Finite Group Databasebeta

← #14792552

Subgroups — #14792552

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622345C211yesmaximal, characteristic
2#13074405C211yesmaximal, characteristic, complemented
3#13071196C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069989C211yesmaximal, characteristic, complemented
6#13069927C211yesmaximal, characteristic, complemented
7#13069927C211yesmaximal, characteristic, complemented
8#13069492C211yesmaximal, characteristic, complemented
9#13069482C211yesmaximal, characteristic, complemented
10#13069313C211yesmaximal, characteristic, complemented
11#13069299C211yesmaximal, characteristic, complemented
12#13068936C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic, complemented
15C2×C11×#433C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×D88C2211yescharacteristic
21C22×D88C2211yescharacteristic
22C11×#433—24no—
23C2×C11×C4⋊C8C2211yescharacteristic, complemented
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic, complemented
28C2×C4×C8×C11C2211yescharacteristic, complemented
29#10622825C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic, complemented
37C2×#66885C2211yescharacteristic, complemented
38C2×#66882C2211yescharacteristic, complemented
39C2×#66881C2211yescharacteristic, complemented
40#10622606—21no—
41#10622605—21no—
42#10622601—21no—
43#10622601—21no—
44#10622572—21no—
45#10622572—21no—
46#10622568—21no—
47#10622568—21no—
48#10622552C2211yescharacteristic
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622552C2211yescharacteristic, complemented
53#10622552C2211yescharacteristic, complemented
54#10622541C2211yescharacteristic, complemented
55#10622541C2211yescharacteristic, complemented
56#10622345—24no—
57#10622189C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622189C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61C24×D11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#117—22no—
79C11×#117—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66983—22no—
89#66983—22no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103#66979—41no—
104#66979—41no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×D88—22no—
114C2×D88—22no—
115C2×D88—22no—
116C2×D88—22no—
117C2×D88—41no—
118C2×D88—41no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8D414yes—
123C11×#97—22no—
124C4×C8×C11—22no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66885—22no—
129#66885—22no—
130#66885—22no—
131#66885—22no—
132#66885—41no—
133#66885—41no—
134#66885—41no—
135#66885—41no—
136#66882—41no—
137#66881—41no—
138#24512—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—21no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11—81no—
149C23×D11—81no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—42no—
163C2×C22⋊D11—81no—
164C2×C22⋊D11—81no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—44no—
188C2×D44—44no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44#4112yes—
194C2×D44#4112yes—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
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×C11C2×D412yes—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C22⋊Dic11—42no—
216C22⋊Dic11—81no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—81no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4—81no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4—81no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228(C2×D11)⋊C4—81no—
229(C2×D11)⋊C4—81no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240Dic11⋊C4—81no—
241Dic11⋊C4—81no—
242C4×Dic11—42no—
243D88—44no—
244D88—44no—
245C2×#447—111no—
246C2×#433D1111yescharacteristic, complemented
247#2624—111no—
248#2309—111no—
249#2067—111no—
250#2065—111no—
251#2054—111no—
252#2054—111no—
253#1972—111no—
254#1970—111no—
255#1936—111no—
256#1934—111no—
257#1875—111no—
258#1854—111no—
259#1786—111no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11#12112yes—
267C23×C11C22×D411yescharacteristic
