Finite Group Databasebeta

← #13072233

Subgroups — #13072233

Order 1408.

952 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4339C211yesmaximal, characteristic, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66937C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622826C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622569C211yesmaximal, characteristic, complemented
12#10622284C211yesmaximal, characteristic, complemented
13#10622279C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C2×#4339—24no—
25C2×#4339—24no—
26C2×#4339—24no—
27C22×D44C2211yescharacteristic
28C22×D44C2211yescharacteristic
29C22×D44C2211yescharacteristic
30C22×C4×D11C2211yescharacteristic
31C22×C4×D11C2211yescharacteristic
32C22×Dic22C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38#66993—24no—
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic
47C2×C4×Dic11C2211yescharacteristic
48C2×C4×Dic11C2211yescharacteristic
49#66938—24no—
50#66937—24no—
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C23×D11C2311yescharacteristic
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
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—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11D414yescomplemented
91C22×Dic11C2311yescharacteristic
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96#4339—232no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11D414yescomplemented
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22D414yescomplemented
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—41no—
118C22⋊Dic11—22no—
119C22⋊Dic11—41no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127Dic11⋊C4—22no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130#2431—111nomaximal, Sylow
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×C11—21no—
143C23×C11—21no—
144C23×C11C2×D412yes—
145C23×C11C2411yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11C2×D412yes—
166C22×D11C2×D412yes—
167D4×C11—44no—
168C2×C4×C11—28no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11C2×D412yes—
182C2×C4×C11C2×D412yes—
183C2×C4×C11#4112yescomplemented
184C22⋊D11—28no—
185C22⋊D11—28no—
186C22⋊D11—44no—
187C22⋊D11—44no—
188C22⋊D11—44no—
189C22⋊D11—44no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11C2×D412yes—
201C2×Dic11C2×D412yes—
202C2×Dic11C2×D412yes—
203C2×Dic11C2×D412yes—
204C2×Dic11#4112yescomplemented
205D44—28no—
206D44—44no—
207D44—44no—
208C4×D11—28no—
209C4×D11—28no—
210Dic22—28no—
211C22×#41—111no—
212C2×#127—111no—
213C2×#124—111no—
214C2×#121—111no—
215#392—111no—
216#392—111no—
217#392—111no—
218#392—111no—
219#391—111no—
220#390—111no—
221#386—111no—
222#386—111no—
223#386—111no—
224#386D1111yescharacteristic, complemented
225C4×C22⋊C4—111no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11C22×D411yescharacteristic
241C22×C11C22×D411yescharacteristic
242C22×C11C22×D411yescharacteristic
243C22×C11C2×#4111yescharacteristic
244C22×C11C2×#4111yescharacteristic
245C22×C11H(5,𝔽2)11yescharacteristic
246C22×C11H(5,𝔽2)11yescharacteristic
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—41no—
272C4×C11—41no—
273Dic11—22no—
274Dic11—22no—
275Dic11—41no—
276Dic11—41no—
277Dic11#12014yes—
278C2×#41—224no—
279C2×#41—224no—
280C2×#41—224no—
281C22×Q8—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4—111no—
287C22×D4—111no—
288C22×D4—111no—
289C22×D4—111no—
290C22×D4—111no—
291C22×D4C2×D1111yescharacteristic
292C23×C4—111no—
293C23×C4—111no—
294C23×C4C2×D1111yescharacteristic
295#127—224no—
296#124—224no—
297#121—224no—
298C2×C4⋊C4—111no—
299C2×C22⋊C4—111no—
300C2×C22⋊C4—111no—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—111no—
307C2×C22⋊C4—111no—
308C2×C22⋊C4C2×D1111yescharacteristic
309C2×C22⋊C4C2×D1111yescharacteristic
