Finite Group Databasebeta

← #14719907

Subgroups — #14719907

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2#13077245C211yesmaximal, characteristic
3C2×#10622332C211yesmaximal, characteristic
4#13066981C211yesmaximal, characteristic
5#13066980C211yesmaximal, characteristic
6#13066979C211yesmaximal, characteristic
7#13066970C214yesmaximal, complemented
8#13066958C214yesmaximal, complemented
9C11×#1472C211yesmaximal, characteristic
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×Q8×Dic11C411yescharacteristic
12C2×#66997C411yescharacteristic
13C2×#66977C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15#10623153—21no—
16#10623153—21no—
17#10623153—21no—
18#10623153—21no—
19#10623153—21no—
20#10623153—21no—
21#10623153—21no—
22#10623153—21no—
23C2×#66942C2212yes—
24C2×#66941C411yescharacteristic
25C2×#66940C411yescharacteristic
26C2×#66940C2212yes—
27C2×#66931C412yes—
28C2×#66930C412yes—
29C11×#407C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31#10622820C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622731—21no—
34M16×Dic11—21no—
35C2×#66879—21no—
36C2×Dic11⋊C8—21no—
37#10622332—21no—
38#10622332—21no—
39#10622332—21no—
40#10622332C2212yes—
41#10622332C2212yes—
42#10622332C2212yes—
43#10622331—21no—
44#10622331C2212yes—
45C11×#324C2214yes—
46#10622166C2214yes—
47#10622107C2214yes—
48#10622107C2214yes—
49C22×Q8×C11C2×C411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11C2×C411yescharacteristic
52C23×Dic11C2×C411yescharacteristic
53C22×Dic22C2×C412yes—
54C22×Dic22C2×C411yescharacteristic
55C2×C11×M16—21no—
56C22×C8×C11—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C22⋊Dic11C2×C412yes—
65Q8×Dic11—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68Q8×Dic11—21no—
69#66997—21no—
70#66997—21no—
71#66997—21no—
72#66997—21no—
73C2×C4⋊Dic11C2×C412yes—
74C2×C4⋊Dic11C2×C411yescharacteristic
75#66977—21no—
76#66977—21no—
77#66977—21no—
78#66977—21no—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2×C412yes—
81C2×Dic11⋊C4C2×C412yes—
82C2×Dic11⋊C4C2×C412yes—
83C2×Dic11⋊C4C2312yes—
84C2×C4×Dic11C2×C412yes—
85C2×C4×Dic11C2×C412yes—
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×#4318—21no—
99C22×C11⋊C8—21no—
100#66942—22no—
101#66942—22no—
102#66942—22no—
103#66942—22no—
104#66941—21no—
105#66941—21no—
106#66941—21no—
107#66941—21no—
108#66940—21no—
109#66940—21no—
110#66940—21no—
111#66940—21no—
112#66940—22no—
113#66940—22no—
114#66940—22no—
115#66940—22no—
116#66931—22no—
117#66931—22no—
118#66931—22no—
119#66931—22no—
120#66930—22no—
121#66930—22no—
122#66930—22no—
123#66930—22no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×C22⋊C8C2312yes—
127C11×C22⋊C8C2312yes—
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130C22⋊(C11⋊C8)C2312yes—
131C22⋊(C11⋊C8)C2312yes—
132#66879—22no—
133#66879—22no—
134#66879—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139C8×Dic11—22no—
140#17404—111nomaximal, Sylow
141C24×C11C22×C411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—24no—
155C22×Dic11—42no—
156C22×Dic11C22⋊C411yescharacteristic
157C22×Dic11C22⋊C411yescharacteristic
158C22×Dic11C22⋊C411yescharacteristic
159C22×Dic11C22⋊C411yescharacteristic
160C22×Dic11C22⋊C411yescharacteristic
161C22×Dic11C22⋊C411yescharacteristic
162C22×Dic11C22⋊C411yescharacteristic
163C22×Dic11C22⋊C411yescharacteristic
164C22×Dic11C22×C412yes—
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C412yes—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—44no—
175C2×Dic22—42no—
176C11×M16—42no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—42no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192Dic11⋊C4—22no—
193Dic11⋊C4—22no—
194Dic11⋊C4—22no—
195Dic11⋊C4—22no—
196Dic11⋊C4—22no—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202C4×Dic11—22no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11C22⋊C411yescharacteristic
207C4×Dic11C22⋊C411yescharacteristic
208C4×Dic11C22⋊C411yescharacteristic
209C4×Dic11C22⋊C411yescharacteristic
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C2×D411yescharacteristic
215C4×Dic11C2×D411yescharacteristic
216C4×Dic11C2×D411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222#4318—42no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—42no—
226C2×#533—111no—
227#2920—111no—
228C2×#432—111no—
229#1472—111no—
230#1472—111no—
231#1472—111no—
232#1472D1111yescharacteristic
233#1470—114no—
234#1467—114no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—41no—
238C23×C11C2×C22⋊C411yescharacteristic
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C23×C411yescharacteristic
241Q8×C11—42no—
242Q8×C11—42no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—42no—
272C2×Dic11#10114yes—
273C2×Dic11C2×C22⋊C411yescharacteristic
274C2×Dic11C2×C22⋊C411yescharacteristic
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281Dic22—44no—
282Dic22—44no—
283Dic22—42no—
284Dic22—42no—
285C8×C11—42no—
286C8×C11—42no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289#533—221no—
290#533—221no—
