Finite Group Databasebeta

← #14719866

Subgroups — #14719866

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#126C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic, complemented
3#13077244C211yesmaximal, characteristic, complemented
4#13066986C211yesmaximal, characteristic, complemented
5#13066985C211yesmaximal, characteristic, complemented
6#13066984C212yesmaximal, complemented
7#13066983C211yesmaximal, characteristic, complemented
8#13066982C212yesmaximal, complemented
9#13066944C212yesmaximal, complemented
10#13066941C212yesmaximal
11C11×#1473C211yesmaximal, characteristic, complemented
12C2×C11×#126C2211yescharacteristic
13D11×#126—21no—
14D11×#126—21no—
15D11×#126—21no—
16D11×#126—21no—
17D11×#126—21no—
18D11×#126—21no—
19D11×#126—21no—
20D11×#126—21no—
21C2×#66951C411yescharacteristic
22C2×#66951C411yescharacteristic
23C2×#66951C2211yescharacteristic
24C2×C4⋊C4×D11C411yescharacteristic
25C2×C4⋊C4×D11C411yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C22⋊C4×D11C411yescharacteristic
28C2×C22⋊C4×D11C411yescharacteristic
29C2×C22⋊C4×D11C2211yescharacteristic
30C2×#66932C411yescharacteristic
31C2×#66932C411yescharacteristic
32C2×#66932C2211yescharacteristic
33C2×#66929C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C11×#432C2211yescharacteristic, complemented
36C11×#431C2211yescharacteristic, complemented
37#10622539C2211yescharacteristic, complemented
38#10622538C2211yescharacteristic, complemented
39#10622450—21no—
40#10622450—21no—
41#10622448—21no—
42#10622446—21no—
43#10622339C2212yes—
44#10622339C2212yes—
45#10622332C2212yescomplemented
46#10622331C2212yescomplemented
47#10622320—21no—
48#10622318—21no—
49C4×#4313—21no—
50#10622298—21no—
51C11×#324C2212yescomplemented
52C11×#323C2212yes—
53#10622166C2212yescomplemented
54#10622163C2212yes—
55#10622107C2212yescomplemented
56#10622107C2212yescomplemented
57#10622106C2212yes—
58#10622106C2212yes—
59C24×D11C2×C411yescharacteristic
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C11×#126—21no—
67C11×#126—21no—
68C11×#126—21no—
69C11×#126—21no—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2311yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×Dic11⋊C4C2×C411yescharacteristic
91C2×Dic11⋊C4C2×C411yescharacteristic
92C2×Dic11⋊C4C2×C411yescharacteristic
93C2×Dic11⋊C4C2×C411yescharacteristic
94C2×Dic11⋊C4C2311yescharacteristic
95C2×C4×Dic11C2×C411yescharacteristic
96C2×C4×Dic11C2×C411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×#4313—22no—
99C2×#4313—22no—
100#66951—21no—
101#66951—21no—
102#66951—21no—
103#66951—21no—
104#66951—21no—
105#66951—21no—
106#66951—21no—
107#66951—21no—
108#66951—21no—
109#66951—21no—
110#66951—21no—
111#66951—21no—
112C4⋊C4×D11—21no—
113C4⋊C4×D11—21no—
114C4⋊C4×D11—21no—
115C4⋊C4×D11—21no—
116C4⋊C4×D11—21no—
117C4⋊C4×D11—21no—
118C4⋊C4×D11—21no—
119C4⋊C4×D11—21no—
120C4⋊C4×D11—21no—
121C4⋊C4×D11—21no—
122C4⋊C4×D11—21no—
123C4⋊C4×D11—21no—
124C22⋊C4×D11—21no—
125C22⋊C4×D11—21no—
126C22⋊C4×D11—21no—
127C22⋊C4×D11—21no—
