Finite Group Databasebeta

← #14797705

Subgroups — #14797705

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622663C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3C22⋊C4×Dic22C211yesmaximal, characteristic
4#13070155C211yesmaximal, characteristic, complemented
5#13070047C211yesmaximal, characteristic
6#13069938C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic
8#13069291C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068869C211yesmaximal, characteristic, complemented
13#13068618C211yesmaximal, characteristic, complemented
14#13068550C211yesmaximal, characteristic
15C11×#2423C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#399—21no—
24C11×#398—21no—
25C11×#391C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#388—21no—
28C11×#387—21no—
29C11×#384C2211yescharacteristic
30C11×#380C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622663—24no—
38C4×#4326—24no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622555—21no—
48C22⋊C4×Dic11—21no—
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622259—21no—
54#10622259—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—21no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—41no—
70C22×Dic22—41no—
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—41no—
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×#4326—22no—
94C2×#4326—22no—
95C2×#4326—22no—
96C2×#4326—22no—
97C2×#4326—41no—
98C2×#4326D414yes—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C4×Dic22—22no—
110C4×Dic22—22no—
111C4×Dic22—41no—
112C4×Dic22—41no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#66899—22no—
120#66899—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—41no—
128#66874—22no—
129#66874—22no—
130#66874—22no—
131#66874—22no—
132#66874—22no—
133#66874—41no—
134#66871—22no—
135#66871—41no—
136C4⋊(C11⋊C8)—41no—
137C4×C11⋊C8—22no—
138#24906—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C2×Dic22—24no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22—44no—
181C2×Dic22—44no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×Dic22C2×D412yes—
185C2×Dic22#4112yes—
186C2×Dic22#4112yes—
187C2×Dic22#4112yes—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—81no—
198C11×C4⋊C4—81no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—81no—
202C11×C22⋊C4Q1614yescomplemented
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—42no—
208C22⋊Dic11—42no—
209#4326—28no—
210#4326—44no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217C4×Dic11—42no—
218C4×Dic11—42no—
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⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8C2×D412yes—
231C2×#451—111no—
232C2×C4×Q16—111no—
233#2423D1111yescharacteristic
234Q8×C22⋊C4—111no—
235#2095—111no—
236#2076—111no—
237#2056—111no—
238#2036—111no—
239#1933—111no—
240#1923—111no—
241#1878—111no—
242#1878—111no—
243#1863—111no—
244#1803—111no—
245#1787—111no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11C2×Q1612yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
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×C11C2×Q1612yes—
288C2×C4×C11C2×Q1612yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—48no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308Dic22—22no—
309Dic22—22no—
310Dic22—22no—
311Dic22—22no—
312Dic22—22no—
313Dic22—48no—
314Dic22—41no—
315Dic22—41no—
316Dic22#12314yes—
317C11⋊C8—22no—
318C11⋊C8—41no—
319C11⋊C8—41no—
320C11⋊C8—41no—
321C23×Q8—111no—
322C22×Q16—111no—
323C22×Q16—111no—
324C2×C22⋊Q8C2×D1111yescharacteristic
325C2×C4×Q8—111no—
326C2×C4×Q8—111no—
327C2×C4×Q8C2×D1111yescharacteristic
328#451—224no—
329C4×Q16—224no—
330C2×#107—111no—
331C2×#107—111no—
332C2×C4⋊C8—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—111no—
341C2×C22⋊C8—111no—
342C2×C22⋊C8—111no—
343C2×C4×C8—111no—
344#399—21no—
345#398—21no—
346#391—111no—
347#391—111no—
348#391—221no—
349#391—221no—
350#391C2×D1111yescharacteristic
351#389C2×D1111yescharacteristic
352#388—21no—
353#387—21no—
354#384C2×D1111yescharacteristic
355#380—111no—
356#380—221no—
357#380C2×D1111yescharacteristic
358C4×C22⋊C4—221no—
359C4×C22⋊C4C2×D1111yescharacteristic
360#340—111no—
361#340—111no—
362#340—111no—
363#340—111no—
364#336—111no—
365#336—111no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11#52511yescharacteristic
374C22×C11D4211yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11C22×Q1611yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57711yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11C2×#12311yescharacteristic
390C4×C11#53811yescharacteristic
391C4×C11#54611yescharacteristic
392C4×C11#55111yescharacteristic
393Dic11—24no—
394Dic11—42no—
