Finite Group Databasebeta

← #14720044

Subgroups — #14720044

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623087C211yesmaximal, characteristic
2#13077651C211yesmaximal, characteristic, complemented
3#13066986C211yesmaximal, characteristic, complemented
4#13066983C211yesmaximal, characteristic, complemented
5#13066981C211yesmaximal, characteristic, complemented
6#13066979C211yesmaximal, characteristic, complemented
7#13066965C211yesmaximal, characteristic, complemented
8#13066962C211yesmaximal, characteristic, complemented
9#13066952C211yesmaximal, characteristic, complemented
10#13066948C211yesmaximal, characteristic, complemented
11#13066942C211yesmaximal, characteristic, complemented
12#13066932C211yesmaximal, characteristic, complemented
13#13066928C211yesmaximal, characteristic, complemented
14C2×#10622106C211yesmaximal, characteristic, complemented
15C11×#2974C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66990C411yescharacteristic
18C2×#66988C411yescharacteristic
19C2×#66982C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23#10623087—21no—
24#10623087—21no—
25#10623087—21no—
26#10623087—21no—
27#10623087—21no—
28#10623087—21no—
29#10623087—21no—
30#10623087—21no—
31C2×#66951C411yescharacteristic
32C2×#66949C411yescharacteristic
33C2×#66938C411yescharacteristic
34C2×#66936C411yescharacteristic
35C2×C22⋊C4×D11C411yescharacteristic
36C2×#66930C411yescharacteristic
37C2×#66929C2211yescharacteristic
38C2×#66925C2211yescharacteristic
39C11×#436—21no—
40C11×#435—21no—
41C11×#435—21no—
42C8×D4×C11—21no—
43C11×#432C2211yescharacteristic, complemented
44C11×#431C2211yescharacteristic, complemented
45C11×#407C2211yescharacteristic
46C11×#407C2211yescharacteristic, complemented
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic, complemented
49#10622820C2211yescharacteristic
50#10622820C2211yescharacteristic, complemented
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622625—21no—
54#10622624—21no—
55#10622624—21no—
56D4×C11⋊C8—21no—
57#10622539C2211yescharacteristic, complemented
58#10622538C2211yescharacteristic, complemented
59#10622107C2211yescharacteristic, complemented
60#10622107C2211yescharacteristic, complemented
61#10622107C2211yescharacteristic, complemented
62#10622107C2211yescharacteristic, complemented
63#10622107C2211yescharacteristic, complemented
64#10622107C2211yescharacteristic, complemented
65#10622107C2211yescharacteristic, complemented
66#10622107C2211yescharacteristic, complemented
67#10622106C2211yescharacteristic
68#10622106C2211yescharacteristic
69#10622106C2211yescharacteristic
70#10622106C2211yescharacteristic
71#10622106C2211yescharacteristic
72#10622106C2211yescharacteristic
73#10622106C2211yescharacteristic
74#10622106C2211yescharacteristic
75C24×D11C2×C411yescharacteristic
76C22×D4×C11C2×C411yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11C2×C411yescharacteristic
80C22×C22⋊D11C2×C411yescharacteristic
81C23×Dic11C2×C411yescharacteristic
82C22×C4×D11C2×C411yescharacteristic
83C22×C4×D11C2×C411yescharacteristic
84C22×Dic22C2×C411yescharacteristic
85C2×C11×M16—21no—
86C2×C11×M16—21no—
87C22×C8×C11—21no—
88C22×C8×C11—21no—
89C4×D4×C11D411yescharacteristic
90C4×D4×C11D411yescharacteristic
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C4×D4×C11D411yescharacteristic
94C4×D4×C11D411yescharacteristic
95C4×D4×C11D411yescharacteristic
96C4×D4×C11D411yescharacteristic
