Finite Group Databasebeta

← #6852280

Subgroups — #6852280

Order 512.

1581 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39608C211yesmaximal, characteristic, complemented
2#35279C211yesmaximal, characteristic, complemented
3#32958C211yesmaximal, characteristic, complemented
4#32364C212yesmaximal, complemented
5#32357C212yesmaximal, complemented
6#31543C212yesmaximal, complemented
7#31518C212yesmaximal, complemented
8#29961C212yesmaximal, complemented
9#28539C211yesmaximal, characteristic, complemented
10#28528C211yesmaximal, characteristic, complemented
11#27959C212yesmaximal, complemented
12#27821C211yesmaximal, characteristic, complemented
13#27815C211yesmaximal, characteristic, complemented
14#27687C212yesmaximal, complemented
15#25813C211yesmaximal, characteristic, complemented
16#25455C211yesmaximal, characteristic, complemented
17#25450C211yesmaximal, characteristic, complemented
18#24815C211yesmaximal, characteristic, complemented
19#24812C211yesmaximal, characteristic, complemented
20#24299C211yesmaximal, characteristic, complemented
21#22626C211yesmaximal, characteristic, complemented
22#22055C212yesmaximal
23C4×#449C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#477C2211yescharacteristic
29C2×#476C2211yescharacteristic
30C2×#476C2211yescharacteristic
31C2×#476C2211yescharacteristic
32C2×#449C2211yescharacteristic
33C2×C4×SD16C2211yescharacteristic
34C2×C4×D8C2211yescharacteristic
35#2857—21no—
36#2857—21no—
37#2857C2211yescharacteristic
38#2763—22no—
39#2692—22no—
40#2628—22no—
41#2628C2212yes—
42#2568C2212yes—
43#2567C2211yescharacteristic
44#2567C2211yescharacteristic
45#2563—21no—
46#2563C2211yescharacteristic
47#2563C2211yescharacteristic
48#2563C2211yescharacteristic
49#2551C2211yescharacteristic
50#2542C2212yes—
51#2508C2212yes—
52#2497—21no—
53#2487—21no—
54#2487—21no—
55#2487—21no—
56#2452C2212yes—
57#2440—21no—
58#2409—22no—
59#2369C2211yescharacteristic
60D4×C4⋊C4C2211yescharacteristic
61#2324C2212yes—
62#2317C2212yes—
63#2311C2212yes—
64C4×#121C2211yescharacteristic
65#2285C2211yescharacteristic
66#2101C2212yes—
67#2100C2212yes—
68#2097C2212yes—
69#2093C2212yes—
70#2092C2212yes—
71#2092C2212yes—
72#2085C2212yes—
73#2085C2212yes—
74#2084C2212yes—
75#2083C2212yes—
76#2068C2212yes—
77#2067C2212yes—
78#2066C2212yes—
79#2065C2212yes—
80#2058C2212yes—
81#2057C2212yes—
82#2057C2212yes—
83#2024C2212yes—
84#2023C2212yes—
85#2023C2212yes—
86#1993C2212yes—
87#1990C2212yes—
88#1990C2211yescharacteristic
89#1990C2211yescharacteristic
90#1987C2211yescharacteristic
91#1987C2211yescharacteristic
92#1973C2212yes—
93#1970C2212yes—
94#1949C2212yes—
95#1947C2212yes—
96#1939C2211yescharacteristic
97#1939C2211yescharacteristic
98#1936C2212yes—
99#1933C2212yes—
100#1928C2212yes—
101#1925C2212yes—
102#1917C2212yes—
103#1916C2212yes—
104#1880C2211yescharacteristic
105#1879C2211yescharacteristic
106#1879C2212yes—
107#1877C2212yes—
108#1875C2211yescharacteristic
109#1874C2212yes—
110#1865C2212yes—
111#1864C2211yescharacteristic
112#1863C2211yescharacteristic
113#1862C2212yes—
114#1854C2212yes—
115#1854C2211yescharacteristic
116#1853C2212yes—
117#1852C2212yes—
118#1852C2212yes—
119#1847C2212yes—
120#1846C2212yes—
121#1804C2212yes—
122#1803C2211yescharacteristic
123#1802C2212yes—
124#1802C2211yescharacteristic
125#1798C2212yes—
126#1797C2211yescharacteristic
127#1788C2211yescharacteristic
128#1788C2212yes—
129#1770C2211yescharacteristic
130C8×C4⋊C4C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#102C2211yescharacteristic
133#1750C2212yes—
134C4×C22⋊C8C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×Q8—21no—
137C22×SD16C2311yescharacteristic
138C22×D8C2311yescharacteristic
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—42no—
143C2×C4⋊Q8—42no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2312yes—
148C2×C4⋊Q8C2312yes—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8—22no—
153C2×#121C2311yescharacteristic
154C4×#41—42no—
155C4×#41—42no—
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×D4—21no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2312yes—
