Finite Group Databasebeta

← #13072222

Subgroups — #13072222

Order 1408.

914 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4341C211yesmaximal, characteristic, complemented
2C2×C11×#121C211yesmaximal, characteristic, complemented
3C2×#66992C211yesmaximal, characteristic, complemented
4C2×#66988C211yesmaximal, characteristic, complemented
5#10622836C211yesmaximal, characteristic, complemented
6#10622833C211yesmaximal, characteristic, complemented
7#10622833C211yesmaximal, characteristic, complemented
8#10622826C211yesmaximal, characteristic, complemented
9C2×C11⋊#95C211yesmaximal, characteristic, complemented
10#10622602C211yesmaximal, characteristic, complemented
11#10622592C211yesmaximal, characteristic, complemented
12#10622572C211yesmaximal, characteristic, complemented
13#10622569C211yesmaximal, characteristic, complemented
14#10622560C211yesmaximal, characteristic, complemented
15#10622559C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C23×Dic11C2211yescharacteristic
24C23×Dic11C2211yescharacteristic
25C23×Dic11C2211yescharacteristic
26C2×#4341—24no—
27C2×#4341—24no—
28C2×#4341—24no—
29C22×C4×D11C2211yescharacteristic
30C22×Dic22C2211yescharacteristic
31C11×#121—24no—
32C2×C11×C4⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊Dic11C2211yescharacteristic
41#66992—24no—
42#66988—24no—
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×Dic11⋊C4C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C24×C11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C2×D4×C11D414yescomplemented
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—41no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11D414yescomplemented
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—41no—
94C22×Dic11D414yescomplemented
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C22×Dic11C2311yescharacteristic
102#4341—232no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×Dic22—22no—
107C2×Dic22—22no—
108C2×Dic22—22no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C22⋊Dic11—22no—
113C22⋊Dic11—22no—
114C22⋊Dic11—22no—
115C22⋊Dic11—22no—
116C22⋊Dic11—22no—
117C22⋊Dic11—41no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—41no—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123Dic11⋊C4—22no—
124#2430—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11C2×D412yes—
143C23×C11C2×D412yes—
144C23×C11C2×D412yes—
145C23×C11C2×D412yes—
146C23×C11C2411yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11C2×D412yes—
154D4×C11—28no—
155D4×C11—44no—
156D4×C11—44no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—44no—
168C2×C4×C11C2×D412yes—
169C2×C4×C11#4112yescomplemented
170C22⋊D11—28no—
171C22⋊D11—28no—
172C22⋊D11—44no—
173C2×Dic11—28no—
174C2×Dic11—28no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—44no—
193C2×Dic11C2×D412yes—
194C2×Dic11C2×D412yes—
195C2×Dic11C2×D412yes—
196C2×Dic11#4112yescomplemented
197C4×D11—28no—
198Dic22—28no—
199C22×#41—111no—
200C2×#123—111no—
201C2×#121—111no—
202C2×#121D1111yescharacteristic, complemented
203#395—111no—
204#394—111no—
205#393—111no—
206#392—111no—
207#386—111no—
208#386—111no—
209#386—111no—
210#386—111no—
211#385—111no—
212#385—111no—
213C2×#95—111no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11#12014yes—
235C22×C11C22×D411yescharacteristic
236C22×C11C22×D411yescharacteristic
237C22×C11C22×D411yescharacteristic
238C22×C11C2×#4111yescharacteristic
239C22×C11C2×#4111yescharacteristic
240C22×C11H(5,𝔽2)11yescharacteristic
241C22×C112−1+411yescharacteristic
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—22no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
248C2×D11—41no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—41no—
252C4×C11—41no—
253Dic11—22no—
254Dic11—22no—
255Dic11—22no—
256Dic11—22no—
257Dic11—41no—
258Dic11—41no—
259Dic11—41no—
260C2×#41—224no—
261C2×#41—224no—
262C2×#41—224no—
263C22×Q8—111no—
264C22×D4—111no—
265C22×D4—111no—
266C22×D4—111no—
267C22×D4C2×D1111yescharacteristic