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11C2×C411yescharacteristic
102C2×C22⋊Dic11C2×C411yescharacteristic
103C2×C22⋊Dic11C2×C411yescharacteristic
104C2×C22⋊Dic11C2×C411yescharacteristic
105#66990—21no—
106#66990—21no—
107#66990—21no—
108#66990—21no—
109#66988—21no—
110#66988—21no—
111#66988—21no—
112#66988—21no—
113#66982—21no—
114#66982—21no—
115#66982—21no—
116#66982—21no—
117C4×C22⋊D11—21no—
118C4×C22⋊D11—21no—
119C4×C22⋊D11—21no—
120C4×C22⋊D11—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4C2×C411yescharacteristic
126C2×(C2×D11)⋊C4C2×C411yescharacteristic
127C2×(C2×D11)⋊C4C2×C411yescharacteristic
128C2×(C2×D11)⋊C4C2×C411yescharacteristic
129C2×(C2×D11)⋊C4C2×C411yescharacteristic
130C2×(C2×D11)⋊C4C2×C411yescharacteristic
131C2×(C2×D11)⋊C4C2311yescharacteristic
132C2×(C2×D11)⋊C4C2311yescharacteristic
133C2×C4⋊Dic11C2×C411yescharacteristic
134#66977—21no—
135#66977—21no—
136#66977—21no—
137#66977—21no—
138C2×Dic11⋊C4C2×C411yescharacteristic
139C2×Dic11⋊C4C2×C411yescharacteristic
140C2×Dic11⋊C4C2×C411yescharacteristic
141C2×Dic11⋊C4C2×C411yescharacteristic
142C2×Dic11⋊C4C2311yescharacteristic
143C2×Dic11⋊C4C2311yescharacteristic
144C2×C4×Dic11C2×C411yescharacteristic
145C2×C4×Dic11C2×C411yescharacteristic
146C2×#4318—21no—
147C2×#4318—21no—
148C22×C11⋊C8—21no—
149C22×C11⋊C8—21no—
150#66951—21no—
151#66951—21no—
152#66951—21no—
153#66951—21no—
154#66949—21no—
155#66949—21no—
156#66949—21no—
157#66949—21no—
158#66938—21no—
159#66938—21no—
160#66938—21no—
161#66938—21no—
162#66936—21no—
163#66936—21no—
164#66936—21no—
165#66936—21no—
166C22⋊C4×D11—21no—
167C22⋊C4×D11—21no—
168C22⋊C4×D11—21no—
169C22⋊C4×D11—21no—
170#66930—21no—
171#66930—21no—
172#66930—21no—
173#66930—21no—
174#66929—21no—
175#66929—21no—
176#66929—21no—
177#66929—21no—
178#66925—21no—
179#66925—21no—
180#66925—21no—
181#66925—21no—
182C11×C4⋊C8—21no—
183C11×C4⋊C8—21no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8—21no—
187C11×C22⋊C8—21no—
188C11×C22⋊C8C2311yescharacteristic
189C11×C22⋊C8C2311yescharacteristic
190C11×C22⋊C8C2311yescharacteristic
191C11×C22⋊C8C2311yescharacteristic
192C11×#97—21no—
193C4×C8×C11—21no—
194C22⋊(C11⋊C8)—21no—
195C22⋊(C11⋊C8)—21no—
196C22⋊(C11⋊C8)—21no—
197C22⋊(C11⋊C8)—21no—
198C22⋊(C11⋊C8)C2311yescharacteristic
199C22⋊(C11⋊C8)C2311yescharacteristic
200C22⋊(C11⋊C8)C2311yescharacteristic
201C22⋊(C11⋊C8)C2311yescharacteristic
202C4⋊(C11⋊C8)—21no—
203C4⋊(C11⋊C8)—21no—
204#66867—21no—
205C4×C11⋊C8—21no—
206#17422—111nomaximal, Sylow
207C24×C11C22×C411yescharacteristic
208C24×C11C22×C411yescharacteristic
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—22no—
212C23×D11—41no—
213C23×D11—42no—
214C23×D11—81no—
215C23×D11C22×C411yescharacteristic
216C23×D11C22×C411yescharacteristic
217C2×D4×C11—42no—
218C2×D4×C11C22⋊C411yescharacteristic
219C2×D4×C11C22⋊C411yescharacteristic
220C2×D4×C11C22⋊C411yescharacteristic
221C2×D4×C11C22⋊C411yescharacteristic
222C22×C4×C11—81no—
223C22×C4×C11—81no—
224C22×C4×C11C22×C411yescharacteristic
225C22×C4×C11C22×C411yescharacteristic
226C22×C4×C11C22×C411yescharacteristic
227C22×C4×C11C22×C411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11—21no—
238C2×C22⋊D11—21no—
239C2×C22⋊D11—21no—
240C2×C22⋊D11—21no—
241C2×C22⋊D11—22no—
242C2×C22⋊D11—41no—
243C2×C22⋊D11—81no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—42no—
247C22×Dic11C22×C411yescharacteristic
248C22×Dic11C22×C411yescharacteristic