164C2×C4×D4C2311yescharacteristic
165C2×#117—21no—
166C2×#117C2311yescharacteristic
167C2×#117C2312yes—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4C2312yes—
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173#500—42no—
174#500—42no—
175#477—42no—
176#476—42no—
177#476—42no—
178#476—42no—
179#449Q818yescomplemented
180C4×SD16—42no—
181C4×D8—42no—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2311yescharacteristic
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2311yescharacteristic
191C2×#106C2312yes—
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2311yescharacteristic
205C2×#102C2312yes—
206C2×#102C2311yescharacteristic
207C2×#102C2311yescharacteristic
208C2×#102C2312yes—
209C2×#102C2311yescharacteristic
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×#97C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2312yes—
217#400—22no—
218#400—22no—
219#400—22no—
220#400—22no—
221#399—22no—
222#399—22no—
223#399—22no—
224#398—22no—
225#396—22no—
226#395—22no—
227#395—22no—
228#395—22no—
229#395—22no—
230#393—22no—
231#393—22no—
232#393—22no—
233#393—22no—
234#393—22no—
235#391—22no—
236#391—22no—
237#391—21no—
238#391—22no—
239#391C2312yes—
240#391C2312yes—
241#390—22no—
242#390C2312yes—
243#390C2312yes—
244#390C2312yes—
245#390C2311yescharacteristic
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389—22no—
252#389—21no—
253#389—21no—
254#389—21no—
255#389C2312yes—
256#389C2311yescharacteristic
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#388—22no—
261#388—21no—
262#387—22no—
263#386—21no—
264#386—22no—
265#386—22no—
266#386—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#384D411yescharacteristic
273#384D411yescharacteristic
274#384C2312yes—
275#384C2312yes—
276#384C2311yescharacteristic
277#382—22no—
278#382D412yes—
279#382C2312yes—
280#382C2312yes—
281#382C2312yes—
282#380—21no—
283#380—21no—
284#380—21no—
285#380—21no—
286#380—21no—
287#380—21no—
288#380—21no—
289#380—21no—
290#380—22no—
291#380—22no—
292#380D411yescharacteristic
293#380D412yes—
294#380D411yescharacteristic
295#380C2312yes—
296#380C2311yescharacteristic
297C4×C4⋊C4—21no—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2312yes—
303C4×C22⋊C4—21no—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325C2×#41—22no—
326C2×#41—41no—
327C2×#41—41no—
328C2×#41—41no—
329C2×#41—41no—
330C2×#41C2×Q814yes—
331C22×Q8—22no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—22no—
336C22×Q8—44no—
337C22×Q8—82no—
338C22×Q8—82no—
339C22×Q8C2411yescharacteristic
340C22×D4—21no—
341C22×D4—21no—
342C22×D4C2411yescharacteristic
343C22×D4C2411yescharacteristic
344C23×C4—21no—
345C23×C4—22no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—22no—
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2411yescharacteristic
353C2×SD16—41no—
354C2×SD16—41no—
355C2×SD16C2×Q814yescomplemented
356C2×D8—41no—
357C2×D8—41no—
358C2×D8C2×Q814yescomplemented
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—42no—
372C4⋊Q8—42no—
373C4⋊Q8—42no—
374C4⋊Q8—42no—
375C4⋊Q8—44no—
376C4⋊Q8—44no—
377C4⋊Q8—82no—
378C22⋊Q8—84no—
379C22⋊Q8—84no—
380C22⋊Q8—82no—
381C22⋊Q8—84no—
382#121—22no—
383#121C2×Q814yes—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—41no—
393C4×D4—41no—
394C4×D4—42no—
395C4×D4—42no—
396C4×D4—44no—
397C4×D4—44no—
398C4×D4—82no—
399#117—42no—
400#117—42no—
401#117—44no—
402#117—41no—
403#117—41no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—82no—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D412yes—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2411yescharacteristic
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—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—44no—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2412yes—
473C2×C42C2412yes—
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476#107—41no—
477#107—42no—
478#107—42no—
479#107—42no—
480#107—42no—
481#107—42no—
482#106—41no—
483#106—42no—
484#106—42no—
485#106—42no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—42no—
489C4⋊C8—42no—
490#103—42no—
491#103—41no—
492#103—41no—