268C22×D4C2×D1111yescharacteristic
269C22×D4C2×D1111yescharacteristic
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—111no—
274C23×C4C2×D1111yescharacteristic
275#123—224no—
276#121—24no—
277#121—224no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4C2×D1111yescharacteristic
282C2×C22⋊C4—111no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4C2×D1111yescharacteristic
292C2×C22⋊C4C2×D1111yescharacteristic
293#95—111no—
294#95—111no—
295#95—111no—
296#95—111no—
297#95—111no—
298#95—111no—
299#95—111no—
300#95—111no—
301C2×C11—24no—
302C2×C11—42no—
303C2×C11—81no—
304C2×C11C2×#12011yescharacteristic
305C2×C11#53211yescharacteristic
306C2×C11#53711yescharacteristic
307C2×C11#54611yescharacteristic
308C2×C11#54611yescharacteristic
309C2×C11#54711yescharacteristic
310C2×C11#54711yescharacteristic
311D11—42no—
312C24—111no—
313C24C22×D1111yescharacteristic
314C24C22×D1111yescharacteristic
315C24C22×D1111yescharacteristic
316#41—2232no—
317C2×Q8—222no—
318C2×Q8—222no—
319C2×Q8—222no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—41no—
328C2×D4—114no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—441no—
337C2×D4C22⋊D1114yescomplemented
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—41no—
341C22×C4—114no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—441no—
360C22×C4C22×D1111yescharacteristic
361C22×C4C22×D1111yescharacteristic
362C22×C4C22×D1111yescharacteristic
363C22×C4C22×D1111yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—222no—
371C22⋊C4—222no—
372C22⋊C4—222no—
373C22⋊C4—222no—
374C22⋊C4—222no—
375C22⋊C4—222no—
376C22⋊C4—222no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C11#243011yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—112no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23D4×D1112yes—
405C23D4×D1112yes—
406C23C2×C22⋊D1112yes—
407C23C2×C22⋊D1112yes—
408C23C23×D1111yescharacteristic
409Q8—228no—
410D4—28no—
411D4—44no—
412D4—44no—
413D4—228no—
414D4—228no—
415D4—444no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—44no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—112no—
431C2×C4—228no—
432C2×C4—228no—
433C2×C4—228no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—444no—
452C2×C4#434112yescomplemented
453C2×C4C2×C22⋊D1112yes—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—441no—
478C22—441no—
479C22—441no—
480C22—441no—
481C22#6699014yes—
482C22C2×D4×D1111yescharacteristic
483C22C2×D4×D1111yescharacteristic
484C22C2×#434111yescharacteristic
485C22#6703711yescharacteristic
486C22#41×D1111yescharacteristic
487C22#6704311yescharacteristic
488C22C22×C22⋊D1111yescharacteristic
489C4—22no—
490C4—22no—
491C4—41no—
492C4—41no—
493C4—222no—
494C4—222no—
495C4—222no—
496C4—222no—
497C4—441no—
498C4—441no—
499C4—441no—
500C2—24no—
501C2—42no—
502C2—81no—
503C2—442no—
504C2#1062312711yescharacteristic
505C2#1062312811yescharacteristic
506C2#1062314111yescharacteristic
507C2#1062314211yescharacteristic
508C2C2×#6699011yescharacteristic
509C2#1062333711yescharacteristic
510C2#1062335511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#4341C2semidirect
2. C2×C11×#121C2semidirect
3. C2×#66992C2semidirect
4. C2×#66988C2semidirect
5. #10622836C2semidirect
6. #10622833C2semidirect
7. #10622833C2semidirect
8. #10622826C2semidirect
9. C2×C11⋊#95C2semidirect
10. #10622602C2semidirect
11. #10622592C2semidirect
12. #10622572C2semidirect
13. #10622569C2semidirect
14. #10622560C2semidirect
15. #10622559C2semidirect
69. C2×D4×C11D4semidirect
85. C2×C22⋊D11D4semidirect
94. C22×Dic11D4semidirect
169. C2×C4×C11#41semidirect
196. C2×Dic11#41semidirect
202. C2×#121D11semidirect
337. C2×D4C22⋊D11semidirect
379. C11#2430semidirect
452. C2×C4#4341semidirect

Maximal subgroups

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

subgroupindex
C22×#43412
C2×C11×#1212
C2×#669922
C2×#669882
#106228362
#106228332
#106228262
C2×C11⋊#952
#106226022
#106225922
#106225722
#106225692
#106225602
#106225592
#243011