291#533—221no—
292#533—221no—
293#533—221no—
294#533—221no—
295#533—221no—
296#533—221no—
297C2×C4⋊Q8—111no—
298C2×C4⋊Q8—111no—
299C2×#125—112no—
300C2×C22⋊Q8—111no—
301C2×C22⋊Q8—112no—
302C2×C22⋊Q8C2×D1111yescharacteristic
303C2×C4×Q8—111no—
304C2×C4×Q8—112no—
305C2×C4×Q8—111no—
306C2×#117—112no—
307C22×C42—111no—
308#432—112no—
309#432—112no—
310#432—112no—
311#432—221no—
312#432—221no—
313#432—221no—
314#431—112no—
315#431—221no—
316#423—221no—
317C2×C4⋊C8—221no—
318#407—111no—
319#407C2×D1111yescharacteristic
320C2×C22⋊C8—111no—
321C2×C22⋊C8C2×D1111yescharacteristic
322C4×M16—221no—
323C2×#97—221no—
324#324—114no—
325#324—114no—
326#324—114no—
327#324C2×D1114yes—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—44no—
336C22×C11C2×#10112yes—
337C22×C11C22×C22⋊C411yescharacteristic
338C22×C11#56812yes—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11#41012yes—
345Dic11—21no—
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—21no—
350Dic11—21no—
351Dic11—42no—
352Dic11—42no—
353Dic11C2×#10112yes—
354Dic11C2×#10112yes—
355C22×Q8—112no—
356C22×Q8—111no—
357C22×Q8C4×D1111yescharacteristic
358C23×C4—111no—
359C23×C4—111no—
360C23×C4C22×D1111yescharacteristic
361C2×M16—21no—
362C2×M16—221no—
363C22×C8—21no—
364C22×C8—221no—
365C4⋊Q8—221no—
366C4⋊Q8—221no—
367C4⋊Q8—221no—
368C4⋊Q8—221no—
369C4⋊Q8—221no—
370C4⋊Q8—221no—
371C4⋊Q8—221no—
372C4⋊Q8—221no—
373#125—222no—
374#125—222no—
375#125—222no—
376#125—222no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—222no—
382C22⋊Q8—222no—
383C22⋊Q8—222no—
384C22⋊Q8—222no—
385C22⋊Q8—221no—
386C22⋊Q8—221no—
387C22⋊Q8—221no—
388C22⋊Q8—221no—
389C4×Q8—221no—
390C4×Q8—221no—
391C4×Q8—221no—
392C4×Q8—221no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—222no—
397C4×Q8—221no—
398C4×Q8—221no—
399C4×Q8—221no—
400C4×Q8—221no—
401#117—222no—
402#117—222no—
403#117—222no—
404#117—222no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—112no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4C4×D1111yescharacteristic
413C2×C4⋊C4C22×D1112yes—
414C2×C22⋊C4—112no—
415C2×C22⋊C4C4×D1112yes—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—112no—
429C2×C42—112no—
430C4⋊C8—222no—
431C4⋊C8—222no—
432C4⋊C8—222no—
433C4⋊C8—222no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—112no—
437C22⋊C8—112no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8C22×D1112yes—
441C22⋊C8C22×D1112yes—
442#97—222no—
443#97—222no—
444#97—222no—
445C4×C8—222no—
446C2×C11—22no—
447C2×C11—22no—
448C2×C11—41no—
449C2×C11#287911yescharacteristic
450C2×C11C2×#41011yescharacteristic
451C2×C11C22×#10111yescharacteristic
452C24C2×C4×D1111yescharacteristic
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—42no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—444no—
461C2×Q8—442no—
462C22×C4—42no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—112no—
476C22×C4—112no—
477C22×C4—224no—
478C22×C4—442no—
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×C4×D1112yes—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487M16—42no—
488M16—442no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—42no—
492C2×C8—222no—
493C2×C8—222no—
494C2×C8—442no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C42—111no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42—111no—
522C42—111no—
523C42—111no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—222no—
534C42—222no—
535C42—222no—
536C42—222no—
537C11#1740411yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—41no—
541C23C22⋊C4×D1111yescharacteristic
542C23C22⋊C4×D1111yescharacteristic
543C23C22×C4×D1111yescharacteristic
544Q8—42no—
545Q8—42no—
546Q8—442no—
547Q8—444no—
548Q8—444no—
549Q8—442no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—111no—
561C2×C4—111no—
562C2×C4—114no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—111no—
566C2×C4—111no—
567C2×C4—111no—
568C2×C4—111no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—442no—
584C2×C4C22⋊C4×D1111yescharacteristic
585C2×C4C22⋊C4×D1111yescharacteristic
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4C2×D4×D1111yescharacteristic
588C8—42no—
589C8—42no—
590C8—442no—
591C8—442no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—44no—
600C22D11×#10112yes—
601C22C2×C22⋊C4×D1111yescharacteristic
602C22#1062328112yes—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—112no—
609C4—112no—
610C4—221no—
611C4—221no—
612C4—221no—
613C4—221no—
614C4—221no—
615C4—221no—
616C4—442no—
617C4—442no—
618C4#1062235312yes—
619C2—22no—
620C2—22no—
621C2—41no—
622C2#1307705811yescharacteristic
623C2C2×#1062235311yescharacteristic
624C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1472C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1472D11
hypocenterC11#17404
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
7. #13066970C2semidirect
8. #13066958C2semidirect
537. C11#17404semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
#130772452
C2×#106223322
#130669812
#130669802
#130669792
#130669702
#130669582
C11×#14722
#1740411