Finite Group Databasebeta

← #13074873

Subgroups — #13074873

Order 1408.

618 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic
2C2×#66939C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66931C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6#10622833C211yesmaximal, characteristic, complemented
7#10622602C211yesmaximal, characteristic, complemented
8#10622598C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622562C211yesmaximal, characteristic, complemented
12#10622561C211yesmaximal, characteristic, complemented
13#10622557C211yesmaximal, characteristic, complemented
14#10622280C211yesmaximal, characteristic, complemented
15#10622269C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×Dic22C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32#66991—24no—
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊Dic11C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×C4×Dic11C2211yescharacteristic
46#66939—24no—
47#66938—24no—
48#66931—24no—
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—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—22no—
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—41no—
71C2×C22⋊D11—41no—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—41no—
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C2×C4×D11—22no—
83C2×C4×D11—22no—
84C2×C4×D11—41no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C11×C4⋊C4—22no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—41no—
93C22⋊Dic11—22no—
94C22⋊Dic11—22no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11D414yes—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4D414yescomplemented
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—22no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—22no—
111#2672—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×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×D11C2×D412yes—
134D4×C11—44no—
135C2×C4×C11—21no—
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×C11C2×D412yes—
149C2×C4×C11#4112yes—
150C22⋊D11—44no—
151C22⋊D11—44no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
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×Dic11—44no—
171C2×Dic11C2×D412yes—
172C2×Dic11C2×D412yes—
173C2×Dic11C2×D412yes—
174C4×D11—44no—
175Dic22—44no—
176C2×#124—111no—
177C2×#123—111no—
178C2×C22⋊Q8—111no—
179C2×#121—111no—
180#399—111no—
181#396—111no—
182#395—111no—
183#394—111no—
184#394—111no—
185#394D1111yescharacteristic, complemented
186#389—111no—
187#388—111no—
188#386—111no—
189#385—111no—
190#380—111no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11C22×D411yescharacteristic
206C22×C11C22×D411yescharacteristic
207C22×C11C2×#4111yescharacteristic
208C22×C11H(5,𝔽2)11yescharacteristic
209C22×C11H(5,𝔽2)11yescharacteristic
210C22×C112−1+411yescharacteristic
211C22×C112−1+411yescharacteristic
212C2×D11—22no—
213C2×D11—22no—
214C2×D11—22no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—41no—
224Dic11—22no—
225Dic11—22no—
226Dic11—22no—
227Dic11—41no—
228Dic11—41no—
229Dic11—41no—
230Dic11—41no—
231C22×Q8—111no—
232C22×D4—111no—
233C22×D4—111no—
234C22×D4C2×D1111yescharacteristic
235C23×C4—111no—
236C23×C4—111no—
237#124—224no—
238#123—224no—
239C22⋊Q8—224no—
240#121—224no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4C2×D1111yescharacteristic
250C2×C22⋊C4—111no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—111no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—111no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4C2×D1111yescharacteristic
260C2×C22⋊C4C2×D1111yescharacteristic
261C2×C22⋊C4C2×D1111yescharacteristic
262C2×C22⋊C4C2×D1111yescharacteristic
263C2×C42—111no—
264#95—111no—
265#95—111no—
266#95—111no—
267#95—111no—
268#95—111no—
269#95C2×D1111yescharacteristic
270C2×C11—42no—
271C2×C11—81no—
272C2×C11#53611yescharacteristic
273C2×C11#53711yescharacteristic
274C2×C11#54211yescharacteristic
275C2×C11D4211yescharacteristic
276C2×C11#54611yescharacteristic
277C2×C11#54711yescharacteristic
278C2×C11#56211yescharacteristic
279D11—42no—
280C24—111no—
281C24C22×D1111yescharacteristic
282C24C22×D1111yescharacteristic
283C2×Q8—222no—
284C2×Q8—222no—
285C2×Q8—441no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—441no—
294C2×D4—441no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—222no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4C22×D1111yescharacteristic
309C22×C4C22×D1111yescharacteristic
310C22×C4C22×D1111yescharacteristic
311C22×C4C22×D1111yescharacteristic
312C22×C4C22×D1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C4⋊C4—222no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—41no—
326C22⋊C4—114no—
327C22⋊C4—114no—
328C22⋊C4—222no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42—222no—
336C11#267211yescharacteristic, complemented, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—112no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23D4×D1112yes—
358C23C23×D1111yescharacteristic
359Q8—444no—
360D4—44no—
361D4—444no—
362D4—444no—
363C2×C4—21no—
364C2×C4—21no—
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—112no—
377C2×C4—112no—
378C2×C4—112no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
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—444no—
398C2×C4—444no—
399C2×C4D4×D1112yes—
400C2×C4#434112yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—222no—
416C22—222no—
417C22—222no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22—441no—
422C22C2×D4×D1111yescharacteristic
423C22C2×D4×D1111yescharacteristic
424C22C2×#434111yescharacteristic
425C22#6703711yescharacteristic
426C22#6704211yescharacteristic
427C22#6704311yescharacteristic
428C22#6704311yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—222no—
435C4—222no—
436C4—222no—
437C4—441no—
438C4—441no—
439C4—441no—
440C4—441no—
441C2—42no—
442C2—81no—
443C2—442no—
444C2#1062312211yescharacteristic
445C2#1062313911yescharacteristic
446C2#1062314011yescharacteristic
447C2#1062314211yescharacteristic
448C2#1062317911yescharacteristic
449C2#1062319811yescharacteristic
450C2#1062321311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66991C2
hypercenter#394D11
hypocenterC11#2672
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66939C2semidirect
3. C2×#66938C2semidirect
4. C2×#66931C2semidirect
5. C11×#394C2semidirect
6. #10622833C2semidirect
7. #10622602C2semidirect
8. #10622598C2semidirect
9. #10622574C2semidirect
10. #10622572C2semidirect
11. #10622562C2semidirect
12. #10622561C2semidirect
13. #10622557C2semidirect
14. #10622280C2semidirect
15. #10622269C2semidirect
101. (C2×D11)⋊C4D4semidirect
185. #394D11semidirect
336. C11#2672semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×#669392
C2×#669382
C2×#669312
C11×#3942
#106228332
#106226022
#106225982
#106225742
#106225722
#106225622
#106225612
#106225572
#106222802
#106222692
#267211