249C22×Dic11C22×C411yescharacteristic
250C22×Dic11C22×C411yescharacteristic
251C22×Dic11C22×C411yescharacteristic
252C22×Dic11C22×C411yescharacteristic
253C2×C4×D11—22no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—41no—
259C2×C4×D11—81no—
260C2×Dic22—21no—
261C2×Dic22—21no—
262C2×Dic22—81no—
263C11×M16—81no—
264C11×M16—81no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—81no—
270C2×C8×C11—81no—
271C11×C4⋊C4C22⋊C411yescharacteristic
272C11×C4⋊C4C22⋊C411yescharacteristic
273C11×C4⋊C4C22⋊C411yescharacteristic
274C11×C4⋊C4C22⋊C411yescharacteristic
275C11×C22⋊C4C22⋊C411yescharacteristic
276C11×C22⋊C4C22⋊C411yescharacteristic
277C11×C22⋊C4C22⋊C411yescharacteristic
278C11×C22⋊C4C22⋊C411yescharacteristic
279C11×C22⋊C4C22⋊C411yescharacteristic
280C11×C22⋊C4C22⋊C411yescharacteristic
281C11×C22⋊C4C22⋊C411yescharacteristic
282C11×C22⋊C4C22⋊C411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C22⋊Dic11—21no—
288C22⋊Dic11—21no—
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291C22⋊Dic11—21no—
292C22⋊Dic11—21no—
293C22⋊Dic11—21no—
294C22⋊Dic11—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—21no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—21no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325C4×Dic11—21no—
326C4×Dic11—21no—
327C4×Dic11—21no—
328C4×Dic11—21no—
329#4318—81no—
330#4318—81no—
331C2×C11⋊C8—21no—
332C2×C11⋊C8—21no—
333C2×C11⋊C8—21no—
334C2×C11⋊C8—21no—
335C2×C11⋊C8—81no—
336C2×C11⋊C8—81no—
337C2×#551—111no—
338#2974—111no—
339#2974D1111yescharacteristic, complemented
340#1473—111no—
341#1473—111no—
342#1472—111no—
343#1472—111no—
344#1468—111no—
345#1468—111no—
346#1465—111no—
347#1464—111no—
348#1462—111no—
349#1459—111no—
350#1458—111no—
351C2×#323—111no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—22no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11C2×C22⋊C411yescharacteristic
361C23×C11C2×C22⋊C411yescharacteristic
362C23×C11C2×C22⋊C411yescharacteristic
363C23×C11C2×C22⋊C411yescharacteristic
364C23×C11C23×C411yescharacteristic
365C22×D11—21no—
366C22×D11—21no—
367C22×D11—21no—
368C22×D11—21no—
369C22×D11—21no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—81no—
379C22×D11—81no—
380C22×D11—84no—
381C22×D11—84no—
382C22×D11#13112yes—
383D4×C11—22no—
384D4×C11—22no—
385D4×C11—41no—
386D4×C11—41no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11C2×C22⋊C411yescharacteristic
402C2×C4×C11C2×C22⋊C411yescharacteristic
403C2×C4×C11C2×C22⋊C411yescharacteristic
404C2×C4×C11C2×C22⋊C411yescharacteristic
405C2×C4×C11C2×C22⋊C411yescharacteristic
406C2×C4×C11C2×C22⋊C411yescharacteristic
407C2×C4×C11C2×C22⋊C411yescharacteristic
408C2×C4×C11C2×C22⋊C411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C22⋊D11—42no—
412C22⋊D11—42no—
413C22⋊D11—81no—
414C22⋊D11—81no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—21no—
418C2×Dic11—21no—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—42no—
426C2×Dic11—42no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C4×D11—42no—
432C4×D11—42no—
433C4×D11—81no—
434C4×D11—81no—
435Dic22—81no—
436Dic22—81no—
437C8×C11—41no—
438C8×C11—41no—
439C8×C11—41no—
440C8×C11—41no—
441C11⋊C8—41no—
442C11⋊C8—41no—
443C11⋊C8—41no—
444C11⋊C8—41no—
445#551—221no—
446#551—221no—
447#551—221no—
448#551—221no—
449#551—221no—
450#551—221no—
451#551—221no—
452#551—221no—
453C2×#126—111no—
454C2×#126—111no—
455C2×#124—111no—
456C2×#123—111no—
457C2×#123—111no—
458C2×#123—111no—
