Finite Group Databasebeta

← #6508637

Subgroups — #6508637

Order 512.

3112 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic
2C2×#3095C211yesmaximal, characteristic, complemented
3C22×#485C211yesmaximal, characteristic, complemented
4#34809C211yesmaximal, characteristic
5#24109C214yesmaximal, complemented
6#24098C212yesmaximal, complemented
7#24097C212yesmaximal, complemented
8#24065C214yesmaximal, complemented
9#24053C214yesmaximal, complemented
10#24042C212yesmaximal, complemented
11#24041C212yesmaximal, complemented
12#24010C214yesmaximal, complemented
13#21768C211yesmaximal, characteristic, complemented
14#21762C211yesmaximal, characteristic, complemented
15#21740C211yesmaximal, characteristic
16#3501—28no—
17#3501—28no—
18C2×#554—22no—
19C2×#554—22no—
20C2×#554C2212yes—
21C2×#554C2212yes—
22C2×D4×Q8C2212yes—
23C2×D4×Q8C2212yes—
24C2×#544—21no—
25C2×#543—21no—
26C2×#543—21no—
27C2×#533C2212yes—
28C22×C22⋊Q8C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#518—21no—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34#3095—28no—
35C2×#484C2212yescomplemented
36C2×#485—28no—
37C2×#485C2214yes—
38C2×#485C2214yes—
39C2×#485C2214yescomplemented
40C2×#483C2212yescomplemented
41C2×#428C2212yescomplemented
42C22×#107C2211yescharacteristic, complemented
43C22×#106C2211yescharacteristic, complemented
44C2×#419C2212yescomplemented
45C22×#103C2211yescharacteristic, complemented
46C22×#103C2211yescharacteristic, complemented
47C2×#407C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49#2487C2212yes—
50#2486C2212yes—
51#2485C2214yes—
52#2484—21no—
53#2483—21no—
54#2482—21no—
55#2405—21no—
56#2395—22no—
57C4×#123—22no—
58#2296C2212yes—
59#2280C2211yescharacteristic
60#2280C2212yes—
61#2058C2214yescomplemented
62#2057C2214yescomplemented
63#2043C2214yescomplemented
64#2043C2214yescomplemented
65#2036C2214yescomplemented
66#2036C2214yescomplemented
67#2035C2214yescomplemented
68#2035C2214yescomplemented
69#1894C2214yescomplemented
70#1892C2212yescomplemented
71#1892C2212yescomplemented
72#1873C2214yes—
73#1873C2214yes—
74#1870C2214yes—
75#1869C2212yes—
76#1869C2212yes—
77#1865C2214yescomplemented
78#1865C2214yescomplemented
79#1863C2214yescomplemented
80#1863C2214yescomplemented
81#1853C2214yescomplemented
82#1852C2214yescomplemented
83#1824C2212yescomplemented
84#1823C2212yescomplemented
85#1817C2212yes—
86#1787C2212yescomplemented
87#1787C2212yescomplemented
88#1787C2214yescomplemented
89#1787C2214yescomplemented
90#1779C2212yes—
91C23×Q8C2312yes—
92C23×Q8C2311yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4D411yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×M16C2312yes—
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100#554—232no—
101#554—232no—
102#554—28no—
103#554—28no—
104#554—28no—
105#554—28no—
106D4×Q8—28no—
107D4×Q8—28no—
108D4×Q8—28no—
109D4×Q8—28no—
110#544—216no—
111#543—216no—
112#543—216no—
113#533—28no—
114#533—28no—
115C2×C4⋊Q8—22no—
116C2×C4⋊Q8—22no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119C2×#125—22no—
120C2×#125—22no—
121C2×#125—22no—
122C2×#123—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8—28no—
133C2×C22⋊Q8—28no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—22no—
137C2×C22⋊Q8—22no—
138C2×C22⋊Q8—22no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8—22no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8D418yes—
143C2×C22⋊Q8D418yes—
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2312yes—
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2312yes—
148C2×C22⋊Q8C2312yes—
149C2×C22⋊Q8C2312yes—
150#518—216no—
151C2×C4×Q8—22no—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×D4—22no—
155C2×C4×D4—22no—
156C2×C4×D4—22no—
157C2×C4×D4—22no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4D412yes—
161C2×C4×D4D412yes—
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C2×#117—22no—
165C2×#117—21no—
166C2×#117—21no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117C2312yes—
170C2×#117C2312yes—
171C2×#117C2312yes—
