Finite Group Databasebeta

← #14660430

Subgroups — #14660430

Order 2816.

1310 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3C2×#10622853C211yesmaximal, characteristic, complemented
4C2×#10622847C211yesmaximal, characteristic, complemented
5#13068332C211yesmaximal, characteristic, complemented
6#13068325C211yesmaximal, characteristic, complemented
7C11×#3449C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×#41C2211yescharacteristic
10C11×#537—22no—
11C11×#536—21no—
12C11×#536C412yescomplemented
13C11×#535—21no—
14C11×#535C412yescomplemented
15C11×#534—22no—
16C11×#532—22no—
17C11×#525—22no—
18C11×#525—22no—
19C2×C11×#117C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24#10622853—22no—
25#10622853—22no—
26#10622849—22no—
27#10622849—22no—
28C2×#66901—22no—
29#10622847—22no—
30#10622847—22no—
31#10622846—22no—
32#10622846—22no—
33C2×#66899—21no—
34C2×#66898—22no—
35C2×#66896—21no—
36C2×C22⋊(C11⋊C8)—22no—
37#10622170—22no—
38#10622167—22no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41C2×C412yes—
62C2×C11×#41D412yes—
63C22×Q8×C11C2×C411yescharacteristic
64C22×Q8×C11D411yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2×C411yescharacteristic
67C22×D4×C11D412yes—
68C22×D4×C11D411yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11D412yes—
71C23×C4×C11C2311yescharacteristic
72C11×C4⋊Q8—22no—
73C11×#127—22no—
74C11×#124—22no—
75C11×#124—22no—
76C11×#123—24no—
77C11×#123—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—24no—
80C11×#121—24no—
81C11×#121—28no—
82C11×#121—24no—
83C11×#120—24no—
84C11×#120—24no—
85C4×D4×C11—28no—
86C11×#117—21no—
87C11×#117—21no—
88C11×#117C2×C412yes—
89C11×#117D412yes—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95#66979—21no—
96#66979—21no—
97#66979—21no—
98#66979—21no—
99#66979—21no—
100#66979—21no—
101#66979D412yescomplemented
102#66979D412yescomplemented
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318D412yescomplemented
113C22×C11⋊C8—21no—
114C22×C11⋊C8—21no—
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8—21no—
118C22×C11⋊C8—21no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8D412yescomplemented
121#66901—28no—
122#66899—24no—
123#66898—28no—
124#66896—24no—
125C22⋊(C11⋊C8)—28no—
126#10999—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C22⋊C412yes—
129C24×C11C2×D411yescharacteristic
130C11×#41—22no—
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—41no—
139C11×#41—41no—
140C11×#41—41no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C11×#41—41no—
158C11×#41—41no—
159C11×#41—41no—
160C11×#41—41no—
161C11×#41—41no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11C22⋊C412yes—
174C2×D4×C11—22no—
175C2×D4×C11—22no—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—28no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—41no—
195C2×D4×C11—41no—
196C2×D4×C11—41no—
197C2×D4×C11—41no—
198C2×D4×C11C22⋊C412yes—
199C22×C4×C11—21no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—41no—
210C22×C4×C11—41no—
211C22×C4×C11—41no—
212C22×C4×C11—41no—
213C22×C4×C11C22⋊C412yes—
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11#4111yescharacteristic
225C22×C4×C11#4111yescharacteristic
226C22×C4×C11#4111yescharacteristic
227C22×C4×C11#4111yescharacteristic
228C22×Dic11—41no—
229C22×Dic11—41no—
230C11×C4⋊C4—28no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4C22⋊C414yes—
233C11×C22⋊C4—28no—
234C11×C22⋊C4—28no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C42×C11—22no—
238C42×C11—22no—
239C22⋊Dic11—22no—
240C22⋊Dic11—22no—
241C22⋊Dic11—41no—
242C22⋊Dic11—41no—
243C4⋊Dic11—22no—
244C4⋊Dic11—22no—
245C4⋊Dic11—41no—
246C4⋊Dic11—41no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11—41no—
250C4×Dic11—41no—
251#4318—22no—
252#4318—22no—
253#4318—41no—
254#4318—41no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8—22no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8—41no—
260C2×C11⋊C8—41no—
261C2×C11⋊C8—41no—
262C2×C11⋊C8—41no—
263C2×C11⋊C8—41no—
264C2×C11⋊C8—41no—
265#3449D1111yescharacteristic
266C2×#421—111no—
267C2×#416—111no—
268C2×#410—111no—
269C2×#408—111no—
270#1735—111no—
271#1733—111no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—42no—
