Finite Group Databasebeta

← #14775564

Subgroups — #14775564

Order 2816.

788 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622314C211yesmaximal, characteristic, complemented
2C2×#10622732C211yesmaximal, characteristic
3#13071890C211yesmaximal, characteristic
4#13069554C211yesmaximal, characteristic, complemented
5#13069338C211yesmaximal, characteristic, complemented
6#13069334C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069180C211yesmaximal, characteristic, complemented
9#13069179C211yesmaximal, characteristic, complemented
10#13068799C211yesmaximal, characteristic
11#13068796C211yesmaximal, characteristic
12#13068490C211yesmaximal, characteristic, complemented
13#13068395C211yesmaximal, characteristic
14#13068384C211yesmaximal, characteristic
15C11×#1753C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26#10622732—24no—
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622562C411yescharacteristic
38#10622561C411yescharacteristic
39#10622561C411yescharacteristic
40#10622560C411yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46#10622314—24no—
47#10622274C411yescharacteristic
48#10622273C411yescharacteristic
49#10622270C411yescharacteristic
50#10622269C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2×C411yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—41no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78#66979—22no—
79#66979—22no—
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×Dic11⋊C4C2×C411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8—22no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—41no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C4×Dic22—22no—
103C4×Dic22—22no—
104C11×C22⋊C8Q814yescomplemented
105C11×#97—22no—
106C4×C8×C11—41no—
107C11×#95C2×C411yescharacteristic
108C11×#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C22⋊(C11⋊C8)—22no—
118#66879—22no—
119#66879—22no—
120#66879—41no—
121Dic11⋊C8—22no—
122Dic11⋊C8—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—41no—
126Dic11⋊C8D414yes—
127C8×Dic11—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—41no—
130#22961—111nomaximal, Sylow
131C24×C11C22×C411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×Q812yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C2×Dic22—22no—
153C2×Dic22—41no—
154C2×Dic22—41no—
155C11×M16—44no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C2×D412yes—
166C2×C8×C11C2×Q812yes—
167C2×C8×C11C2×Q812yes—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—41no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—41no—
183Dic11⋊C4—22no—
184Dic11⋊C4—22no—
185Dic11⋊C4—22no—
186Dic11⋊C4—41no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11C2×D412yes—
196C4×Dic11#4112yes—
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—
208C2×C11⋊C8—44no—
209C2×C11⋊C8C2×D412yes—
210C2×#446—111no—
211C2×#424—111no—
212#2396—111no—
213#1985—111no—
214#1940—111no—
215#1939—111no—
216#1939—111no—
217#1917—111no—
218#1917—111no—
219#1851—111no—
220#1850—111no—
221#1771—111no—
222#1753D1111yescharacteristic
223#1752—111no—
224#1750—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C4×Q812yes—
232C23×C11C23×C411yescharacteristic
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
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×C11C4×Q812yes—
251C2×C4×C11#13112yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×Q811yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
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×Dic11C4×D412yes—
281C2×Dic11C4×D412yes—
282Dic22—44no—
283C8×C11—22no—
284C8×C11—22no—
285C8×C11—22no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×M16C2×D1111yescharacteristic
292C23×C8—111no—
293C2×C4×Q8—111no—
294C2×#117—111no—
295#446—224no—
296#424—224no—
297C2×C4⋊C8—111no—
298C2×C4⋊C8—111no—
299C2×C4⋊C8—111no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—111no—
305C2×C22⋊C8—111no—
306C2×C22⋊C8C2×D1111yescharacteristic
307C2×#97—111no—
308C2×#97—111no—
309C2×#97—111no—
310C2×#97C2×D1111yescharacteristic
311C2×C4×C8—111no—
312C2×C4×C8C2×D1111yescharacteristic
313#400—111no—
314#399—111no—
315#398—111no—
316#398—111no—
317#396—111no—
318#396—111no—
319#395—111no—
320#393—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4—111no—
325C4×C22⋊C4C2×D1111yescharacteristic
326#336—111no—
327#336—111no—
328#336—111no—
329#336—111no—
330#336—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×C4×Q811yescharacteristic
345C22×C11#52011yescharacteristic
