Finite Group Databasebeta

← #14802014

Subgroups — #14802014

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622335C211yesmaximal, characteristic
2C2×#10622729C211yesmaximal, characteristic
3#13073094C211yesmaximal, characteristic
4#13071619C211yesmaximal, characteristic
5#13070089C211yesmaximal, characteristic, complemented
6#13070026C211yesmaximal, characteristic, complemented
7#13070010C211yesmaximal, characteristic, complemented
8#13069939C211yesmaximal, characteristic, complemented
9#13069375C211yesmaximal, characteristic, complemented
10#13069258C211yesmaximal, characteristic, complemented
11#13068956C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622729—24no—
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622563—21no—
38#10622563—21no—
39#10622559—21no—
40C22⋊C4×Dic11—21no—
41#10622548C2211yescharacteristic
42#10622548C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622335—24no—
49#10622274—21no—
50#10622274—21no—
51#10622268—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977—22no—
97#66977—22no—
98#66977D414yes—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×Dic44—22no—
106C2×Dic44—22no—
107C2×Dic44—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×C4⋊C8—22no—
111C11×C4⋊C8—41no—
112C11×C22⋊C8—22no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66882—22no—
124#66882—22no—
125#66882—22no—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#25206—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—81no—
158C22×Dic11—81no—
159C22×Dic11—81no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C2×D412yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—44no—
184C2×C8×C11#4112yes—
185C11×C22⋊C4—22no—
186C11×C22⋊C4Q1614yescomplemented
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11—81no—
206C4⋊Dic11—81no—
207C4⋊Dic11—81no—
208C4⋊Dic11—81no—
209C4⋊Dic11C2×D412yes—
210C4⋊Dic11#4112yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217Dic44—44no—
218C2×#484—111no—
219C2×#467—111no—
220#2502—111no—
221#2360—111no—
222#2083—111no—
223#2072—111no—
224#2068—111no—
225#2056—111no—
226#1947—111no—
227#1928—111no—
228#1878—111no—
229#1872—111no—
230#1850D1111yescharacteristic
231#1803—111no—
232C2×#340—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11#12112yes—
238C23×C11C2×Q1612yes—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
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—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11#12112yes—
258C2×C4×C11C2×Q1612yes—
259C2×C4×C11C2×Q1612yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
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—84no—
291C2×Dic11—84no—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—22no—
301C8×C11—41no—
302C8×C11—41no—
303C8×C11—41no—
304C22×Q16—111no—
305C23×C8C2×D1111yescharacteristic
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8—111no—
308C2×C4×Q8—111no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4—111no—
311#484—224no—
312#467—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×C4⋊C8C2×D1111yescharacteristic
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×C22⋊C8C2×D1111yescharacteristic
325#398—221no—
326#398—221no—
327#391—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—221no—
332#387—221no—
333#385—221no—
334#385—221no—
335#385—221no—
336#384—111no—
337#384—111no—
338C4×C4⋊C4—111no—
339C4×C22⋊C4—221no—
340C4×C22⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336C2×D1111yescharacteristic
348#336C2×D1111yescharacteristic
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11#46214yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C22×Q1611yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11#52911yescharacteristic
369C4×C11#53911yescharacteristic
370C4×C11#54611yescharacteristic
371C4×C11#54711yescharacteristic
372Dic11—42no—
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×Q8—111no—
382C23×C4—221no—
383C23×C4—221no—
384C23×C4C22×D1111yescharacteristic
385C2×Q16—222no—
386C2×Q16—222no—
387C2×Q16—441no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—41no—
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C22⋊Q8—114no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C4×Q8—222no—
400C4×Q8—441no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—441no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4D4411yescharacteristic
424C2×C22⋊C4D4411yescharacteristic
425C2×C42—221no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429#107—222no—
430#107—222no—
431#107—222no—
432C4⋊C8—22no—
433C4⋊C8—41no—
434#103—222no—
435#103—222no—
436#103—222no—
437#103—222no—
438#103—222no—
439#103—441no—
440C22⋊C8—22no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95D4411yescharacteristic
450#95D4411yescharacteristic
451C2×C11—24no—
452C2×C11#242511yescharacteristic
453C2×C11C2×#46211yescharacteristic
454C2×C11#304511yescharacteristic
455C2×C11#329911yescharacteristic
456C2×C11#331411yescharacteristic
457C2×C11#333811yescharacteristic
458C2×C11#334411yescharacteristic
459C24C2×D4411yescharacteristic
460C2×Q8—112no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—881no—
488C22×C4—881no—
489C22×C4—881no—
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4D4×D1112yes—
496C22×C4#434312yes—
497C22×C4C23×D1111yescharacteristic
498Q16—444no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—44no—
511C2×C8#434112yes—
512C4⋊C4—112no—
513C4⋊C4—112no—
514C4⋊C4—224no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4—881no—
532C4⋊C4—881no—
533C4⋊C4—881no—
534C22⋊C4—22no—
535C22⋊C4—224no—
536C22⋊C4—442no—
537C22⋊C4Dic4414yescomplemented
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—442no—
543C42—881no—
544C11#2520611yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23#6694812yes—
550C23C2×Dic4412yes—
551C23#6696212yes—
552C23C22×D4411yescharacteristic
553Q8—222no—
554Q8—222no—
555Q8—441no—
556Q8—441no—
557Q8—441no—
558Q8—441no—
559Q8—441no—
560Q8—441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—884no—
602C2×C4—884no—
603C2×C4#6694812yes—
604C2×C4C2×Dic4412yes—
605C2×C4C2×Dic4412yes—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4C2×#434311yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—22no—
613C8—41no—
614C8—41no—
615C8—41no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22#1062246214yes—
623C22C2×#6694811yescharacteristic
624C22#1062308511yescharacteristic
625C22#1062308611yescharacteristic
626C22C22×Dic4411yescharacteristic
627C22C2×#6696211yescharacteristic
628C22#1062328211yescharacteristic
629C22#1062328311yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—41no—
635C4—442no—
636C4—442no—
637C4—442no—
638C4—881no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062312211yescharacteristic
644C4#1062315511yescharacteristic
645C4#1062317611yescharacteristic
646C4#1062318611yescharacteristic
647C2—24no—
648C2#1307216511yescharacteristic
649C2C2×#1062246211yescharacteristic
650C2#1307815711yescharacteristic
651C2#1308049311yescharacteristic
652C2#1308069911yescharacteristic
653C2#1308100911yescharacteristic
654C2#1308107311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1850D11
hypocenterC11#25206
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
5. #13070089C2semidirect
6. #13070026C2semidirect
7. #13070010C2semidirect
8. #13069939C2semidirect
9. #13069375C2semidirect
10. #13069258C2semidirect
11. #13068956C2semidirect
13. #13068622C2semidirect
186. C11×C22⋊C4Q16semidirect
537. C22⋊C4Dic44semidirect
544. C11#25206semidirect

Maximal subgroups

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

subgroupindex
C2×#106223352
C2×#106227292
#130730942
#130716192
#130700892
#130700262
#130700102
#130699392
#130693752
#130692582
#130689562
#130689212
#130686222
C2×#106221892
C11×#18502
#2520611