277C23×C11—44no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—82no—
281C23×C11C2×C22⋊C411yescharacteristic
282C23×C11#12011yescharacteristic
283C23×C11#12011yescharacteristic
284C23×C11#12011yescharacteristic
285C23×C11#12111yescharacteristic
286C23×C11#12111yescharacteristic
287C23×C11#12311yescharacteristic
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11—41no—
294Q8×C11—41no—
295Q8×C11—41no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11—42no—
301D4×C11—42no—
302D4×C11—42no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—88no—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—82no—
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11#12011yescharacteristic
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12111yescharacteristic
344C2×C4×C11#12111yescharacteristic
345C2×C4×C11#12111yescharacteristic
346C2×C4×C11#12111yescharacteristic
347C2×C4×C11#12111yescharacteristic
348C2×C4×C11#12111yescharacteristic
349C2×C4×C11#12111yescharacteristic
350C2×C4×C11#12311yescharacteristic
351C2×C4×C11#12311yescharacteristic
352C2×C4×C11#12311yescharacteristic
353C2×C4×C11#12411yescharacteristic
354C2×C4×C11#12411yescharacteristic
355C2×C4×C11#12711yescharacteristic
356C2×C4×C11#12711yescharacteristic
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—82no—
360C2×Dic11—82no—
361C11⋊C8—42no—
362C11⋊C8—42no—
363C22×#41C2×D1111yescharacteristic
364C22×#41C2×D1111yescharacteristic
365C22×M16—111no—
366C23×C8—111no—
367#537—22no—
368#536—21no—
369#536Dic1112yescomplemented
370#535—21no—
371#535Dic1112yescomplemented
372#534—22no—
373#532—22no—
374#525—22no—
375#525—22no—
376C2×#117—111no—
377C2×#117—111no—
378C2×#117C2×D1111yescharacteristic
379#421—222no—
380#421—222no—
381C2×#104—222no—
382#416—222no—
383#416—222no—
384C2×#103—221no—
385C2×#102—221no—
386#410—222no—
387#410—222no—
388C2×#99—222no—
389#408—222no—
390#408—222no—
391C2×C22⋊C8—222no—
392#340—222no—
393#339—222no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—44no—
402C22×C11—44no—
403C22×C11—44no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—82no—
407C22×C11—82no—
408C22×C11—82no—
409C22×C11#37911yescharacteristic
410C22×C11#38611yescharacteristic
411C22×C11#38611yescharacteristic
412C22×C11#39211yescharacteristic
413C22×C11#39211yescharacteristic
414C22×C11#39411yescharacteristic
415C22×C11#39411yescharacteristic
416C4×C11—44no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11#38611yescharacteristic
420C4×C11#38611yescharacteristic
421C4×C11#39011yescharacteristic
422C4×C11#39011yescharacteristic
423C4×C11#39211yescharacteristic
424C4×C11#39211yescharacteristic
425C4×C11#39411yescharacteristic
426C4×C11#39411yescharacteristic
427Dic11—82no—
428Dic11—82no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41C2×Dic1112yes—
452C2×#41C22⋊D1112yes—
453C22×Q8C2×Dic1111yescharacteristic
454C22×Q8C22⋊D1111yescharacteristic
455C22×D4—21no—
456C22×D4C2×Dic1111yescharacteristic
457C22×D4C22⋊D1112yes—
458C22×D4C22⋊D1111yescharacteristic
459C23×C4—21no—
460C23×C4C22⋊D1112yes—
461C23×C4C22×D1111yescharacteristic
462C2×M16—112no—
463C2×M16—221no—
464C2×M16—221no—
465C2×M16—221no—
466C2×M16—221no—
467C2×M16—221no—
468C22×C8—112no—
469C22×C8—221no—
470C22×C8—221no—
471C22×C8—221no—
472C22×C8—221no—
473C22×C8—221no—
474C22×C8—221no—
475C22×C8—221no—
476C4⋊Q8—22no—
477#127—22no—
478#124—22no—
479#124—22no—
480#123—24no—
481#123—24no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484#121—24no—
485#121—28no—
486#121—24no—
487#120—24no—
488#120—24no—
489C4×D4—28no—
490#117—21no—
491#117—21no—
492#117—112no—
493#117—112no—
494#117—221no—
495#117—221no—
496#117—221no—
497#117—221no—
498#117—221no—
499#117—221no—
500#117C2×Dic1112yes—
501#117C22⋊D1112yes—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22⋊D1112yes—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C42—21no—
509C2×C42—221no—
510C2×C42—221no—
511#104—228no—
512#103—224no—
513#102—224no—
514#99—228no—
515C22⋊C8—228no—
516C2×C11—21no—
517C2×C11—21no—
518C2×C11—21no—
519C2×C11—21no—
520C2×C11—21no—
521C2×C11—21no—
522C2×C11—82no—
523C2×C11—82no—
524C2×C11#143811yescharacteristic
525C2×C11#179412yes—
526C24—21no—
527C24C22⋊Dic1112yes—
528C24C2×C22⋊D1111yescharacteristic
