Finite Group Databasebeta

← #14796195

Subgroups — #14796195

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622747C211yesmaximal, characteristic, complemented
2C2×#10622747C211yesmaximal, characteristic, complemented
3C2×#10622734C211yesmaximal, characteristic, complemented
4#13072067C211yesmaximal, characteristic, complemented
5#13072034C211yesmaximal, characteristic
6#13070010C211yesmaximal, characteristic, complemented
7#13069989C211yesmaximal, characteristic, complemented
8#13069813C211yesmaximal, characteristic, complemented
9#13069799C211yesmaximal, characteristic, complemented
10#13069470C211yesmaximal, characteristic, complemented
11#13069349C211yesmaximal, characteristic, complemented
12#13068931C211yesmaximal, characteristic, complemented
13#13068926C211yesmaximal, characteristic, complemented
14#13068649C211yesmaximal, characteristic, complemented
15C2×C11×#436C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C11×#436—24no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31#10622836—21no—
32#10622833—21no—
33#10622825C2211yescharacteristic
34#10622825C2211yescharacteristic
35#10622747—24no—
36#10622747—24no—
37#10622734—24no—
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66882C2211yescharacteristic
43C2×#66882C2211yescharacteristic
44C2×#66881C2211yescharacteristic
45C2×#66881C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49#10622603—21no—
50#10622597—21no—
51#10622572—21no—
52#10622570—21no—
53#10622561—21no—
54#10622555—21no—
55#10622552C2211yescharacteristic
56#10622542C2211yescharacteristic
57#10622541C2211yescharacteristic
58#10622541C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622189C2211yescharacteristic
63C22×D4×C11D411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C22×D44C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16D414yescomplemented
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#66983—22no—
93#66983—22no—
94#66983—22no—
95#66983—41no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100#66979—22no—
101#66979—41no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977—22no—
113#66977—22no—
114#66977—41no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C2×#4314—22no—
121C2×#4314—22no—
122C2×#4314—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C4×C8×C11—22no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133#66885—22no—
134#66885—22no—
135#66885—41no—
136#66882—22no—
137#66882—22no—
138#66882D414yescomplemented
139#66881—22no—
140#66881—22no—
141#66880—22no—
142#66880—22no—
143#66880—41no—
144#24795—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C24×C11C2×D411yescharacteristic
147C23×D11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—41no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—81no—
172C2×C22⋊D11—81no—
173C2×C22⋊D11—81no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—42no—
182C22×Dic11—42no—
183C22×Dic11—81no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C11×M16—28no—
197C11×M16—44no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C2×D412yes—
207C2×C8×C11C2×D412yes—
208C2×C8×C11C2×D412yes—
209C2×C8×C11#4112yes—
210C11×C4⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C42×C11—21no—
214C42×C11—21no—
215C22⋊Dic11—42no—
216C22⋊Dic11—42no—
217C22⋊Dic11—42no—
218C22⋊Dic11—81no—
219C22⋊Dic11—81no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—81no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—42no—
235C4⋊Dic11C2×D412yes—
236C4⋊Dic11C2×D412yes—
237Dic11⋊C4—42no—
238Dic11⋊C4—42no—
239Dic11⋊C4—81no—
240Dic11⋊C4—81no—
241C4×Dic11—42no—
242#4314—44no—
243C2×#468—111no—
244C2×#468—111no—