172C22×C4⋊C4—22no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4D411yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C22⋊C4—22no—
182C22×C22⋊C4—21no—
183C22×C22⋊C4—21no—
184C22×C22⋊C4—21no—
185C22×C22⋊C4D411yescharacteristic
186C22×C22⋊C4D411yescharacteristic
187C22×C42—21no—
188C22×C42C2311yescharacteristic
189#485—216no—
190#485—216no—
191#485—216no—
192#484—28no—
193#483—28no—
194#428—28no—
195C2×#107—24no—
196C2×#107C2314yes—
197C2×#107C2314yes—
198C2×#106—24no—
199C2×#106C2314yes—
200C2×#106C2314yes—
201#419—28no—
202C2×#103—24no—
203C2×#103—24no—
204C2×#103C2314yes—
205C2×#103C2314yes—
206C2×#103C2314yes—
207C2×#103C2314yes—
208C2×#103C2314yes—
209C2×#103C2314yes—
210C2×#103C2314yes—
211C2×#103C2314yes—
212#407—24no—
213C2×C22⋊C8—24no—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C22⋊C8C2314yes—
219C2×C22⋊C8C2314yes—
220#400—22no—
221#399—22no—
222#398—22no—
223#397—22no—
224#397—24no—
225#394—24no—
226#389C2314yes—
227#389C2314yes—
228#388—24no—
229#387—24no—
230#386—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#381—21no—
235#381—22no—
236#381—22no—
237#380C2312yes—
238#380C2312yes—
239#380C2314yes—
240#380C2314yes—
241#379—22no—
242#379—21no—
243C4×C4⋊C4—24no—
244C4×C22⋊C4—21no—
245C4×C22⋊C4—24no—
246C4×C22⋊C4—21no—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#336C2314yes—
252#336C2314yes—
253C25C2×D411yescharacteristic
254C25C2×D411yescharacteristic
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8—42no—
266C22×Q8—42no—
267C22×Q8—44no—
268C22×Q8—44no—
269C22×Q8C2×D414yes—
270C22×Q8C2×D414yes—
271C22×Q8C2412yes—
272C22×Q8C2412yes—
273C22×D4—24no—
274C22×D4—28no—
275C22×D4C2×D412yes—
276C22×D4C2×D412yes—
277C23×C4—22no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D412yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×M16—24no—
305C2×M16—42no—
306C2×M16—42no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—42no—
310C22×C8—42no—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2414yes—
314C4⋊Q8—216no—
315C4⋊Q8—216no—
316C4⋊Q8—24no—
317C4⋊Q8—24no—
318C4⋊Q8—24no—
319C4⋊Q8—24no—
320#125—216no—
321#125—216no—
322#125—216no—
323#123—48no—
324C22⋊Q8—216no—
325C22⋊Q8—216no—
326C22⋊Q8—216no—
327C22⋊Q8—216no—
328C22⋊Q8—216no—
329C22⋊Q8—216no—
330C22⋊Q8—216no—
331C22⋊Q8—216no—
332C22⋊Q8—216no—
333C22⋊Q8—216no—
334C22⋊Q8—216no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—28no—
338C22⋊Q8—28no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8C2×D418yes—
348C22⋊Q8C2×D418yes—
349C22⋊Q8C2×D418yes—
350C22⋊Q8C2×D418yes—
351C4×Q8—216no—
352C4×Q8—24no—
353C4×Q8—24no—
354C4×Q8—24no—
355C4×Q8—24no—
356C4×D4—216no—
357C4×D4—216no—
358C4×D4—216no—
359C4×D4—216no—
360C4×D4—28no—
361C4×D4—28no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—24no—
365C4×D4—24no—
366#117—216no—
367#117—24no—
368#117—24no—
369#117—24no—
370#117—24no—
371#117—42no—
372#117—42no—
373#117—44no—
374#117—44no—
375C2×C4⋊C4—216no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4C2×D412yes—
406C2×C4⋊C4C2×D412yes—
407C2×C4⋊C4C2×D414yes—
408C2×C4⋊C4C2×D414yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2414yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C22⋊C4—216no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4C2×D412yes—
434C2×C22⋊C4C2×D412yes—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—44no—
445C2×C42C2×D412yes—
446C2×C42C2412yes—
447#107—28no—
448#107—28no—
449#106—28no—
450#106—28no—
451#103—28no—
452#103—28no—
453#103—28no—
454#103—28no—
455#103—44no—
456#103—44no—
457#103—44no—
458#103—44no—
459C22⋊C8—24no—
460C22⋊C8—24no—
461C22⋊C8—24no—
462C22⋊C8—24no—
463C22⋊C8—44no—
464C22⋊C8—44no—
465#95—24no—
466#95—24no—
467#95—22no—
468#95—22no—
469#95—24no—
470#95—24no—
471C24—22no—
472C24—24no—
473C24—24no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24#12014yes—
479C24C22×D411yescharacteristic
480C24C22×D411yescharacteristic
481C24C22×D412yes—
482C24C22×D411yescharacteristic
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—24no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—24no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—48no—
