Finite Group Databasebeta

← #14792582

Subgroups — #14792582

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622352C211yesmaximal, characteristic
2#13074413C211yesmaximal, characteristic
3#13071200C211yesmaximal, characteristic
4#13070010C211yesmaximal, characteristic, complemented
5#13069996C211yesmaximal, characteristic, complemented
6#13069939C211yesmaximal, characteristic, complemented
7#13069939C211yesmaximal, characteristic, complemented
8#13069487C211yesmaximal, characteristic, complemented
9#13069477C211yesmaximal, characteristic, complemented
10#13069306C211yesmaximal, characteristic, complemented
11#13069292C211yesmaximal, characteristic, complemented
12#13068926C211yesmaximal, characteristic
13#13068817C211yesmaximal, characteristic
14#13068552C211yesmaximal, characteristic
15C2×C11×#433C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×Dic44C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C11×#433—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40#10622595—21no—
41#10622593—21no—
42#10622587—21no—
43#10622587—21no—
44#10622565—21no—
45#10622565—21no—
46#10622556—21no—
47#10622556—21no—
48#10622542C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622541C2211yescharacteristic
56#10622352—24no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—41no—
69C22×Dic22—41no—
70C22×Dic22C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66979—41no—
89#66979—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977—22no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×Dic44—22no—
102C2×Dic44—22no—
103C2×Dic44—22no—
104C2×Dic44—22no—
105C2×Dic44—41no—
106C2×Dic44—41no—
107C11×C4⋊C8—22no—
108C11×C4⋊C8—22no—
109C11×C22⋊C8—22no—
110C11×C22⋊C8D414yes—
111C11×#97—22no—
112C4×C8×C11—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66882—41no—
129#66881—41no—
130#66880—22no—
131#66880—22no—
132#66880—22no—
133#66880—22no—
134#66880—41no—
135#66880—41no—
136#66880—41no—
137#66880—41no—
138#24514—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C2×Dic22—24no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
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—21no—
179C2×Dic22—21no—
180C2×Dic22—44no—
181C2×Dic22—44no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22#4112yes—
187C2×Dic22#4112yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C2×D412yes—
199C2×C8×C11C2×D412yes—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C22⋊Dic11—42no—
209C22⋊Dic11—42no—
210C22⋊Dic11—81no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221Dic11⋊C4—42no—
222Dic11⋊C4—81no—
223Dic11⋊C4—81no—
224C4×Dic11—42no—
225Dic44—44no—
226Dic44—44no—
227C2×#451—111no—
228C2×#433D1111yescharacteristic
229#2625—111no—
230#2310—111no—
231#2068—111no—
232#2066—111no—
233#2056—111no—
234#2056—111no—
235#1971—111no—
236#1969—111no—
237#1935—111no—
238#1933—111no—
239#1873—111no—
240#1854—111no—
241#1787—111no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11#12112yes—
249C23×C11C22×D411yescharacteristic
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
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—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11#12112yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—48no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300Dic22—22no—
301Dic22—22no—
302Dic22—22no—
303Dic22—22no—
304Dic22—48no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309Dic22—41no—
310Dic22—41no—
311Dic22—41no—
312Dic22—41no—
313C8×C11—22no—
314C8×C11—22no—
315C8×C11—41no—
316C8×C11—41no—
317C23×Q8—111no—
318C22×Q16—111no—
319C22×Q16—111no—
320C2×C22⋊Q8—111no—
321C2×#117—111no—
322C2×#117C2×D1111yescharacteristic
323#451—224no—
324#433—24no—
325C2×#107—111no—
326C2×#106—111no—
327C2×C4⋊C8C2×D1111yescharacteristic
328C2×C4⋊C8C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×C22⋊C8C2×D1111yescharacteristic
338C2×C22⋊C8C2×D1111yescharacteristic
339C2×#97C2×D1111yescharacteristic
340C2×C4×C8C2×D1111yescharacteristic
341#400—221no—
342#398—221no—
343#397—221no—
344#397—221no—
345#391—111no—
346#391—111no—
347#391—111no—
348#391—111no—
349#391—111no—
350#391—111no—
351#391—221no—
352#391—221no—
353#389—111no—
354#389—111no—
355#381—221no—
356#381—221no—
357#380—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×#12111yescharacteristic
370C22×C11#52511yescharacteristic
371C22×C11#53511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C22×C11#57811yescharacteristic
375C22×C11#57811yescharacteristic
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11#54611yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#55111yescharacteristic
