Finite Group Databasebeta

← #14720084

Subgroups — #14720084

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623071C211yesmaximal, characteristic
2#13077651C211yesmaximal, characteristic, complemented
3#13066986C211yesmaximal, characteristic, complemented
4#13066983C211yesmaximal, characteristic, complemented
5#13066977C211yesmaximal, characteristic, complemented
6#13066975C211yesmaximal, characteristic, complemented
7#13066965C211yesmaximal, characteristic, complemented
8#13066962C211yesmaximal, characteristic, complemented
9#13066952C211yesmaximal, characteristic, complemented
10#13066948C211yesmaximal, characteristic, complemented
11#13066945C211yesmaximal, characteristic, complemented
12#13066932C211yesmaximal, characteristic, complemented
13#13066928C211yesmaximal, characteristic, complemented
14C2×#10622107C211yesmaximal, characteristic, complemented
15C11×#2974C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66992C411yescharacteristic
18C2×#66992C411yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66982C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23#10623071—21no—
24#10623071—21no—
25#10623071—21no—
26#10623071—21no—
27#10623071—21no—
28#10623071—21no—
29#10623071—21no—
30#10623071—21no—
31C2×#66947C411yescharacteristic
32C2×#66942C411yescharacteristic
33C2×#66937C411yescharacteristic
34C2×(C22⋊D11)⋊C4C411yescharacteristic
35C2×(C22⋊D11)⋊C4C411yescharacteristic
36C2×#66932C411yescharacteristic
37C2×#66929C2211yescharacteristic
38C2×#66925C2211yescharacteristic
39C11×#436—21no—
40C11×#435—21no—
41C11×#435—21no—
42C8×D4×C11—21no—
43C11×#432C2211yescharacteristic
44C11×#431C2211yescharacteristic
45C11×#407C2211yescharacteristic
46C11×#407C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49#10622820C2211yescharacteristic
50#10622820C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53#10622625—21no—
54#10622624—21no—
55#10622624—21no—
56D4×C11⋊C8—21no—
57#10622539C2211yescharacteristic
58#10622538C2211yescharacteristic
59#10622107C2211yescharacteristic
60#10622107C2211yescharacteristic
61#10622107C2211yescharacteristic
62#10622107C2211yescharacteristic
63#10622107C2211yescharacteristic
64#10622107C2211yescharacteristic
65#10622107C2211yescharacteristic
66#10622107C2211yescharacteristic
67#10622106C2211yescharacteristic
68#10622106C2211yescharacteristic
69#10622106C2211yescharacteristic
70#10622106C2211yescharacteristic
71#10622106C2211yescharacteristic
72#10622106C2211yescharacteristic
73#10622106C2211yescharacteristic
74#10622106C2211yescharacteristic
75C22×D4×C11C2×C411yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11C2×C411yescharacteristic
79C22×C22⋊D11C2×C411yescharacteristic
80C22×C22⋊D11C2×C411yescharacteristic
81C22×C22⋊D11C2×C411yescharacteristic
82C23×Dic11C2×C411yescharacteristic
83C23×Dic11C2×C411yescharacteristic
84C22×D44C2×C411yescharacteristic
85C22×C4×D11C2×C411yescharacteristic
86C22×C4×D11C2×C411yescharacteristic
87C2×C11×M16—21no—
88C2×C11×M16—21no—
89C22×C8×C11—21no—
90C22×C8×C11—21no—
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C4×D4×C11D411yescharacteristic
94C4×D4×C11D411yescharacteristic
95C4×D4×C11D411yescharacteristic
96C4×D4×C11D411yescharacteristic
97C4×D4×C11D411yescharacteristic
98C4×D4×C11D411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11C2×C411yescharacteristic
104C2×C22⋊Dic11C2×C411yescharacteristic
105#66992—21no—