346C22×C11C2×#13111yescharacteristic
347C22×C11#56811yescharacteristic
348C22×C11#56811yescharacteristic
349C22×C11#56811yescharacteristic
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11#54611yescharacteristic
356C4×C11D4×Q811yescharacteristic
357C4×C11#55211yescharacteristic
358C4×C11#55411yescharacteristic
359Dic11—22no—
360Dic11—22no—
361Dic11—41no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365Dic11—41no—
366Dic11—41no—
367C22×Q8—111no—
368C23×C4C22×D1111yescharacteristic
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—41no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—222no—
377C22×C8—222no—
378C22×C8—441no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383C4×Q8—222no—
384C4×Q8—222no—
385#117—222no—
386#117—222no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
400C2×C22⋊C4—111no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4C4×D1111yescharacteristic
403C2×C22⋊C4C4×D1111yescharacteristic
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C4⋊C8—114no—
411C4⋊C8—222no—
412C4⋊C8—222no—
413C4⋊C8—222no—
414C4⋊C8—222no—
415C4⋊C8—222no—
416C4⋊C8—441no—
417C4⋊C8—441no—
418C22⋊C8—222no—
419C22⋊C8Dic2214yescomplemented
420#97—22no—
421#97—222no—
422#97—222no—
423#97—441no—
424C4×C8—41no—
425C4×C8—222no—
426#95—111no—
427#95—111no—
428#95—111no—
429#95—111no—
430#95—111no—
431#95—111no—
432#95—111no—
433#95—111no—
434#95C4×D1111yescharacteristic
435#95C4×D1111yescharacteristic
436C2×C11—42no—
437C2×C11#236011yescharacteristic
438C2×C11#293011yescharacteristic
439C2×C11#293511yescharacteristic
440C2×C11#296111yescharacteristic
441C2×C11#296211yescharacteristic
442C2×C11#299211yescharacteristic
443C2×C11#299511yescharacteristic
444C24C2×C4×D1111yescharacteristic
445C2×Q8—222no—
446C2×Q8—441no—
447C2×Q8—441no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4C2×Dic2212yes—
461C22×C4C2×C4×D1111yescharacteristic
462C22×C4C2×C4×D1111yescharacteristic
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4#433912yes—
467C22×C4C23×D1111yescharacteristic
468M16—44no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—112no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—444no—
491C2×C8C2×Dic2212yes—
492C2×C8C2×Dic2212yes—
493C2×C8D4×D1112yes—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—441no—
502C4⋊C4—441no—
503C4⋊C4—441no—
504C4⋊C4—441no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—112no—
516C42—112no—
517C42—221no—
518C42—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—221no—
523C11#2296111yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23C4×Dic2212yes—
531C23C22×C4×D1111yescharacteristic
532Q8—444no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4C4×Dic2212yes—
575C2×C4#6696012yes—
576C2×C4C22×Dic2211yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6703711yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#6704311yescharacteristic
582C8—22no—
583C8—22no—
584C8—22no—
585C8—41no—
586C8—222no—
587C8—441no—
588C8—441no—
589C8—441no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22C2×C4×Dic2211yescharacteristic
598C22C4×D4×D1111yescharacteristic
599C22#1062307711yescharacteristic
600C22C2×#6696011yescharacteristic
601C22#1062327611yescharacteristic
602C22#1062328111yescharacteristic
603C22#1062328111yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—222no—
610C4—222no—
611C4—441no—
612C4—441no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4—441no—
617C4#1062302111yescharacteristic
618C4#1062306211yescharacteristic
619C4D4×Dic2211yescharacteristic
620C4#1062307011yescharacteristic
621C2—42no—
622C2#1307162211yescharacteristic
623C2#1307731611yescharacteristic
624C2#1307736111yescharacteristic
625C2#1307755411yescharacteristic
626C2#1307756311yescharacteristic
627C2#1307775611yescharacteristic
628C2#1307778211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1753C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22961
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069554C2semidirect
5. #13069338C2semidirect
6. #13069334C2semidirect
7. #13069333C2semidirect
8. #13069180C2semidirect
9. #13069179C2semidirect
12. #13068490C2semidirect
104. C11×C22⋊C8Q8semidirect
419. C22⋊C8Dic22semidirect
523. C11#22961semidirect

Maximal subgroups

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

subgroupindex
C2×#106223142
C2×#106227322
#130718902
#130695542
#130693382
#130693342
#130693332
#130691802
#130691792
#130687992
#130687962
#130684902
#130683952
#130683842
C11×#17532
#2296111