Finite Group Databasebeta

← #7188585

Subgroups — #7188585

Order 512.

1781 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59127C211yesmaximal, characteristic, complemented
2#39351C211yesmaximal, characteristic, complemented
3#32226C212yesmaximal, complemented
4#31738C212yesmaximal, complemented
5#31518C212yesmaximal, complemented
6#31350C212yesmaximal, complemented
7#29071C212yesmaximal, complemented
8#28637C211yesmaximal, characteristic, complemented
9#27813C211yesmaximal, characteristic, complemented
10#27813C212yesmaximal, complemented
11#26720C212yesmaximal, complemented
12#26656C212yesmaximal, complemented
13#26440C211yesmaximal, characteristic, complemented
14#26276C211yesmaximal, characteristic, complemented
15#25933C211yesmaximal, characteristic, complemented
16#25903C211yesmaximal, characteristic, complemented
17#25318C211yesmaximal, characteristic, complemented
18#24650C211yesmaximal, characteristic
19#23754C211yesmaximal, characteristic, complemented
20#23216C211yesmaximal, characteristic, complemented
21#23050C211yesmaximal, characteristic, complemented
22Q8×#102C211yesmaximal, characteristic, complemented
23#21833C211yesmaximal, characteristic, complemented
24C2×D4×Q8—21no—
25C2×D4×Q8C2211yescharacteristic
26C2×#542—21no—
27C22×C4⋊Q8C2211yescharacteristic
28C2×#486C2211yescharacteristic
29C2×#486C2211yescharacteristic
30C2×#459C2211yescharacteristic
31C2×C8×Q8C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2856C2211yescharacteristic
34#2723—22no—
35#2677—22no—
36#2672—22no—
37#2624—21no—
38#2551C2211yescharacteristic
39#2551C2212yes—
40#2548C2211yescharacteristic
41#2546C2211yescharacteristic
42#2542C2212yes—
43#2542C2211yescharacteristic
44#2512C2212yes—
45#2491C2212yes—
46#2452—21no—
47#2452C2212yes—
48#2449—22no—
49#2448—21no—
50#2440C2212yes—
51#2434—21no—
52#2429—21no—
53#2422C2212yes—
54#2409—21no—
55#2366C2211yescharacteristic
56#2365C2211yescharacteristic
57#2361C2212yes—
58Q8×C4⋊C4C2211yescharacteristic
59C4×C22⋊Q8C2211yescharacteristic
60C4×#121C2211yescharacteristic
61#2285C2211yescharacteristic
62#2099C2212yes—
63#2099C2212yes—
64#2099C2211yescharacteristic
65#2093C2211yescharacteristic
66#2086C2212yes—
67#2083C2212yes—
68#2083C2211yescharacteristic
69#2075C2211yescharacteristic
70#2075C2211yescharacteristic
71#2071C2211yescharacteristic
72#2071C2212yes—
73#2067C2212yes—
74#2067C2212yes—
75#2057C2212yes—
76#2054C2212yes—
77#2033C2211yescharacteristic
78#2033C2212yes—
79#2033C2211yescharacteristic
80#2023C2212yes—
81#2023C2212yes—
82#2023C2212yes—
83#2023C2212yes—
84#2023C2212yes—
85#1999C2212yes—
86#1990C2212yes—
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1990C2212yes—
90#1990C2212yes—
91#1990C2212yes—
92#1988C2211yescharacteristic
93#1988C2212yes—
94#1988C2211yescharacteristic
95#1988C2211yescharacteristic
96#1988C2211yescharacteristic
97#1988C2212yes—
98#1984C2211yescharacteristic
99#1982C2211yescharacteristic
100#1970C2212yes—
101#1947C2211yescharacteristic
102#1939C2211yescharacteristic
103#1934C2212yes—
104#1934C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1934C2212yes—
108#1925C2212yes—
109#1923C2212yes—
110#1923C2212yes—
111#1918C2212yes—
112#1918C2212yes—
113#1918C2212yes—
114#1916C2212yes—
115#1879C2212yes—
116#1879C2212yes—
117#1879C2212yes—
118#1874C2212yes—
119#1874C2212yes—
120#1862C2212yes—
121#1823C2212yes—
122#1823C2212yes—
123#1802C2212yes—
124#1802C2211yescharacteristic
125#1802C2212yes—
126C4×#107C2211yescharacteristic
127C4×#107C2211yescharacteristic
128C8×C4⋊C4C2212yes—
129C8×C4⋊C4C2211yescharacteristic
130C4×#102C2212yes—
131C4×#102C2211yescharacteristic
132C4×#102C2212yes—
133C4×#102C2211yescharacteristic
134C4×C22⋊C8C2211yescharacteristic
135C23×Q8—21no—
136C23×Q8—21no—
137C22×D8C2312yes—
138D4×Q8—24no—
139D4×Q8—42no—
140D4×Q8—48no—
141#542—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—22no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—24no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—42no—
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×C4⋊Q8C2311yescharacteristic
153C2×C4⋊Q8C2312yes—
