Finite Group Databasebeta

← #13071949

Subgroups — #13071949

Order 1408.

864 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4339C211yesmaximal, characteristic
2C2×#66947C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×#66936C211yesmaximal, characteristic, complemented
5C11×#385C211yesmaximal, characteristic, complemented
6#10622823C211yesmaximal, characteristic, complemented
7#10622602C211yesmaximal, characteristic, complemented
8#10622592C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622569C211yesmaximal, characteristic, complemented
12#10622281C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622277C211yesmaximal, characteristic, complemented
15#10622269C211yesmaximal, characteristic, complemented
16C23×C4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C2×#4339—24no—
20C2×#4339—24no—
21C2×#4339—24no—
22C22×D44C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C22×C4×D11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic
27C22×Dic22C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×C4⋊Dic11C2211yescharacteristic
41C2×C4⋊Dic11C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×Dic11⋊C4C2211yescharacteristic
46#66947—24no—
47C4⋊C4×D11—24no—
48#66936—24no—
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11D414yes—
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81#4339—232no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44D414yes—
85C2×C4×D11—22no—
86C2×C4×D11—22no—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—22no—
95C2×C4×D11—22no—
96C2×C4×D11D414yes—
97C2×Dic22—22no—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117Dic11⋊C4—22no—
118#2406—111nomaximal, Sylow
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C2×D412yes—
126C23×C11C2411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11C2×D412yes—
138C22×D11C2×D412yes—
139C22×D11C2×D412yes—
140C22×D11C2×D412yes—
141C2×C4×C11—28no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11C2×D412yes—
158C2×C4×C11C2×D412yes—
159C2×C4×C11#4112yescomplemented
160C22⋊D11—28no—
161C22⋊D11—28no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11C2×D412yes—
178C2×Dic11C2×D412yes—
179C2×Dic11#4112yescomplemented
180D44—28no—
181C4×D11—28no—
182C4×D11—28no—
183C4×D11—28no—
184C4×D11—44no—
185Dic22—28no—
186C22×#41—111no—
187C2×#123—111no—
188C2×#123—111no—
189C22×C4⋊C4—111no—
190#395—111no—
191#395—111no—
192#394—111no—
193#394—111no—
194#386—111no—
195#386—111no—
196#385—111no—
197#385—111no—
198#385—111no—
199#385D1111yescharacteristic, complemented
200#381—111no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11C22×D411yescharacteristic
209C22×C11C22×D411yescharacteristic
210C22×C11C22×D411yescharacteristic
211C22×C11C2×#4111yescharacteristic
212C22×C11C2×#4111yescharacteristic
213C22×C112−1+411yescharacteristic
214C22×C112−1+411yescharacteristic
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11#12014yes—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—41no—
235Dic11—22no—
236Dic11—22no—
237Dic11—22no—
238Dic11—41no—
239Dic11—41no—
240Dic11—41no—
241C2×#41—224no—
242C2×#41—224no—
243C2×#41—224no—
244C22×Q8—111no—
245C22×D4—111no—
246C22×D4—111no—
247C22×D4—111no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—111no—
251C23×C4—111no—
252C23×C4C2×D1111yescharacteristic
253#123—224no—
254#123—224no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—224no—
262C2×C4⋊C4C2×D1111yescharacteristic
263C2×C4⋊C4C2×D1111yescharacteristic
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4C2×D1111yescharacteristic
273C2×C22⋊C4C2×D1111yescharacteristic
274#95—111no—
275#95—111no—
276#95—111no—
277#95—111no—
278#95—111no—
279#95—111no—
280#95C2×D1111yescharacteristic
281#95C2×D1111yescharacteristic
282C2×C11—42no—
283C2×C11C2×#12011yescharacteristic
284C2×C11#52511yescharacteristic
285C2×C11#53611yescharacteristic
286C2×C11#54711yescharacteristic
287C2×C11#54711yescharacteristic
288C2×C11#54711yescharacteristic
289C2×C11#54711yescharacteristic
290D11—24no—
291D11—42no—
292C24—111no—
293C24—111no—
294C24C22×D1111yescharacteristic
295#41—2232no—
296C2×Q8—222no—
297C2×Q8—222no—
298C2×Q8—222no—
299C2×D4—114no—
300C2×D4—114no—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—222no—
306C2×D4—222no—
307C2×D4—222no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—114no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4—222no—
321C22×C4—222no—
322C22×C4—222no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4C22×D1111yescharacteristic
330C22×C4C22×D1111yescharacteristic
331C22×C4C22×D1111yescharacteristic
332C22×C4C22×D1111yescharacteristic
333C22×C4C22×D1111yescharacteristic
334C22×C4C22×D1111yescharacteristic
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—222no—
348C22⋊C4—222no—
349C22⋊C4—222no—
350C22⋊C4—222no—
351C22⋊C4—222no—
352C22⋊C4—222no—
353C11#240611yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—112no—
361C23—112no—
362C23—112no—
363C23—112no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23D4×D1112yes—
375C23C23×D1111yescharacteristic
376Q8—228no—
377D4—228no—
378D4—228no—
379D4—228no—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—112no—
397C2×C4—112no—
398C2×C4—112no—
399C2×C4—228no—
400C2×C4—228no—
401C2×C4—228no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—444no—
418C2×C4#433912yescomplemented
419C2×C4D4×D1112yes—
420C2×C4D4×D1112yes—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—114no—
429C22—222no—
430C22—222no—
431C22—222no—
432C22—222no—
433C22—222no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22C2×#433911yescharacteristic
443C22C2×D4×D1111yescharacteristic
444C22C2×D4×D1111yescharacteristic
445C22C2×D4×D1111yescharacteristic
446C22#6704011yescharacteristic
447C22#41×D1111yescharacteristic
448C22#6704311yescharacteristic
449C4—22no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—222no—
456C4—222no—
457C4—222no—
458C4—441no—
459C4—441no—
460C4—441no—
461C2—42no—
462C2—224no—
463C2—442no—
464C2#1062303811yescharacteristic
465C2#1062307811yescharacteristic
466C2#1062308211yescharacteristic
467C2D11×#12011yescharacteristic
468C2#1062315911yescharacteristic
469C2#1062316211yescharacteristic
470C2#1062318611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC22×#4339C2
hypercenter#385D11
hypocenterC11#2406
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#66947C2semidirect
3. C2×C4⋊C4×D11C2semidirect
4. C2×#66936C2semidirect
5. C11×#385C2semidirect
6. #10622823C2semidirect
7. #10622602C2semidirect
8. #10622592C2semidirect
9. #10622574C2semidirect
10. #10622572C2semidirect
11. #10622569C2semidirect
12. #10622281C2semidirect
13. #10622278C2semidirect
14. #10622277C2semidirect
15. #10622269C2semidirect
159. C2×C4×C11#41semidirect
179. C2×Dic11#41semidirect
199. #385D11semidirect
353. C11#2406semidirect
418. C2×C4#4339semidirect

Maximal subgroups

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

subgroupindex
C22×#43392
C2×#669472
C2×C4⋊C4×D112
C2×#669362
C11×#3852
#106228232
#106226022
#106225922
#106225742
#106225722
#106225692
#106222812
#106222782
#106222772
#106222692
#240611