106#66992—21no—
107#66992—21no—
108#66992—21no—
109#66992—21no—
110#66992—21no—
111#66992—21no—
112#66992—21no—
113#66983—21no—
114#66983—21no—
115#66983—21no—
116#66983—21no—
117#66982—21no—
118#66982—21no—
119#66982—21no—
120#66982—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11—21no—
123C4×C22⋊D11—21no—
124C4×C22⋊D11—21no—
125C2×(C2×D11)⋊C4C2×C411yescharacteristic
126C2×(C2×D11)⋊C4C2×C411yescharacteristic
127C2×(C2×D11)⋊C4C2×C411yescharacteristic
128C2×(C2×D11)⋊C4C2×C411yescharacteristic
129C2×(C2×D11)⋊C4C2311yescharacteristic
130C2×(C2×D11)⋊C4C2311yescharacteristic
131C2×C4⋊Dic11C2×C411yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4C2×C411yescharacteristic
137C2×Dic11⋊C4C2×C411yescharacteristic
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#66947—21no—
151#66947—21no—
152#66947—21no—
153#66947—21no—
154#66942—21no—
155#66942—21no—
156#66942—21no—
157#66942—21no—
158#66937—21no—
159#66937—21no—
160#66937—21no—
161#66937—21no—
162(C22⋊D11)⋊C4—21no—
163(C22⋊D11)⋊C4—21no—
164(C22⋊D11)⋊C4—21no—
165(C22⋊D11)⋊C4—21no—
166(C22⋊D11)⋊C4—21no—
167(C22⋊D11)⋊C4—21no—
168(C22⋊D11)⋊C4—21no—
169(C22⋊D11)⋊C4—21no—
170#66932—21no—
171#66932—21no—
172#66932—21no—
173#66932—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#17427—111nomaximal, Sylow
207C24×C11C22×C411yescharacteristic
208C24×C11C22×C411yescharacteristic
209C23×D11C22×C411yescharacteristic
210C23×D11C22×C411yescharacteristic
211C2×D4×C11—42no—
212C2×D4×C11C22⋊C411yescharacteristic
213C2×D4×C11C22⋊C411yescharacteristic
214C2×D4×C11C22⋊C411yescharacteristic
215C2×D4×C11C22⋊C411yescharacteristic
216C22×C4×C11—81no—
217C22×C4×C11—81no—
218C22×C4×C11C22×C411yescharacteristic
219C22×C4×C11C22×C411yescharacteristic
220C22×C4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11—22no—
232C2×C22⋊D11—21no—
233C2×C22⋊D11—21no—
234C2×C22⋊D11—21no—
235C2×C22⋊D11—21no—
236C2×C22⋊D11—21no—
237C2×C22⋊D11—21no—
238C2×C22⋊D11—21no—
239C2×C22⋊D11—21no—
240C2×C22⋊D11—41no—
241C2×C22⋊D11—42no—
242C2×C22⋊D11—42no—
243C2×C22⋊D11—81no—
244C22×Dic11—22no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—41no—
250C22×Dic11—81no—
251C22×Dic11C22×C411yescharacteristic
252C22×Dic11C22×C411yescharacteristic
253C22×Dic11C22×C411yescharacteristic
254C22×Dic11C22×C411yescharacteristic
255C22×Dic11C22×C411yescharacteristic
256C22×Dic11C22×C411yescharacteristic
257C2×D44—21no—
258C2×D44—21no—
259C2×D44—81no—
260C2×C4×D11—22no—
261C2×C4×D11—21no—
262C2×C4×D11—21no—
263C2×C4×D11—21no—
264C2×C4×D11—21no—
265C2×C4×D11—41no—
266C2×C4×D11—81no—
267C11×M16—81no—
268C11×M16—81no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—81no—
274C2×C8×C11—81no—
275C11×C4⋊C4C22⋊C411yescharacteristic
276C11×C4⋊C4C22⋊C411yescharacteristic
277C11×C4⋊C4C22⋊C411yescharacteristic
278C11×C4⋊C4C22⋊C411yescharacteristic
279C11×C22⋊C4C22⋊C411yescharacteristic
280C11×C22⋊C4C22⋊C411yescharacteristic
281C11×C22⋊C4C22⋊C411yescharacteristic
282C11×C22⋊C4C22⋊C411yescharacteristic
283C11×C22⋊C4C22⋊C411yescharacteristic
284C11×C22⋊C4C22⋊C411yescharacteristic
285C11×C22⋊C4C22⋊C411yescharacteristic
286C11×C22⋊C4C22⋊C411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
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—
307C4⋊Dic11—21no—
308C4⋊Dic11—21no—
309Dic11⋊C4—21no—
310Dic11⋊C4—21no—
311Dic11⋊C4—21no—
312Dic11⋊C4—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×#553—111no—
338#2974—111no—