496C2×Q8—84no—
497C2×Q8—82no—
498C2×Q8—82no—
499C2×Q8—84no—
500C2×Q8—84no—
501C2×Q8—82no—
502C2×Q8—82no—
503C2×Q8—84no—
504C2×Q8—84no—
505C2×Q8—88no—
506C2×Q8C22×D414yes—
507C2×Q8C22×D414yes—
508C2×D4—232no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4#13718yes—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—44no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—44no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—84no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—84no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—84no—
565C22×C4#12014yes—
566C22×C4#12014yes—
567C22×C4#12014yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C2511yescharacteristic
581M16—48no—
582C2×C8—22no—
583C2×C8—24no—
584C2×C8—22no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—44no—
590C2×C8—44no—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C4⋊C4—28no—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—48no—
618C4⋊C4—84no—
619C4⋊C4C22×D414yes—
620C4⋊C4C22×D414yes—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—48no—
636C22⋊C4—82no—
637C22⋊C4—84no—
638C42—28no—
639C42—28no—
640C42—24no—
641C42—22no—
642C42—22no—
643C42—44no—
644C42—44no—
645C42—44no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—28no—
660C23—44no—
661C23—44no—
662C23—82no—
663C23—88no—
664C23—88no—
665C23—82no—
666C23C2×#12012yes—
667C23C2×#12012yes—
668C23C2×#12012yes—
669C23C2×#13714yes—
670C23C2×#13714yes—
671C23C23×D411yescharacteristic
672Q8—24no—
673Q8—24no—
674Q8—28no—
675Q8—42no—
676Q8—42no—
677Q8—44no—
678Q8—84no—
679Q8—84no—
680Q8—88no—
681Q8—88no—
682D4—216no—
683D4—216no—
684C2×C4—28no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—84no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—88no—
732C2×C4—88no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4C2×#12012yes—
736C2×C4C2×#12012yes—
737C2×C4C2×#12012yes—
738C2×C4C2×#13714yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C23×D411yescharacteristic
741C2×C4#58512yes—
742C2×C4#58512yes—
743C8—42no—
744C8—42no—
745C8—44no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—28no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—24no—
755C22—22no—
756C22—22no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—88no—
763C22—88no—
764C22#300414yes—
765C22C22×#12011yescharacteristic
766C22#348512yes—
767C22C22×#13712yes—
768C22#358412yes—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—24no—
773C4—42no—
774C4—44no—
775C4—44no—
776C4—42no—
777C4—44no—
778C4—44no—
779C4—84no—
780C4—82no—
781C4—82no—
782C4#348511yescharacteristic
783C4#348511yescharacteristic
784C4#348512yes—
785C2—24no—
786C2—44no—
787C2—42no—
788C2—42no—
789C2#3544611yescharacteristic
790C2C2×#300411yescharacteristic
791C2#6036611yescharacteristic
792C2#6174214yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3095C2semidirect
3. C22×#485C2semidirect
5. #24109C2semidirect
6. #24098C2semidirect
7. #24097C2semidirect
8. #24065C2semidirect
9. #24053C2semidirect
10. #24042C2semidirect
11. #24041C2semidirect
12. #24010C2semidirect
13. #21768C2semidirect
14. #21762C2semidirect
35. C2×#484C22semidirect
39. C2×#485C22semidirect
40. C2×#483C22semidirect
41. C2×#428C22semidirect
42. C22×#107C22semidirect
43. C22×#106C22semidirect
44. C2×#419C22semidirect
45. C22×#103C22semidirect
46. C22×#103C22semidirect
61. #2058C22semidirect
62. #2057C22semidirect
63. #2043C22semidirect
64. #2043C22semidirect
65. #2036C22semidirect
66. #2036C22semidirect
67. #2035C22semidirect
68. #2035C22semidirect
69. #1894C22semidirect
70. #1892C22semidirect
71. #1892C22semidirect
77. #1865C22semidirect
78. #1865C22semidirect
79. #1863C22semidirect
80. #1863C22semidirect
81. #1853C22semidirect
82. #1852C22semidirect
83. #1824C22semidirect
84. #1823C22semidirect
86. #1787C22semidirect
87. #1787C22semidirect
88. #1787C22semidirect
89. #1787C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
C2×#30952
C22×#4852
#348092
#241092
#240982
#240972
#240652
#240532
#240422
#240412
#240102
#217682
#217622
#217402