Finite Group Databasebeta

← #7631622

Subgroups — #7631622

Order 512.

11156 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3485C212yesmaximal, complemented
2C22×#547C211yesmaximal, characteristic, complemented
3C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
4#36259C218yesmaximal, complemented
5#36153C218yesmaximal, complemented
6#36020C218yesmaximal, complemented
7#36009C218yesmaximal, complemented
8#35633C214yesmaximal, complemented
9#35447C218yesmaximal, complemented
10#35316C212yesmaximal, complemented
11#35000C214yesmaximal, complemented
12#34935C212yesmaximal, complemented
13C2×#2486C214yesmaximal, complemented
14#34181C211yesmaximal, characteristic, complemented
15#34172C212yesmaximal, complemented
16C22×H(5,𝔽2)C2211yescharacteristic
17C23×#41C2212yes—
18#3485—232no—
19C2×#547—216no—
20C2×#547C22116yescomplemented
21C2×#547C2218yescomplemented
22C2×#547C2218yescomplemented
23C2×#546C22116yescomplemented
24C2×#536C2214yes—
25C2×#534C2218yes—
26C22×C4⋊Q8C2211yescharacteristic, complemented
27C2×#525C2214yes—
28C22×#123C2218yes—
29C22×#123C2214yescomplemented
30C22×C22⋊Q8C2212yescomplemented
31C22×#121C2212yescomplemented
32C4×H(5,𝔽2)—216no—
33C2×#520C2212yes—
34C2×#520C2214yescomplemented
35C2×#518C2212yes—
36C2×#518C2214yes—
37C2×#518C2211yescharacteristic
38C2×#518C2214yescomplemented
39C2×C4×#41C2212yes—
40C2×C4×#41C2214yescomplemented
41C22×C4×D4C2214yes—
42C22×C4×D4C2211yescharacteristic
43C22×C4×D4C2214yescomplemented
44C22×C4×D4C2211yescharacteristic, complemented
45C23×C4⋊C4C2212yescomplemented
46#2857C2218yescomplemented
47#2854C2218yescomplemented
48#2847C2218yescomplemented
49#2621C2218yescomplemented
50#2618C2218yescomplemented
51#2617C2218yescomplemented
52#2547C2214yescomplemented
53#2547C2214yescomplemented
54#2546C2214yescomplemented
55#2546C2214yescomplemented
56#2543C22116yescomplemented
57#2538C2214yescomplemented
58#2537C2214yescomplemented
59#2536C2214yescomplemented
60#2535C2214yescomplemented
61#2534C22116yescomplemented
62#2534C2218yescomplemented
63#2486C22116yescomplemented
64#2486C22116yescomplemented
65#2486C2214yescomplemented
66#2486C2218yescomplemented
67#2486C22116yescomplemented
68#2486C2218yescomplemented
69#2429C22116yescomplemented
70#2427C22116yescomplemented
71#2425C22132yescomplemented
72#2425C22132yescomplemented
73#2417C22116yescomplemented
74#2416C22116yescomplemented
75#2415C22116yescomplemented
76#2413C22132yescomplemented
77#2412C22132yescomplemented
78#2408C2214yescomplemented
79#2392C2218yescomplemented
80C2×#398C2218yescomplemented
81C2×#397C2218yescomplemented
82#2349C2218yescomplemented
83D4×C4⋊C4C2218yescomplemented
84#2339C22116yescomplemented
85#2339C22116yescomplemented
86#2316C2212yescomplemented
87#2315C2214yescomplemented
88#2310C2214yescomplemented
89#2308C2218yescomplemented
90C4×#121C2218yescomplemented
