Finite Group Databasebeta

← #14780310

Subgroups — #14780310

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071902C211yesmaximal, characteristic
2#13069554C211yesmaximal, characteristic, complemented
3#13069554C211yesmaximal, characteristic, complemented
4#13069230C211yesmaximal, characteristic, complemented
5#13069230C211yesmaximal, characteristic, complemented
6#13069228C211yesmaximal, characteristic, complemented
7#13069228C211yesmaximal, characteristic, complemented
8#13068912C211yesmaximal, characteristic
9#13068907C211yesmaximal, characteristic
10#13068800C211yesmaximal, characteristic, complemented
11#13068797C211yesmaximal, characteristic, complemented
12#13068795C211yesmaximal, characteristic, complemented
13#13068792C211yesmaximal, characteristic, complemented
14#13068736C211yesmaximal, characteristic, complemented
15C11×#1832C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#376C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C4×(C2×D11)⋊C4C2211yescharacteristic
34C4×(C2×D11)⋊C4C2211yescharacteristic
35C4×(C2×D11)⋊C4C2211yescharacteristic
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622287C411yescharacteristic
40#10622287C411yescharacteristic
41#10622286C411yescharacteristic
42#10622286C411yescharacteristic
43#10622285C411yescharacteristic
44#10622285C411yescharacteristic
45#10622272C411yescharacteristic
46#10622272C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2×C411yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22C2×C411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C2×#4313—41no—
91C2×#4313—41no—
92C2×#4313—41no—
93C2×C8×D11—41no—
94C2×C8×D11—41no—
95C2×C8×D11—41no—
96C4×D44—41no—
97C4×D44—41no—
98C4×Dic22—41no—
99C4×Dic22—41no—
100C11×C4⋊C8—41no—
101C11×C4⋊C8—41no—
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11×#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114(C2×D11)⋊C8—41no—
115(C2×D11)⋊C8—41no—
116(C2×D11)⋊C8—41no—
117(C2×D11)⋊C8—41no—
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66879—41no—
121#66879—41no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124C4⋊(C11⋊C8)—41no—
125C4⋊(C11⋊C8)—41no—
126#23354—111nomaximal, Sylow
127C23×D11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×D44—22no—
143C2×D44—41no—
144C2×D44—41no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×Dic22—41no—
158C2×Dic22—41no—
159C2×Dic22—41no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188C4⋊Dic11—41no—
189C4⋊Dic11—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208#4313—44no—
209C8×D11—44no—
210#2398—111no—
211#1985—111no—
212#1985—111no—
213#1924—111no—
214#1924—111no—
215#1924—111no—
216#1924—111no—
217#1870—111no—
218#1869—111no—
219#1851—111no—
220#1851—111no—
221#1850—111no—
222#1850—111no—
223#1832—111no—
224#1832D1111yescharacteristic, complemented
225C23×C11C23×C411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11#13112yes—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282D44—44no—
283C4×D11—41no—
284C4×D11—41no—
285C4×D11—41no—
286C4×D11—41no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—41no—
291Dic22—44no—
292C8×C11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×M16—111no—
301C23×C8—111no—
302C2×C4×Q8—111no—
303C2×C4×D4—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×#97—111no—
317C2×#97—111no—
318#400—111no—
319#400—111no—
320#397—111no—
321#397—111no—
322#394—111no—
323#394—111no—
324#393—111no—
325#393—111no—
326C4×C22⋊C4—111no—
327C4×C22⋊C4—111no—
328C4×C22⋊C4—111no—
329C4×C22⋊C4—111no—
330#376C2×D1111yescharacteristic
331#336—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
343C22×C11#51811yescharacteristic
344C22×C11#52011yescharacteristic
345C22×C11#52011yescharacteristic
346C22×C11C2×#13111yescharacteristic
347C22×C11#56811yescharacteristic
348C22×C11#56811yescharacteristic
349C22×C11#56811yescharacteristic
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11H(3,𝔽4)11yescharacteristic
