Finite Group Databasebeta

← #14800882

Subgroups — #14800882

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622655C211yesmaximal, characteristic, complemented
2C2×#10622653C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5#13071981C211yesmaximal, characteristic, complemented
6#13070008C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069819C211yesmaximal, characteristic, complemented
9#13069619C211yesmaximal, characteristic, complemented
10#13069496C211yesmaximal, characteristic, complemented
11#13069305C211yesmaximal, characteristic, complemented
12#13069047C211yesmaximal, characteristic, complemented
13#13069045C211yesmaximal, characteristic, complemented
14#13068804C211yesmaximal, characteristic, complemented
15C11×#2416C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C11×#396—21no—
29C11×#394—21no—
30C11×#390C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#386—21no—
33C11×#380C2211yescharacteristic
34#10622833—21no—
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622655—24no—
41#10622653—24no—
42#10622624—24no—
43#10622592—21no—
44C2×#66874—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622560—21no—
54#10622559—21no—
55#10622542C2211yescharacteristic
56#10622542C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—21no—
71C22×Dic22—22no—
72C22×Dic22—22no—
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—21no—
76C22×Dic22—41no—
77C22×Dic22—41no—
78C22×Dic22C2311yescharacteristic
79C22×Dic22C2311yescharacteristic
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—41no—
84C11×#121—44no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—41no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×#4324—22no—
107C2×#4324—22no—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324—41no—
111C2×#4324—41no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114#66977—22no—
115#66977—22no—
116#66977—41no—
117#66977—41no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—41no—
123C22×C11⋊C8—22no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—41no—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C11×#95—21no—
131C11×#95—21no—
132#66896—22no—
133#66896—41no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)D414yescomplemented
141#66874—22no—
142#66874—22no—
143#66874—22no—
144#66874—22no—
145#66874—22no—
146#66874D414yescomplemented
147#66871—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151#25130—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11C2×D411yescharacteristic
154C24×C11C2×D411yescharacteristic
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—81no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D412yes—
191C22×C4×C11#4112yes—
192C22×C4×C11C2411yescharacteristic
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C22×Dic11—42no—
200C2×Dic22—28no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—44no—
212C2×Dic22—44no—
213C2×Dic22—42no—
214C2×Dic22—42no—
215C2×Dic22—44no—
216C2×Dic22—42no—
217C2×Dic22C2×D412yes—
218C2×Dic22#4112yes—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4C2×D412yes—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—81no—
235C42×C11—21no—
236C42×C11—21no—
237C22⋊Dic11—42no—
238C22⋊Dic11—42no—
239C22⋊Dic11—42no—
240#4324—44no—
241#4324—44no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246Dic11⋊C4—42no—
247Dic11⋊C4—42no—
248#4318—44no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—44no—
259C2×C11⋊C8C2×D412yes—
260C2×C11⋊C8C2×D412yes—
261C2×C11⋊C8C2×D412yes—
262C2×#468—111no—
263C2×#448—111no—
264C2×#435—111no—
265C22×#103—111no—
266#2416D1111yescharacteristic
267#2409—111no—
268#2068—111no—
269#2055—111no—
270#2036—111no—
271#2000—111no—
272#1973—111no—
273#1935—111no—
274#1894—111no—
275#1893—111no—
276#1852—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11#12112yes—
296C23×C11AGL(1,ℤ/8)12yes—
297C23×C11#13712yes—
298C23×C11C22×D411yescharacteristic
299D4×C11—44no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—84no—
305D4×C11—84no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—84no—
335C2×C4×C11#12112yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—48no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355Dic22—22no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22—48no—
360Dic22—41no—
361Dic22—41no—
362Dic22—41no—
363Dic22—41no—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C11⋊C8—22no—
367C11⋊C8—41no—
368C23×Q8—111no—
369C22×SD16—111no—
370C22×SD16—111no—
371C22×M16—111no—
372C23×C8—111no—
373C2×C22⋊Q8—111no—
374C2×C22⋊Q8—111no—
375C2×#121—21no—
376C2×#121C2×D1111yescharacteristic
377C2×#121C2×D1111yescharacteristic
378C2×C4×D4C2×D1111yescharacteristic
379C22×C4⋊C4C2×D1111yescharacteristic
380#468—224no—
381#448—224no—
382#435—224no—
383C2×#107—111no—
384C2×#107—111no—
385C2×C4⋊C8—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#103—224no—
393C2×#102—111no—
394C2×#102—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×#97—111no—
398#396—21no—
399#395—221no—
400#394—21no—
401#393—221no—
402#391—111no—
403#391—111no—
404#390C2×D1111yescharacteristic
405#389C2×D1111yescharacteristic
406#386—21no—
407#386—221no—
408#385—221no—
409#380—111no—
410#380C2×D1111yescharacteristic
411#340—111no—
412#340—111no—
413#340—111no—
414#340—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11#46814yescomplemented
436C22×C11C2×#12111yescharacteristic
437C22×C11D4211yescharacteristic
438C22×C11#54611yescharacteristic
439C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