339#2974D1111yescharacteristic, complemented
340#1473—111no—
341#1473—111no—
342#1471—111no—
343#1471—111no—
344#1468—111no—
345#1468—111no—
346#1465—111no—
347#1464—111no—
348#1463—111no—
349#1459—111no—
350#1458—111no—
351C2×#324—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—21no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375D4×C11—22no—
376D4×C11—22no—
377D4×C11—41no—
378D4×C11—41no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C2×C22⋊C411yescharacteristic
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C2×C22⋊C411yescharacteristic
397C2×C4×C11C2×C22⋊C411yescharacteristic
398C2×C4×C11C2×C22⋊C411yescharacteristic
399C2×C4×C11C2×C22⋊C411yescharacteristic
400C2×C4×C11C2×C22⋊C411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C22⋊D11—42no—
404C22⋊D11—42no—
405C22⋊D11—42no—
406C22⋊D11—42no—
407C22⋊D11—42no—
408C22⋊D11—42no—
409C22⋊D11—81no—
410C22⋊D11—81no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—21no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—21no—
418C2×Dic11—21no—
419C2×Dic11—21no—
420C2×Dic11—42no—
421C2×Dic11—42no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—81no—
427C2×Dic11—81no—
428C2×Dic11#13112yes—
429D44—81no—
430D44—81no—
431C4×D11—42no—
432C4×D11—42no—
433C4×D11—81no—
434C4×D11—81no—
435C8×C11—41no—
436C8×C11—41no—
437C8×C11—41no—
438C8×C11—41no—
439C11⋊C8—41no—
440C11⋊C8—41no—
441C11⋊C8—41no—
442C11⋊C8—41no—
443#553—221no—
444#553—221no—
445#553—221no—
446#553—221no—
447#553—221no—
448#553—221no—
449#553—221no—
450#553—221no—
451C2×#126—111no—
452C2×#126—111no—
453C2×#125—111no—
454C2×#123—111no—
455C2×#123—111no—
456C2×#121—111no—
457C2×#121—111no—
458C2×#121—111no—
459C2×#121—111no—
460C2×C4×D4—111no—
461C2×C4×D4—111no—
462C2×C4×D4—111no—
463C2×C4×D4C2×D1111yescharacteristic
464C2×#117—111no—
465C22×C4⋊C4—111no—
466#436—21no—
467#436—221no—
468#435—21no—
469#435—21no—
470#435—221no—
471#435—221no—
472C8×D4—21no—
473C8×D4—221no—
474#432—111no—
475#432C2×D1111yescharacteristic
476#431—111no—
477#431C2×D1111yescharacteristic
478#407—111no—
479#407—111no—
480#407C2×D1111yescharacteristic
481#407C2×D1111yescharacteristic
482C2×C22⋊C8—111no—
483C2×C22⋊C8—111no—
484C2×C22⋊C8C2×D1111yescharacteristic
485C2×C22⋊C8C2×D1111yescharacteristic
486#324—111no—
487#324—111no—
488#324—111no—
489#324—111no—
490#324—111no—
491#324—111no—
492#324—111no—
493#324—111no—
494#323—111no—
495#323—111no—
496#323—111no—
497#323—111no—
498#323—111no—
499#323—111no—
500#323—111no—
501#323—111no—
502C22×C11—21no—
503C22×C11—21no—
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—42no—
516C22×C11—42no—
517C22×C11—81no—
518C22×C11—81no—
519C22×C11#41312yes—
520C22×C11C22×C22⋊C411yescharacteristic
521C22×C11C2×#13111yescharacteristic
522C22×C11#56811yescharacteristic
523C2×D11—41no—
524C2×D11—41no—
525C2×D11—41no—
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—41no—
529C2×D11—81no—
530C2×D11—81no—
531C2×D11—81no—
532C2×D11—81no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—21no—
537C4×C11—21no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—21no—
541C4×C11—21no—
542C4×C11—21no—
543Dic11—22no—
544Dic11—41no—
545Dic11—41no—
546Dic11—41no—
547Dic11—41no—
548Dic11—41no—
549C22×D4—111no—
550C22×D4—111no—
551C22×D4—111no—
552C22×D4—111no—
553C22×D4—111no—
554C22×D4C4×D1111yescharacteristic
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C2×M16—21no—