91C2×#389C2218yescomplemented
92#2285C2212yescomplemented
93#2280C2214yescomplemented
94C2×#381C2218yescomplemented
95C2×#380C2218yescomplemented
96C2×#380C2214yescomplemented
97C2×H(5,𝔽2)—28no—
98C2×H(5,𝔽2)—28no—
99C2×H(5,𝔽2)D4116yescomplemented
100C22×#41—216no—
101C22×#41—216no—
102C22×#41—216no—
103C22×#41C23116yes—
104C22×#41C2312yes—
105C22×#41C2314yes—
106C23×Q8C2312yes—
107C23×D4C2314yes—
108C23×D4C2314yes—
109C23×D4C2314yes—
110C23×D4C2311yescharacteristic
111C23×D4C2311yescharacteristic
112C24×C4C2314yes—
113C24×C4C2312yes—
114C24×C4C2314yes—
115C24×C4C2312yes—
116#547—2128no—
117#547—264no—
118#547—264no—
119#546—2128no—
120#536—232no—
121#534—264no—
122C2×C4⋊Q8—28no—
123C2×C4⋊Q8C2314yes—
124C2×C4⋊Q8C2314yes—
125C2×C4⋊Q8C2318yes—
126C2×#124C2318yes—
127#525—232no—
128C2×#123—264no—
129C2×#123—232no—
130C2×#123C23116yes—
131C2×#123C2318yes—
132C2×#123C23116yes—
133C2×#123C23132yes—
134C2×#123C23132yes—
135C2×C22⋊Q8—216no—
136C2×C22⋊Q8C23116yes—
137C2×C22⋊Q8C23116yes—
138C2×C22⋊Q8C2318yes—
139C2×#121—216no—
140C2×#121C2318yes—
141C2×#121C2318yes—
142C2×#121C2318yes—
143C2×#121C23132yes—
144C2×#121C2318yes—
145C2×#120C23116yes—
146C2×#120C2318yes—
147#520—232no—
148#520—216no—
149#518—28no—
150#518—216no—
151#518—232no—
152#518—232no—
153C4×#41—232no—
154C4×#41—216no—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2314yes—
158C2×C4×D4—232no—
159C2×C4×D4—232no—
160C2×C4×D4—28no—
161C2×C4×D4D4116yescomplemented
162C2×C4×D4C2314yes—
163C2×C4×D4C2314yes—
164C2×C4×D4C23116yes—
165C2×C4×D4C2314yes—
166C2×C4×D4C23116yes—
167C2×C4×D4C2314yes—
168C2×C4×D4C2318yes—
169C2×C4×D4C2318yes—
170C2×C4×D4C2318yes—
171C2×C4×D4C2312yes—
172C2×C4×D4C2318yes—
173C2×C4×D4C2314yes—
174C2×C4×D4C2314yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2312yes—
177C2×C4×D4C2318yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2314yes—
180C2×#117C2312yes—
181C2×#117C2314yes—
182C2×#117C2314yes—
183C2×#117C2318yes—
184C2×#117C2314yes—
185C22×C4⋊C4—216no—
186C22×C4⋊C4C2314yes—
187C22×C4⋊C4C2318yes—
188C22×C4⋊C4C23116yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2314yes—
192C22×C4⋊C4C2318yes—
193C22×C4⋊C4C2314yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2318yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C22⋊C4C2314yes—
198C22×C22⋊C4C2318yes—
199C22×C22⋊C4C2314yes—
200C22×C22⋊C4C23116yes—
201C22×C22⋊C4C2318yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2314yes—
204C22×C22⋊C4C2312yes—
205C22×C42C2314yes—
206C22×C42C2314yes—
207C22×C42C2311yescharacteristic
208#398C23116yes—
209#398C23116yes—
210#398C2318yes—
211#398C23132yes—
212#397C23116yes—
213#397C23116yes—
214#397C2318yes—
215#397C23132yes—
216#396C23132yes—
217#396C23116yes—
218#394C23132yes—
219#394C2318yes—
220#394C23116yes—
221#392C2318yes—
222#391C23116yes—
223#391C2318yes—
224#391C2318yes—
225#390C2318yes—