440C22×C11C2×#13711yescharacteristic
441C22×C11#57711yescharacteristic
442C22×C11#57811yescharacteristic
443C4×C11—22no—
444C4×C11—41no—
445C4×C11—42no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11—81no—
449C4×C11—81no—
450C4×C11#52511yescharacteristic
451C4×C11#53811yescharacteristic
452C4×C11D4211yescharacteristic
453C4×C11#54611yescharacteristic
454Dic11—42no—
455Dic11—42no—
456Dic11—81no—
457Dic11—81no—
458C22×Q8—111no—
459C22×Q8—111no—
460C22×Q8—222no—
461C22×Q8—222no—
462C22×Q8—221no—
463C22×Q8—222no—
464C22×Q8—222no—
465C22×Q8—441no—
466C22×Q8—441no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4C22⋊D1111yescharacteristic
470C22×D4C22×D1111yescharacteristic
471C23×C4—21no—
472C23×C4—221no—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C2×SD16—222no—
476C2×SD16—222no—
477C2×SD16—222no—
478C2×SD16—222no—
479C2×SD16—441no—
480C2×SD16—441no—
481C2×M16—222no—
482C2×M16—222no—
483C2×M16—441no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8—222no—
489C22×C8—222no—
490C22×C8—441no—
491C22⋊Q8—222no—
492C22⋊Q8—222no—
493C22⋊Q8—441no—
494C22⋊Q8—441no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—41no—
499#121—44no—
500C4×D4—22no—
501C4×D4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4C22⋊D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4C22⋊D1111yescharacteristic
523C2×C22⋊C4C22⋊D1111yescharacteristic
524C2×C42C22×D1111yescharacteristic
525#107—222no—
526#107—441no—
527C4⋊C8—222no—
528#103—114no—
529#103—222no—
530#103—222no—
531#103—222no—
532#103—222no—
533#103—222no—
534#102—222no—
535#102—441no—
536C22⋊C8—114no—
537C22⋊C8—222no—
538#97—222no—
539#95—21no—
540#95—21no—
541#95—221no—
542#95—221no—
543#95—221no—
544#95—221no—
545#95—221no—
546C2×C11—24no—
547C2×C11—81no—
548C2×C11—161no—
549C2×C11#242411yescharacteristic
550C2×C11C2×#46811yescharacteristic
551C2×C11#306311yescharacteristic
552C2×C11#326511yescharacteristic
553C2×C11#327011yescharacteristic
554C2×C11#330811yescharacteristic
555C2×C11#332011yescharacteristic
556C24—21no—
557C24C2×C22⋊D1111yescharacteristic
558C24C2×C22⋊D1111yescharacteristic
559C2×Q8—112no—
560C2×Q8—112no—
561C2×Q8—228no—
562C2×Q8—221no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8—221no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—442no—
573C2×Q8—442no—
574C2×Q8—444no—
575C2×Q8—444no—
576C2×Q8—444no—
577C2×Q8—442no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4D4×D1112yes—
617C22×C4#434112yes—
618C22×C4C2×C22⋊D1111yescharacteristic
619C22×C4C2×C22⋊D1111yescharacteristic
620C22×C4C2×C22⋊D1111yescharacteristic
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C23×D1111yescharacteristic
623SD16—444no—
624SD16—444no—
625M16—444no—
626C2×C8—112no—
627C2×C8—112no—
628C2×C8—112no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—444no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—442no—
652C4⋊C4—442no—
653C4⋊C4D4×D1112yes—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—442no—
662C22⋊C4—442no—
663C22⋊C4—442no—
664C42—21no—
665C42—21no—
666C11#2513011yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23#6698512yes—
686C23#6699212yes—
687C23#6700412yes—
688C23C22×C22⋊D1111yescharacteristic
689Q8—222no—
690Q8—222no—
691Q8—222no—
692Q8—222no—
693Q8—448no—
694Q8—441no—
695Q8—441no—
696Q8—441no—
697Q8—441no—
698D4—44no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—84no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—448no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4#6699212yes—
748C2×C4C2×D4×D1111yescharacteristic
749C2×C4C2×D4×D1111yescharacteristic
750C2×C4C2×#434111yescharacteristic
751C2×C4#6703711yescharacteristic
752C2×C4#41×D1111yescharacteristic
753C2×C4#6704211yescharacteristic
754C8—222no—
755C8—222no—
756C8—222no—
757C8—441no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22#1062265514yescomplemented
779C22C2×#6698511yescharacteristic
780C22D4×C22⋊D1111yescharacteristic
781C22C2×#6699211yescharacteristic
782C22C2×#6700411yescharacteristic
783C22#1062336011yescharacteristic
784C22#1062336711yescharacteristic
785C22#1062336911yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—442no—
794C4—442no—
795C4—881no—
796C4—881no—
797C4#1062313711yescharacteristic
798C4#1062314011yescharacteristic
799C4#1062314111yescharacteristic
800C4#1062314811yescharacteristic
801C2—24no—
802C2—81no—
803C2—161no—
804C2#1307215811yescharacteristic
805C2C2×#1062265511yescharacteristic
806C2#1307830911yescharacteristic
807C2#1308010711yescharacteristic
808C2#1308018211yescharacteristic
809C2#1308060111yescharacteristic
810C2#1308078111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2416C2
socleC23×C11C22×D4
hypercenter#2416D11
hypocenterC11#25130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#10622655C2semidirect
2. C2×#10622653C2semidirect
3. C2×#10622624C2semidirect
4. C22×#66874C2semidirect
5. #13071981C2semidirect
6. #13070008C2semidirect
7. #13069933C2semidirect
8. #13069819C2semidirect
9. #13069619C2semidirect
10. #13069496C2semidirect
11. #13069305C2semidirect
12. #13069047C2semidirect
13. #13069045C2semidirect
14. #13068804C2semidirect
140. C22⋊(C11⋊C8)D4semidirect
146. #66874D4semidirect
435. C22×C11#468semidirect
666. C11#25130semidirect
778. C22#10622655semidirect

Maximal subgroups

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

subgroupindex
C2×#106226552
C2×#106226532
C2×#106226242
C22×#668742
#130719812
#130700082
#130699332
#130698192
#130696192
#130694962
#130693052
#130690472
#130690452
#130688042
C11×#24162
#2513011