Finite Group Databasebeta

← #7631871

Subgroups — #7631871

Order 512.

9256 conjugacy classes of subgroups.

The subgroup lattice has 711 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#546C211yesmaximal, characteristic
2C2×#3428C211yesmaximal, characteristic, complemented
3#36216C2116yesmaximal, complemented
4#35987C218yesmaximal, complemented
5#35976C218yesmaximal, complemented
6#35679C212yesmaximal, complemented
7#35672C212yesmaximal, complemented
8#35351C214yesmaximal, complemented
9#35350C214yesmaximal, complemented
10#35262C212yesmaximal, complemented
11#35097C214yesmaximal, complemented
12#34809C212yesmaximal, complemented
13C2×#2482C214yesmaximal, complemented
14#34248C212yesmaximal, complemented
15#34172C211yesmaximal, characteristic, complemented
16#34171C212yesmaximal, complemented
17C23×#41C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C2×#546—216no—
20C2×#546C2218yes—
21C2×#546C2218yes—
22C22×#124C2211yescharacteristic
23C22×#123C2212yes—
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2212yes—
26C22×#121C2211yescharacteristic
27C22×#120C2212yes—
28#3428—216no—
29C2×#520C2214yescomplemented
30C2×#520C2214yescomplemented
31C2×#519C2212yescomplemented
32C2×#518C2212yes—
33C2×#518C2212yes—
34C2×#518C2214yescomplemented
35C2×C4×#41C2218yescomplemented
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C22×#117C2214yescomplemented
39C22×#117C2212yescomplemented
40C23×C22⋊C4C2212yes—
41#2854C2218yescomplemented
42#2853C22116yescomplemented
43#2624C2218yescomplemented
44#2623C2218yescomplemented
45#2623C2218yescomplemented
46#2504C2214yescomplemented
47#2501C2214yescomplemented
48#2500C2218yescomplemented
49#2498C22116yescomplemented
50#2498C22116yescomplemented
51#2487C2214yescomplemented
52#2486C2214yescomplemented
53#2485C2218yescomplemented
54#2484C2218yescomplemented
55#2484C2214yescomplemented
56#2483C2214yescomplemented
57#2482C2218yes—
58#2482C2214yes—
59#2482C2218yescomplemented
60#2482C2218yescomplemented
61#2482C2218yescomplemented
62#2482C22116yescomplemented
63#2482C22116yescomplemented
64#2448C22116yescomplemented
65#2448C22116yescomplemented
66#2444C22132yescomplemented
67#2443C22132yescomplemented
68#2423C22116yescomplemented
69#2421C22116yescomplemented
70#2418C22132yescomplemented
71#2418C22132yescomplemented
72#2405C2214yes—
73#2405C2218yescomplemented
74#2395C2218yescomplemented
75C2×#399C2218yescomplemented
76C2×#397C2218yescomplemented
77#2349C22116yescomplemented
78D4×C4⋊C4C22116yescomplemented
79#2339C2218yescomplemented
80#2339C2218yescomplemented
81D4×C22⋊C4C22116yescomplemented
82D4×C22⋊C4C22116yescomplemented
83#2317C2214yescomplemented
84#2315C2218yescomplemented
85#2310C2212yescomplemented
86#2309C2214yes—
87#2308C2218yes—
88#2308C2214yescomplemented
89C4×#123C2218yescomplemented
90#2296C2214yescomplemented
91C2×#388C22116yescomplemented
92C2×#385C2218yescomplemented
93#2280C2214yes—
94#2280C2212yescomplemented
