Finite Group Databasebeta

← #6579390

Subgroups — #6579390

Order 512.

2108 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3139C211yesmaximal, characteristic, complemented
2C22×#487C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic
5#33236C211yesmaximal, characteristic, complemented
6#33049C211yesmaximal, characteristic, complemented
7#33043C211yesmaximal, characteristic, complemented
8#28748C211yesmaximal, characteristic, complemented
9#28719C211yesmaximal, characteristic, complemented
10#27782C214yesmaximal, complemented
11#27277C214yesmaximal, complemented
12#27268C214yesmaximal, complemented
13#25904C211yesmaximal, characteristic, complemented
14#25902C211yesmaximal, characteristic, complemented
15#25856C211yesmaximal, characteristic, complemented
16#25856C211yesmaximal, characteristic, complemented
17#22425C214yesmaximal
18#21647C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic
20C2×D4×Q8C2212yes—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3139—28no—
26C2×#491C2214yes—
27C2×#487—28no—
28C2×#487C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2214yes—
35C2×#487C2211yescharacteristic
36C2×#487C2211yescharacteristic
37C2×#487C2211yescharacteristic
38C2×#435C2212yes—
39C2×#419C2214yes—
40C22×#103C2214yes—
41C2×C4×M16C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2868C2211yescharacteristic
44#2862C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2551—21no—
50#2551—21no—
51#2550C2212yes—
52#2546C2212yes—
53#2492—21no—
54#2451—21no—
55#2446—21no—
56#2442C2212yes—
57#2440—21no—
58#2440—21no—
59#2440—21no—
60#2440—21no—
61#2439C2212yes—
62#2434C2212yes—
63#2434C2212yes—
64#2429—21no—
65#2417—21no—
66#2409—21no—
67#2360—21no—
68#2352C2212yes—
69D4×C4⋊C4—21no—
70D4×C4⋊C4—21no—
71Q8×C22⋊C4—21no—
72C4×C4⋊Q8C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic
74C42×D4C2211yescharacteristic
75#2074C2214yes—
76#2043C2214yes—
77#2043C2214yes—
78#2043C2214yes—
79#2026C2214yes—
80#2024C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1981C2214yes—
85#1960C2214yes—
86#1960C2214yes—
87#1956C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1935C2214yes—
91#1935C2214yes—
92#1933C2214yes—
93#1894C2214yes—
94#1892C2214yes—
95#1873C2214yes—
96#1872C2214yes—
97#1834C2211yescharacteristic
98#1805C2214yes—
99#1787C2214yes—
100#1787C2214yes—
101#1771C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C23×Q8—21no—
110C23×Q8C2312yes—
111C23×Q8C2312yes—
112C22×M16C2312yes—
113C23×C8C2312yes—
114D4×Q8—216no—
115#533—24no—
116#533—42no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—42no—
128C2×C4⋊Q8—42no—
129C2×C4⋊Q8—42no—
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2312yes—
133C2×C4⋊Q8C2312yes—
134C2×C4⋊Q8C2312yes—
135C2×C4⋊Q8C2311yescharacteristic
136C2×C4⋊Q8C2312yes—
137C2×C4⋊Q8C2311yescharacteristic
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2312yes—
140C2×C4⋊Q8C2311yescharacteristic
141C2×#125C2312yes—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8C2312yes—
149C2×C22⋊Q8C2312yes—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8C2312yes—
154C2×C4×D4—22no—
155C2×C4×D4D411yescharacteristic
156C2×C4×D4D411yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×#117C2312yes—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#491—216no—
168#487—24no—
169#487—24no—
170#487—24no—
171#487—24no—
172#487—216no—
173#487—24no—
174#487—24no—
175#487—42no—
176#487—42no—
177#487D418yescomplemented
178#435—28no—
179C2×C4⋊C8C2312yes—
180#419—216no—
181C2×#103—216no—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C4×M16—24no—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×#97C2312yes—
200C2×C4×C8—24no—
201C2×C4×C8C2312yes—
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206#400—22no—
207#398—22no—
208#398—22no—
209#398—22no—
210#398—22no—
211#396—22no—
212#395—22no—
213#395—22no—
214#395—22no—
215#395—22no—
216#395—22no—
217#393—22no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—22no—
226#391—22no—
227#391C2312yes—
228#391C2312yes—
229#391C2312yes—
230#389—22no—
231#389—22no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#384—21no—
255#384—21no—
256#384—21no—
257#384—21no—
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#382C2312yes—
261#382C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—22no—
269#380C2312yes—
270#380C2312yes—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4D411yescharacteristic
275C4×C4⋊C4D411yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C22⋊C4—22no—
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C43C2311yescharacteristic
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—24no—
300C22×Q8—24no—
301C22×Q8—28no—
302C22×Q8—28no—
303C22×Q8—42no—
304C22×Q8—42no—
305C22×Q8—44no—
306C22×Q8—44no—
307C22×Q8—44no—
308C22×Q8—44no—
309C22×Q8—82no—
310C22×Q8C2412yes—