128C22⋊C4×D11—21no—
129C22⋊C4×D11—21no—
130C22⋊C4×D11—21no—
131C22⋊C4×D11—21no—
132C22⋊C4×D11—21no—
133C22⋊C4×D11—21no—
134C22⋊C4×D11—21no—
135C22⋊C4×D11—21no—
136#66932—21no—
137#66932—21no—
138#66932—21no—
139#66932—21no—
140#66932—21no—
141#66932—21no—
142#66932—21no—
143#66932—21no—
144#66932—21no—
145#66932—21no—
146#66932—21no—
147#66932—21no—
148#66929—21no—
149#66929—21no—
150#66929—21no—
151#66929—21no—
152C42×D11D411yescharacteristic
153C42×D11D411yescharacteristic
154C42×D11D411yescharacteristic
155C42×D11D411yescharacteristic
156C42×D11D411yescharacteristic
157C42×D11D411yescharacteristic
158C42×D11D411yescharacteristic
159C42×D11D411yescharacteristic
160C11×C4⋊C8—21no—
161C11×C4⋊C8—21no—
162C11×C22⋊C8C2312yes—
163C11×C22⋊C8C2312yes—
164C11×#97—21no—
165C4×C8×C11—21no—
166C22⋊(C11⋊C8)C2312yes—
167C22⋊(C11⋊C8)C2312yes—
168(C2×D11)⋊C8—22no—
169(C2×D11)⋊C8—22no—
170#66879—22no—
171Dic11⋊C8—22no—
172Dic11⋊C8—22no—
173C8×Dic11—22no—
174C4⋊(C11⋊C8)—21no—
175C4⋊(C11⋊C8)—21no—
176#66867—21no—
177C4×C11⋊C8—21no—
178#17398—111nomaximal, Sylow
179C24×C11C22×C411yescharacteristic
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—42no—
183C23×D11—42no—
184C23×D11—42no—
185C23×D11C22×C411yescharacteristic
186C23×D11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×Dic11C22×C411yescharacteristic
194C22×Dic11C22×C411yescharacteristic
195C22×Dic11C22×C411yescharacteristic
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11C22⋊C411yescharacteristic
212C2×C4×D11C22⋊C411yescharacteristic
213C2×C4×D11C22⋊C411yescharacteristic
214C2×C4×D11C22⋊C411yescharacteristic
215C2×C4×D11C22⋊C411yescharacteristic
216C2×C4×D11C22⋊C411yescharacteristic
217C2×C4×D11C22⋊C411yescharacteristic
218C2×C4×D11C22⋊C411yescharacteristic
219C2×C4×D11C2×D411yescharacteristic
220C2×C4×D11C2×D411yescharacteristic
221C2×C4×D11C2×D411yescharacteristic
222C2×C4×D11C2×D411yescharacteristic
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C22⋊C4—21no—
232C11×C22⋊C4—21no—
233C11×C22⋊C4—21no—
234C11×C22⋊C4—21no—
235C11×C22⋊C4—21no—
236C11×C22⋊C4—21no—
237C42×C11C2×D411yescharacteristic
238C42×C11C2×D411yescharacteristic
239C42×C11C2×D411yescharacteristic
240C42×C11C2×D411yescharacteristic
241C22⋊Dic11—21no—
242C22⋊Dic11—21no—
243C22⋊Dic11—21no—
244C22⋊Dic11—21no—
245C22⋊Dic11—21no—
246C22⋊Dic11—21no—
247(C2×D11)⋊C4—21no—
248(C2×D11)⋊C4—21no—
249(C2×D11)⋊C4—21no—
250(C2×D11)⋊C4—21no—
251(C2×D11)⋊C4—21no—
252(C2×D11)⋊C4—21no—
253(C2×D11)⋊C4—21no—
254(C2×D11)⋊C4—21no—
255(C2×D11)⋊C4—21no—
256(C2×D11)⋊C4—21no—
257(C2×D11)⋊C4—21no—
258(C2×D11)⋊C4—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265Dic11⋊C4—21no—
266Dic11⋊C4—21no—
267Dic11⋊C4—21no—
268Dic11⋊C4—21no—
269Dic11⋊C4—21no—
270Dic11⋊C4—21no—
271Dic11⋊C4—21no—
272Dic11⋊C4—21no—
273Dic11⋊C4—21no—
274Dic11⋊C4—21no—
275Dic11⋊C4—21no—
276Dic11⋊C4—21no—
277C4×Dic11C22⋊C411yescharacteristic
278C4×Dic11C22⋊C411yescharacteristic
279C4×Dic11C22⋊C411yescharacteristic
280C4×Dic11C22⋊C411yescharacteristic
281C4×Dic11C22⋊C411yescharacteristic