226#389C23116yes—
227#389C23116yes—
228#389C23116yes—
229#389C23132yes—
230#389C2318yes—
231#388C23132yes—
232#388C23116yes—
233#386C23116yes—
234#386C23116yes—
235#386C23132yes—
236#386C23132yes—
237#386C23116yes—
238#385C23132yes—
239#384C2314yes—
240#382C2314yes—
241#381C23116yes—
242#381C23132yes—
243#381C2318yes—
244#380C2314yes—
245#380C2318yes—
246#380C2318yes—
247#380C23116yes—
248#380C2318yes—
249#380C2318yes—
250#380C23116yes—
251#380C2318yes—
252#380C2314yes—
253#380C23132yes—
254#380C2318yes—
255#379C2318yes—
256C4×C4⋊C4C2314yes—
257C4×C4⋊C4C2314yes—
258C4×C22⋊C4C23116yes—
259C2×#95C23116yes—
260C2×#95C23116yes—
261C2×#95C2318yes—
262C25C2412yes—
263C25C2414yes—
264C25C2412yes—
265H(5,𝔽2)—2128no—
266C2×#41—216no—
267C2×#41—264no—
268C2×#41—264no—
269C2×#41—216no—
270C2×#41—264no—
271C2×#41—28no—
272C2×#41—28no—
273C2×#41—4128no—
274C2×#41C2×D4116yes—
275C2×#41C2×D4132yescomplemented
276C22×Q8—28no—
277C22×Q8—28no—
278C22×Q8—28no—
279C22×Q8C2418yes—
280C22×Q8C2412yes—
281C22×D4—216no—
282C22×D4—216no—
283C22×D4—216no—
284C22×D4—216no—
285C22×D4—216no—
286C22×D4—216no—
287C22×D4—216no—
288C22×D4—24no—
289C22×D4—44no—
290C22×D4C2×D4132yes—
291C22×D4C2×D418yes—
292C22×D4C2×D418yes—
293C22×D4C2×D4132yescomplemented
294C22×D4#4118yes—
295C22×D4C2412yes—
296C22×D4C24116yes—
297C22×D4C2414yes—
298C22×D4C2418yes—
299C22×D4C2412yes—
300C22×D4C2412yes—
301C22×D4C24116yes—
302C22×D4C2414yes—
303C23×C4—216no—
304C23×C4—216no—
305C23×C4—216no—
306C23×C4—28no—
307C23×C4—28no—
308C23×C4—28no—
309C23×C4—216no—
310C23×C4—48no—
311C23×C4—416no—
312C23×C4C2×D4116yes—
313C23×C4C2412yes—
314C23×C4C2414yes—
315C23×C4C24116yes—
316C23×C4C2414yes—
317C23×C4C2418yes—
318C23×C4C2414yes—
319C23×C4C2414yes—
320C23×C4C2411yescharacteristic
321C23×C4C2414yes—
322C23×C4C24116yes—
323C23×C4C2414yes—
324C23×C4C2414yes—
325C23×C4C2414yes—
326C23×C4C2418yes—
327C23×C4C2411yescharacteristic
328C23×C4C2412yes—
329C23×C4C2414yes—
330C23×C4C2411yescharacteristic
331C4⋊Q8—232no—
332C4⋊Q8—216no—
333C4⋊Q8—216no—
334#124—232no—
335#123—232no—
336#123—264no—
337#123—2128no—
338#123—264no—
339#123—2128no—
340C22⋊Q8—232no—
341C22⋊Q8—264no—
342C22⋊Q8—264no—
343#121—232no—
344#121—2128no—
345#121—232no—
346#121—232no—
347#121—416no—
348#120—264no—
349#120—232no—
350C4×Q8—216no—
351C4×Q8—28no—
352C4×Q8—28no—
353C4×D4—216no—
354C4×D4—216no—
355C4×D4—264no—
356C4×D4—232no—
357C4×D4—216no—
358C4×D4—232no—
359C4×D4—232no—
360C4×D4—216no—
361C4×D4—264no—
362C4×D4—216no—
363C4×D4—232no—
364C4×D4—232no—
365C4×D4—28no—
366C4×D4—216no—
367C4×D4—216no—
368C4×D4—28no—
369C4×D4C2×D4132yes—
370C4×D4C2×D4132yes—
371#117—28no—
372#117—216no—
373#117—216no—
374#117—232no—
375#117—216no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—216no—
379C2×C4⋊C4—232no—
380C2×C4⋊C4—232no—