395Dic11—81no—
396Dic11—81no—
397C22×Q8—111no—
398C22×Q8—111no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—221no—
404C22×Q8—441no—
405C22×Q8—441no—
406C22×Q8C22×D1111yescharacteristic
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409C2×Q16—114no—
410C2×Q16—222no—
411C2×Q16—222no—
412C2×Q16—222no—
413C2×Q16—222no—
414C2×Q16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—111no—
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421C4×Q8—22no—
422C4×Q8—41no—
423C4×Q8—222no—
424C4×Q8—222no—
425C4×Q8—441no—
426C4×Q8—441no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4C22⋊D1111yescharacteristic
443C2×C22⋊C4C22⋊D1111yescharacteristic
444C2×C42—21no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42C22×D1111yescharacteristic
448C2×C42C22×D1111yescharacteristic
449#107—222no—
450#107—441no—
451C4⋊C8—441no—
452#103—222no—
453#103—222no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458#103—441no—
459#103—441no—
460C22⋊C8—222no—
461C22⋊C8—441no—
462C4×C8—222no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95C22⋊D1111yescharacteristic
473#95C22⋊D1111yescharacteristic
474C2×C11—42no—
475C2×C11#241811yescharacteristic
476C2×C11#310411yescharacteristic
477C2×C11#312111yescharacteristic
478C2×C11#327111yescharacteristic
479C2×C11D4×Q1611yescharacteristic
480C2×C11#329911yescharacteristic
481C2×C11#332711yescharacteristic
482C24C2×C22⋊D1111yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—112no—
489C2×Q8—112no—
490C2×Q8—112no—
491C2×Q8—112no—
492C2×Q8—224no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—442no—
502C2×Q8—442no—
503C2×Q8—444no—
504C2×Q8—444no—
505C2×Q8—444no—
506C2×Q8—444no—
507C2×Q8D4×D1112yes—
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—21no—
518C22×C4—221no—
519C22×C4—224no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C2×C22⋊D1111yescharacteristic
528C22×C4C2×C22⋊D1111yescharacteristic
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C23×D1111yescharacteristic
531Q16—228no—
532Q16—444no—
533C2×C8—112no—
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—
543C2×C8—221no—
544C2×C8—221no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—442no—
561C4⋊C4—442no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C22⋊C4—442no—
566C22⋊C4#432614yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—442no—
573C42—442no—
574C11#2490611yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23C2×#432612yes—
582C23C22×C22⋊D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587Q8—114no—
588Q8—222no—
589Q8—222no—
590Q8—222no—
591Q8—222no—
592Q8—222no—
593Q8—448no—
594Q8—441no—
595Q8—441no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
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—41no—
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—41no—
624C2×C4—41no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—448no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4C2×#432612yes—
639C2×C4C2×#432612yes—
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#41×D1111yescharacteristic
645C2×C4#6704211yescharacteristic
646C8—222no—
647C8—441no—
648C8—441no—
649C8—441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22D4×C22⋊D1111yescharacteristic
658C22C22×#432611yescharacteristic
659C22#1062335311yescharacteristic
660C22#1062335911yescharacteristic
661C22#1062336011yescharacteristic
662C22#1062336711yescharacteristic
663C22#1062336911yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—224no—
674C4—442no—
675C4—881no—
676C4—881no—
677C4D11×#12311yescharacteristic
678C4#1062318511yescharacteristic
679C4#1062318811yescharacteristic
680C4#1062319011yescharacteristic
681C2—42no—
682C2#1307207511yescharacteristic
683C2#1307865111yescharacteristic
684C2#1307883911yescharacteristic
685C2#1308019711yescharacteristic
686C2D4×#432611yescharacteristic
687C2#1308048611yescharacteristic
688C2#1308087811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2423C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2423D11
hypocenterC11#24906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2423

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
4. #13070155C2semidirect
6. #13069938C2semidirect
8. #13069291C2semidirect
10. #13068960C2semidirect
11. #13068957C2semidirect
12. #13068869C2semidirect
13. #13068618C2semidirect
202. C11×C22⋊C4Q16semidirect
566. C22⋊C4#4326semidirect
574. C11#24906semidirect

Maximal subgroups

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

subgroupindex
C2×#106226632
C2×C4×#43262
C22⋊C4×Dic222
#130701552
#130700472
#130699382
#130698162
#130692912
#130692242
#130689602
#130689572
#130688692
#130686182
#130685502
C11×#24232
#2490611