Finite Group Databasebeta

← #6478085

Subgroups — #6478085

Order 512.

1535 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35083C211yesmaximal, characteristic
2C2×#2369C211yesmaximal, characteristic, complemented
3#33146C211yesmaximal, characteristic, complemented
4#33111C211yesmaximal, characteristic
5#33100C211yesmaximal, characteristic, complemented
6#33096C211yesmaximal, characteristic
7#29968C211yesmaximal, characteristic, complemented
8#29760C211yesmaximal, characteristic
9#29641C211yesmaximal, characteristic, complemented
10#29638C211yesmaximal, characteristic
11#27147C212yesmaximal, complemented
12#27132C212yesmaximal, complemented
13#27021C212yesmaximal, complemented
14#27002C212yesmaximal, complemented
15#26876C212yesmaximal, complemented
16#26863C212yesmaximal, complemented
17#26710C212yesmaximal, complemented
18#26693C212yesmaximal, complemented
19#22081C211yesmaximal, characteristic
20#22078C211yesmaximal, characteristic, complemented
21#21914C211yesmaximal, characteristic, complemented
22#21579C211yesmaximal, characteristic, complemented
23C4×#480C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C2×#483C2211yescharacteristic
26C2×#483C2211yescharacteristic
27C2×#480C2211yescharacteristic
28C2×#480C2211yescharacteristic
29#2857C2211yescharacteristic
30#2855C2211yescharacteristic
31#2854C2211yescharacteristic
32#2850C2211yescharacteristic
33#2654—21no—
34#2650—21no—
35#2512C2211yescharacteristic
36#2511C2211yescharacteristic
37#2509C2211yescharacteristic
38#2508C2211yescharacteristic
39#2488—21no—
40#2481—21no—
41#2452C2211yescharacteristic
42#2451C2211yescharacteristic
43#2449—21no—
44#2448C2211yescharacteristic
45#2447C2211yescharacteristic
46#2419—21no—
47#2369—21no—
48#2369—21no—
49#2369—21no—
50#2369—21no—
51#2369C2212yes—
52#2369C2212yes—
53#2369C2212yes—
54#2369C2212yes—
55#2334—21no—
56#2332—21no—
57C4×C22⋊Q8C2211yescharacteristic
58C4×#121C2211yescharacteristic
59C2×#391—21no—
60C2×#391—21no—
61C2×#389—21no—
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×C4×C4⋊C4—21no—
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69#2100C2212yes—
70#2088C2212yes—
71#2088C2212yes—
72#2085C2212yes—
73#2068C2212yes—
74#2065C2212yes—
75#2058C2212yes—
76#2058C2212yes—
77#2058C2212yes—
78#2057C2212yes—
79#2057C2212yes—
80#2042C2212yes—
81#2024C2212yes—
82#2024C2212yes—
83#2023C2212yes—
84#2023C2212yes—
85#1988C2212yes—
86#1983C2212yes—
87#1949C2212yes—
88#1947C2212yes—
89#1943C2212yes—
90#1941C2212yes—
91#1936C2212yes—
92#1933C2212yes—
93#1928C2212yes—
94#1928C2212yes—
95#1928C2212yes—
96#1927C2212yes—
97#1926C2212yes—
98#1926C2212yes—
99#1925C2212yes—
100#1925C2212yes—
101#1921C2212yes—
102#1921C2212yes—
103#1920C2212yes—
104#1919C2212yes—
105#1919C2212yes—
106#1919C2212yes—
107#1918C2212yes—
108#1918C2212yes—
109#1918C2212yes—
110#1918C2212yes—
111#1917C2212yes—
112#1917C2212yes—
113#1916C2212yes—
114#1916C2212yes—
115#1874C2211yescharacteristic
116#1874C2211yescharacteristic
117#1872C2211yescharacteristic
118#1872C2211yescharacteristic
119#1865C2212yes—
120#1864C2212yes—
121#1853C2211yescharacteristic
122#1853C2211yescharacteristic
123#1852C2211yescharacteristic
124#1852C2211yescharacteristic
125#1823C2211yescharacteristic
126#1823C2211yescharacteristic
127#1823C2211yescharacteristic
128#1823C2211yescharacteristic
129#1817C2211yescharacteristic
130#1817C2211yescharacteristic
131#1797C2211yescharacteristic
132#1797C2211yescharacteristic
133#1776C2212yes—
134C4×#107C2212yes—
135#1763C2212yes—
136C4×#102C2212yes—
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8—21no—
140C2×C4⋊Q8—24no—
141C2×C4⋊Q8—24no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×#126—21no—
148C2×#124C2311yescharacteristic
149C2×#123—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8C2311yescharacteristic
153C2×#121C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—21no—
156C2×C4×D4C2311yescharacteristic
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4D411yescharacteristic
161C22×C4⋊C4D411yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C42—21no—
167C22×C42—21no—
168C22×C42—21no—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#483—24no—
173#483—24no—
174#480—24no—
175#480—24no—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2311yescharacteristic
196C2×C22⋊C8C2311yescharacteristic
197C2×C22⋊C8C2311yescharacteristic
198C2×#97C2312yes—
199C2×C4×C8C2312yes—
200#400—21no—
201#400—21no—
202#400—21no—
203#400—21no—
204#400—21no—
205#399—21no—
206#398—21no—
207#398—21no—
208#397—21no—
209#397—21no—
210#397—21no—
211#397—21no—
212#396—21no—
213#396—21no—
214#395—21no—
215#393—21no—
216#391—21no—
217#391—21no—
218#391—22no—
219#391—22no—
220#391—22no—
221#391—22no—
222#391—22no—
223#391—22no—
224#391—22no—
225#391—22no—
226#391C2311yescharacteristic
227#391C2311yescharacteristic
228#391C2311yescharacteristic
229#391C2311yescharacteristic
230#390C2311yescharacteristic
231#390C2311yescharacteristic
232#390C2311yescharacteristic
233#390C2311yescharacteristic
234#389—21no—
235#389—22no—
236#389—22no—
237#389—22no—
238#389—22no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2312yes—
249#389C2312yes—