381C2×C4⋊C4—216no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—216no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4C2×D418yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2414yes—
390C2×C4⋊C4C2414yes—
391C2×C4⋊C4C24116yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2414yes—
394C2×C4⋊C4C2418yes—
395C2×C4⋊C4C24116yes—
396C2×C4⋊C4C2418yes—
397C2×C4⋊C4C24132yes—
398C2×C4⋊C4C2418yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2414yes—
401C2×C4⋊C4C2418yes—
402C2×C4⋊C4C24116yes—
403C2×C4⋊C4C2418yes—
404C2×C4⋊C4C2414yes—
405C2×C22⋊C4—216no—
406C2×C22⋊C4—232no—
407C2×C22⋊C4—264no—
408C2×C22⋊C4—216no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—216no—
411C2×C22⋊C4—232no—
412C2×C22⋊C4C2×D4116yes—
413C2×C22⋊C4C2414yes—
414C2×C22⋊C4C2418yes—
415C2×C22⋊C4C2414yes—
416C2×C22⋊C4C2418yes—
417C2×C22⋊C4C2414yes—
418C2×C22⋊C4C2418yes—
419C2×C22⋊C4C24116yes—
420C2×C22⋊C4C24116yes—
421C2×C22⋊C4C2418yes—
422C2×C22⋊C4C24132yes—
423C2×C22⋊C4C24116yes—
424C2×C22⋊C4C24116yes—
425C2×C22⋊C4C24116yes—
426C2×C22⋊C4C24116yes—
427C2×C22⋊C4C2418yes—
428C2×C42—216no—
429C2×C42—216no—
430C2×C42C2×D418yes—
431C2×C42C2414yes—
432C2×C42C2418yes—
433C2×C42C2414yes—
434C2×C42C2418yes—
435C2×C42C2414yes—
436C2×C42C2412yes—
437C2×C42C2412yes—
438#95C24116yes—
439#95C24116yes—
440#95C2418yes—
441#95C24132yes—
442#95C24116yes—
443#95C24132yes—
444#95C2418yes—
445C24—28no—
446C24—28no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—44no—
451C24—44no—
452C24—48no—
453C24—44no—
454C24—48no—
455C24—44no—
456C24C22×D4116yes—
457C24C22×D418yes—
458C24C22×D418yes—
459C24C2×#4118yes—
460C24C2514yes—
461C24C2514yes—
462C24C2511yescharacteristic
463C24C2514yes—
464#41—2128no—
465#41—264no—
466#41—4256no—
467C2×Q8—24no—
468C2×Q8—216no—
469C2×Q8—216no—
470C2×Q8—24no—
471C2×Q8—216no—
472C2×Q8—432no—
473C2×Q8C22×D418yes—
474C2×D4—2128no—
475C2×D4—28no—
476C2×D4—216no—
477C2×D4—28no—
478C2×D4—216no—
479C2×D4—2128no—
480C2×D4—232no—
481C2×D4—232no—
482C2×D4—232no—
483C2×D4—232no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—28no—
489C2×D4—44no—
490C2×D4—416no—
491C2×D4—416no—
492C2×D4—416no—
493C2×D4—464no—
494C2×D4#121164yescomplemented
495C2×D4C22×D4116yes—
496C2×D4C22×D4132yes—
497C2×D4C22×D418yes—
498C2×D4C22×D4116yes—
499C2×D4C22×D4116yes—
500C2×D4C2×#41116yes—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—216no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—28no—
509C22×C4—232no—
510C22×C4—232no—
511C22×C4—24no—
512C22×C4—28no—
513C22×C4—24no—
514C22×C4—28no—
515C22×C4—232no—
516C22×C4—28no—
517C22×C4—232no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—216no—
522C22×C4—216no—
523C22×C4—216no—
524C22×C4—28no—
525C22×C4—216no—
526C22×C4—432no—
527C22×C4—44no—
528C22×C4—48no—
529C22×C4—42no—
530C22×C4—416no—
531C22×C4—416no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—416no—
536C22×C4—464no—
537C22×C4—432no—
538C22×C4—832no—
