C3×C4#88412yes—
384C3×C4#93712yes—
385C3×C4#93812yes—
386Dic3—64no—
387Dic3—64no—
388Dic3—64no—
389Dic3—122no—
390Dic3—122no—
391Dic3—122no—
392C32#186911yescharacteristic, complemented, Sylow
393C23—22no—
394C23—21no—
395C23—22no—
396C23—21no—
397C23—92no—
398C23—92no—
399C23—92no—
400C23—182no—
401C23—182no—
402C23#371012yescomplemented
403C23C2×#62411yescharacteristic
404D4—188no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—92no—
411C2×C4—92no—
412C2×C4—181no—
413C2×C4—182no—
414C2×C4—181no—
415C2×C4—184no—
416C2×C4—182no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—181no—
420C2×C4#380412yes—
421C2×C4D3×#6712yes—
422C2×C4#381111yescharacteristic
423C2×C4#381111yescharacteristic
424C8—64no—
425C8—122no—
426C2×C3—22no—
427C2×C3—22no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—44no—
432C2×C3—44no—
433C2×C3D3×C22⋊C812yes—
434C2×C3#67⋊C812yes—
435C2×C3#472712yes—
436C2×C3#472812yes—
437C2×C3#495612yes—
438C2×C3C8×#6712yes—
439C2×C3#512712yes—
440D3—68no—
441D3—124no—
442C22—24no—
443C22—22no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—94no—
448C22—184no—
449C22—184no—
450C22—182no—
451C22—182no—
452C22C2×#371011yescharacteristic
453C22#6381712yes—
454C22#6381811yescharacteristic
455C22#6395212yes—
456C22#6397411yescharacteristic
457C4—41no—
458C4—182no—
459C4—182no—
460C4—361no—
461C4#6395812yes—
462C4#6397511yescharacteristic
463C4#6398311yescharacteristic
464C3—21no—
465C3#6995712yescomplemented
466C2—42no—
467C2—184no—
468C2#1059114812yes—
469C2#1059114912yes—
470C2#1059115211yescharacteristic
471C2#1059115311yescharacteristic
472C2#1059172211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1869
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3710C2semidirect
3. C2×C3×#830C2semidirect
4. C2×#63557C2semidirect
5. #10589156C2semidirect
26. C2×#830D3semidirect
40. C2×#638C8semidirect
58. C2×C3×C3⋊C8D4semidirect
93. C23×C32C2×C8semidirect
116. C2×C3⋊Dic3C2×C8semidirect
188. C2×C3⋊C8#67semidirect
204. C2×C3⋊D3C22⋊C8semidirect
239. C23×C3D3×C8semidirect
392. C32#1869semidirect
402. C23#3710semidirect
465. C3#69957semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×#37102
C2×C3×#8302
C2×#635572
#105891562
#699573