459C2×C22⋊Q8—111no—
460C2×C22⋊Q8—111no—
461C2×#120—111no—
462C2×C4×D4—111no—
463C2×C4×D4C2×D1111yescharacteristic
464C2×#117—111no—
465C2×#117—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468#436—21no—
469#436—221no—
470#435—21no—
471#435—21no—
472#435—221no—
473#435—221no—
474C8×D4—21no—
475C8×D4—221no—
476#432—111no—
477#432C2×D1111yescharacteristic, complemented
478#431—111no—
479#431C2×D1111yescharacteristic, complemented
480#407—111no—
481#407—111no—
482#407C2×D1111yescharacteristic
483#407C2×D1111yescharacteristic, complemented
484C2×C22⋊C8—111no—
485C2×C22⋊C8—111no—
486C2×C22⋊C8C2×D1111yescharacteristic
487C2×C22⋊C8C2×D1111yescharacteristic, complemented
488#324—111no—
489#324—111no—
490#324—111no—
491#324—111no—
492#324—111no—
493#324—111no—
494#324—111no—
495#324—111no—
496#323—111no—
497#323—111no—
498#323—111no—
499#323—111no—
500#323—111no—
501#323—111no—
502#323—111no—
503#323—111no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—81no—
520C22×C11—81no—
521C22×C11#41312yes—
522C22×C11C22×C22⋊C411yescharacteristic
523C22×C11C2×#13111yescharacteristic
524C22×C11#56811yescharacteristic
525C2×D11—22no—
526C2×D11—42no—
527C2×D11—41no—
528C2×D11—41no—
529C2×D11—42no—
530C2×D11—41no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—84no—
534C2×D11—84no—
535C2×D11—81no—
536C2×D11—81no—
537C4×C11—21no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—21no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—21no—
547Dic11—41no—
548Dic11—41no—
549Dic11—41no—
550Dic11—41no—
551Dic11—41no—
552Dic11—41no—
553C25—111no—
554C22×Q8—111no—
555C22×D4—111no—
556C22×D4—111no—
557C22×D4C4×D1111yescharacteristic
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C2×M16—21no—
564C2×M16—21no—
565C2×M16—221no—
566C2×M16—221no—
567C22×C8—21no—
568C22×C8—21no—
569C22×C8—221no—
570C22×C8—221no—
571#126—221no—
572#126—221no—
573#126—221no—
574#126—221no—
575#126—221no—
576#126—221no—
577#126—221no—
578#126—221no—
579#124—221no—
580#124—221no—
581#124—221no—
582#124—221no—
583#123—221no—
584#123—221no—
585#123—221no—
586#123—221no—
587#123—221no—
588#123—221no—
589#123—221no—
590#123—221no—
591#123—221no—
592#123—221no—
593#123—221no—
594#123—221no—
595C22⋊Q8—221no—
596C22⋊Q8—221no—
597C22⋊Q8—221no—
598C22⋊Q8—221no—
599C22⋊Q8—221no—
600C22⋊Q8—221no—
601C22⋊Q8—221no—
602C22⋊Q8—221no—
603#120—221no—
604#120—221no—
605#120—221no—
606#120—221no—
607C4×D4—221no—
608C4×D4—221no—
609C4×D4—221no—
610C4×D4—221no—
611C4×D4D4411yescharacteristic
612C4×D4D4411yescharacteristic
613C4×D4D4411yescharacteristic
614C4×D4D4411yescharacteristic
615C4×D4C22⋊D1111yescharacteristic
616C4×D4C22⋊D1111yescharacteristic
617C4×D4C22⋊D1111yescharacteristic
618C4×D4C22⋊D1111yescharacteristic
619#117—221no—
620#117—221no—
621#117—221no—
622#117—221no—
623#117—221no—
624#117—221no—
625#117—221no—
626#117—221no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4C4×D1111yescharacteristic
635C2×C22⋊C4—111no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—111no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—111no—
642C2×C22⋊C4—111no—
643C2×C22⋊C4—111no—
644C2×C22⋊C4—111no—
645C2×C22⋊C4—111no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4C4×D1111yescharacteristic
656C2×C22⋊C4C4×D1111yescharacteristic
657C2×C42—111no—
658C2×C42—111no—
659C2×C42C22×D1111yescharacteristic
660C4⋊C8—21no—
661C4⋊C8—21no—
662C4⋊C8—221no—