371C4×C11#56211yescharacteristic
372C4×C11#56211yescharacteristic
373C4×C11#56311yescharacteristic
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—41no—
380C22×Q8—111no—
381C22×D4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C2×M16—441no—
385C2×M16—441no—
386C2×M16—441no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—441no—
392C22×C8—441no—
393C22×C8—441no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C4×Q8—441no—
399C4×Q8—441no—
400C4×D4—441no—
401C4×D4—441no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—111no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427C22⋊C8—441no—
428C22⋊C8—441no—
429C22⋊C8—441no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432C22⋊C8—441no—
433#97—441no—
434#97—441no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—111no—
440#95—111no—
441#95—111no—
442#95—111no—
443#95C4×D1111yescharacteristic
444#95C4×D1111yescharacteristic
445#95C4×D1111yescharacteristic
446#95C4×D1111yescharacteristic
447C2×C11#237911yescharacteristic
448C2×C11#297611yescharacteristic
449C2×C11#297811yescharacteristic
450C2×C11#299211yescharacteristic
451C2×C11#299211yescharacteristic
452C2×C11#299511yescharacteristic
453C2×C11#299511yescharacteristic
454D11—42no—
455D11—81no—
456C24—111no—
457C24—111no—
458C2×Q8—441no—
459C2×Q8—441no—
460C2×Q8—441no—
461C2×D4—222no—
462C2×D4—441no—
463C2×D4—441no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—444no—
515C4⋊C4—441no—
516C4⋊C4—441no—
517C4⋊C4—441no—
518C4⋊C4—441no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—441no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C22⋊C4—441no—
528C22⋊C4—441no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C11#2335411yescharacteristic, complemented, Sylow
540C23—112no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23C22×C4×D1111yescharacteristic
555Q8—444no—
556D4—444no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4#6703711yescharacteristic
602C2×C4#6704011yescharacteristic
603C2×C4#6704211yescharacteristic
604C2×C4#6704211yescharacteristic
605C2×C4#6704211yescharacteristic
606C2×C4#6704311yescharacteristic
607C8—41no—
608C8—41no—
609C8—41no—
610C8—41no—
611C8—441no—
612C8—441no—
613C8—441no—
614C8—441no—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—441no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22#1062303511yescharacteristic
630C22#1062305211yescharacteristic
631C22#1062305411yescharacteristic
632C22D11×#13111yescharacteristic
633C22#1062328111yescharacteristic
634C22#1062328111yescharacteristic
635C22#1062328111yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—441no—
643C4—441no—
644C4—441no—
645C4—441no—
646C4—441no—
647C4—441no—
648C4#1062321411yescharacteristic
649C4#1062321511yescharacteristic
650C4#1062323011yescharacteristic
651C4#1062323111yescharacteristic
652C2—442no—
653C2—881no—
654C2#1307178711yescharacteristic
655C2#1307766211yescharacteristic
656C2#1307767711yescharacteristic
657C2#1307775011yescharacteristic
658C2#1307775311yescharacteristic
659C2#1307778111yescharacteristic
660C2#1307778411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1832C2
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1832D11
hypocenterC11#23354
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1832

Complements

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

NH ≅ G/Ntype
2. #13069554C2semidirect
3. #13069554C2semidirect
4. #13069230C2semidirect
5. #13069230C2semidirect
6. #13069228C2semidirect
7. #13069228C2semidirect
10. #13068800C2semidirect
11. #13068797C2semidirect
12. #13068795C2semidirect
13. #13068792C2semidirect
14. #13068736C2semidirect
15. C11×#1832C2semidirect
224. #1832D11semidirect
539. C11#23354semidirect

Maximal subgroups

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

subgroupindex
#130719022
#130695542
#130692302
#130692282
#130689122
#130689072
#130688002
#130687972
#130687952
#130687922
#130687362
C11×#18322
#2335411