154C2×#127C2311yescharacteristic
155C2×#126—22no—
156C2×#124—21no—
157C2×#124—22no—
158C2×#123—22no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8—22no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—22no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8—22no—
167C2×C22⋊Q8D411yescharacteristic
168C2×#121—21no—
169C2×#121—21no—
170C2×#121C2311yescharacteristic
171C2×#121C2312yes—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×D4—21no—
176C2×C4×D4—21no—
177C2×C4×D4—22no—
178C2×C4×D4C2311yescharacteristic
179C2×C4×D4C2312yes—
180C2×C4×D4C2312yes—
181C2×#117—21no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4C2312yes—
184C22×C42C2311yescharacteristic
185#486—24no—
186#486—42no—
187#459—42no—
188C8×Q8—42no—
189#431—42no—
190C2×#107C2311yescharacteristic
191C2×#107C2311yescharacteristic
192C2×#107C2311yescharacteristic
193C2×#107C2312yes—
194C2×#107C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2312yes—
199C2×#102C2311yescharacteristic
200C2×#102C2312yes—
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2312yes—
217C2×C4×C8C2312yes—
218C2×C4×C8C2312yes—
219#399—22no—
220#399—22no—
221#399—22no—
222#398—22no—
223#398—22no—
224#397—22no—
225#397—22no—
226#396—22no—
227#396—22no—
228#395—22no—
229#395—22no—
230#395—22no—
231#395—22no—
232#394—22no—
233#394—22no—
234#394—22no—
235#393—22no—
236#393—22no—
237#391—21no—
238#391—21no—
239#391D411yescharacteristic
240#390—21no—
241#390—21no—
242#390—21no—
243#390—21no—
244#390C2312yes—
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#390C2311yescharacteristic
249#390C2312yes—
250#389—21no—
251#389—22no—
252#389—21no—
253#389—22no—
254#389D411yescharacteristic
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#389C2311yescharacteristic
259#389C2312yes—
260#388—21no—
261#388—22no—
262#388—22no—
263#388—22no—
264#387—22no—
265#387D412yes—
266#386—21no—
267#386—22no—
268#386—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385D412yes—
274#384C2312yes—
275#384C2312yes—
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#382—21no—
280#380—21no—
281#380D411yescharacteristic
282#380C2311yescharacteristic
283#380C2311yescharacteristic
284#380C2311yescharacteristic
285C4×C4⋊C4—21no—
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2312yes—
293C4×C22⋊C4—21no—
294C4×C22⋊C4C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#336C2312yes—
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—44no—
329C22×Q8—44no—
330C22×Q8—44no—
331C22×Q8—44no—
332C22×Q8—82no—
333C22×Q8—82no—
334C22×Q8C2×D411yescharacteristic
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4C2412yes—
340C22×D4C2411yescharacteristic
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2411yescharacteristic
348C2×D8—24no—
349C2×D8—42no—
350C2×D8—42no—
351C22×C8C2412yes—
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2411yescharacteristic
356C22×C8C2412yes—
357C4⋊Q8—24no—
358C4⋊Q8—24no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—42no—
363C4⋊Q8—42no—
364C4⋊Q8—42no—
365C4⋊Q8—42no—
366C4⋊Q8—44no—
367C4⋊Q8—44no—
368C4⋊Q8—44no—
369C4⋊Q8—44no—
370C4⋊Q8—48no—
371C4⋊Q8#4114yes—
372#127—22no—
373#127—22no—
374#126—48no—
375#124—44no—
376#124—48no—
377#123—48no—
378C22⋊Q8—48no—
379C22⋊Q8—44no—
380C22⋊Q8—48no—
381C22⋊Q8—48no—
382C22⋊Q8—44no—
383C22⋊Q8—48no—
384C22⋊Q8—84no—
385C22⋊Q8—82no—
386C22⋊Q8D818yescomplemented
387#121—22no—
388#121—22no—
389#121—44no—
390#121—42no—
391#121—42no—
392#121—82no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—44no—
396C4×Q8—44no—
397C4×D4—24no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—42no—
401C4×D4—42no—
402C4×D4—42no—
403C4×D4—44no—
404C4×D4—44no—
405C4×D4—48no—
406#117—44no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4C2×D412yes—
468C2×C22⋊C4C2×D412yes—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2412yes—
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—22no—
483#107—22no—
484#107—41no—
485#107—41no—
486#107—42no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—42no—
490C4⋊C8—42no—
491#102—22no—
492#102—22no—
493#102—24no—
494#102—24no—
495#102—24no—