562C2×M16—21no—
563C2×M16—221no—
564C2×M16—221no—
565C22×C8—21no—
566C22×C8—21no—
567C22×C8—221no—
568C22×C8—221no—
569#126—221no—
570#126—221no—
571#126—221no—
572#126—221no—
573#126—221no—
574#126—221no—
575#126—221no—
576#126—221no—
577#125—221no—
578#125—221no—
579#125—221no—
580#125—221no—
581#123—221no—
582#123—221no—
583#123—221no—
584#123—221no—
585#123—221no—
586#123—221no—
587#123—221no—
588#123—221no—
589#121—221no—
590#121—221no—
591#121—221no—
592#121—221no—
593#121—221no—
594#121—221no—
595#121—221no—
596#121—221no—
597#121—221no—
598#121—221no—
599#121—221no—
600#121—221no—
601#121—221no—
602#121—221no—
603#121—221no—
604#121—221no—
605C4×D4—221no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—221no—
609C4×D4—221no—
610C4×D4—221no—
611C4×D4—221no—
612C4×D4—221no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4—221no—
616C4×D4—221no—
617C4×D4D4411yescharacteristic
618C4×D4D4411yescharacteristic
619C4×D4D4411yescharacteristic
620C4×D4D4411yescharacteristic
621C4×D4C22⋊D1111yescharacteristic
622C4×D4C22⋊D1111yescharacteristic
623C4×D4C22⋊D1111yescharacteristic
624C4×D4C22⋊D1111yescharacteristic
625#117—221no—
626#117—221no—
627#117—221no—
628#117—221no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4—221no—
640C2×C4⋊C4—221no—
641C2×C4⋊C4—221no—
642C2×C4⋊C4C4×D1111yescharacteristic
643C2×C22⋊C4—111no—
644C2×C22⋊C4—111no—
645C2×C22⋊C4—111no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—111no—
648C2×C22⋊C4—111no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4C4×D1111yescharacteristic
652C2×C22⋊C4C4×D1111yescharacteristic
653C2×C42—111no—
654C2×C42—111no—
655C2×C42C22×D1111yescharacteristic
656C4⋊C8—21no—
657C4⋊C8—21no—
658C4⋊C8—221no—
659C4⋊C8—221no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—111no—
665C22⋊C8—111no—
666C22⋊C8—111no—
667C22⋊C8—111no—
668C22⋊C8—221no—
669C22⋊C8—221no—
670C22⋊C8—221no—
671C22⋊C8—221no—
672C22⋊C8C22×D1111yescharacteristic
673C22⋊C8C22×D1111yescharacteristic
674C22⋊C8C22×D1111yescharacteristic
675C22⋊C8C22×D1111yescharacteristic
676#97—21no—
677#97—221no—
678C4×C8—21no—
679C4×C8—221no—
680C2×C11—21no—
681C2×C11—21no—
682C2×C11—22no—
683C2×C11—41no—
684C2×C11—41no—
685C2×C11—41no—
686C2×C11#288011yescharacteristic
687C2×C11#288311yescharacteristic
688C2×C11C2×#41311yescharacteristic
689D11—81no—
690D11—81no—
691C24—111no—
692C24—111no—
693C24C2×C4×D1111yescharacteristic
694C24C2×C4×D1111yescharacteristic
695C2×D4—42no—
696C2×D4—222no—
697C2×D4—221no—
698C2×D4—221no—
699C2×D4—221no—
700C2×D4—221no—
701C2×D4—221no—
702C2×D4—221no—
703C2×D4—221no—
704C2×D4—221no—
705C2×D4—221no—
706C2×D4—221no—
707C2×D4—441no—
708C2×D4—442no—
709C2×D4—442no—
710C2×D4—881no—
711C2×D4—881no—
712C2×D4(C2×D11)⋊C411yescharacteristic
713C2×D4(C2×D11)⋊C411yescharacteristic
714C2×D4(C2×D11)⋊C411yescharacteristic
715C2×D4(C2×D11)⋊C411yescharacteristic
716C22×C4—81no—
717C22×C4—81no—
718C22×C4—111no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—441no—
735C22×C4—441no—
736C22×C4—881no—
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—221no—
782C4⋊C4—221no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4(C2×D11)⋊C411yescharacteristic
786C4⋊C4(C2×D11)⋊C411yescharacteristic
787C4⋊C4(C2×D11)⋊C411yescharacteristic
788C4⋊C4(C2×D11)⋊C411yescharacteristic
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(C2×D11)⋊C411yescharacteristic
806C22⋊C4(C2×D11)⋊C411yescharacteristic
