Finite Group Databasebeta

← #14797648

Subgroups — #14797648

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622841C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3#13072119C211yesmaximal, characteristic
4#13070164C211yesmaximal, characteristic, complemented
5#13070042C211yesmaximal, characteristic
6#13069938C211yesmaximal, characteristic, complemented
7#13069812C211yesmaximal, characteristic
8#13069295C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068631C211yesmaximal, characteristic, complemented
14#13068551C211yesmaximal, characteristic
15Q8×C11×C22⋊C4C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#391—21no—
24C11×#391—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#380—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622841—24no—
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C4×#4326—24no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622565—21no—
47#10622558—21no—
48#10622549C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622271—21no—
54#10622265—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—41no—
76C4×Q8×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×#4326—22no—
91C2×#4326—22no—
92C2×#4326—22no—
93C2×#4326—22no—
94C2×#4326—41no—
95C2×#4326D414yes—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977—41no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C4×Dic22—22no—
110C4×Dic22—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66899—22no—
122#66899—22no—
123#66899—41no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—41no—
132#66874—22no—
133#66874—41no—
134#66872—41no—
135#66871—22no—
136C4⋊(C11⋊C8)—41no—
137C4×C11⋊C8—22no—
138#24902—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—24no—
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×C11—21no—
149C2×Q8×C11—42no—
150C2×Q8×C11—42no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11C2×D412yes—
156C2×Q8×C11#4112yes—
157C2×Q8×C11#4112yes—
158C2×Q8×C11#4112yes—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22C2×D412yes—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—42no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—42no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—42no—
202C42×C11—42no—
203C22⋊Dic11—42no—
204C22⋊Dic11—42no—
205#4326—28no—
206#4326—44no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216C4×Dic11—42no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8C2×D412yes—
229C2×#451—111no—
230C2×C4×Q16—111no—
231#2421—111no—
232Q8×C22⋊C4D1111yescharacteristic
233#2097—111no—
234#2075—111no—
235#2056—111no—
236#2035—111no—
237#1933—111no—
238#1923—111no—
239#1878—111no—
240#1878—111no—
241#1865—111no—
242#1805—111no—
243#1787—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11#13512yes—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—48no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11#12314yes—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—48no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11#13712yes—
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C11H(5,𝔽2)11yescharacteristic
299C2×Dic11—22no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311Dic22—22no—
312Dic22—22no—
313Dic22—41no—
314Dic22—41no—
315C11⋊C8—22no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C23×Q8C2×D1111yescharacteristic
320C22×Q16—111no—
321C22×Q16—111no—
322C2×C22⋊Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8C2×D1111yescharacteristic
325C2×C4×Q8C2×D1111yescharacteristic
326#451—224no—
327C4×Q16—224no—
328C2×#107—111no—
329C2×#106—111no—
330C2×C4⋊C8—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C4×C8—111no—
342#400—221no—
343#397—221no—
344#391—21no—
345#391—21no—
346#391—111no—
347#391C2×D1111yescharacteristic
348#391C2×D1111yescharacteristic
349#389—111no—
350#388—221no—
351#387—221no—
352#382—111no—
353#380—21no—
354#380—111no—
355#380C2×D1111yescharacteristic
356C4×C22⋊C4—21no—
357C4×C22⋊C4C2×D1111yescharacteristic
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#336—111no—
363#336—111no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11#52511yescharacteristic
372C22×C11D4211yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11C2×#13511yescharacteristic
375C22×C11C2×#13711yescharacteristic
376C22×C11#57811yescharacteristic
377C22×C11#57811yescharacteristic
378C4×C11—24no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11C2×#12311yescharacteristic
388C4×C11#53811yescharacteristic
389C4×C11#54611yescharacteristic
390C4×C11#55111yescharacteristic
391Dic11—42no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—21no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—41no—
401C22×Q8—41no—
402C22×Q8—111no—
403C22×Q8C22×D1111yescharacteristic
404C22×Q8C22×D1111yescharacteristic
405C23×C4—21no—
406C23×C4C22×D1111yescharacteristic
407C2×Q16—114no—
408C2×Q16—222no—
409C2×Q16—222no—
410C2×Q16—222no—
411C2×Q16—222no—
412C2×Q16—441no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—111no—
416C22×C8—111no—
417C22⋊Q8—222no—
418C22⋊Q8—441no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—41no—
422C4×Q8—41no—
423C4×Q8—222no—
424C4×Q8—441no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4C22⋊D1111yescharacteristic
439C2×C22⋊C4C22⋊D1111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—221no—
443C2×C42C22×D1111yescharacteristic
444C2×C42C22×D1111yescharacteristic
445#107—222no—
446#106—441no—
447C4⋊C8—441no—
448#103—222no—
449#103—222no—
450#103—222no—
451#103—222no—
452#103—222no—
453#103—222no—
454#103—441no—
455#103—441no—
456C22⋊C8—222no—
457C22⋊C8—441no—
458C4×C8—222no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95C22⋊D1111yescharacteristic
471#95C22⋊D1111yescharacteristic
472C2×C11—42no—
473C2×C11#241811yescharacteristic
474C2×C11#310811yescharacteristic
475C2×C11#312711yescharacteristic
476C2×C11#327011yescharacteristic
477C2×C11#328511yescharacteristic
478C2×C11#330011yescharacteristic
479C2×C11#332811yescharacteristic
480C24C2×C22⋊D1111yescharacteristic
481C2×Q8—24no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—112no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8#433912yes—
503C2×Q8#433912yes—
504C2×Q8D4×D1112yes—
505C2×Q8#434112yes—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C2×C22⋊D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529Q16—228no—
530Q16—444no—
531C2×C8—112no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—42no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—42no—
569C42—442no—
570C11#2490211yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#6700312yes—
578C23C22×C22⋊D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—48no—
585Q8—41no—
586Q8—41no—
587Q8—222no—
588Q8—222no—
589Q8—441no—
590Q8—441no—
591Q8#6693614yes—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—48no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—222no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4#6699512yes—
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×#433911yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×#434111yescharacteristic
640C2×C4#6703711yescharacteristic
641C2×C4#6703711yescharacteristic
642C8—222no—
643C8—441no—
644C8—441no—
645C8—441no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22#1062332211yescharacteristic
654C22D4×C22⋊D1111yescharacteristic
655C22#1062333711yescharacteristic
656C22C2×#6699511yescharacteristic
657C22C2×#6700311yescharacteristic
658C22#1062336911yescharacteristic
659C22#1062336911yescharacteristic
660C4—22no—
661C4—24no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—442no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4C2×#6693611yescharacteristic
674C4#1062302111yescharacteristic
675C4#1062302511yescharacteristic
676C4#1062302611yescharacteristic
677C2—42no—
678C2#1307207811yescharacteristic
679C2#1307869611yescharacteristic
680C2#1307891611yescharacteristic
681C2#1308018711yescharacteristic
682C2#1308035311yescharacteristic
683C2#1308050311yescharacteristic
684C2#1308089911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterQ8×C22⋊C4D11
hypocenterC11#24902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
4. #13070164C2semidirect
6. #13069938C2semidirect
8. #13069295C2semidirect
10. #13068960C2semidirect
11. #13068957C2semidirect
12. #13068884C2semidirect
13. #13068631C2semidirect
570. C11#24902semidirect

Maximal subgroups

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

subgroupindex
C2×#106228412
C2×C4×#43262
#130721192
#130701642
#130700422
#130699382
#130698122
#130692952
#130692242
#130689602
#130689572
#130688842
#130686312
#130685512
Q8×C11×C22⋊C42
#2490211