Finite Group Databasebeta

← #13073559

Subgroups — #13073559

Order 1408.

948 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66993C212yesmaximal, complemented
3C2×#66993C211yesmaximal, characteristic, complemented
4C2×#66991C211yesmaximal, characteristic, complemented
5C2×#66983C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
7C2×#66948C211yesmaximal, characteristic, complemented
8#10622836C212yesmaximal, complemented
9C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622573C212yesmaximal, complemented
11#10622570C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C22×C22⋊D11C2212yes—
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2212yes—
20C22×D44C2211yescharacteristic
21C22×D44C2212yes—
22C22×C4×D11C2211yescharacteristic
23C11×#121—24no—
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2212yes—
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2212yes—
28#66993—28no—
29#66993—24no—
30#66991—24no—
31#66983—24no—
32C4×C22⋊D11—24no—
33C2×(C2×D11)⋊C4C2212yes—
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2212yes—
36C2×C4⋊Dic11C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×C4×Dic11C2212yes—
39C2×C4×Dic11C2211yescharacteristic
40#66948—24no—
41C11⋊#95C2212yes—
42C24×C11C2312yes—
43C24×C11C2311yescharacteristic
44C23×D11C2312yes—
45C23×D11C2311yescharacteristic
46C2×D4×C11—24no—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—24no—
50C2×D4×C11—22no—
51C2×D4×C11—42no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2312yes—
57C22×C4×C11C2311yescharacteristic
58C2×C22⋊D11—22no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—24no—
62C2×C22⋊D11—24no—
63C2×C22⋊D11—24no—
64C2×C22⋊D11—22no—
65C2×C22⋊D11—24no—
66C2×C22⋊D11—24no—
67C2×C22⋊D11—24no—
68C2×C22⋊D11—42no—
69C2×C22⋊D11—42no—
70C2×C22⋊D11—42no—
71C2×C22⋊D11—42no—
72C2×C22⋊D11D414yescomplemented
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2312yes—
76C22×Dic11C2311yescharacteristic
77C2×D44—24no—
78C2×D44—24no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—42no—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C11×C4⋊C4D414yescomplemented
87C11×C22⋊C4—24no—
88C22⋊Dic11—22no—
89C22⋊Dic11—24no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—24no—
92(C2×D11)⋊C4—24no—
93C4⋊Dic11D414yescomplemented
94Dic11⋊C4—22no—
95C4×Dic11—24no—
96C4×Dic11D414yescomplemented
97#2541—111nomaximal, Sylow
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—22no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11C2×D412yes—
112C23×C11C2411yescharacteristic
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—22no—
120C22×D11—22no—
121C22×D11—22no—
122C22×D11—22no—
123C22×D11—22no—
124C22×D11—22no—
125C22×D11—22no—
126C22×D11C2×D412yes—
127D4×C11—48no—
128D4×C11—44no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—44no—
135C2×C4×C11C2×D412yes—
136C2×C4×C11C2×D412yes—
137C2×C4×C11C2×D414yes—
138C2×C4×C11C2×D412yes—
139C22⋊D11—28no—
140C22⋊D11—48no—
141C22⋊D11—48no—
142C22⋊D11—48no—
143C22⋊D11—48no—
144C2×Dic11—22no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—22no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11C2×D412yes—
152C2×Dic11C2×D414yes—
153C2×Dic11C2×D412yes—
154C2×Dic11C2×D412yes—
155C2×Dic11#4112yes—
156D44—48no—
157D44—44no—
158C4×D11—44no—
159C2×#127—111no—
160C2×#127—112no—
161C2×#121—111no—
162C2×#121—111no—
163C2×#121—111no—
164C2×#121D1111yescharacteristic, complemented
165C2×C4×D4—111no—
166#392—112no—
167#392—112no—
168#390—112no—
169C4×C4⋊C4—111no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11C22×D411yescharacteristic
185C22×C11C22×D411yescharacteristic
186C22×C11C22×D411yescharacteristic
187C22×C11C22×D411yescharacteristic
188C22×C11C2×#4111yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—42no—
205C4×C11—24no—
206C4×C11—41no—
207C4×C11#12714yescomplemented
208Dic11—22no—
209Dic11—24no—
210Dic11—41no—
211Dic11#12114yescomplemented
212C22×D4—111no—
213C22×D4—112no—
214C22×D4—112no—
215C22×D4—112no—
216C22×D4—112no—
217C22×D4—111no—
218C22×D4—112no—
219C22×D4C2×D1111yescharacteristic
220C22×D4C2×D1112yes—
221C23×C4—111no—