245C2×#436D1111yescharacteristic, complemented
246C2×#428—111no—
247#2417—111no—
248#2414—111no—
249#2068—111no—
250#2065—111no—
251#2035—111no—
252#2033—111no—
253#1968—111no—
254#1942—111no—
255#1874—111no—
256#1873—111no—
257#1809—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11#12112yes—
272C23×C11C22×D411yescharacteristic
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280D4×C11—44no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11#12112yes—
300C2×C4×C11#13712yes—
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11H(5,𝔽2)11yescharacteristic
306C2×C4×C112−1+411yescharacteristic
307C22⋊D11—84no—
308C22⋊D11—84no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—84no—
331D44—41no—
332D44—41no—
333D44—41no—
334D44—41no—
335Dic22—41no—
336Dic22—41no—
337Dic22—41no—
338Dic22—41no—
339C8×C11—22no—
340C8×C11—41no—
341C8×C11—41no—
342C8×C11#12114yes—
343C22×SD16—111no—
344C22×M16C2×D1111yescharacteristic
345C22×M16C2×D1111yescharacteristic
346C2×C22⋊Q8—111no—
347C2×C22⋊Q8—111no—
348C2×#121—111no—
349C2×#121—111no—
350C2×C4×D4C2×D1111yescharacteristic
351C2×#117—111no—
352C22×C4⋊C4—111no—
353#468—224no—
354#468—224no—
355#436—24no—
356#428—224no—
357C2×#107—111no—
358C2×#107—111no—
359C2×#107—111no—
360C2×#106—111no—
361C2×#106—111no—
362C2×C4⋊C8C2×D1111yescharacteristic
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×C22⋊C8C2×D1111yescharacteristic
370C2×C22⋊C8C2×D1111yescharacteristic
371C2×C4×C8C2×D1111yescharacteristic
372#398—221no—
373#396—221no—
374#394—221no—
375#392—221no—
376#391—111no—
377#390—111no—
378#390—221no—
379#389—111no—
380#389—111no—
381#388—221no—
382#386—221no—
383#380—111no—
384#380—111no—
385#380—221no—
386#340—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11C2×#12111yescharacteristic
405C22×C11D4211yescharacteristic
406C22×C11#54711yescharacteristic
407C22×C11C2×#13711yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57711yescharacteristic
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11C2×#12111yescharacteristic
423C4×C11#53711yescharacteristic
424C4×C11#54811yescharacteristic
425C4×C11#55311yescharacteristic
426Dic11—42no—
427Dic11—42no—
428Dic11—81no—
429Dic11—81no—
430Dic11—81no—
431Dic11—81no—
432Dic11—81no—
433C22×Q8—111no—
434C22×D4—111no—
435C22×D4—221no—
436C22×D4—221no—
437C22×D4D4411yescharacteristic
438C23×C4—221no—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C2×SD16—222no—
442C2×SD16—222no—
443C2×SD16—222no—
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16C22⋊D1114yescomplemented
450C22×C8C22×D1111yescharacteristic
451C22×C8C22×D1111yescharacteristic
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454C22⋊Q8—222no—
455C22⋊Q8—222no—
456C22⋊Q8—222no—
457C22⋊Q8—441no—
458#121—222no—
459#121—222no—
460#121—222no—
461#121—441no—
462C4×D4—22no—
463C4×D4—22no—
464#117—222no—
465#117—441no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—441no—
479C2×C4⋊C4D4411yescharacteristic
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4D4411yescharacteristic
490C2×C22⋊C4D4411yescharacteristic
491C2×C42—221no—
492C2×C42C22×D1111yescharacteristic
493#107—114no—
494#107—222no—
495#107—222no—
496#106—222no—
497#106—222no—
498C4⋊C8—22no—
499#103—222no—
500#103—222no—
501#103—441no—
502#102—222no—
503#102—222no—
504#102—441no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C4×C8—22no—
508#95—221no—
509#95—221no—
510#95—221no—
511#95—221no—
512#95—221no—
513#95—221no—
514C2×C11—42no—
515C2×C11—81no—
516C2×C11#241611yescharacteristic
517C2×C11#305611yescharacteristic
518C2×C11#306211yescharacteristic
519C2×C11#327311yescharacteristic
520C2×C11#327811yescharacteristic
