Finite Group Databasebeta

← #13076913

Subgroups — #13076913

Order 1408.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66992C211yesmaximal, characteristic
2C22×C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66931C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622833C211yesmaximal, characteristic, complemented
7#10622826C211yesmaximal, characteristic, complemented
8#10622571C211yesmaximal, characteristic, complemented
9#10622570C211yesmaximal, characteristic, complemented
10#10622564C211yesmaximal, characteristic, complemented
11#10622557C211yesmaximal, characteristic, complemented
12#10622283C211yesmaximal, characteristic, complemented
13#10622282C211yesmaximal, characteristic, complemented
14#10622263C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C23×Dic11C2211yescharacteristic
22C22×Dic22C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30#66992—24no—
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11—24no—
41C2×C4×Dic11C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44C2×C4×Dic11C2211yescharacteristic
45#66938—24no—
46#66931—24no—
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
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⋊D11—22no—
75C22×Dic11—22no—
76C22×Dic11—22no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C22×Dic11D414yes—
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C22⋊Dic11—22no—
95C22⋊Dic11—22no—
96C22⋊Dic11—22no—
97C22⋊Dic11—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103C4⋊Dic11—22no—
104Dic11⋊C4—22no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11D414yescomplemented
111#2850—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11C2×D412yes—
124C23×C11#4112yes—
125C23×C11#4112yes—
126C23×C11C2411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134D4×C11—44no—
135C2×C4×C11—28no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
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×C11C2×D412yes—
150C2×C4×C11#4112yes—
151C22⋊D11—44no—
152C22⋊D11—44no—
153C2×Dic11—28no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—28no—
161C2×Dic11—21no—
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×Dic11C2×D412yes—
171C2×Dic11C2×D412yes—
172C2×Dic11C2×D412yes—
173C2×Dic11C2×D412yes—
174C2×Dic11#4112yes—
175C2×Dic11#4112yes—
176Dic22—44no—
177C2×#124—111no—
178C2×C22⋊Q8—111no—
179C2×#121—111no—
180C22×C42—111no—
181#391—111no—
182#390—111no—
183#388—111no—
184#388—111no—
185#388—111no—
186#388—111no—
187#386—111no—
188#386—111no—
189#386—111no—
190#386D1111yescharacteristic, complemented
191#382—111no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11#12414yescomplemented
206C22×C11C22×D411yescharacteristic
207C22×C11C22×D411yescharacteristic
208C22×C11C2×#4111yescharacteristic
209C22×C11C2×#4111yescharacteristic
210C22×C11C2×#4111yescharacteristic
211C22×C11C2×#4111yescharacteristic
212C22×C11C2×#4111yescharacteristic
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—41no—
225Dic11—22no—
226Dic11—22no—
227Dic11—22no—
228Dic11—41no—
229Dic11—41no—
230Dic11—41no—
231Dic11#12114yes—
232C22×Q8—111no—
233C22×D4—111no—
234C22×D4—111no—
235C22×D4C2×D1111yescharacteristic
236C23×C4—111no—
237C23×C4—111no—
238C23×C4C2×D1111yescharacteristic
239#124—224no—
240C22⋊Q8—224no—
241#121—224no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—111no—
250C2×C22⋊C4—111no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—111no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4C2×D1111yescharacteristic
256C2×C22⋊C4C2×D1111yescharacteristic
257C2×C22⋊C4C2×D1111yescharacteristic
258C2×C42—111no—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—111no—
262C2×C42—224no—
263#95—111no—
264#95—111no—
265#95—111no—
266#95—111no—
267#95—111no—
268#95—111no—
269#95C2×D1111yescharacteristic
270#95C2×D1111yescharacteristic
271C2×C11—24no—
272C2×C11—81no—
273C2×C11C2×#12111yescharacteristic
274C2×C11#52511yescharacteristic
275C2×C11#52511yescharacteristic
276C2×C11C2×#12411yescharacteristic
277C2×C11#52911yescharacteristic
278C2×C11#52911yescharacteristic
279C2×C11#53211yescharacteristic
280D11—81no—
281C24—111no—
282C24C22×D1111yescharacteristic
283C24C22×D1111yescharacteristic
284C2×Q8—222no—
285C2×Q8—222no—
286C2×Q8—222no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—222no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—111no—
300C22×C4—114no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4—222no—
312C22×C4C22×D1111yescharacteristic
313C22×C4C22×D1111yescharacteristic
314C22×C4C22×D1111yescharacteristic
315C22×C4C22×D1111yescharacteristic
316C22×C4C22×D1111yescharacteristic
317C4⋊C4—222no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—222no—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C22⋊C4—222no—
333C42—114no—
334C42—222no—
335C42—222no—
336C42—222no—
337C11#285011yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23#433912yes—
357C23D4×D1112yes—
358C23#434112yes—
359C23C23×D1111yescharacteristic
360Q8—444no—
361D4—44no—
362D4—444no—
363D4—444no—
364C2×C4—28no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—112no—
379C2×C4—112no—
380C2×C4—112no—
381C2×C4—112no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—228no—
385C2×C4—228no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4D4×D1112yes—
402C2×C4#434112yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—441no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22#6693814yescomplemented
424C22C2×#433911yescharacteristic
425C22C2×D4×D1111yescharacteristic
426C22C2×D4×D1111yescharacteristic
427C22C2×#434111yescharacteristic
428C22C2×#434111yescharacteristic
429C22#41×D1111yescharacteristic
430C22#41×D1111yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—114no—
437C4—222no—
438C4—222no—
439C4—222no—
440C4—441no—
441C4—441no—
442C4—441no—
443C2—24no—
444C2—81no—
445C2—881no—
446C2C2×#6693811yescharacteristic
447C2#1062306911yescharacteristic
448C2#1062307811yescharacteristic
449C2#1062311711yescharacteristic
450C2#1062312711yescharacteristic
451C2D11×#12111yescharacteristic
452C2#1062318011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66992C2
hypercenter#386D11
hypocenterC11#2850
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic11C2semidirect
3. C2×#66938C2semidirect
4. C2×#66931C2semidirect
5. C11×#386C2semidirect
6. #10622833C2semidirect
7. #10622826C2semidirect
8. #10622571C2semidirect
9. #10622570C2semidirect
10. #10622564C2semidirect
11. #10622557C2semidirect
12. #10622283C2semidirect
13. #10622282C2semidirect
14. #10622263C2semidirect
15. #10622259C2semidirect
110. C4×Dic11D4semidirect
190. #386D11semidirect
205. C22×C11#124semidirect
337. C11#2850semidirect
423. C22#66938semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C22×C4×Dic112
C2×#669382
C2×#669312
C11×#3862
#106228332
#106228262
#106225712
#106225702
#106225642
#106225572
#106222832
#106222822
#106222632
#106222592
#285011