Finite Group Databasebeta

← #14764138

Subgroups — #14764138

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622322C211yesmaximal, characteristic
2C2×#10622453C211yesmaximal, characteristic
3#13071096C211yesmaximal, characteristic
4#13069339C211yesmaximal, characteristic, complemented
5#13069338C211yesmaximal, characteristic, complemented
6#13069336C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13069333C211yesmaximal, characteristic, complemented
9#13069332C211yesmaximal, characteristic, complemented
10#13069331C211yesmaximal, characteristic, complemented
11#13068599C211yesmaximal, characteristic
12#13068597C211yesmaximal, characteristic
13#13068595C211yesmaximal, characteristic
14#13068593C211yesmaximal, characteristic
15C11×#1940C211yesmaximal, characteristic, complemented
16C2×#66925C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622602C411yescharacteristic
37#10622602C411yescharacteristic
38#10622585C411yescharacteristic
39#10622585C411yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622453—24no—
48#10622322—24no—
49#10622281C411yescharacteristic
50#10622281C411yescharacteristic
51#10622260C411yescharacteristic
52#10622260C411yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×C4⋊Dic11C2×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×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66925—41no—
97#66925—41no—
98#66925D414yes—
99#66925Q814yes—
100C42×D11—41no—
101C42×D11—41no—
102C11×C4⋊C8—22no—
103C11×C4⋊C8—41no—
104C11×C4⋊C8—41no—
105C11×#97—22no—
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—22no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117(C2×D11)⋊C8—22no—
118#66879—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124Dic11⋊C8—41no—
125C8×Dic11—22no—
126C4⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—41no—
128C4⋊(C11⋊C8)—41no—
129C4×C11⋊C8—22no—
130#21958—111nomaximal, Sylow
131C23×D11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11—41no—
156C2×C4×D11C2×D412yes—
157C2×C4×D11C2×Q812yes—
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×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—41no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11C2×D412yes—
177C42×C11C2×Q812yes—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4C4⋊C414yes—
181(C2×D11)⋊C4C4⋊C414yes—
182C4⋊Dic11—22no—
183C4⋊Dic11—41no—
184Dic11⋊C4—22no—
185Dic11⋊C4—22no—
186Dic11⋊C4—41no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4C4⋊C414yes—
191Dic11⋊C4C4⋊C414yes—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—41no—
197C4×Dic11—41no—
198C4×Dic11C2×D412yes—
199C4×Dic11C2×Q812yes—
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—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×#433—111no—
213C2×#433—111no—
214#2296—111no—
215#1940—111no—
216#1940—111no—
217#1940—111no—
218#1940D1111yescharacteristic, complemented
219#1939—111no—
220#1939—111no—
221#1939—111no—
222#1939—111no—
223#1798—111no—
224#1798—111no—
225#1797—111no—
226#1797—111no—
227C23×C11C23×C411yescharacteristic
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11C2×C4⋊C412yes—
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—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11C2×C4⋊C412yes—
251C2×C4×C11C2×C4⋊C412yes—
252C2×C4×C11#13112yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×C4×C112−1+411yescharacteristic
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×Dic11C2×C4⋊C412yes—
277C2×Dic11C2×C4⋊C412yes—
278C2×Dic11C2×C4⋊C412yes—
279C2×Dic11#13112yes—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—44no—
285C4×D11—44no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11—41no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C2×#117—111no—
295C2×#117—111no—
296C22×C42—111no—
297#433—224no—
298#433—224no—
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×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×C4⋊C8C2×D1111yescharacteristic
311C2×C22⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×#97—111no—
316C2×#97C2×D1111yescharacteristic
317C2×C4×C8—111no—
318C2×C4×C8—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#389—111no—
323#385—111no—
324#385—111no—
325#385—111no—
326#385—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4C2×D1111yescharacteristic
331#336—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336C2×D1111yescharacteristic
338#336C2×D1111yescharacteristic
339C22×C11C22×C4⋊C411yescharacteristic
340C22×C11#51811yescharacteristic
341C22×C11#51911yescharacteristic
342C22×C11C2×#13111yescharacteristic
343C22×C11C2×#13111yescharacteristic