311C22×Q8C2412yes—
312C22×Q8C2412yes—
313C22×D4C2×D411yescharacteristic
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—42no—
326C22×C8—24no—
327C22×C8—24no—
328C22×C8—42no—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C4⋊Q8—24no—
334C4⋊Q8—24no—
335C4⋊Q8—24no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—28no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—42no—
348C4⋊Q8—44no—
349C4⋊Q8—44no—
350C4⋊Q8—44no—
351C4⋊Q8—44no—
352C4⋊Q8—44no—
353C4⋊Q8—42no—
354C4⋊Q8—42no—
355C4⋊Q8—44no—
356C4⋊Q8—44no—
357C4⋊Q8—48no—
358C4⋊Q8C2×D414yes—
359C4⋊Q8C2×D414yes—
360#125—24no—
361#125—42no—
362C22⋊Q8—28no—
363C22⋊Q8—28no—
364C22⋊Q8—44no—
365C22⋊Q8—44no—
366C22⋊Q8—44no—
367C22⋊Q8—48no—
368C22⋊Q8—48no—
369C22⋊Q8—82no—
370C4×Q8—28no—
371C4×Q8—44no—
372C4×Q8—44no—
373C4×Q8—82no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—48no—
377C4×D4#4118yes—
378#117—24no—
379#117—42no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
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—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457C4⋊C8—24no—
458#103—28no—
459#103—28no—
460#103—28no—
461#103—28no—
462#103—28no—
463#103—28no—
464#103—44no—
465#103—44no—
466#103—44no—
467#103—44no—
468#103—44no—
469#103C2×D4116yes—
470C22⋊C8—24no—
471C22⋊C8—24no—
472#97—24no—
473#97—24no—
474#97—42no—
475C4×C8—24no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8C2×D414yes—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501#95C2×D411yescharacteristic
502C24C22×D411yescharacteristic
503C24C22×D411yescharacteristic
504C2×Q8—24no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—24no—
514C2×Q8—24no—
515C2×Q8—24no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—416no—
520C2×Q8—416no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—82no—
533C2×Q8—82no—
534C2×Q8—82no—
535C2×Q8—88no—
536C2×Q8—88no—
537C2×Q8—816no—
538C2×Q8C22×D414yes—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4#12414yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4#13714yes—
576C22×C4#13714yes—
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2511yescharacteristic
592M16—48no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—48no—
605C2×C8C22×D414yes—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4#12414yes—
647C4⋊C4C22×D414yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—82no—
657C22⋊C4#12414yes—
658C22⋊C4#12414yes—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—22no—
672C42—44no—
673C42—44no—
674C42—82no—
675C42C22×D412yes—
676C42C2×#4114yes—
677C42H(5,𝔽2)12yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23C2×#12412yes—
689C23C2×#12412yes—
690C23C2×#13712yes—
691C23C2×#13712yes—
692C23C23×D411yescharacteristic
693Q8—28no—
694Q8—44no—
695Q8—48no—
696Q8—44no—
697Q8—44no—
698Q8—44no—
699Q8—44no—
700Q8—88no—
701Q8—88no—
702Q8—88no—
703Q8—84no—
704Q8—84no—
705D4—28no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—88no—
763C2×C4—88no—
764C2×C4—88no—
765C2×C4C2×#12412yes—
766C2×C4C2×#12412yes—
767C2×C4C2×#12412yes—
768C2×C4C2×#12412yes—
769C2×C4D4212yes—
770C2×C4D4212yes—
771C2×C4C2×#13712yes—
772C2×C4C2×#13712yes—
773C2×C4C2×#13712yes—
774C2×C4C2×#13712yes—
775C2×C4#57712yes—
776C2×C4#57812yes—
777C2×C4C23×D411yescharacteristic
778C2×C4C22×#4112yes—
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4#58512yes—
781C8—24no—
782C8—42no—
783C8—42no—
784C8—42no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22#313914yescomplemented
799C22C22×#12411yescharacteristic
800C22C2×D4211yescharacteristic
801C22#350011yescharacteristic
802C22C22×#13711yescharacteristic
803C22C22×#13711yescharacteristic
804C22C2×#57711yescharacteristic
805C22C2×#57811yescharacteristic
806C4—22no—
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—44no—
817C4—41no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4#326614yes—
825C4#327014yes—
826C4D4×#4112yes—
827C4#351412yes—
828C2—24no—
829C2—42no—
830C2D4×#12411yescharacteristic
831C2C2×#313911yescharacteristic
832C2#6062311yescharacteristic
833C2C2×#326611yescharacteristic
834C2C2×#327011yescharacteristic
835C2#6253611yescharacteristic
836C2#6254011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3139C2semidirect
2. C22×#487C2semidirect
5. #33236C2semidirect
6. #33049C2semidirect
7. #33043C2semidirect
8. #28748C2semidirect
9. #28719C2semidirect
10. #27782C2semidirect
11. #27277C2semidirect
12. #27268C2semidirect
13. #25904C2semidirect
14. #25902C2semidirect
15. #25856C2semidirect
16. #25856C2semidirect
18. #21647C2semidirect
177. #487D4semidirect
798. C22#3139semidirect

Maximal subgroups

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

subgroupindex
C2×#31392
C22×#4872
#361292
D4×C4⋊Q82
#332362
#330492
#330432
#287482
#287192
#277822
#272772
#272682
#259042
#259022
#258562
#224252
#216472
C4×#4352