282C4×Dic11C22⋊C411yescharacteristic
283C4×Dic11C22⋊C411yescharacteristic
284C4×Dic11C22⋊C411yescharacteristic
285C4×Dic11C2×D411yescharacteristic
286C4×Dic11C2×D411yescharacteristic
287C4×Dic11C2×D411yescharacteristic
288C4×Dic11C2×D411yescharacteristic
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291#4313—44no—
292#4313—44no—
293C22×#126—111no—
294#2920—111no—
295#2920—111no—
296#1473—111no—
297#1473—111no—
298#1473—112no—
299#1473—112no—
300#1473—111no—
301#1473D1111yescharacteristic, complemented
302#1463—112no—
303#1462—112no—
304C23×C11—21no—
305C23×C11—22no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11C23×C411yescharacteristic
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—21no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—88no—
323C22×D11C2×C22⋊C411yescharacteristic
324C22×D11C2×C22⋊C411yescharacteristic
325C2×C4×C11—22no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11C2×C22⋊C411yescharacteristic
335C2×C4×C11C2×C22⋊C411yescharacteristic
336C2×C4×C11C2×C22⋊C411yescharacteristic
337C2×C4×C11C2×C22⋊C411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×Dic11—22no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—22no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11C2×C22⋊C411yescharacteristic
350C2×Dic11C2×C22⋊C411yescharacteristic
351C2×Dic11C2×C22⋊C411yescharacteristic
352C2×Dic11C2×C22⋊C411yescharacteristic
353C2×Dic11C2×C22⋊C411yescharacteristic
354C2×Dic11C2×C22⋊C411yescharacteristic
355C4×D11—22no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—41no—
360C4×D11—41no—
361C4×D11—41no—
362C4×D11—41no—
363C4×D11—41no—
364C4×D11—41no—
365C4×D11—41no—
366C4×D11—41no—
367C4×D11—42no—
368C4×D11—42no—
369C4×D11—42no—
370C4×D11—42no—
371C4×D11—42no—
372C4×D11—42no—
373C8×C11—42no—
374C8×C11—42no—
375C11⋊C8—42no—
376C11⋊C8—42no—
377C2×#126—111no—
378C2×#126—111no—
379C2×#126—111no—
380C2×#126—111no—
381C2×#126—111no—
382C2×#126—111no—
383C2×#126—111no—
384C2×#126—221no—
385C2×#126—221no—
386C2×#126—221no—
387C2×#126—221no—
388C2×#126—221no—
389C2×#126—221no—
390C2×#126—221no—
391C2×#126—221no—
392C2×#126C2×D1111yescharacteristic
393C22×C4⋊C4—111no—
394C22×C4⋊C4—111no—
395C22×C4⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—111no—
399C22×C42—111no—
400#432—111no—
401#432—112no—
402#432—221no—
403#432—221no—
404#432C2×D1111yescharacteristic, complemented
405#431—111no—
406#431—112no—
407#431—221no—
408#431—221no—
409#431C2×D1111yescharacteristic, complemented
410#423—221no—
411#423—221no—
412#407—112no—
413#407—112no—
414C4×M16—221no—
415C4×M16—221no—
416#324—112no—
417#324—112no—
418#324—112no—
419#324C2×D1112yescomplemented
420#323—112no—
421#323—112no—
422#323—112no—
423#323C2×D1112yes—
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—82no—
430C22×C11C22×C22⋊C411yescharacteristic
431C22×C11#56812yes—
432C2×D11—28no—
433C2×D11—21no—
434C2×D11—21no—
435C2×D11—21no—
436C2×D11—21no—
437C2×D11—41no—
438C2×D11—41no—
439C2×D11—41no—
440C2×D11—84no—
441C2×D11—84no—
442C2×D11—82no—
443C2×D11#41012yes—