384C4×C11#55111yescharacteristic
385Dic11—42no—
386Dic11—42no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—111no—
394C22×Q8—111no—
395C22×Q8—111no—
396C22×Q8—222no—
397C22×Q8—222no—
398C22×Q8—221no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—441no—
402C22×Q8—441no—
403C23×C4—221no—
404C23×C4C22×D1111yescharacteristic
405C2×Q16—222no—
406C2×Q16—222no—
407C2×Q16—222no—
408C2×Q16—222no—
409C2×Q16—441no—
410C2×Q16—441no—
411C22×C8C22×D1111yescharacteristic
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22⋊Q8—222no—
416C22⋊Q8—222no—
417#117—22no—
418#117—22no—
419#117—441no—
420#117—441no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4D4411yescharacteristic
430C2×C4⋊C4D4411yescharacteristic
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4D4411yescharacteristic
435C2×C22⋊C4D4411yescharacteristic
436C2×C42—221no—
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439#107—441no—
440#106—441no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443#103—222no—
444#103—222no—
445#103—222no—
446#103—222no—
447#103—441no—
448#103—441no—
449#103—441no—
450#103—441no—
451C22⋊C8—22no—
452C22⋊C8C22⋊D1114yes—
453#97—22no—
454C4×C8—22no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11—42no—
471C2×C11#241111yescharacteristic
472C2×C11#305911yescharacteristic
473C2×C11#306311yescharacteristic
474C2×C11#312111yescharacteristic
475C2×C11#312711yescharacteristic
476C2×C11#322311yescharacteristic
477C2×C11#322511yescharacteristic
478C24C2×D4411yescharacteristic
479C2×Q8—112no—
480C2×Q8—112no—
481C2×Q8—224no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—444no—
499C2×Q8—444no—
500C2×Q8—444no—
501C2×Q8—444no—
502C2×Q8—442no—
503C2×Q8—442no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—224no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4C2×D4411yescharacteristic
520C22×C4C2×D4411yescharacteristic
521C22×C4C2×D4411yescharacteristic
522C22×C4C2×D4411yescharacteristic
523C22×C4C2×D4411yescharacteristic
524C22×C4#433912yes—
525C22×C4C2×C22⋊D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—444no—
528Q16—444no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8C2×C22⋊D1112yes—
540C2×C8C2×C22⋊D1112yes—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—442no—
554C4⋊C4—881no—
555C4⋊C4—881no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—881no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—442no—
566C11#2451411yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#6698312yes—
574C23C22×D4411yescharacteristic
575Q8—222no—
576Q8—222no—
577Q8—222no—
578Q8—222no—
579Q8—448no—
580Q8—441no—
581Q8—441no—
582Q8—441no—
583Q8—441no—
584Q8—441no—
585Q8—441no—
586Q8—441no—
587Q8—441no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
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—222no—
607C2×C4—222no—
608C2×C4—448no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4#6698312yes—
632C2×C4C2×#433911yescharacteristic
633C2×C4#41×D1111yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C2×C4#6704211yescharacteristic
636C2×C4#6704211yescharacteristic
637C2×C4C22×C22⋊D1111yescharacteristic
638C8—22no—
639C8—22no—
640C8—41no—
641C8—41no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22#1062305511yescharacteristic
650C22#1062305611yescharacteristic
651C22#1062328211yescharacteristic
652C22#1062328411yescharacteristic
653C22#1062328411yescharacteristic
654C22#1062328411yescharacteristic
655C22C2×#6698311yescharacteristic
656C4—22no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—442no—
662C4—442no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4#1062305811yescharacteristic
670C4#1062305811yescharacteristic
671C4#1062336011yescharacteristic
672C4#1062336011yescharacteristic
673C2—42no—
674C2#1307199511yescharacteristic
675C2#1307827111yescharacteristic
676C2#1307830711yescharacteristic
677C2#1307884711yescharacteristic
678C2#1307891711yescharacteristic
679C2#1307970111yescharacteristic
680C2#1307972711yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#433D11
hypocenterC11#24514
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
4. #13070010C2semidirect
5. #13069996C2semidirect
6. #13069939C2semidirect
7. #13069939C2semidirect
8. #13069487C2semidirect
9. #13069477C2semidirect
10. #13069306C2semidirect
11. #13069292C2semidirect
566. C11#24514semidirect

Maximal subgroups

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

subgroupindex
C2×#106223522
#130744132
#130712002
#130700102
#130699962
#130699392
#130694872
#130694772
#130693062
#130692922
#130689262
#130688172
#130685522
C2×C11×#4332
#2451411