344C22×C11#56811yescharacteristic
345C22×C11#56811yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11#53711yescharacteristic
360C4×C11#53711yescharacteristic
361C4×C11#54411yescharacteristic
362C4×C11#54411yescharacteristic
363Dic11—22no—
364Dic11—22no—
365Dic11—22no—
366Dic11—22no—
367Dic11—41no—
368Dic11—41no—
369Dic11—41no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8C22×D1111yescharacteristic
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381#117—114no—
382#117—114no—
383#117—441no—
384#117—441no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
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⋊C4C4×D1111yescharacteristic
396C2×C4⋊C4C4×D1111yescharacteristic
397C2×C22⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
400C2×C22⋊C4—111no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—441no—
407C2×C42—441no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1111yescharacteristic
411C4⋊C8—22no—
412C4⋊C8—41no—
413C4⋊C8—41no—
414C4⋊C8—222no—
415C4⋊C8—222no—
416C4⋊C8—222no—
417C4⋊C8—441no—
418C4⋊C8—441no—
419C4⋊C8—441no—
420C4⋊C8—441no—
421C4⋊C8—441no—
422C4⋊C8—441no—
423C22⋊C8—222no—
424C22⋊C8—222no—
425C22⋊C8—222no—
426C22⋊C8—222no—
427#97—22no—
428#97—222no—
429C4×C8—222no—
430C4×C8—222no—
431#95—111no—
432#95—111no—
433#95—111no—
434#95—111no—
435#95—111no—
436#95—111no—
437#95C4×D1111yescharacteristic
438#95C4×D1111yescharacteristic
439C2×C11#231611yescharacteristic
440C2×C11#290611yescharacteristic
441C2×C11#290611yescharacteristic
442C2×C11#297711yescharacteristic
443C2×C11#297811yescharacteristic
444C2×C11#298511yescharacteristic
445C2×C11#298511yescharacteristic
446D11—42no—
447C24—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—222no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4—441no—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4C2×C4×D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—114no—
501C4⋊C4—114no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—441no—
506C4⋊C4—441no—
507C4⋊C4—441no—
508C4⋊C4—441no—
509C4⋊C4—441no—
510C22⋊C4—114no—
511C22⋊C4—114no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—112no—
519C42—112no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42—441no—
525C42—441no—
526C42D4×D1112yes—
527C42Q8×D1112yes—
528C11#2195811yescharacteristic, complemented, Sylow
529C23—112no—
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23C22×C4×D1111yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
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—21no—
551C2×C4—21no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
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—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—444no—
578C2×C4—444no—
579C2×C4C4⋊C4×D1112yes—
580C2×C4C4⋊C4×D1112yes—
581C2×C4#6696012yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#6703711yescharacteristic
584C2×C4C2×Q8×D1111yescharacteristic
585C2×C4#6704011yescharacteristic
586C2×C4#6704211yescharacteristic
587C2×C4#6704311yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—441no—
593C8—441no—
594C8—441no—
595C8—441no—
596C22—222no—
597C22—222no—
598C22—222no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22C2×C4⋊C4×D1111yescharacteristic
604C22#1062307611yescharacteristic
605C22#1062310311yescharacteristic
606C22C2×#6696011yescharacteristic
607C22#1062327611yescharacteristic
608C22D11×#13111yescharacteristic
609C22#1062328111yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—222no—
617C4—222no—
618C4—222no—
619C4—222no—
620C4—441no—
621C4—441no—
622C4—441no—
623C4#1062313911yescharacteristic
624C4#1062316011yescharacteristic
625C4#1062322011yescharacteristic
626C4#1062326011yescharacteristic
627C2—442no—
628C2#1307123111yescharacteristic
629C2#1307718311yescharacteristic
630C2#1307718511yescharacteristic
631C2#1307766711yescharacteristic
632C2#1307767511yescharacteristic
633C2#1307770911yescharacteristic
634C2#1307771211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1940C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1940D11
hypocenterC11#21958
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
4. #13069339C2semidirect
5. #13069338C2semidirect
6. #13069336C2semidirect
7. #13069335C2semidirect
8. #13069333C2semidirect
9. #13069332C2semidirect
10. #13069331C2semidirect
15. C11×#1940C2semidirect
218. #1940D11semidirect
528. C11#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#106223222
C2×#106224532
#130710962
#130693392
#130693382
#130693362
#130693352
#130693332
#130693322
#130693312
#130685992
#130685972
#130685952
#130685932
C11×#19402
#2195811