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2312yes—
253#389C2312yes—
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#388—21no—
257#388—21no—
258#388—21no—
259#388—21no—
260#388—21no—
261#388—21no—
262#388—21no—
263#388—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#387—21no—
270#387—21no—
271#387—21no—
272#386—21no—
273#386—21no—
274#386—21no—
275#386—21no—
276#385—21no—
277#385—21no—
278#385—21no—
279#385—21no—
280#384C2311yescharacteristic
281#382—21no—
282#382C2311yescharacteristic
283#381—21no—
284#381—21no—
285#380—21no—
286#380C2311yescharacteristic
287#380C2311yescharacteristic
288C4×C4⋊C4—22no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4—22no—
291C4×C4⋊C4—22no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4D411yescharacteristic
303C4×C4⋊C4C2312yes—
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2312yes—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95D411yescharacteristic
323C2×#95D411yescharacteristic
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—28no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—21no—
352C22×Q8—82no—
353C22×Q8—82no—
354C22×Q8C2411yescharacteristic
355C22×D4—21no—
356C22×D4C2411yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2411yescharacteristic
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C4⋊Q8—28no—
374C4⋊Q8—28no—
375C4⋊Q8—24no—
376C4⋊Q8—24no—
377C4⋊Q8—24no—
378C4⋊Q8—24no—
379C4⋊Q8—42no—
380#126—44no—
381#124—42no—
382#123—82no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—44no—
386C22⋊Q8—82no—
387#121—22no—
388#121—22no—
389C4×Q8—42no—
390C4×D4—42no—
391C4×D4—82no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
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—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—82no—
423C2×C4⋊C4—82no—
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4#4114yes—
433C2×C4⋊C4#4114yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—42no—
471C2×C42—42no—
472C2×C42—44no—
473C2×C42—82no—
474C2×C42—82no—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487#107—24no—
488#107—24no—
489#107—24no—
490#107—24no—
491#106—24no—
492#106—24no—
493#106—42no—
494#106—42no—
495C4⋊C8—42no—
496C4⋊C8—42no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—42no—
501#102—24no—
502#102—24no—
503#102—24no—
504#102—42no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509#97—42no—
510C4×C8—42no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551C24—21no—
552C24C22×D411yescharacteristic
553C2×Q8—28no—
554C2×Q8—28no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—82no—
561C2×Q8—82no—
562C2×Q8—82no—
563C2×Q8—82no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8—816no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2511yescharacteristic
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C4⋊C4—24no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4#13714yes—
692C4⋊C4C2×#4114yes—
693C4⋊C4C2×#4114yes—
694C4⋊C42−1+414yes—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—41no—
721C42—41no—
722C42—41no—
723C42—41no—
724C42—44no—
725C42—42no—
726C42—44no—
727C42—82no—
728C42—82no—
729C42—82no—
730C42—82no—
731C42—81no—
732C42—81no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23#52512yes—
745C23#57612yes—
746C23#57712yes—
747C23C23×D411yescharacteristic
748Q8—42no—
749Q8—42no—
750Q8—88no—
751Q8—88no—
752Q8—162no—
753D4—42no—
754D4—42no—
755D4—84no—
756C2×C4—28no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—48no—
799C2×C4—44no—
800C2×C4—48no—
801C2×C4—48no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—84no—
835C2×C4—162no—
836C2×C4#52512yes—
837C2×C4C2×#13712yes—
838C2×C4C2×#13712yes—
839C2×C4C2×#13712yes—
840C2×C4#57512yes—
841C2×C4C22×#4111yescharacteristic
842C2×C4C22×#4111yescharacteristic
843C2×C4C2×2−1+412yes—
844C2×C4#58512yes—
845C8—42no—
846C8—42no—
847C8—42no—
848C8—42no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22#311814yes—
863C22C2×#52511yescharacteristic
864C22#348511yescharacteristic
865C22#348611yescharacteristic
866C22C22×#13711yescharacteristic
867C22C2×#57511yescharacteristic
868C22C2×#57611yescharacteristic
869C22C2×#57711yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4#346112yes—
895C4#350712yes—
896C2—24no—
897C2—161no—
898C2#3509211yescharacteristic
899C2C2×#311811yescharacteristic
900C2#6056011yescharacteristic
901C2#6172611yescharacteristic
902C2#6173111yescharacteristic
903C2#6183511yescharacteristic
904C2#6183811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2369C2semidirect
3. #33146C2semidirect
5. #33100C2semidirect
7. #29968C2semidirect
9. #29641C2semidirect
11. #27147C2semidirect
12. #27132C2semidirect
13. #27021C2semidirect
14. #27002C2semidirect
15. #26876C2semidirect
16. #26863C2semidirect
17. #26710C2semidirect
18. #26693C2semidirect
20. #22078C2semidirect
21. #21914C2semidirect
22. #21579C2semidirect

Maximal subgroups

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

subgroupindex
#350832
C2×#23692
#331462
#331112
#331002
#330962
#299682
#297602
#296412
#296382
#271472
#271322
#270212
#270022
#268762
#268632
#267102
#266932
#220812
#220782
#219142
#215792
C4×#4802