95C2×#381C2214yescomplemented
96C2×#379C2218yes—
97C26C2312yes—
98C22×#41—216no—
99C22×#41D4116yes—
100C22×#41C2314yes—
101C22×#41C2314yes—
102C23×Q8C2311yescharacteristic
103C23×D4—28no—
104C23×D4—216no—
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C23×D4C2318yes—
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C23×D4C2312yes—
111C23×D4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116#546—264no—
117#546—264no—
118C2×#124—28no—
119C2×#124C2318yes—
120C2×#123—216no—
121C2×#123C2318yes—
122C2×#123C2318yes—
123C2×#123C2318yes—
124C2×#123C23116yescomplemented
125C2×C22⋊Q8—28no—
126C2×C22⋊Q8C2318yes—
127C2×#121—216no—
128C2×#121—28no—
129C2×#121C2314yes—
130C2×#121C2314yes—
131C2×#121C23116yes—
132C2×#120—216no—
133C2×#120C23116yes—
134#520—232no—
135#520—232no—
136#519—216no—
137#518—216no—
138#518—232no—
139#518—216no—
140C4×#41—264no—
141C2×C4×Q8C2318yescomplemented
142C2×C4×Q8C2318yescomplemented
143C2×C4×D4—28no—
144C2×C4×D4—28no—
145C2×C4×D4C23116yes—
146C2×C4×D4C2318yes—
147C2×C4×D4C2318yes—
148C2×C4×D4C2318yes—
149C2×C4×D4C2314yes—
150C2×C4×D4C2314yes—
151C2×C4×D4C23116yescomplemented
152C2×C4×D4C23116yescomplemented
153C2×#117—232no—
154C2×#117—216no—
155C2×#117C2314yes—
156C2×#117C2314yes—
157C2×#117C2314yes—
158C2×#117C2318yes—
159C2×#117C2314yescomplemented
160C2×#117C2318yescomplemented
161C2×#117C2314yescomplemented
162C2×#117C2318yescomplemented
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2314yescomplemented
167C22×C4⋊C4C2314yescomplemented
168C22×C4⋊C4C2312yescomplemented
169C22×C4⋊C4C2312yescomplemented
170C22×C4⋊C4C23116yescomplemented
171C22×C22⋊C4—216no—
172C22×C22⋊C4C2318yes—
173C22×C22⋊C4C2318yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2318yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2318yes—
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C23116yes—
185C22×C22⋊C4C23116yes—
186C22×C42C2311yescharacteristic
187C22×C42C2318yescomplemented
188C22×C42C2314yescomplemented
189#400C2318yescomplemented
190#400C23116yescomplemented
191#399C2318yes—
192#399C23116yes—
193#399C23116yescomplemented
194#399C23116yescomplemented
195#399C23116yescomplemented
196#398C2318yescomplemented
197#398C23116yescomplemented
198#397C2318yes—
199#397C23116yes—
200#397C23116yescomplemented
201#397C23116yescomplemented
202#397C23116yescomplemented
203#397C23116yescomplemented
204#394C23116yes—
205#394C23132yescomplemented
206#391C23116yescomplemented
207#390C23116yes—
208#390C2318yes—
209#390C2318yes—
210#389C23116yescomplemented
211#389C2318yescomplemented
212#389C2318yescomplemented
213#388C23132yes—
214#388C23116yes—
215#388C23132yescomplemented
216#388C23132yescomplemented
217#388C23132yescomplemented
218#387C23116yescomplemented
219#387C23132yescomplemented
220#386C23116yes—
221#386C23116yes—
222#386C23132yes—
223#386C2318yes—
224#386C23132yescomplemented
225#386C23116yescomplemented
226#385C2318yes—
