Finite Group Databasebeta

← #14765804

Subgroups — #14765804

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622314C211yesmaximal, characteristic, complemented
2C2×#10622453C211yesmaximal, characteristic
3#13071892C211yesmaximal, characteristic
4#13069550C211yesmaximal, characteristic, complemented
5#13069338C211yesmaximal, characteristic, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic
9#13069229C211yesmaximal, characteristic
10#13069223C211yesmaximal, characteristic
11#13069220C211yesmaximal, characteristic
12#13069170C211yesmaximal, characteristic, complemented
13#13068599C211yesmaximal, characteristic
14#13068487C211yesmaximal, characteristic, complemented
15C11×#1917C211yesmaximal, characteristic, complemented
16C2×#66925C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C8C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622607C411yescharacteristic
34#10622605C411yescharacteristic
35#10622593C411yescharacteristic
36#10622592C411yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622453—24no—
46#10622314—24no—
47#10622289C411yescharacteristic
48#10622286C411yescharacteristic
49#10622271C411yescharacteristic
50#10622270C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22C2×C411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
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×C4⋊Dic11C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66925—22no—
95#66925—22no—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×C4⋊C8—22no—
99C11×#97—22no—
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11⋊#95C2×C411yescharacteristic
103C11⋊#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110(C2×D11)⋊C8—22no—
111(C2×D11)⋊C8—22no—
112(C2×D11)⋊C8—41no—
113(C2×D11)⋊C8—41no—
114#66879—41no—
115#66879D414yes—
116Dic11⋊C8—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—41no—
120C8×Dic11—22no—
121C8×Dic11—22no—
122C4⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)—22no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#22109—111nomaximal, Sylow
127C23×D11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—41no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
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×C11C2×D412yes—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—41no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171(C2×D11)⋊C4—22no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4—22no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177C4⋊Dic11—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11C2×D412yes—
191C4×Dic11#4112yes—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—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⋊C8C2×D412yes—
204C2×#446—111no—
205C2×#433—111no—
206#2396—111no—
207#1984—111no—
208#1940—111no—
209#1939—111no—
210#1939—111no—
211#1924—111no—
212#1924—111no—
213#1923—111no—
214#1923—111no—
215#1917D1111yescharacteristic, complemented
216#1916—111no—
217#1798—111no—
218#1771—111no—
219C23×C11C23×C411yescharacteristic
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11#13112yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
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×Dic11C4×D412yes—
270C2×Dic11C4×D412yes—
271C2×Dic11#13112yes—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276Dic22—44no—
277C8×C11—22no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C2×C4×Q8—111no—
286C2×#117—111no—
287#446—224no—
288#433—224no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—111no—
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×C22⋊C8—111no—
298C2×C22⋊C8—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306C2×C4×C8—111no—
307#400—111no—
308#399—111no—
309#398—111no—
310#398—111no—
311#396—111no—
312#396—111no—
313#395—111no—
314#393—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4—111no—
319C4×C22⋊C4—111no—
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336C2×D1111yescharacteristic
327#336C2×D1111yescharacteristic
328#336C2×D1111yescharacteristic
329#336C2×D1111yescharacteristic
330C22×C11C2×C4×D411yescharacteristic
331C22×C11#51911yescharacteristic
332C22×C11#52011yescharacteristic
333C22×C11C2×#13111yescharacteristic
334C22×C11C2×#13111yescharacteristic
335C22×C11#56811yescharacteristic
336C22×C11#56811yescharacteristic
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C4×C11—22no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11#53611yescharacteristic
351C4×C11#53711yescharacteristic
352C4×C11#54111yescharacteristic
353C4×C11#54211yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—22no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361C22×Q8—111no—
362C23×C4—111no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C4×Q8—222no—
372C4×Q8—222no—
373#117—222no—
374#117—222no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4C4×D1111yescharacteristic
385C2×C4⋊C4C4×D1111yescharacteristic
386C2×C22⋊C4—111no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C22⋊C4—111no—
390C2×C22⋊C4—111no—
391C2×C22⋊C4—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C4⋊C8—22no—
399C4⋊C8—222no—
400C4⋊C8—222no—
401C4⋊C8—222no—
402C4⋊C8—222no—
403C4⋊C8—222no—
404C4⋊C8—441no—
405C4⋊C8—441no—
406C22⋊C8—222no—
407C22⋊C8—222no—
408C22⋊C8—441no—
409C22⋊C8—441no—
410#97—22no—
411#97—114no—
412#97—441no—
413C4×C8—222no—
414C4×C8—222no—
415C4×C8—441no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—111no—
420#95—111no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95C4×D1111yescharacteristic
425#95C4×D1111yescharacteristic
426C2×C11#232311yescharacteristic
427C2×C11#293311yescharacteristic
428C2×C11#293511yescharacteristic
429C2×C11#298611yescharacteristic
430C2×C11#298711yescharacteristic
431C2×C11#299211yescharacteristic
432C2×C11#299311yescharacteristic
433D11—81no—
434C24—111no—
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8—441no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8D4×D1112yes—
482C4⋊C4—22no—
483C4⋊C4—41no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—441no—
492C4⋊C4—441no—
493C22⋊C4—222no—
494C22⋊C4—222no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—112no—
506C42—112no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C11#2210911yescharacteristic, complemented, Sylow
512C23—221no—
513C23—221no—
514C23—221no—
515C23—221no—
516C23—221no—
517C23—221no—
518C23—221no—
519C23C22×C4×D1111yescharacteristic
520Q8—444no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4#6696012yes—
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4#6704011yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704211yescharacteristic
568C2×C4#6704311yescharacteristic
569C2×C4#6704311yescharacteristic
570C8—22no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—222no—
575C8—441no—
576C8—441no—
577C8—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22#1062305411yescharacteristic
586C22C4×D4×D1111yescharacteristic
587C22#1062310311yescharacteristic
588C22C2×#6696011yescharacteristic
589C22#1062327611yescharacteristic
590C22D11×#13111yescharacteristic
591C22#1062328111yescharacteristic
592C4—22no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—222no—
599C4—222no—
600C4—222no—
601C4—441no—
602C4—441no—
603C4—441no—
604C4—441no—
605C4#1062316011yescharacteristic
606C4#1062317911yescharacteristic
607C4#1062322711yescharacteristic
608C4#1062324111yescharacteristic
609C2—881no—
610C2#1307129711yescharacteristic
611C2#1307733911yescharacteristic
612C2#1307736111yescharacteristic
613C2#1307771411yescharacteristic
614C2#1307771911yescharacteristic
615C2#1307775711yescharacteristic
616C2#1307775911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1917C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1917D11
hypocenterC11#22109
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069550C2semidirect
5. #13069338C2semidirect
6. #13069335C2semidirect
7. #13069333C2semidirect
12. #13069170C2semidirect
14. #13068487C2semidirect
15. C11×#1917C2semidirect
215. #1917D11semidirect
511. C11#22109semidirect

Maximal subgroups

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

subgroupindex
C2×#106223142
C2×#106224532
#130718922
#130695502
#130693382
#130693352
#130693332
#130692302
#130692292
#130692232
#130692202
#130691702
#130685992
#130684872
C11×#19172
#2210911