663C4⋊C8—221no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—111no—
669C22⋊C8—111no—
670C22⋊C8—111no—
671C22⋊C8—111no—
672C22⋊C8—221no—
673C22⋊C8—221no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8C22×D1111yescharacteristic
677C22⋊C8C22×D1111yescharacteristic
678C22⋊C8C22×D1111yescharacteristic
679C22⋊C8C22×D1111yescharacteristic
680#97—21no—
681#97—221no—
682C4×C8—21no—
683C4×C8—221no—
684C2×C11—21no—
685C2×C11—21no—
686C2×C11—22no—
687C2×C11—41no—
688C2×C11—41no—
689C2×C11—41no—
690C2×C11#288011yescharacteristic
691C2×C11#288311yescharacteristic
692C2×C11C2×#41311yescharacteristic
693D11—42no—
694D11—81no—
695C24—111no—
696C24—111no—
697C24—222no—
698C24—221no—
699C24—221no—
700C24—441no—
701C24—442no—
702C24—881no—
703C24C2×C4×D1111yescharacteristic
704C24C2×C4×D1111yescharacteristic
705C2×Q8—221no—
706C2×Q8—221no—
707C2×Q8—881no—
708C2×D4—42no—
709C2×D4—222no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—221no—
714C2×D4—441no—
715C2×D4—881no—
716C2×D4(C2×D11)⋊C411yescharacteristic
717C2×D4(C2×D11)⋊C411yescharacteristic
718C2×D4(C2×D11)⋊C411yescharacteristic
719C2×D4(C2×D11)⋊C411yescharacteristic
720C22×C4—81no—
721C22×C4—81no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—111no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—222no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—441no—
736C22×C4—442no—
737C22×C4—881no—
738C22×C4C2×C4×D1111yescharacteristic
739C22×C4C2×C4×D1111yescharacteristic
740C22×C4C2×C4×D1111yescharacteristic
741C22×C4C2×C4×D1111yescharacteristic
742C22×C4C2×D4411yescharacteristic
743C22×C4C2×D4411yescharacteristic
744C22×C4C2×D4411yescharacteristic
745C22×C4C2×D4411yescharacteristic
746C22×C4C2×C22⋊D1111yescharacteristic
747C22×C4C2×C22⋊D1111yescharacteristic
748C22×C4C2×C22⋊D1111yescharacteristic
749C22×C4C2×C22⋊D1111yescharacteristic
750C22×C4C23×D1111yescharacteristic
751M16—81no—
752M16—81no—
753M16—881no—
754M16—881no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—81no—
760C2×C8—81no—
761C2×C8—221no—
762C2×C8—221no—
763C2×C8—221no—
764C2×C8—221no—
765C2×C8—881no—
766C2×C8—881no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—221no—
770C4⋊C4—221no—
771C4⋊C4—221no—
772C4⋊C4—221no—
773C4⋊C4—221no—
774C4⋊C4—221no—
775C4⋊C4—221no—
776C4⋊C4—221no—
777C4⋊C4—221no—
778C4⋊C4—221no—
779C4⋊C4—221no—
780C4⋊C4—221no—
781C4⋊C4(C2×D11)⋊C411yescharacteristic
782C4⋊C4(C2×D11)⋊C411yescharacteristic
783C4⋊C4(C2×D11)⋊C411yescharacteristic
784C4⋊C4(C2×D11)⋊C411yescharacteristic
785C22⋊C4—221no—
786C22⋊C4—221no—
787C22⋊C4—221no—
788C22⋊C4—221no—
789C22⋊C4—221no—
790C22⋊C4—221no—
791C22⋊C4—221no—
792C22⋊C4—221no—
793C22⋊C4—221no—
794C22⋊C4—221no—
795C22⋊C4—221no—
796C22⋊C4—221no—
797C22⋊C4—221no—
798C22⋊C4—221no—
799C22⋊C4—221no—
800C22⋊C4—221no—
801C22⋊C4—221no—
802C22⋊C4—221no—
803C22⋊C4—221no—
804C22⋊C4—221no—
805C22⋊C4—221no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C22⋊C4—221no—
809C22⋊C4(C2×D11)⋊C411yescharacteristic
810C22⋊C4(C2×D11)⋊C411yescharacteristic
811C22⋊C4(C2×D11)⋊C411yescharacteristic
812C22⋊C4(C2×D11)⋊C411yescharacteristic
813C22⋊C4(C2×D11)⋊C411yescharacteristic
814C22⋊C4(C2×D11)⋊C411yescharacteristic
815C22⋊C4(C2×D11)⋊C411yescharacteristic
816C22⋊C4(C2×D11)⋊C411yescharacteristic
817C42—221no—
818C42—221no—
819C42—221no—
820C42—221no—
821C42C2×D4411yescharacteristic
822C42C2×D4411yescharacteristic
823C42C2×C22⋊D1111yescharacteristic
824C42C2×C22⋊D1111yescharacteristic