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—48no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—84no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11#12112yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C22⋊D11—84no—
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—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337D44—22no—
338D44—22no—
339D44—22no—
340D44—22no—
341D44—48no—
342D44—41no—
343D44—41no—
344D44—41no—
345D44—41no—
346D44—41no—
347D44—41no—
348D44—41no—
349D44—41no—
350C8×C11—22no—
351C8×C11—22no—
352C8×C11—41no—
353C8×C11—41no—
354C23×D4—111no—
355C22×D8—111no—
356C22×D8—111no—
357C2×#121—111no—
358C2×#117—111no—
359C2×#117C2×D1111yescharacteristic
360#447—224no—
361#433—24no—
362C2×#107—111no—
363C2×#106—111no—
364C2×C4⋊C8C2×D1111yescharacteristic, complemented
365C2×C4⋊C8C2×D1111yescharacteristic, complemented
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×C22⋊C8C2×D1111yescharacteristic
376C2×#97C2×D1111yescharacteristic, complemented
377C2×C4×C8C2×D1111yescharacteristic, complemented
378#399—221no—
379#397—221no—
380#394—221no—
381#394—221no—
382#390—111no—
383#390—111no—
384#390—111no—
385#390—111no—
386#390—111no—
387#390—111no—
388#390—221no—
389#390—221no—
390#389—111no—
391#389—111no—
392#380—111no—
393#379—221no—
394#379—221no—
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11C2×#12111yescharacteristic
407C22×C11#52511yescharacteristic
408C22×C11#53511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57611yescharacteristic
411C22×C11#57611yescharacteristic
412C22×C11#57711yescharacteristic
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—816no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C4×C11—22no—
436C4×C11—41no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11#54611yescharacteristic
441C4×C11#54611yescharacteristic
442C4×C11#55111yescharacteristic
443C4×C11#55111yescharacteristic
444Dic11—81no—
445Dic11—81no—
446Dic11—81no—
447Dic11—81no—
448Dic11—81no—
449C25—221no—
450C22×D4—111no—
451C22×D4—111no—
452C22×D4—111no—
453C22×D4—222no—
454C22×D4—222no—
455C22×D4—221no—
456C22×D4—221no—
457C22×D4—222no—
458C22×D4—222no—
459C22×D4—441no—
460C22×D4—441no—
461C23×C4C22×D1111yescharacteristic
462C2×D8—222no—
463C2×D8—222no—
464C2×D8—222no—
465C2×D8—222no—
466C2×D8—441no—
467C2×D8—441no—
468C22×C8C22×D1111yescharacteristic
469C22×C8C22×D1111yescharacteristic
470C22×C8C22×D1111yescharacteristic
471C22×C8C22×D1111yescharacteristic
472#121—222no—
473#121—222no—
474#117—22no—
475#117—22no—
476#117—441no—
477#117—441no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4D4411yescharacteristic
486C2×C4⋊C4D4411yescharacteristic
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4D4411yescharacteristic
503C2×C22⋊C4D4411yescharacteristic
504C2×C42—221no—
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1111yescharacteristic
507#107—441no—
508#106—441no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511#102—222no—
512#102—222no—
513#102—222no—
514#102—222no—
515#102—441no—
516#102—441no—
517#102—441no—
518#102—441no—
519C22⋊C8—22no—
520C22⋊C8C22⋊D1114yes—
521#97—22no—
522C4×C8—22no—
523#95—221no—
524#95—221no—
525#95—221no—
526C2×C11—42no—
527C2×C11#241111yescharacteristic
528C2×C11#305811yescharacteristic
529C2×C11#306211yescharacteristic
530C2×C11#311811yescharacteristic
531C2×C11#312211yescharacteristic
532C2×C11#322011yescharacteristic
533C2×C11#322411yescharacteristic
534D11—82no—
535D11—82no—
536D11—161no—
537C24—224no—
538C24—221no—
539C24—221no—
540C24—221no—
541C24—442no—
542C24—442no—
543C24—881no—
544C24—881no—
545C24—881no—
546C24—881no—
547C24C2×D4411yescharacteristic
548C2×D4—112no—
549C2×D4—112no—
550C2×D4—224no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—444no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—442no—
572C2×D4—442no—
573C2×D4—442no—
574C2×D4—881no—