539C22×C4C22×D4116yes—
540C22×C4C22×D414yes—
541C22×C4C22×D4116yes—
542C22×C4C22×D4116yes—
543C22×C4C22×D414yes—
544C22×C4C22×D418yes—
545C22×C4C22×D4116yes—
546C22×C4C22×D414yes—
547C22×C4C22×D414yes—
548C22×C4C2×#4114yes—
549C22×C4C2514yes—
550C22×C4C2514yes—
551C22×C4C25116yes—
552C22×C4C2514yes—
553C22×C4C2518yes—
554C22×C4C2511yescharacteristic
555C22×C4C2512yes—
556C22×C4C2514yes—
557C22×C4C2514yes—
558C22×C4C2512yes—
559C22×C4C2511yescharacteristic
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—232no—
565C4⋊C4—216no—
566C4⋊C4—28no—
567C4⋊C4—24no—
568C4⋊C4—232no—
569C4⋊C4—264no—
570C4⋊C4—216no—
571C4⋊C4—28no—
572C4⋊C4—24no—
573C4⋊C4—216no—
574C4⋊C4—216no—
575C4⋊C4—416no—
576C4⋊C4—48no—
577C4⋊C4C22×D4116yes—
578C22⋊C4—28no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—232no—
582C22⋊C4—232no—
583C22⋊C4—264no—
584C22⋊C4—216no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—216no—
588C22⋊C4—232no—
589C22⋊C4—232no—
590C22⋊C4—416no—
591C22⋊C4—416no—
592C22⋊C4C22×D4132yes—
593C42—28no—
594C42—216no—
595C42—28no—
596C42—28no—
597C42—216no—
598C42C22×D418yes—
599C42C22×D418yes—
600C23—28no—
601C23—22no—
602C23—28no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—28no—
607C23—28no—
608C23—232no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—28no—
613C23—28no—
614C23—48no—
615C23—416no—
616C23—48no—
617C23—416no—
618C23—432no—
619C23—48no—
620C23—48no—
621C23—48no—
622C23—88no—
623C23—88no—
624C23—88no—
625C23—816no—
626C23—88no—
627C23C2×#121132yes—
628C23C23×D418yes—
629C23C23×D412yes—
630C23C23×D418yes—
631C23C23×D412yes—
632C23C23×D418yes—
633C23C22×#4112yes—
634C23C22×#4118yes—
635C23C2611yescharacteristic
636Q8—216no—
637Q8—432no—
638D4—264no—
639D4—232no—
640D4—216no—
641D4—48no—
642D4—464no—
643D4—48no—
644D4—832no—
645D4C2×#121164yes—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—232no—
652C2×C4—232no—
653C2×C4—28no—
654C2×C4—232no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—216no—
658C2×C4—24no—
659C2×C4—28no—
660C2×C4—24no—
661C2×C4—28no—
662C2×C4—24no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—216no—
666C2×C4—28no—
667C2×C4—216no—
668C2×C4—416no—
669C2×C4—48no—
670C2×C4—44no—
671C2×C4—48no—
672C2×C4—416no—
673C2×C4—464no—
674C2×C4—432no—
675C2×C4—416no—
676C2×C4—88no—
677C2×C4—816no—
678C2×C4—832no—
679C2×C4—88no—
680C2×C4—88no—
681C2×C4C2×#121116yes—
682C2×C4C23×D414yes—
683C2×C4C23×D418yes—
684C2×C4C23×D412yes—
685C2×C4C23×D418yes—
686C2×C4C23×D414yes—
687C2×C4C23×D414yes—
688C2×C4C23×D412yes—
689C2×C4C22×#4114yes—
690C2×C4#58514yes—
691C22—216no—
692C22—24no—
693C22—24no—
694C22—216no—
695C22—22no—
696C22—28no—
697C22—22no—
698C22—28no—
699C22—216no—
700C22—28no—
701C22—432no—
702C22—48no—
703C22—44no—
704C22—44no—
705C22—48no—
706C22—48no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—832no—
711C22—816no—