807C22⋊C4(C2×D11)⋊C411yescharacteristic
808C22⋊C4(C2×D11)⋊C411yescharacteristic
809C22⋊C4(C2×D11)⋊C411yescharacteristic
810C22⋊C4(C2×D11)⋊C411yescharacteristic
811C22⋊C4(C2×D11)⋊C411yescharacteristic
812C22⋊C4(C2×D11)⋊C411yescharacteristic
813C42—221no—
814C42—221no—
815C42—221no—
816C42—221no—
817C42C2×D4411yescharacteristic
818C42C2×D4411yescharacteristic
819C42C2×C22⋊D1111yescharacteristic
820C42C2×C22⋊D1111yescharacteristic
821C11#1742711yescharacteristic, complemented, Sylow
822C23—22no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—221no—
831C23—221no—
832C23—221no—
833C23—221no—
834C23—221no—
835C23—221no—
836C23—441no—
837C23—441no—
838C23—441no—
839C23—441no—
840C23C2×(C2×D11)⋊C411yescharacteristic
841C23C2×(C2×D11)⋊C411yescharacteristic
842C23C2×(C2×D11)⋊C411yescharacteristic
843C23C2×(C2×D11)⋊C411yescharacteristic
844C23C22×C4×D1111yescharacteristic
845D4—22no—
846D4—22no—
847D4—41no—
848D4—41no—
849D4—442no—
850D4—442no—
851D4—442no—
852D4—442no—
853D4—442no—
854D4—442no—
855D4—881no—
856D4—881no—
857D4—881no—
858D4—881no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—112no—
874C2×C4—221no—
875C2×C4—221no—
876C2×C4—221no—
877C2×C4—221no—
878C2×C4—221no—
879C2×C4—221no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—442no—
884C2×C4—442no—
885C2×C4—442no—
886C2×C4—442no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—881no—
892C2×C4—881no—
893C2×C4—881no—
894C2×C4—881no—
895C2×C4C2×(C2×D11)⋊C411yescharacteristic
896C2×C4C2×(C2×D11)⋊C411yescharacteristic
897C2×C4C2×(C2×D11)⋊C411yescharacteristic
898C2×C4C2×(C2×D11)⋊C411yescharacteristic
899C2×C4C2×(C2×D11)⋊C411yescharacteristic
900C2×C4C2×(C2×D11)⋊C411yescharacteristic
901C2×C4C2×(C2×D11)⋊C411yescharacteristic
902C2×C4C2×(C2×D11)⋊C411yescharacteristic
903C2×C4C22×D4411yescharacteristic
904C2×C4C22×C22⋊D1111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C8—441no—
910C8—441no—
911C8—441no—
912C8—441no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—441no—
931C22—441no—
932C22—441no—
933C22—441no—
934C22—441no—
935C22—441no—
936C22—881no—
937C22—881no—
938C22—881no—
939C22—881no—
940C22#1062274512yes—
941C22D11×#13111yescharacteristic
942C22#1062328111yescharacteristic
943C22C22×(C2×D11)⋊C411yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—21no—
951C4—21no—
952C4—21no—
953C4—21no—
954C4—222no—
955C4—441no—
956C4—441no—
957C4—441no—
958C4—441no—
959C4—441no—
960C2—21no—
961C2—21no—
962C2—22no—
963C2—41no—
964C2—41no—
965C2—41no—
966C2—881no—
967C2—881no—
968C2#1307706311yescharacteristic
969C2#1307707611yescharacteristic
970C2C2×#1062274511yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2974C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623071C2
cosocleC22×C4×C11C24
hypercenter#2974D11
hypocenterC11#17427
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. #13066977C2semidirect
6. #13066975C2semidirect
7. #13066965C2semidirect
8. #13066962C2semidirect
9. #13066952C2semidirect
10. #13066948C2semidirect
11. #13066945C2semidirect
12. #13066932C2semidirect
13. #13066928C2semidirect
14. C2×#10622107C2semidirect
15. C11×#2974C2semidirect
339. #2974D11semidirect
821. C11#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#106230712
#130776512
#130669862
#130669832
#130669772
#130669752
#130669652
#130669622
#130669522
#130669482
#130669452
#130669322
#130669282
C2×#106221072
C11×#29742
#1742711