310C2×C22⋊C4C2×D1111yescharacteristic
311C2×C42—111no—
312C2×C42—111no—
313#95—111no—
314#95—111no—
315#95—111no—
316#95—111no—
317#95C2×D1111yescharacteristic
318#95C2×D1111yescharacteristic
319C2×C11—42no—
320C2×C11—81no—
321C2×C11C2×#12011yescharacteristic
322C2×C11#53211yescharacteristic
323C2×C11#53511yescharacteristic
324C2×C11#54611yescharacteristic
325C2×C11#54611yescharacteristic
326C2×C11#55011yescharacteristic
327C2×C11#55011yescharacteristic
328D11—42no—
329D11—42no—
330D11—81no—
331C24—111no—
332C24—111no—
333C24—111no—
334C24C22×D1111yescharacteristic
335C24C22×D1111yescharacteristic
336#41—2232no—
337C2×Q8—114no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—114no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—441no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—114no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4C22×D1111yescharacteristic
385C22×C4C22×D1111yescharacteristic
386C22×C4C22×D1111yescharacteristic
387C22×C4C22×D1111yescharacteristic
388C22×C4C22×D1111yescharacteristic
389C4⋊C4—222no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—41no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—222no—
403C42—222no—
404C11#243111yescharacteristic, complemented, Sylow
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—112no—
419C23—112no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—221no—
439C23D4×D1112yes—
440C23C23×D1111yescharacteristic
441Q8—228no—
442D4—44no—
443D4—228no—
444D4—228no—
445D4—228no—
446D4—444no—
447D4—444no—
448D4—444no—
449D4—444no—
450D4—444no—
451D4—444no—
452C2×C4—28no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—228no—
471C2×C4—228no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4#433912yescomplemented
483C2×C4D4×D1112yes—
484C2×C4D4×D1112yes—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—222no—
500C22—222no—
501C22—222no—
502C22—222no—
503C22—222no—
504C22—222no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22—441no—
510C22—441no—
511C22—441no—
512C22—441no—
513C22—441no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—441no—
518C22—441no—
519C22—441no—
520C22C2×#433911yescharacteristic
521C22C2×D4×D1111yescharacteristic
522C22C2×D4×D1111yescharacteristic
523C22C2×D4×D1111yescharacteristic
524C22#6703711yescharacteristic
525C22#41×D1111yescharacteristic
526C22#6704211yescharacteristic
527C4—22no—
528C4—22no—
529C4—22no—
530C4—41no—
531C4—41no—
532C4—114no—
533C4—222no—
534C4—222no—
535C4—441no—
536C4—441no—
537C2—42no—
538C2—81no—
539C2—442no—
540C2—442no—
541C2—881no—
542C2#1062302111yescharacteristic
543C2#1062307911yescharacteristic
544C2#1062308411yescharacteristic
545C2D11×#12011yescharacteristic
546C2#1062313011yescharacteristic
547C2#1062313811yescharacteristic
548C2#1062318511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2431
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#4339C2semidirect
2. C2×#66993C2semidirect
3. C2×#66938C2semidirect
4. C2×#66937C2semidirect
5. C11×#386C2semidirect
6. #10622836C2semidirect
7. #10622826C2semidirect
8. #10622573C2semidirect
9. #10622573C2semidirect
10. #10622570C2semidirect
11. #10622569C2semidirect
12. #10622284C2semidirect
13. #10622279C2semidirect
14. #10622278C2semidirect
15. #10622259C2semidirect
90. C2×C22⋊D11D4semidirect
111. C2×C4×D11D4semidirect
114. C2×Dic22D4semidirect
183. C2×C4×C11#41semidirect
204. C2×Dic11#41semidirect
224. #386D11semidirect
404. C11#2431semidirect
482. C2×C4#4339semidirect

Maximal subgroups

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

subgroupindex
C22×#43392
C2×#669932
C2×#669382
C2×#669372
C11×#3862
#106228362
#106228262
#106225732
#106225702
#106225692
#106222842
#106222792
#106222782
#106222592
#243111