575C2×D4—881no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4C2×D4411yescharacteristic
586C22×C4C2×D4411yescharacteristic
587C22×C4C2×D4411yescharacteristic
588C22×C4C2×D4411yescharacteristic
589C22×C4C2×D4411yescharacteristic
590C22×C4#433912yes—
591C22×C4C2×C22⋊D1112yes—
592C22×C4C23×D1111yescharacteristic
593D8—444no—
594D8—444no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8C2×C22⋊D1112yes—
606C2×C8C2×C22⋊D1112yes—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—881no—
620C4⋊C4—881no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—442no—
624C22⋊C4—442no—
625C22⋊C4—881no—
626C22⋊C4—881no—
627C22⋊C4—881no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C22⋊C4—881no—
631C22⋊C4—881no—
632C22⋊C4—881no—
633C22⋊C4—881no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C22⋊C4—881no—
637C22⋊C4—881no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—442no—
643C11#2451211yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—222no—
651C23—222no—
652C23—448no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—884no—
673C23—884no—
674C23—884no—
675C23—884no—
676C23—884no—
677C23—884no—
678C23#6698312yes—
679C23C22×D4411yescharacteristic
680D4—222no—
681D4—222no—
682D4—222no—
683D4—222no—
684D4—448no—
685D4—441no—
686D4—441no—
687D4—441no—
688D4—441no—
689D4—441no—
690D4—441no—
691D4—441no—
692D4—441no—
693D4—884no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4#6698312yes—
728C2×C4C2×#433911yescharacteristic
729C2×C4#41×D1111yescharacteristic
730C2×C4#41×D1111yescharacteristic
731C2×C4#6704211yescharacteristic
732C2×C4#6704211yescharacteristic
733C2×C4C22×C22⋊D1111yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—8816no—
752C22—881no—
753C22—881no—
754C22—881no—
755C22—881no—
756C22—881no—
757C22—881no—
758C22—881no—
759C22—881no—
760C22—881no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—881no—
766C22—881no—
767C22#1062305511yescharacteristic
768C22#1062305611yescharacteristic
769C22#1062328211yescharacteristic
770C22#1062328311yescharacteristic
771C22#1062328311yescharacteristic
772C22#1062328311yescharacteristic
773C22C2×#6698311yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—881no—
780C4—881no—
781C4—881no—
782C4—881no—
783C4—881no—
784C4#1062305811yescharacteristic
785C4#1062305811yescharacteristic
786C4#1062336011yescharacteristic
787C4#1062336011yescharacteristic
788C2—42no—
789C2—882no—
790C2—882no—
791C2—1761no—
792C2#1307199511yescharacteristic
793C2#1307826411yescharacteristic
794C2#1307829611yescharacteristic
795C2#1307880211yescharacteristic
796C2#1307886011yescharacteristic
797C2#1307966811yescharacteristic
798C2#1307971211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
hypercenterC2×#433D11
hypocenterC11#24512
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13074405C2semidirect
3. #13071196C2semidirect
4. #13070003C2semidirect
5. #13069989C2semidirect
6. #13069927C2semidirect
7. #13069927C2semidirect
8. #13069492C2semidirect
9. #13069482C2semidirect
10. #13069313C2semidirect
11. #13069299C2semidirect
12. #13068936C2semidirect
13. #13068817C2semidirect
14. #13068548C2semidirect
15. C2×C11×#433C2semidirect
23. C2×C11×C4⋊C8C22semidirect
24. C2×C11×C4⋊C8C22semidirect
27. C2×C11×#97C22semidirect
28. C2×C4×C8×C11C22semidirect
36. C2×#66885C22semidirect
37. C2×#66885C22semidirect
38. C2×#66882C22semidirect
39. C2×#66881C22semidirect
52. #10622552C22semidirect
53. #10622552C22semidirect
54. #10622541C22semidirect
55. #10622541C22semidirect
57. #10622189C22semidirect
58. #10622189C22semidirect
59. #10622189C22semidirect
60. #10622189C22semidirect
246. C2×#433D11semidirect
364. C2×C4⋊C8C2×D11semidirect
365. C2×C4⋊C8C2×D11semidirect
376. C2×#97C2×D11semidirect
377. C2×C4×C8C2×D11semidirect
643. C11#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#106223452
#130744052
#130711962
#130700032
#130699892
#130699272
#130694922
#130694822
#130693132
#130692992
#130689362
#130688172
#130685482
C2×C11×#4332
#2451211