222C23×C4C2×D1111yescharacteristic
223#127—224no—
224#127—228no—
225#121—24no—
226#121—224no—
227#121—224no—
228#121—224no—
229C4×D4—224no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4C2×D1111yescharacteristic
233C2×C22⋊C4—111no—
234C2×C22⋊C4—112no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—112no—
237C2×C22⋊C4—112no—
238C2×C22⋊C4C2×D1112yes—
239C2×C42—111no—
240C2×C42—112no—
241#95—112no—
242C2×C11—42no—
243C2×C11—82no—
244C2×C11C2×#12111yescharacteristic
245C2×C11C2×#12711yescharacteristic
246C2×C11#53511yescharacteristic
247C2×C11D4211yescharacteristic
248C2×C11D4211yescharacteristic
249C2×C11#55011yescharacteristic
250C2×C11#55011yescharacteristic
251D11—42no—
252D11—82no—
253C24—111no—
254C24—112no—
255C24C22×D1112yes—
256C24C22×D1111yescharacteristic
257C2×D4—24no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—24no—
261C2×D4—22no—
262C2×D4—42no—
263C2×D4—114no—
264C2×D4—224no—
265C2×D4—222no—
266C2×D4—222no—
267C2×D4—224no—
268C2×D4—224no—
269C2×D4—224no—
270C2×D4—224no—
271C2×D4—224no—
272C2×D4—224no—
273C2×D4—224no—
274C2×D4—224no—
275C2×D4—222no—
276C2×D4—222no—
277C2×D4—224no—
278C2×D4—222no—
279C2×D4—442no—
280C2×D4—442no—
281C2×D4—442no—
282C2×D4—442no—
283C2×D4—442no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—112no—
290C22×C4—111no—
291C22×C4—222no—
292C22×C4—222no—
293C22×C4—222no—
294C22×C4C22×D1111yescharacteristic
295C22×C4C22×D1112yes—
296C22×C4C22×D1111yescharacteristic
297C4⋊C4—114no—
298C4⋊C4—222no—
299C4⋊C4C22⋊D1114yescomplemented
300C22⋊C4—24no—
301C22⋊C4—222no—
302C22⋊C4—224no—
303C22⋊C4—222no—
304C22⋊C4—224no—
305C22⋊C4—224no—
306C42—114no—
307C42—224no—
308C11#254111yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—112no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23—221no—
327C23—221no—
328C23—221no—
329C23—222no—
330C23—222no—
331C23—222no—
332C23—222no—
333C23—222no—
334C23—222no—
335C23—222no—
336C23D4×D1112yes—
337C23C23×D1111yescharacteristic
338D4—48no—
339D4—44no—
340D4—228no—
341D4—448no—
342D4—448no—
343D4—448no—
344D4—448no—
345D4—448no—
346D4—444no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—112no—
354C2×C4—112no—
355C2×C4—112no—
356C2×C4—112no—
357C2×C4—114no—
358C2×C4—222no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—222no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—444no—
366C2×C4D4×D1112yes—
367C2×C4D4×D1112yes—
368C2×C4C2×C22⋊D1114yes—
369C2×C4C2×C22⋊D1112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—222no—
385C22—222no—
386C22—222no—
387C22—441no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—442no—
392C22—442no—
393C22—442no—
394C22—442no—
395C22—442no—
396C22—442no—
397C22—442no—
398C22C2×D4×D1111yescharacteristic
399C22C2×D4×D1111yescharacteristic
400C22C2×D4×D1111yescharacteristic
401C22#6703711yescharacteristic
402C22#41×D1111yescharacteristic
403C22#6704211yescharacteristic
404C22C22×C22⋊D1111yescharacteristic
405C4—24no—
406C4—41no—
407C4—114no—
408C4—222no—
409C4—224no—
410C4—441no—
411C4#6699314yescomplemented
412C2—42no—
413C2—82no—
414C2—442no—
415C2—882no—
416C2#1062313011yescharacteristic
417C2D11×#12111yescharacteristic
418C2#1062313811yescharacteristic
419C2#1062314011yescharacteristic
420C2D4×C22⋊D1111yescharacteristic
421C2C2×#6699311yescharacteristic
422C2#1062336511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2541
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66993C2semidirect
3. C2×#66993C2semidirect
4. C2×#66991C2semidirect
5. C2×#66983C2semidirect
6. C2×C4×C22⋊D11C2semidirect
7. C2×#66948C2semidirect
8. #10622836C2semidirect
9. C4⋊C4×Dic11C2semidirect
10. #10622573C2semidirect
11. #10622570C2semidirect
72. C2×C22⋊D11D4semidirect
86. C11×C4⋊C4D4semidirect
93. C4⋊Dic11D4semidirect
96. C4×Dic11D4semidirect
164. C2×#121D11semidirect
207. C4×C11#127semidirect
211. Dic11#121semidirect
299. C4⋊C4C22⋊D11semidirect
308. C11#2541semidirect
411. C4#66993semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669932
C2×#669912
C2×#669832
C2×C4×C22⋊D112
C2×#669482
#106228362
C4⋊C4×Dic112
#106225732
#106225702
#254111