496#102—42no—
497#102—41no—
498#102—42no—
499#102—41no—
500#102—42no—
501#102—42no—
502#102—42no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505C22⋊C8—42no—
506C4×C8—22no—
507C4×C8—22no—
508C4×C8—42no—
509C4×C8—42no—
510C4×C8—42no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—21no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527#95C2×D412yes—
528#95C2×D412yes—
529C24—21no—
530C24—22no—
531C24C22×D411yescharacteristic
532C2×Q8—22no—
533C2×Q8—24no—
534C2×Q8—22no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—42no—
542C2×Q8—44no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—82no—
546C2×Q8—82no—
547C2×Q8—82no—
548C2×Q8—82no—
549C2×Q8—816no—
550C2×Q8—816no—
551C2×Q8C2×D814yes—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D42−1+412yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4C2×D814yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2511yescharacteristic
620D8—84no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4C2×D814yes—
683C4⋊C4C2×D818yes—
684C4⋊C4C2×#4114yes—
685C4⋊C42−1+412yes—
686C22⋊C4—24no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—42no—
700C22⋊C4—44no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4C2×D818yes—
708C42—22no—
709C42—22no—
710C42—21no—
711C42—22no—
712C42—21no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—42no—
717C42—42no—
718C42—44no—
719C42—42no—
720C42—44no—
721C42C2×#4112yes—
722C42H(5,𝔽2)12yes—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23C22×D812yes—
744C23C23×D411yescharacteristic
745Q8—28no—
746Q8—48no—
747Q8—88no—
748Q8—88no—
749Q8—84no—
750Q8—164no—
751D4—22no—
752D4—22no—
753D4—48no—
754D4—42no—
755D4—41no—
756D4—42no—
757D4—41no—
758D4—42no—
759D4—42no—
760D4—84no—
761D4—162no—
762D4—164no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—28no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—44no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—88no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4—164no—
822C2×C4#54612yes—
823C2×C4#54612yes—
824C2×C4C22×D814yes—
825C2×C4C22×D814yes—
826C2×C4C22×D812yes—
827C2×C4C22×D812yes—
828C2×C4#57712yes—
829C2×C4#57712yes—
830C2×C4C22×#4111yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4#58511yescharacteristic
835C2×C4#58511yescharacteristic
836C8—41no—
837C8—41no—
838C8—41no—
839C8—42no—
840C8—41no—
841C8—42no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22C2×#54611yescharacteristic
864C22#348611yescharacteristic
865C22#350011yescharacteristic
866C22C23×D811yescharacteristic
867C22C2×#57711yescharacteristic
868C22C2×#57711yescharacteristic
869C22#358611yescharacteristic
870C4—22no—
871C4—22no—
872C4—24no—
873C4—22no—
874C4—24no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—44no—
879C4—41no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—82no—
888C4#329414yes—
889C4#351611yescharacteristic
890C4#351811yescharacteristic
891C4#355411yescharacteristic
892C4#356111yescharacteristic
893C2—42no—
894C2—82no—
895C2—162no—
896C2#4528911yescharacteristic
897C2C2×#329411yescharacteristic
898C2#6118511yescharacteristic
899C2#6181711yescharacteristic
900C2#6187111yescharacteristic
901C2#6252911yescharacteristic
902C2#6261611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24650C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59127C2semidirect
2. #39351C2semidirect
3. #32226C2semidirect
4. #31738C2semidirect
5. #31518C2semidirect
6. #31350C2semidirect
7. #29071C2semidirect
8. #28637C2semidirect
9. #27813C2semidirect
10. #27813C2semidirect
11. #26720C2semidirect
12. #26656C2semidirect
13. #26440C2semidirect
14. #26276C2semidirect
15. #25933C2semidirect
16. #25903C2semidirect
17. #25318C2semidirect
19. #23754C2semidirect
20. #23216C2semidirect
21. #23050C2semidirect
22. Q8×#102C2semidirect
23. #21833C2semidirect
386. C22⋊Q8D8semidirect

Maximal subgroups

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

subgroupindex
#591272
#393512
#322262
#317382
#315182
#313502
#290712
#286372
#278132
#267202
#266562
#264402
#262762
#259332
#259032
#253182
#246502
#237542
#232162
#230502
Q8×#1022
#218332