444C2×D11#41312yes—
445C4×C11—21no—
446C4×C11—21no—
447C4×C11—21no—
448C4×C11—21no—
449C4×C11—21no—
450C4×C11—21no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—41no—
454Dic11—21no—
455Dic11—21no—
456Dic11—21no—
457Dic11—21no—
458Dic11—21no—
459Dic11—21no—
460Dic11—41no—
461Dic11—41no—
462Dic11—41no—
463C25—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—111no—
470C2×M16—222no—
471C2×M16—222no—
472#126—21no—
473#126—21no—
474#126—21no—
475#126—21no—
476#126—221no—
477#126—221no—
478#126—221no—
479#126—221no—
480#126—221no—
481#126—221no—
482#126—221no—
483#126—221no—
484#126—221no—
485#126—221no—
486#126—221no—
487#126—221no—
488#126—221no—
489#126—221no—
490#126—221no—
491#126—221no—
492#126—221no—
493#126—221no—
494#126—221no—
495#126—221no—
496#126—221no—
497#126—221no—
498#126—221no—
499#126—221no—
500#126—221no—
501#126—221no—
502#126—221no—
503#126—221no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4C4×D1111yescharacteristic
526C2×C4⋊C4C4×D1111yescharacteristic
527C2×C4⋊C4C22×D1111yescharacteristic
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—111no—
531C2×C22⋊C4—111no—
532C2×C22⋊C4—111no—
533C2×C22⋊C4—111no—
534C2×C22⋊C4—111no—
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4C4×D1111yescharacteristic
550C2×C22⋊C4C4×D1111yescharacteristic
551C2×C22⋊C4C22×D1111yescharacteristic
552C2×C42—111no—
553C2×C42—111no—
554C2×C42—111no—
555C2×C42—111no—
556C2×C42—111no—
557C2×C42—111no—
558C2×C42—111no—
559C2×C42—111no—
560C2×C42—111no—
561C2×C42—111no—
562C2×C42—111no—
563C2×C42C22×D1111yescharacteristic
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—222no—
567C4⋊C8—222no—
568C4⋊C8—221no—
569C4⋊C8—221no—
570C22⋊C8—112no—
571C22⋊C8—112no—
572C22⋊C8—222no—
573C22⋊C8—222no—
574C22⋊C8C22×D1112yes—
575C22⋊C8C22×D1112yes—
576#97—21no—
577#97—222no—
578#97—221no—
579C4×C8—21no—
580C4×C8—222no—
581C4×C8—221no—
582C2×C11—22no—
583C2×C11—81no—
584C2×C11#287911yescharacteristic
585C2×C11C2×#41011yescharacteristic
586C2×C11C2×#41311yescharacteristic
587D11—22no—
588D11—22no—
589D11—81no—
590C24—111no—
591C24—111no—
592C24—221no—
593C24—221no—
594C24—442no—
595C24—442no—
596C24—442no—
597C24C2×C4×D1111yescharacteristic
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—111no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—442no—
623C22×C4—442no—
624C22×C4—442no—
625C22×C4—442no—
626C22×C4—442no—
627C22×C4—442no—
628C22×C4C2×C4×D1111yescharacteristic
629C22×C4C2×C4×D1111yescharacteristic
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C23×D1111yescharacteristic
634M16—444no—
635M16—444no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—222no—
639C2×C8—222no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—221no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—221no—
656C4⋊C4—221no—
657C4⋊C4—221no—
658C4⋊C4—221no—
659C4⋊C4—221no—
660C4⋊C4—221no—
661C4⋊C4—221no—
662C4⋊C4—221no—
663C4⋊C4—221no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—221no—
671C22⋊C4—221no—
672C22⋊C4—221no—
673C22⋊C4—221no—