712C22C22×#121116yes—
713C22C22×#12114yes—
714C22C24×D411yescharacteristic
715C22C24×D411yescharacteristic
716C22C23×#4111yescharacteristic
717C22C2×#58512yes—
718C222−1+612yes—
719C4—22no—
720C4—28no—
721C4—24no—
722C4—28no—
723C4—416no—
724C4—44no—
725C4—44no—
726C4—44no—
727C4—48no—
728C4C22×#12118yes—
729C4#348514yescomplemented
730C2—24no—
731C2—216no—
732C2—48no—
733C2—84no—
734C2C23×#12111yescharacteristic
735C2C2×#348511yescharacteristic
736C2#6285911yescharacteristic
737C2#6298812yes—
738C2#6299112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3485C2semidirect
2. C22×#547C2semidirect
3. C2×C4×H(5,𝔽2)C2semidirect
4. #36259C2semidirect
5. #36153C2semidirect
6. #36020C2semidirect
7. #36009C2semidirect
8. #35633C2semidirect
9. #35447C2semidirect
10. #35316C2semidirect
11. #35000C2semidirect
12. #34935C2semidirect
13. C2×#2486C2semidirect
14. #34181C2semidirect
15. #34172C2semidirect
20. C2×#547C22semidirect
21. C2×#547C22semidirect
22. C2×#547C22semidirect
23. C2×#546C22semidirect
26. C22×C4⋊Q8C22semidirect
29. C22×#123C22semidirect
30. C22×C22⋊Q8C22semidirect
31. C22×#121C22semidirect
34. C2×#520C22semidirect
38. C2×#518C22semidirect
40. C2×C4×#41C22semidirect
43. C22×C4×D4C22semidirect
44. C22×C4×D4C22semidirect
45. C23×C4⋊C4C22semidirect
46. #2857C22semidirect
47. #2854C22semidirect
48. #2847C22semidirect
49. #2621C22semidirect
50. #2618C22semidirect
51. #2617C22semidirect
52. #2547C22semidirect
53. #2547C22semidirect
54. #2546C22semidirect
55. #2546C22semidirect
56. #2543C22semidirect
57. #2538C22semidirect
58. #2537C22semidirect
59. #2536C22semidirect
60. #2535C22semidirect
61. #2534C22semidirect
62. #2534C22semidirect
63. #2486C22semidirect
64. #2486C22semidirect
65. #2486C22semidirect
66. #2486C22semidirect
67. #2486C22semidirect
68. #2486C22semidirect
69. #2429C22semidirect
70. #2427C22semidirect
71. #2425C22semidirect
72. #2425C22semidirect
73. #2417C22semidirect
74. #2416C22semidirect
75. #2415C22semidirect
76. #2413C22semidirect
77. #2412C22semidirect
78. #2408C22semidirect
79. #2392C22semidirect
80. C2×#398C22semidirect
81. C2×#397C22semidirect
82. #2349C22semidirect
83. D4×C4⋊C4C22semidirect
84. #2339C22semidirect
85. #2339C22semidirect
86. #2316C22semidirect
87. #2315C22semidirect
88. #2310C22semidirect
89. #2308C22semidirect
90. C4×#121C22semidirect
91. C2×#389C22semidirect
92. #2285C22semidirect
93. #2280C22semidirect
94. C2×#381C22semidirect
95. C2×#380C22semidirect
96. C2×#380C22semidirect
99. C2×H(5,𝔽2)D4semidirect
161. C2×C4×D4D4semidirect
275. C2×#41C2×D4semidirect
293. C22×D4C2×D4semidirect
494. C2×D4#121semidirect
729. C4#3485semidirect

Maximal subgroups

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

subgroupindex
C2×#34852
C22×#5472
C2×C4×H(5,𝔽2)2
#362592
#361532
#360202
#360092
#356332
#354472
#353162
#350002
#349352
C2×#24862
#341812
#341722