Finite Group Databasebeta

← #13072347

Subgroups — #13072347

Order 1408.

674 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×C11×#121C211yesmaximal, characteristic
2C2×#66988C211yesmaximal, characteristic, complemented
3C2×D4×Dic11C211yesmaximal, characteristic, complemented
4C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#10622835C211yesmaximal, characteristic, complemented
6#10622833C211yesmaximal, characteristic, complemented
7#10622833C211yesmaximal, characteristic, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622823C211yesmaximal, characteristic, complemented
10#10622596C211yesmaximal, characteristic, complemented
11#10622591C211yesmaximal, characteristic, complemented
12#10622565C211yesmaximal, characteristic, complemented
13#10622562C211yesmaximal, characteristic, complemented
14#10622559C211yesmaximal, characteristic, complemented
15#10622557C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C23×Dic11C2211yescharacteristic
22C23×Dic11C2211yescharacteristic
23C11×#121—24no—
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36#66988—24no—
37D4×Dic11—24no—
38C2×C4⋊Dic11C2211yescharacteristic
39C2×Dic11⋊C4—24no—
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×Dic11⋊C4C2211yescharacteristic
46C2×C4×Dic11C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C2×D4×C11D414yes—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—41no—
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×Dic11—22no—
75C22×Dic11—22no—
76C22×Dic11—22no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C22×Dic11—22no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C11×C4⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C22⋊Dic11—22no—
95C22⋊Dic11—22no—
96C22⋊Dic11—22no—
97C22⋊Dic11—22no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—22no—
102C22⋊Dic11—41no—
103C4⋊Dic11—22no—
104Dic11⋊C4—22no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—22no—
108Dic11⋊C4—41no—
109Dic11⋊C4D414yescomplemented
110C4×Dic11—22no—
111#2443—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×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11C2×D412yes—
130C23×C11C2×D412yes—
131C23×C11#4112yes—
132C23×C11#4112yes—
133C23×C11C2411yescharacteristic
134D4×C11—28no—
135D4×C11—44no—
136D4×C11—44no—
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—44no—
148C2×C4×C11C2×D412yes—
149C2×C4×C11C2×D412yes—
150C2×Dic11—28no—
151C2×Dic11—21no—
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—21no—
171C2×Dic11—21no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11C2×D412yes—
175C2×Dic11C2×D412yes—
176C2×Dic11#4112yes—
177C2×#123—111no—
178C2×#121D1111yescharacteristic
179C2×C4×D4—111no—
180C22×C4⋊C4—111no—
181#399—111no—
182#398—111no—
183#397—111no—
184#394—111no—
185#388—111no—
186#387—111no—
187#386—111no—
188#386—111no—
189#386—111no—
190#385—111no—
191#385—111no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11#12314yescomplemented
213C22×C11C22×D411yescharacteristic
214C22×C11C22×D411yescharacteristic
215C22×C11C2×#4111yescharacteristic
216C22×C11C2×#4111yescharacteristic
217C22×C11C2×#4111yescharacteristic
218C22×C11H(5,𝔽2)11yescharacteristic
219C22×C112−1+411yescharacteristic
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—41no—
223C4×C11—41no—
224Dic11—22no—
225Dic11—22no—
226Dic11—22no—
227Dic11—41no—
228Dic11—41no—
229Dic11—41no—
230Dic11—41no—
231Dic11—41no—
232C22×D4C2×D1111yescharacteristic
233C22×D4C2×D1111yescharacteristic
234C22×D4C2×D1111yescharacteristic
235C23×C4—111no—
236C23×C4—111no—
237C23×C4—111no—
238C23×C4C2×D1111yescharacteristic
239#123—224no—
240#121—24no—
241C4×D4—224no—
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⋊C4—224no—
250C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
260C2×C22⋊C4C2×D1111yescharacteristic
261C2×C22⋊C4C2×D1111yescharacteristic
262C2×C42—111no—
263#95—111no—
264#95—111no—
265#95—111no—
266#95—111no—
267#95—111no—
268#95—111no—
269#95—111no—
270#95—111no—
271C2×C11—24no—
272C2×C11—42no—
273C2×C11—81no—
274C2×C11C2×#12311yescharacteristic
275C2×C11#52511yescharacteristic
276C2×C11#53911yescharacteristic
277C2×C11D4211yescharacteristic
278C2×C11#54711yescharacteristic
279C2×C11#54811yescharacteristic
280C2×C11#55311yescharacteristic
281C24C22×D1111yescharacteristic
282C24C22×D1111yescharacteristic
283C24C22×D1111yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—41no—
292C2×D4C22⋊D1114yes—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—222no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4C22×D1111yescharacteristic
314C22×C4C22×D1111yescharacteristic
315C22×C4C22×D1111yescharacteristic
316C22×C4C22×D1111yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—114no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—222no—
323C4⋊C4—222no—
324C4⋊C4—441no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C22⋊C4—222no—
333C22⋊C4—222no—
334C22⋊C4—222no—
335C22⋊C4—441no—
336C42—222no—
337C11#244311yescharacteristic, 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—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23#434112yes—
356C23#434112yes—
357C23C2×C22⋊D1112yes—
358C23C2×C22⋊D1112yes—
359C23C23×D1111yescharacteristic
360D4—28no—
361D4—44no—
362D4—44no—
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—44no—
374C2×C4—112no—
375C2×C4—112no—
376C2×C4—112no—
377C2×C4—228no—
378C2×C4—221no—
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—221no—
398C2×C4—221no—
399C2×C4—444no—
400C2×C4—444no—
401C2×C4D4×D1112yes—
402C2×C4C2×C22⋊D1112yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22#6698814yescomplemented
424C22C2×D4×D1111yescharacteristic
425C22C2×#434111yescharacteristic
426C22C2×#434111yescharacteristic
427C22#6703711yescharacteristic
428C22#41×D1111yescharacteristic
429C22#6704311yescharacteristic
430C22C22×C22⋊D1111yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—222no—
436C4—222no—
437C4—222no—
438C4—441no—
439C4—441no—
440C4—441no—
441C4—441no—
442C4—441no—
443C2—24no—
444C2—42no—
445C2—81no—
446C2#1062312911yescharacteristic
447C2#1062313211yescharacteristic
448C2#1062313311yescharacteristic
449C2#1062313711yescharacteristic
450C2C2×#6698811yescharacteristic
451C2D4×C22⋊D1111yescharacteristic
452C2#1062335511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2443
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C2×D4×Dic11C2semidirect
4. C22×Dic11⋊C4C2semidirect
5. #10622835C2semidirect
6. #10622833C2semidirect
7. #10622833C2semidirect
8. #10622833C2semidirect
9. #10622823C2semidirect
10. #10622596C2semidirect
11. #10622591C2semidirect
12. #10622565C2semidirect
13. #10622562C2semidirect
14. #10622559C2semidirect
15. #10622557C2semidirect
109. Dic11⋊C4D4semidirect
212. C22×C11#123semidirect
337. C11#2443semidirect
423. C22#66988semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669882
C2×D4×Dic112
C22×Dic11⋊C42
#106228352
#106228332
#106228232
#106225962
#106225912
#106225652
#106225622
#106225592
#106225572
#244311