227#385C23116yes—
228#385C2318yes—
229#385C23116yescomplemented
230#385C23116yescomplemented
231#385C23132yescomplemented
232#385C2318yescomplemented
233#384C2318yescomplemented
234#382C2318yescomplemented
235#381C2318yes—
236#381C2318yes—
237#381C2314yes—
238#381C2318yescomplemented
239#381C2318yescomplemented
240#381C2318yescomplemented
241#380C2318yes—
242#380C2318yes—
243#380C23132yescomplemented
244#380C2314yescomplemented
245#380C2314yescomplemented
246#379C23116yes—
247#379C2314yes—
248#379C23132yes—
249#379C2318yes—
250C4×C4⋊C4C23116yescomplemented
251C4×C22⋊C4C23116yes—
252C4×C22⋊C4C2314yescomplemented
253C4×C22⋊C4C2314yescomplemented
254C2×#95C2318yescomplemented
255C2×#95C2318yescomplemented
256C2×#95C23116yescomplemented
257C25—28no—
258C25—216no—
259C25—48no—
260C25—84no—
261C25C2411yescharacteristic
262C25C2418yes—
263C25C2412yes—
264C25C2411yescharacteristic
265C25C2412yes—
266C2×#41—2128no—
267C2×#41—232no—
268C2×#41—232no—
269C2×#41C2×D4132yes—
270C2×#41C2×D4132yes—
271C22×Q8—28no—
272C22×Q8C2×D418yes—
273C22×Q8C2414yes—
274C22×D4—216no—
275C22×D4—24no—
276C22×D4—28no—
277C22×D4—216no—
278C22×D4—28no—
279C22×D4—232no—
280C22×D4—264no—
281C22×D4—24no—
282C22×D4—28no—
283C22×D4—44no—
284C22×D4—464no—
285C22×D4—84no—
286C22×D4C2×D4116yes—
287C22×D4C2×D418yes—
288C22×D4#41116yes—
289C22×D4C2418yes—
290C22×D4C2414yes—
291C22×D4C2414yes—
292C22×D4C2418yes—
293C22×D4C2418yes—
294C22×D4C2414yes—
295C23×C4—216no—
296C23×C4—28no—
297C23×C4—28no—
298C23×C4—24no—
299C23×C4—28no—
300C23×C4—84no—
301C23×C4C2×D4116yes—
302C23×C4C2×D418yes—
303C23×C4C2411yescharacteristic
304C23×C4C2414yes—
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2414yes—
308C23×C4C2414yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2418yes—
315C23×C4C2418yes—
316C23×C4C24116yes—
317C23×C4C2418yes—
318C23×C4C2414yes—
319C23×C4C2414yes—
320C23×C4C2411yescharacteristic
321#124—232no—
322#123—232no—
323#123—232no—
324#123—416no—
325#123—816no—
326C22⋊Q8—232no—
327#121—264no—
328#121—216no—
329#121—216no—
330#120—264no—
331C4×Q8—232no—
332C4×Q8—232no—
333C4×D4—232no—
334C4×D4—232no—
335C4×D4—232no—
336C4×D4—264no—
337C4×D4—264no—
338C4×D4—264no—
339C4×D4—216no—
340C4×D4—216no—
341#117—216no—
342#117—232no—
343#117—216no—
344#117—232no—
345#117—216no—
346#117—232no—
347#117—216no—
348#117—216no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—216no—
353C2×C4⋊C4—216no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—816no—
357C2×C4⋊C4C2414yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2418yes—
361C2×C4⋊C4C2414yes—
362C2×C4⋊C4C2414yes—
363C2×C4⋊C4C2414yes—
364C2×C4⋊C4C2414yes—
365C2×C4⋊C4C2418yes—
366C2×C4⋊C4C2418yes—
367C2×C4⋊C4C2418yes—
368C2×C4⋊C4C24116yes—
369C2×C4⋊C4C24132yes—
370C2×C4⋊C4C24116yes—
371C2×C22⋊C4—216no—
372C2×C22⋊C4—232no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—232no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—232no—