521C2×C11#335111yescharacteristic
522C2×C11#335711yescharacteristic
523D11—161no—
524C24—221no—
525C24C2×D4411yescharacteristic
526C24C2×D4411yescharacteristic
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—221no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—442no—
543C2×D4—442no—
544C2×D4—442no—
545C2×D4—881no—
546C2×D4—881no—
547C2×D4—881no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—442no—
566C22×C4—442no—
567C22×C4—881no—
568C22×C4C2×D4411yescharacteristic
569C22×C4C2×D4411yescharacteristic
570C22×C4C2×D4411yescharacteristic
571C22×C4C2×D4411yescharacteristic
572C22×C4#433912yes—
573C22×C4C2×C22⋊D1112yes—
574C22×C4C23×D1111yescharacteristic
575SD16—444no—
576M16—28no—
577M16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8D4×D1112yes—
587C2×C8#434112yes—
588C2×C8C2×C22⋊D1112yes—
589C2×C8C2×C22⋊D1112yes—
590C4⋊C4—22no—
591C4⋊C4—112no—
592C4⋊C4—112no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—442no—
604C4⋊C4—442no—
605C4⋊C4—442no—
606C4⋊C4—881no—
607C4⋊C4—881no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—442no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—881no—
617C22⋊C4—881no—
618C22⋊C4—881no—
619C42—21no—
620C42—21no—
621C42—442no—
622C11#2479511yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23#6698312yes—
644C23C22×D4411yescharacteristic
645Q8—441no—
646Q8—441no—
647Q8—441no—
648Q8—441no—
649D4—44no—
650D4—441no—
651D4—441no—
652D4—441no—
653D4—441no—
654D4—884no—
655D4—884no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—884no—
696C2×C4#6696212yes—
697C2×C4#6698312yes—
698C2×C4C2×#433911yescharacteristic
699C2×C4C2×D4×D1111yescharacteristic
700C2×C4C2×#434111yescharacteristic
701C2×C4#6704211yescharacteristic
702C2×C4#6704311yescharacteristic
703C2×C4C22×C22⋊D1111yescharacteristic
704C8—22no—
705C8—41no—
706C8—41no—
707C8#6699214yes—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22—881no—
729C22D4×D4411yescharacteristic
730C22#1062308611yescharacteristic
731C22C2×#6696211yescharacteristic
732C22#1062327911yescharacteristic
733C22#1062328211yescharacteristic
734C22#1062328311yescharacteristic
735C22C2×#6698311yescharacteristic
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—442no—
741C4—442no—
742C4—881no—
743C4—881no—
744C4—881no—
745C4—881no—
746C4—881no—
747C4#1062308311yescharacteristic
748C4#1062309611yescharacteristic
749C4C2×#6699211yescharacteristic
750C4#1062336411yescharacteristic
751C2—42no—
752C2—81no—
753C2—1761no—
754C2#1307205611yescharacteristic
755C2#1307824611yescharacteristic
756C2#1307829611yescharacteristic
757C2#1308022811yescharacteristic
758C2#1308028411yescharacteristic
759C2#1308117811yescharacteristic
760C2#1308124311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
prime radical#13072034C2
hypercenterC2×#436D11
hypocenterC11#24795
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#10622747C2semidirect
2. C2×#10622747C2semidirect
3. C2×#10622734C2semidirect
4. #13072067C2semidirect
6. #13070010C2semidirect
7. #13069989C2semidirect
8. #13069813C2semidirect
9. #13069799C2semidirect
10. #13069470C2semidirect
11. #13069349C2semidirect
12. #13068931C2semidirect
13. #13068926C2semidirect
14. #13068649C2semidirect
15. C2×C11×#436C2semidirect
76. C2×C11×M16D4semidirect
138. #66882D4semidirect
245. C2×#436D11semidirect
449. C2×M16C22⋊D11semidirect
622. C11#24795semidirect

Maximal subgroups

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

subgroupindex
C2×#106227472
C2×#106227342
#130720672
#130720342
#130700102
#130699892
#130698132
#130697992
#130694702
#130693492
#130689312
#130689262
#130686492
C2×C11×#4362
#2479511