493#103—42no—
494#103C2×Q814yescomplemented
495#102—42no—
496#102—41no—
497#102—41no—
498#102—41no—
499#102—41no—
500#102—42no—
501#102—42no—
502#102—42no—
503#102C2×Q814yescomplemented
504C22⋊C8—24no—
505C22⋊C8—22no—
506C22⋊C8C2×Q814yes—
507#97—42no—
508C4×C8—22no—
509C4×C8—22no—
510C4×C8—42no—
511#95—21no—
512#95—21no—
513#95—22no—
514#95—22no—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534C24—21no—
535C24—21no—
536C24C22×D411yescharacteristic
537#41—44no—
538#41—44no—
539#41—44no—
540#41—44no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—44no—
547C2×Q8—44no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8—42no—
551C2×Q8—44no—
552C2×Q8—81no—
553C2×Q8—81no—
554C2×Q8—81no—
555C2×Q8—81no—
556C2×Q8—81no—
557C2×Q8—82no—
558C2×Q8—82no—
559C2×Q8—82no—
560C2×Q8—81no—
561C2×Q8—816no—
562C2×Q8C22×Q812yes—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4C22×Q812yes—
580C2×D4C22×Q812yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×Q812yes—
629C22×C42−1+412yes—
630C22×C4C2511yescharacteristic
631SD16—44no—
632D8—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8C22×Q812yes—
650C2×C8C22×Q812yes—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—82no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4C22×Q812yes—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—81no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C22⋊C4—82no—
712C22⋊C4—81no—
713C22⋊C4—82no—
714C42—22no—
715C42—22no—
716C42—21no—
717C42—21no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—82no—
727C42H(5,𝔽2)12yes—
728C42H(5,𝔽2)12yes—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23D4×Q812yes—
750C23C23×D411yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755Q8—88no—
756Q8—84no—
757Q8—84no—
758Q8—162no—
759Q8—164no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—48no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—84no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—44no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—88no—
830C2×C4—84no—
831C2×C4—84no—
832C2×C4—164no—
833C2×C4#53512yes—
834C2×C4#53512yes—
835C2×C4D4×Q812yes—
836C2×C4#57612yes—
837C2×C4#57712yes—
838C2×C4#57812yes—
839C2×C4C23×Q811yescharacteristic
840C2×C4C2×H(5,𝔽2)11yescharacteristic
841C2×C4C2×H(5,𝔽2)11yescharacteristic
842C2×C4C2×2−1+411yescharacteristic
843C2×C4#58511yescharacteristic
844C2×C4#58511yescharacteristic
845C8—22no—
846C8—22no—
847C8—41no—
848C8—41no—
849C8—42no—
850C8—42no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22C2×#53511yescharacteristic
873C22C2×D4×Q811yescharacteristic
874C22#348511yescharacteristic
875C22C2×#57611yescharacteristic
876C22C2×#57711yescharacteristic
877C22C2×#57811yescharacteristic
878C22#358511yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—41no—
887C4—42no—
888C4—42no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4#322514yes—
898C4#350111yescharacteristic
899C4#350111yescharacteristic
900C4#354111yescharacteristic
901C4#354111yescharacteristic
902C2—42no—
903C2—82no—
904C2—82no—
905C2#3959411yescharacteristic
906C2C2×#322511yescharacteristic
907C2#6081111yescharacteristic
908C2#6137311yescharacteristic
909C2#6138211yescharacteristic
910C2#6178811yescharacteristic
911C2#6181611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39608C2semidirect
2. #35279C2semidirect
3. #32958C2semidirect
4. #32364C2semidirect
5. #32357C2semidirect
6. #31543C2semidirect
7. #31518C2semidirect
8. #29961C2semidirect
9. #28539C2semidirect
10. #28528C2semidirect
11. #27959C2semidirect
12. #27821C2semidirect
13. #27815C2semidirect
14. #27687C2semidirect
15. #25813C2semidirect
16. #25455C2semidirect
17. #25450C2semidirect
18. #24815C2semidirect
19. #24812C2semidirect
20. #24299C2semidirect
21. #22626C2semidirect
179. #449Q8semidirect
355. C2×SD16C2×Q8semidirect
358. C2×D8C2×Q8semidirect
494. #103C2×Q8semidirect
503. #102C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#396082
#352792
#329582
#323642
#323572
#315432
#315182
#299612
#285392
#285282
#279592
#278212
#278152
#276872
#258132
#254552
#254502
#248152
#248122
#242992
#226262
#220552
C4×#4492