381C2×C22⋊C4—232no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—432no—
384C2×C22⋊C4—816no—
385C2×C22⋊C4C2412yes—
386C2×C22⋊C4C2412yes—
387C2×C22⋊C4C2418yes—
388C2×C22⋊C4C2418yes—
389C2×C22⋊C4C2414yes—
390C2×C22⋊C4C2414yes—
391C2×C22⋊C4C2418yes—
392C2×C22⋊C4C2418yes—
393C2×C22⋊C4C24116yes—
394C2×C22⋊C4C24116yes—
395C2×C22⋊C4C2418yes—
396C2×C22⋊C4C2418yes—
397C2×C22⋊C4C2414yes—
398C2×C22⋊C4C24116yes—
399C2×C22⋊C4C2418yes—
400C2×C22⋊C4C24116yes—
401C2×C22⋊C4C24132yes—
402C2×C22⋊C4C24132yes—
403C2×C22⋊C4C2418yes—
404C2×C22⋊C4C2418yes—
405C2×C42—232no—
406C2×C42—216no—
407C2×C42—24no—
408C2×C42C2418yes—
409C2×C42C2418yes—
410C2×C42C24116yes—
411C2×C42C2418yes—
412C2×C42C2414yes—
413#95C2418yes—
414#95C2418yes—
415#95C24116yes—
416#95C24132yes—
417#95C24116yes—
418#95C24116yes—
419#95C24116yes—
420#95C24116yes—
421#95C24116yes—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—216no—
428C24—216no—
429C24—232no—
430C24—28no—
431C24—44no—
432C24—44no—
433C24—42no—
434C24—416no—
435C24—42no—
436C24—42no—
437C24—44no—
438C24—48no—
439C24—44no—
440C24—432no—
441C24—432no—
442C24—864no—
443C24—816no—
444C24C22×D414yes—
445C24C22×D418yes—
446C24C2×#41116yes—
447C24C2514yes—
448C24C2512yes—
449C24C2512yes—
450C24C2511yescharacteristic
451C24C2514yes—
452#41—2128no—
453#41—2128no—
454C2×Q8—232no—
455C2×Q8—216no—
456C2×Q8C22×D4116yes—
457C2×D4—264no—
458C2×D4—232no—
459C2×D4—28no—
460C2×D4—216no—
461C2×D4—232no—
462C2×D4—28no—
463C2×D4—216no—
464C2×D4—28no—
465C2×D4—216no—
466C2×D4—44no—
467C2×D4—416no—
468C2×D4—416no—
469C2×D4—432no—
470C2×D4—4128no—
471C2×D4—416no—
472C2×D4—816no—
473C2×D4#123164yescomplemented
474C2×D4C22×D4132yes—
475C2×D4C22×D4116yes—
476C2×D4C2×#41132yes—
477C22×C4—264no—
478C22×C4—24no—
479C22×C4—28no—
480C22×C4—216no—
481C22×C4—216no—
482C22×C4—232no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—216no—
493C22×C4—216no—
494C22×C4—216no—
495C22×C4—232no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—42no—
499C22×C4—44no—
500C22×C4—42no—
501C22×C4—416no—
502C22×C4—416no—
503C22×C4—416no—
504C22×C4—416no—
505C22×C4—416no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—416no—
509C22×C4—816no—
510C22×C4C22×D4116yes—
511C22×C4C22×D418yes—
512C22×C4C22×D414yes—
513C22×C4C22×D418yes—
514C22×C4C22×D4116yes—
515C22×C4C22×D418yes—
516C22×C4C22×D414yes—
517C22×C4C2×#4118yes—
518C22×C4C2512yes—
519C22×C4C25116yes—
520C22×C4C2518yes—
521C22×C4C2512yes—
522C22×C4C2512yes—
523C22×C4C2514yes—
524C22×C4C2518yes—
525C22×C4C2511yescharacteristic
526C22×C4C2514yes—
527C22×C4C2511yescharacteristic
528C22×C4C2512yes—
529C4⋊C4—28no—
530C4⋊C4—28no—
531C4⋊C4—216no—
532C4⋊C4—216no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—216no—
539C4⋊C4—216no—
540C4⋊C4—416no—
541C4⋊C4—432no—
542C4⋊C4—416no—
543C22⋊C4—216no—
544C22⋊C4—216no—
545C22⋊C4—232no—
546C22⋊C4—216no—
547C22⋊C4—28no—
548C22⋊C4—216no—
549C22⋊C4—232no—