674C22⋊C4—221no—
675C22⋊C4—221no—
676C22⋊C4—221no—
677C22⋊C4—221no—
678C22⋊C4—221no—
679C22⋊C4—221no—
680C22⋊C4—221no—
681C22⋊C4—221no—
682C22⋊C4—221no—
683C22⋊C4—221no—
684C22⋊C4—221no—
685C22⋊C4—221no—
686C22⋊C4—221no—
687C22⋊C4—221no—
688C42—111no—
689C42—111no—
690C42—111no—
691C42—111no—
692C42—111no—
693C42—111no—
694C42—111no—
695C42—111no—
696C42—111no—
697C42—111no—
698C42—111no—
699C42—111no—
700C42D4×D1111yescharacteristic
701C42D4×D1111yescharacteristic
702C42D4×D1111yescharacteristic
703C42D4×D1111yescharacteristic
704C11#1739811yescharacteristic, complemented, Sylow
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—111no—
710C23—111no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—221no—
715C23—222no—
716C23—441no—
717C23—441no—
718C23—442no—
719C23—442no—
720C23—442no—
721C23—442no—
722C23—442no—
723C23—442no—
724C23—888no—
725C23C22×C4×D1111yescharacteristic
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—111no—
736C2×C4—111no—
737C2×C4—111no—
738C2×C4—111no—
739C2×C4—111no—
740C2×C4—111no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—222no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4C22⋊C4×D1111yescharacteristic
769C2×C4C22⋊C4×D1111yescharacteristic
770C2×C4C22⋊C4×D1111yescharacteristic
771C2×C4C22⋊C4×D1111yescharacteristic
772C2×C4C2×D4×D1111yescharacteristic
773C2×C4C2×D4×D1111yescharacteristic
774C8—42no—
775C8—42no—
776C8—442no—
777C8—442no—
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—82no—
784C22—112no—
785C22—112no—
786C22—228no—
787C22—221no—
788C22—221no—
789C22—221no—
790C22—221no—
791C22—441no—
792C22—441no—
793C22—441no—
794C22—882no—
795C22—884no—
796C22—884no—
797C22C2×C22⋊C4×D1111yescharacteristic
798C22#1062328112yes—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—221no—
809C4—221no—
810C4—221no—
811C4—221no—
812C4—221no—
813C4—221no—
814C4—441no—
815C4—441no—
816C4—441no—
817C2—22no—
818C2—81no—
819C2—222no—
820C2—222no—
821C2—881no—
822C2#1307705811yescharacteristic
823C2D11×#41011yescharacteristic
824C2D11×#41311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1473C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1473D11
hypocenterC11#17398
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #13077246C2semidirect
3. #13077244C2semidirect
4. #13066986C2semidirect
5. #13066985C2semidirect
6. #13066984C2semidirect
7. #13066983C2semidirect
8. #13066982C2semidirect
9. #13066944C2semidirect
11. C11×#1473C2semidirect
35. C11×#432C22semidirect
36. C11×#431C22semidirect
37. #10622539C22semidirect
38. #10622538C22semidirect
45. #10622332C22semidirect
46. #10622331C22semidirect
51. C11×#324C22semidirect
53. #10622166C22semidirect
55. #10622107C22semidirect
56. #10622107C22semidirect
301. #1473D11semidirect
404. #432C2×D11semidirect
409. #431C2×D11semidirect
419. #324C2×D11semidirect
704. C11#17398semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1262
#130772462
#130772442
#130669862
#130669852
#130669842
#130669832
#130669822
#130669442
#130669412
C11×#14732
#1739811