825C11#1742211yescharacteristic, complemented, Sylow
826C23—22no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—112no—
835C23—221no—
836C23—221no—
837C23—221no—
838C23—221no—
839C23—221no—
840C23—442no—
841C23—442no—
842C23—441no—
843C23—441no—
844C23—442no—
845C23—441no—
846C23—441no—
847C23—442no—
848C23—881no—
849C23—881no—
850C23—884no—
851C23—884no—
852C23C2×(C2×D11)⋊C411yescharacteristic
853C23C2×(C2×D11)⋊C411yescharacteristic
854C23C2×(C2×D11)⋊C411yescharacteristic
855C23C2×(C2×D11)⋊C411yescharacteristic
856C23C22×C4×D1111yescharacteristic
857Q8—881no—
858Q8—881no—
859D4—22no—
860D4—22no—
861D4—41no—
862D4—41no—
863D4—442no—
864D4—442no—
865D4—881no—
866D4—881no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—221no—
891C2×C4—442no—
892C2×C4—442no—
893C2×C4—442no—
894C2×C4—442no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—881no—
900C2×C4—881no—
901C2×C4C2×(C2×D11)⋊C411yescharacteristic
902C2×C4C2×(C2×D11)⋊C411yescharacteristic
903C2×C4C2×(C2×D11)⋊C411yescharacteristic
904C2×C4C2×(C2×D11)⋊C411yescharacteristic
905C2×C4C2×(C2×D11)⋊C411yescharacteristic
906C2×C4C2×(C2×D11)⋊C411yescharacteristic
907C2×C4C2×(C2×D11)⋊C411yescharacteristic
908C2×C4C2×(C2×D11)⋊C411yescharacteristic
909C2×C4C22×D4411yescharacteristic
910C2×C4C22×C22⋊D1111yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—441no—
916C8—441no—
917C8—441no—
918C8—441no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—42no—
933C22—42no—
934C22—81no—
935C22—81no—
936C22—222no—
937C22—442no—
938C22—442no—
939C22—441no—
940C22—441no—
941C22—441no—
942C22—441no—
943C22—441no—
944C22—884no—
945C22—881no—
946C22—881no—
947C22—884no—
948C22#1062274512yes—
949C22D11×#13111yescharacteristic
950C22#1062328111yescharacteristic
951C22C22×(C2×D11)⋊C411yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—441no—
963C4—441no—
964C4—441no—
965C4—441no—
966C4—441no—
967C4—441no—
968C2—21no—
969C2—21no—
970C2—22no—
971C2—41no—
972C2—41no—
973C2—41no—
974C2—442no—
975C2—881no—
976C2#1307706311yescharacteristic
977C2#1307707611yescharacteristic
978C2C2×#1062274511yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2974C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenter#2974D11
hypocenterC11#17422
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13077651C2semidirect
3. #13066986C2semidirect
4. #13066983C2semidirect
5. #13066981C2semidirect
6. #13066979C2semidirect
7. #13066965C2semidirect
8. #13066962C2semidirect
9. #13066952C2semidirect
10. #13066948C2semidirect
11. #13066942C2semidirect
12. #13066932C2semidirect
13. #13066928C2semidirect
14. C2×#10622106C2semidirect
15. C11×#2974C2semidirect
43. C11×#432C22semidirect
44. C11×#431C22semidirect
46. C11×#407C22semidirect
48. C2×C11×C22⋊C8C22semidirect
50. #10622820C22semidirect
52. C2×C22⋊(C11⋊C8)C22semidirect
57. #10622539C22semidirect
58. #10622538C22semidirect
59. #10622107C22semidirect
60. #10622107C22semidirect
61. #10622107C22semidirect
62. #10622107C22semidirect
63. #10622107C22semidirect
64. #10622107C22semidirect
65. #10622107C22semidirect
66. #10622107C22semidirect
339. #2974D11semidirect
477. #432C2×D11semidirect
479. #431C2×D11semidirect
483. #407C2×D11semidirect
487. C2×C22⋊C8C2×D11semidirect
825. C11#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#106230872
#130776512
#130669862
#130669832
#130669812
#130669792
#130669652
#130669622
#130669522
#130669482
#130669422
#130669322
#130669282
C2×#106221062
C11×#29742
#1742211