550C22⋊C4—232no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—216no—
554C22⋊C4—28no—
555C22⋊C4—28no—
556C22⋊C4—216no—
557C22⋊C4—216no—
558C22⋊C4—432no—
559C22⋊C4—416no—
560C22⋊C4—432no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C42—216no—
564C42—232no—
565C42—216no—
566C42—28no—
567C42—216no—
568C23—28no—
569C23—22no—
570C23—28no—
571C23—22no—
572C23—28no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—28no—
581C23—24no—
582C23—28no—
583C23—28no—
584C23—28no—
585C23—48no—
586C23—48no—
587C23—432no—
588C23—44no—
589C23—44no—
590C23—416no—
591C23—432no—
592C23—464no—
593C23—44no—
594C23—48no—
595C23—48no—
596C23—44no—
597C23—432no—
598C23—48no—
599C23—88no—
600C23—832no—
601C23—816no—
602C23—816no—
603C23—8128no—
604C23C2×#123132yes—
605C23C23×D414yes—
606C23C23×D412yes—
607C23C23×D418yes—
608C23C22×#4114yes—
609C23C22×#41116yes—
610C23#58514yes—
611C23C2611yescharacteristic
612Q8—232no—
613D4—264no—
614D4—416no—
615D4—432no—
616D4—416no—
617D4—816no—
618D4C2×#123164yes—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—216no—
624C2×C4—232no—
625C2×C4—232no—
626C2×C4—216no—
627C2×C4—216no—
628C2×C4—28no—
629C2×C4—28no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—216no—
635C2×C4—24no—
636C2×C4—216no—
637C2×C4—216no—
638C2×C4—24no—
639C2×C4—216no—
640C2×C4—216no—
641C2×C4—24no—
642C2×C4—28no—
643C2×C4—44no—
644C2×C4—48no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—416no—
648C2×C4—832no—
649C2×C4—816no—
650C2×C4—88no—
651C2×C4—816no—
652C2×C4—88no—
653C2×C4—816no—
654C2×C4C2×#123116yes—
655C2×C4C23×D412yes—
656C2×C4C23×D418yes—
657C2×C4C23×D412yes—
658C2×C4C23×D414yes—
659C2×C4C22×#4118yes—
660C22—232no—
661C22—28no—
662C22—22no—
663C22—28no—
664C22—22no—
665C22—28no—
666C22—28no—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—24no—
671C22—432no—
672C22—416no—
673C22—44no—
674C22—48no—
675C22—42no—
676C22—42no—
677C22—416no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—88no—
682C22—864no—
683C22—816no—
684C22C22×#12314yes—
685C22C22×#123116yes—
686C22C24×D411yescharacteristic
687C22C23×#4112yes—
688C22C2×#58512yes—
689C22H(7,𝔽2)12yes—
690C4—22no—
691C4—22no—
692C4—28no—
693C4—416no—
694C4—42no—
695C4—48no—
696C4—42no—
697C4—44no—
698C4—48no—
699C4—42no—
700C4C22×#12318yes—
701C2—24no—
702C2—216no—
703C2—44no—
704C2—44no—
705C2—84no—
706C2C23×#12311yescharacteristic
707C2#6281111yescharacteristic
708C2#6285211yescharacteristic
709C2#6299014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#546C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3428C2semidirect
3. #36216C2semidirect
4. #35987C2semidirect
5. #35976C2semidirect
6. #35679C2semidirect
7. #35672C2semidirect
8. #35351C2semidirect
9. #35350C2semidirect
10. #35262C2semidirect
11. #35097C2semidirect
12. #34809C2semidirect
13. C2×#2482C2semidirect
14. #34248C2semidirect
15. #34172C2semidirect
16. #34171C2semidirect
29. C2×#520C22semidirect
30. C2×#520C22semidirect
