Finite Group Databasebeta

← #14776260

Subgroups — #14776260

Order 2816.

906 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×#10622703C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic
4#13071536C211yesmaximal, characteristic
5#13069437C211yesmaximal, characteristic
6#13069384C211yesmaximal, characteristic
7#13069309C211yesmaximal, characteristic
8#13069295C211yesmaximal, characteristic
9#13068960C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic
11#13068884C211yesmaximal, characteristic
12#13068870C211yesmaximal, characteristic
13#13068491C211yesmaximal, characteristic
14#13068449C211yesmaximal, characteristic
15C11×#2365C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389—21no—
27C11×#387—21no—
28C11×#387—21no—
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622703C418yescomplemented
39#10622643—24no—
40C4×#4326—24no—
41#10622585—21no—
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622549C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622263—21no—
55#10622262—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2×C414yes—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4326—22no—
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326C2×C414yes—
90C2×#4326C2×C414yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C4×Dic22C2×C414yes—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#66899—22no—
120#66899—22no—
121#66899—41no—
122#66899—41no—
123#66899C2×C414yes—
124#66899C2×C414yes—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129#66874—22no—
130#66874D414yes—
131#66872—22no—
132#66871—22no—
133C4⋊(C11⋊C8)C2×C414yes—
134#66867—22no—
135#66867—22no—
136C4×C11⋊C8—22no—
137#23014—111nomaximal, Sylow
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C22×C412yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22C22×C412yes—
169C2×Dic22C2×D412yes—
170C2×Dic22#4112yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C2×D412yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C42×C11—42no—
187C42×C11—42no—
188C42×C11C22×C412yes—
189C42×C11#4112yes—
190#4326—28no—
191#4326—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203C4×Dic11—24no—
204C4×Dic11—42no—
205C4×Dic11—42no—
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×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C22×C412yes—
216C2×C11⋊C8C22×C412yes—
217C2×C11⋊C8C2×D412yes—
218C2×#462—111no—
219C2×#441—111no—
220C2×C4×Q16—111no—
221#2365D1111yescharacteristic
222#2351—111no—
223#1960—111no—
224#1949—111no—
225#1935—111no—
226#1933—111no—
227#1878—111no—
228#1878—111no—
229#1865—111no—
230#1863—111no—
231#1771—111no—
232#1763—111no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
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—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C4×D412yes—
270C2×C4×C11C4×D412yes—
271C2×C4×C11#13712yes—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290Dic22—22no—
291Dic22—22no—
292Dic22—22no—
293Dic22C4×D414yes—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16—111no—
299C22×Q16—111no—
300C2×C4⋊Q8C2×D1111yescharacteristic
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×C4×Q8C2×D1111yescharacteristic
306#462—118no—
307#441—224no—
308C4×Q16—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323#391C2×D1111yescharacteristic
324#391C2×D1111yescharacteristic
325#389—21no—
326#389—111no—
327#389—111no—
328#389—221no—
329#389—221no—
330#387—21no—
331#387—21no—
332#382—111no—
333#382—221no—
334C4×C4⋊C4—21no—
335C4×C4⋊C4—221no—
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C4⋊C4C2×D1111yescharacteristic
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344C22×C11C2×C4×D411yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57811yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11C2×C4×D411yescharacteristic
362C4×C11#52011yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#55311yescharacteristic
365Dic11—24no—
366Dic11—42no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8—111no—
370C22×Q8C22×D1111yescharacteristic
371C22×Q8C22×D1111yescharacteristic
372C2×Q16—114no—
373C2×Q16—114no—
374C2×Q16—222no—
375C2×Q16—222no—
376C2×Q16—222no—
377C2×Q16—222no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8—111no—
382C4⋊Q8—22no—
383C4⋊Q8C4×D1114yes—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×Q8—114no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22⋊D1111yescharacteristic
407C2×C4⋊C4C22⋊D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#107—222no—
420#106—222no—
421C4⋊C8—114no—
422#103—114no—
423#103—114no—
424#103—114no—
425#103—222no—
426#103—222no—
427#103—222no—
428#103—441no—
429#103—441no—
430#97—222no—
431#97—222no—
432C4×C8—222no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95C22⋊D1111yescharacteristic
443#95C22⋊D1111yescharacteristic
444C2×C11#236111yescharacteristic
445C2×C11C4×#13711yescharacteristic
446C2×C11#295011yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#327011yescharacteristic
449C2×C11#337411yescharacteristic
450C2×C11#337711yescharacteristic
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—112no—
462C2×Q8—112no—
463C2×Q8—112no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8C2×C4×D1112yes—
468C2×Q8C2×C4×D1112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484Q16—228no—
485Q16—228no—
486C2×C8—112no—
487C2×C8—112no—
488C2×C8—112no—
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—24no—
499C4⋊C4—24no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—112no—
508C4⋊C4—224no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4D4×D1112yes—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—42no—
525C42—42no—
526C42—224no—
527C42—442no—
528C42—442no—
529C42C2×C4×D1112yes—
530C42#433912yes—
531C11#2301411yescharacteristic, complemented, Sylow
532C23C22×C22⋊D1111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—114no—
542Q8—222no—
543Q8—222no—
544Q8—222no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4C4×C22⋊D1112yes—
585C2×C4C4×C22⋊D1112yes—
586C2×C4#6699512yes—
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4#6703711yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#6704311yescharacteristic
593C8—222no—
594C8—222no—
595C8—222no—
596C8—441no—
597C22C2×C4×C22⋊D1111yescharacteristic
598C22D4×C22⋊D1111yescharacteristic
599C22C2×#6699511yescharacteristic
600C22#1062335311yescharacteristic
601C22#1062336211yescharacteristic
602C22#1062336911yescharacteristic
603C22#1062336911yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—81no—
614C4—224no—
615C4—442no—
616C4—881no—
617C4—881no—
618C4C4×D4×D1111yescharacteristic
619C4#1062307711yescharacteristic
620C4#1062308211yescharacteristic
621C4#1062308911yescharacteristic
622C2#1307162811yescharacteristic
623C2C4×#6699511yescharacteristic
624C2#1307748211yescharacteristic
625C2#1308016711yescharacteristic
626C2#1308018711yescharacteristic
627C2#1308141511yescharacteristic
628C2#1308145211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#2365D11
hypocenterC11#23014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
38. #10622703C4semidirect
531. C11#23014semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×#106226432
C2×C4×#43262
#130715362
#130694372
#130693842
#130693092
#130692952
#130689602
#130688842
#130688702
#130684912
#130684492
C11×#23652
#2301411