Finite Group Databasebeta

← #13072177

Subgroups — #13072177

Order 1408.

632 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66949C211yesmaximal, characteristic, complemented
2C2×#66940C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66937C211yesmaximal, characteristic
5C11×#396C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622603C211yesmaximal, characteristic, complemented
8#10622601C211yesmaximal, characteristic, complemented
9#10622585C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622570C211yesmaximal, characteristic, complemented
13#10622557C211yesmaximal, characteristic, complemented
14#10622289C211yesmaximal, characteristic, complemented
15#10622279C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×Dic22C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44C2×C4×Dic11C2211yescharacteristic
45C2×C4×Dic11C2211yescharacteristic
46C2×C4×Dic11C2211yescharacteristic
47#66949—24no—
48#66940—24no—
49#66938—24no—
50#66937—24no—
51C11×#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—22no—
65C2×C22⋊D11—22no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—41no—
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—41no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×Dic22—22no—
83C2×Dic22—22no—
84C2×Dic22D414yescomplemented
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—41no—
91C22⋊Dic11—22no—
92C22⋊Dic11—22no—
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—41no—
102Dic11⋊C4—22no—
103Dic11⋊C4—22no—
104Dic11⋊C4—22no—
105Dic11⋊C4—41no—
106Dic11⋊C4D414yes—
107C4×Dic11—22no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11—22no—
111#2426—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11C2411yescharacteristic
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11#4112yes—
134C2×C4×C11—21no—
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×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11C2×D412yes—
151C2×C4×C11C2×D412yes—
152C22⋊D11—44no—
153C22⋊D11—44no—
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×Dic11C2×D412yes—
167C2×Dic11C2×D412yes—
168C2×Dic11C2×D412yes—
169C2×Dic11C2×D412yes—
170C2×Dic11#4112yes—
171C2×Dic11#4112yes—
172D44—44no—
173C4×D11—44no—
174Dic22—28no—
175C2×#124—111no—
176C2×C22⋊Q8—111no—
177C2×#121—111no—
178C2×C4×Q8—111no—
179#396—111no—
180#396D1111yescharacteristic, complemented
181#394—111no—
182#394—111no—
183#390—111no—
184#390—111no—
185#390—111no—
186#389—111no—
187#388—111no—
188#388—111no—
189C4×C22⋊C4—111no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C22×D411yescharacteristic
198C22×C11C22×D411yescharacteristic
199C22×C11C2×#4111yescharacteristic
200C22×C11C2×#4111yescharacteristic
201C22×C11C2×#4111yescharacteristic
202C22×C11H(5,𝔽2)11yescharacteristic
203C22×C112−1+411yescharacteristic
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—41no—
224Dic11—22no—
225Dic11—22no—
226Dic11—22no—
227Dic11—41no—
228Dic11—41no—
229Dic11#12114yes—
230C22×Q8—111no—
231C22×D4—111no—
232C22×D4—111no—
233C22×D4—111no—
234C23×C4—111no—
235#124—224no—
236C22⋊Q8—224no—
237#121—224no—
238C4×Q8—224no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4C2×D1111yescharacteristic
245C2×C4⋊C4C2×D1111yescharacteristic
246C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
256C2×C22⋊C4—111no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4C2×D1111yescharacteristic
259C2×C22⋊C4C2×D1111yescharacteristic
260C2×C22⋊C4C2×D1111yescharacteristic
261C2×C42—111no—
262C2×C42—111no—
263C2×C42—111no—
264C2×C42—111no—
265#95—111no—
266#95—111no—
267#95—111no—
268#95C2×D1111yescharacteristic
269C2×C11—81no—
270C2×C11C2×#12111yescharacteristic
271C2×C11#52911yescharacteristic
272C2×C11#54211yescharacteristic
273C2×C11#54611yescharacteristic
274C2×C11#54811yescharacteristic
275C2×C11#54811yescharacteristic
276C2×C11#55011yescharacteristic
277D11—42no—
278D11—81no—
279C24—111no—
280C24—111no—
281C24C22×D1111yescharacteristic
282C2×Q8—114no—
283C2×Q8—222no—
284C2×Q8—222no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—441no—
293C2×D4—441no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4C22×D1111yescharacteristic
304C22×C4C22×D1111yescharacteristic
305C22×C4C22×D1111yescharacteristic
306C22×C4C22×D1111yescharacteristic
307C22×C4C22×D1111yescharacteristic
308C22×C4C22×D1111yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—114no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—441no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—41no—
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⋊C4—222no—
330C22⋊C4—441no—
331C42—222no—
332C42—222no—
333C42—222no—
334C42—222no—
335C11#242611yescharacteristic, complemented, Sylow
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—112no—
344C23—221no—
345C23—221no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23C23×D1111yescharacteristic
358Q8—228no—
359D4—444no—
360D4—444no—
361D4—444no—
362C2×C4—21no—
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—21no—
377C2×C4—21no—
378C2×C4—112no—
379C2×C4—112no—
380C2×C4—112no—
381C2×C4—112no—
382C2×C4—112no—
383C2×C4—112no—
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—444no—
397C2×C4D4×D1112yes—
398C2×C4D4×D1112yes—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—222no—
407C22—222no—
408C22—222no—
409C22—441no—
410C22—441no—
411C22—441no—
412C22—441no—
413C22—441no—
414C22—441no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22C2×D4×D1111yescharacteristic
421C22C2×D4×D1111yescharacteristic
422C22#6703711yescharacteristic
423C22#6704011yescharacteristic
424C22#41×D1111yescharacteristic
425C22#41×D1111yescharacteristic
426C22#41×D1111yescharacteristic
427C4—22no—
428C4—22no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—114no—
434C4—222no—
435C4—222no—
436C4—222no—
437C4—441no—
438C4—441no—
439C2—81no—
440C2—442no—
441C2—881no—
442C2#1062313011yescharacteristic
443C2D11×#12111yescharacteristic
444C2#1062314111yescharacteristic
445C2#1062316411yescharacteristic
446C2#1062316411yescharacteristic
447C2#1062317111yescharacteristic
448C2#1062323711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC2×#66937C2
hypercenter#396D11
hypocenterC11#2426
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#66949C2semidirect
2. C2×#66940C2semidirect
3. C2×#66938C2semidirect
5. C11×#396C2semidirect
6. #10622604C2semidirect
7. #10622603C2semidirect
8. #10622601C2semidirect
9. #10622585C2semidirect
10. #10622572C2semidirect
11. #10622570C2semidirect
12. #10622570C2semidirect
13. #10622557C2semidirect
14. #10622289C2semidirect
15. #10622279C2semidirect
84. C2×Dic22D4semidirect
180. #396D11semidirect
335. C11#2426semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669402
C2×#669382
C2×#669372
C11×#3962
#106226042
#106226032
#106226012
#106225852
#106225722
#106225702
#106225572
#106222892
#106222792
#242611