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—41no—
538#41—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8C22⋊Dic1112yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—28no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4C22⋊Dic1112yes—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—441no—
613C22×C4—441no—
614C22×C4C22⋊Dic1112yes—
615C22×C4D4×D1111yescharacteristic
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4D4×D1111yescharacteristic
619C22×C4#434111yescharacteristic
620C22×C4#434111yescharacteristic
621C22×C4#434111yescharacteristic
622C22×C4#434111yescharacteristic
623C22×C4C22×Dic1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629M16—222no—
630M16—222no—
631M16—441no—
632M16—441no—
633C2×C8—222no—
634C2×C8—222no—
635C2×C8—222no—
636C2×C8—222no—
637C2×C8—441no—
638C2×C8—441no—
639C2×C8—441no—
640C2×C8—441no—
641C2×C8—441no—
642C2×C8—441no—
643C4⋊C4—28no—
644C4⋊C4—22no—
645C4⋊C4—222no—
646C4⋊C4—222no—
647C4⋊C4—441no—
648C4⋊C4—441no—
649C4⋊C4C22⋊Dic1114yes—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—222no—
655C22⋊C4—222no—
656C22⋊C4—441no—
657C22⋊C4—441no—
658C42—22no—
659C42—22no—
660C42—222no—
661C42—222no—
662C42—441no—
663C42—441no—
664C11#1099911yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—44no—
671C23—41no—
672C23—41no—
673C23—82no—
674C23#6698811yescharacteristic
675C23#6699011yescharacteristic
676C23#6699211yescharacteristic
677C23#6699211yescharacteristic
678C23C2×C22⋊Dic1111yescharacteristic
679C23#6700611yescharacteristic
680C23#6700611yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—88no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—82no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—882no—
725C2×C4—882no—
726C2×C4D4×Dic1111yescharacteristic
727C2×C4D4×Dic1111yescharacteristic
728C2×C4D4×Dic1111yescharacteristic
729C2×C4D4×Dic1111yescharacteristic
730C2×C4#6698811yescharacteristic
731C2×C4#6698811yescharacteristic
732C2×C4#6698811yescharacteristic
733C2×C4#6698911yescharacteristic
734C2×C4#6698911yescharacteristic
735C2×C4#6699011yescharacteristic
736C2×C4#6699011yescharacteristic
737C2×C4#6699011yescharacteristic
738C2×C4#6699111yescharacteristic
739C2×C4#6699111yescharacteristic
740C2×C4#6699111yescharacteristic
741C2×C4#6699111yescharacteristic
742C2×C4#6699211yescharacteristic
743C2×C4#6699211yescharacteristic
744C2×C4#6699211yescharacteristic
745C2×C4#6699211yescharacteristic
746C2×C4#6699211yescharacteristic
747C2×C4#6699211yescharacteristic
748C2×C4#6699311yescharacteristic
749C2×C4#6699311yescharacteristic
750C2×C4C2×C22⋊Dic1111yescharacteristic
751C2×C4C2×C22⋊Dic1111yescharacteristic
752C2×C4#6700611yescharacteristic
753C2×C4#6700611yescharacteristic
754C8—442no—
755C8—442no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#1062283311yescharacteristic
772C22#1062283311yescharacteristic
773C22#1062283511yescharacteristic
774C22#1062283511yescharacteristic
775C22#1062283611yescharacteristic
776C22#1062283611yescharacteristic
777C22#1062286011yescharacteristic
778C4—44no—
779C4—42no—
780C4—42no—
781C4—882no—
782C4—882no—
783C4#1062283311yescharacteristic
784C4#1062283311yescharacteristic
785C4#1062283411yescharacteristic
786C4#1062283411yescharacteristic
787C4#1062283511yescharacteristic
788C4#1062283511yescharacteristic
789C4#1062283611yescharacteristic
790C4#1062283611yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—82no—
798C2—82no—
799C2#1306685711yescharacteristic
800C2#1306858012yes—
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3449C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenter#3449D11
hypocenterC11#10999
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10622849C2semidirect
2. C2×#10622846C2semidirect
3. C2×#10622853C2semidirect
4. C2×#10622847C2semidirect
5. #13068332C2semidirect
6. #13068325C2semidirect
12. C11×#536C4semidirect
14. C11×#535C4semidirect
101. #66979D4semidirect
102. #66979D4semidirect
112. C2×#4318D4semidirect
120. C22×C11⋊C8D4semidirect
369. #536Dic11semidirect
371. #535Dic11semidirect
664. C11#10999semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
C2×#106228462
C2×#106228532
C2×#106228472
#130683322
#130683252
C11×#34492
#1099911