31. C2×#519C22semidirect
34. C2×#518C22semidirect
35. C2×C4×#41C22semidirect
38. C22×#117C22semidirect
39. C22×#117C22semidirect
41. #2854C22semidirect
42. #2853C22semidirect
43. #2624C22semidirect
44. #2623C22semidirect
45. #2623C22semidirect
46. #2504C22semidirect
47. #2501C22semidirect
48. #2500C22semidirect
49. #2498C22semidirect
50. #2498C22semidirect
51. #2487C22semidirect
52. #2486C22semidirect
53. #2485C22semidirect
54. #2484C22semidirect
55. #2484C22semidirect
56. #2483C22semidirect
59. #2482C22semidirect
60. #2482C22semidirect
61. #2482C22semidirect
62. #2482C22semidirect
63. #2482C22semidirect
64. #2448C22semidirect
65. #2448C22semidirect
66. #2444C22semidirect
67. #2443C22semidirect
68. #2423C22semidirect
69. #2421C22semidirect
70. #2418C22semidirect
71. #2418C22semidirect
73. #2405C22semidirect
74. #2395C22semidirect
75. C2×#399C22semidirect
76. C2×#397C22semidirect
77. #2349C22semidirect
78. D4×C4⋊C4C22semidirect
79. #2339C22semidirect
80. #2339C22semidirect
81. D4×C22⋊C4C22semidirect
82. D4×C22⋊C4C22semidirect
83. #2317C22semidirect
84. #2315C22semidirect
85. #2310C22semidirect
88. #2308C22semidirect
89. C4×#123C22semidirect
90. #2296C22semidirect
91. C2×#388C22semidirect
92. C2×#385C22semidirect
94. #2280C22semidirect
95. C2×#381C22semidirect
124. C2×#123C23semidirect
141. C2×C4×Q8C23semidirect
142. C2×C4×Q8C23semidirect
151. C2×C4×D4C23semidirect
152. C2×C4×D4C23semidirect
159. C2×#117C23semidirect
160. C2×#117C23semidirect
161. C2×#117C23semidirect
162. C2×#117C23semidirect
166. C22×C4⋊C4C23semidirect
167. C22×C4⋊C4C23semidirect
168. C22×C4⋊C4C23semidirect
169. C22×C4⋊C4C23semidirect
170. C22×C4⋊C4C23semidirect
187. C22×C42C23semidirect
188. C22×C42C23semidirect
189. #400C23semidirect
190. #400C23semidirect
193. #399C23semidirect
194. #399C23semidirect
195. #399C23semidirect
196. #398C23semidirect
197. #398C23semidirect
200. #397C23semidirect
201. #397C23semidirect
202. #397C23semidirect
203. #397C23semidirect
205. #394C23semidirect
206. #391C23semidirect
210. #389C23semidirect
211. #389C23semidirect
212. #389C23semidirect
215. #388C23semidirect
216. #388C23semidirect
217. #388C23semidirect
218. #387C23semidirect
219. #387C23semidirect
224. #386C23semidirect
225. #386C23semidirect
229. #385C23semidirect
230. #385C23semidirect
231. #385C23semidirect
232. #385C23semidirect
233. #384C23semidirect
234. #382C23semidirect
238. #381C23semidirect
239. #381C23semidirect
240. #381C23semidirect
243. #380C23semidirect
244. #380C23semidirect
245. #380C23semidirect
250. C4×C4⋊C4C23semidirect
252. C4×C22⋊C4C23semidirect
253. C4×C22⋊C4C23semidirect
254. C2×#95C23semidirect
255. C2×#95C23semidirect
256. C2×#95C23semidirect
473. C2×D4#123semidirect

Maximal subgroups

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

subgroupindex
C22×#5462
C2×#34282
#362162
#359872
#359762
#356792
#356722
#353512
#353502
#352622
#350972
#348092
C2×#24822
#342482
#341722
#341712