Finite Group Databasebeta

← #6446455

Subgroups — #6446455

Order 512.

1621 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34929C211yesmaximal, characteristic
2C4×#557C211yesmaximal, characteristic, complemented
3#27303C211yesmaximal, characteristic, complemented
4#27298C211yesmaximal, characteristic, complemented
5#27007C211yesmaximal, characteristic
6#26998C211yesmaximal, characteristic
7#26865C211yesmaximal, characteristic, complemented
8#26856C211yesmaximal, characteristic, complemented
9#26458C211yesmaximal, characteristic, complemented
10#26377C211yesmaximal, characteristic
11#26373C211yesmaximal, characteristic
12#26294C211yesmaximal, characteristic, complemented
13#26056C211yesmaximal, characteristic, complemented
14#25849C211yesmaximal, characteristic, complemented
15#25465C211yesmaximal, characteristic
16#25073C211yesmaximal, characteristic
17#24827C211yesmaximal, characteristic
18#24346C211yesmaximal, characteristic
19#23841C211yesmaximal, characteristic, complemented
20#23839C211yesmaximal, characteristic, complemented
21#23784C211yesmaximal, characteristic
22#23780C211yesmaximal, characteristic
23#21731C211yesmaximal, characteristic, complemented
24#21617C211yesmaximal, characteristic
25#21616C211yesmaximal, characteristic, complemented
26#21616C211yesmaximal, characteristic, complemented
27#21615C211yesmaximal, characteristic, complemented
28#21346C211yesmaximal, characteristic, complemented
29#21124C211yesmaximal, characteristic
30#21124C211yesmaximal, characteristic
31C4×#440C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#533—21no—
34C2×#501C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42#2556—21no—
43#2556—21no—
44#2551C2211yescharacteristic
45#2546C2211yescharacteristic
46#2542C2211yescharacteristic
47#2538C2211yescharacteristic
48#2506C2211yescharacteristic
49#2506C2211yescharacteristic
50#2492—21no—
51#2452C2211yescharacteristic
52#2452C2211yescharacteristic
53#2429—21no—
54#2396—21no—
55#2396—21no—
56#2370—21no—
57#2370—21no—
58#2370C2211yescharacteristic
59#2370C2211yescharacteristic
60#2365—21no—
61#2365C2211yescharacteristic
62#2355—21no—
63#2355C2211yescharacteristic
64#2351C2211yescharacteristic
65#2351C2211yescharacteristic
66Q8×C4⋊C4C2211yescharacteristic
67C4×C4⋊Q8—21no—
68C4×C4⋊Q8C2211yescharacteristic
69C4×C4⋊Q8C2211yescharacteristic
70C4×C4⋊Q8C2211yescharacteristic
71C4×C4⋊Q8C2211yescharacteristic
72C4×#125—21no—
73C4×#125—21no—
74C4×#125C2211yescharacteristic
75C4×#125C2211yescharacteristic
76C4×C22⋊Q8—21no—
77#2293C2211yescharacteristic
78#2293C2211yescharacteristic
79C42×Q8—21no—
80C42×Q8C2211yescharacteristic
81C42×Q8C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83C42×Q8C2211yescharacteristic
84C42×D4C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2086C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2083C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2058C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2025C2211yescharacteristic
116#2023C2211yescharacteristic
117#1993C2211yescharacteristic
118#1992C2211yescharacteristic
119#1989C2211yescharacteristic
120#1988C2211yescharacteristic
121#1987C2211yescharacteristic
122#1987C2211yescharacteristic
123#1985C2211yescharacteristic
124#1985C2211yescharacteristic
125#1949C2211yescharacteristic
126#1948C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1942C2211yescharacteristic
130#1942C2211yescharacteristic
131#1941C2211yescharacteristic
132#1941C2211yescharacteristic
133#1940C2211yescharacteristic
134#1940C2211yescharacteristic
135#1926C2211yescharacteristic
136#1926C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1920C2211yescharacteristic
142#1920C2211yescharacteristic
143#1920C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1918C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1918C2211yescharacteristic
150#1918C2211yescharacteristic
151#1916C2211yescharacteristic
152#1916C2211yescharacteristic
153#1916C2211yescharacteristic
154#1916C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1864C2211yescharacteristic
166#1863C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1862C2211yescharacteristic
171#1847C2211yescharacteristic
172#1804C2211yescharacteristic
173#1803C2211yescharacteristic
174#1803C2211yescharacteristic
175#1803C2211yescharacteristic
176#1776C2211yescharacteristic
177#1776C2211yescharacteristic
178#1776C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186C4×#107C2211yescharacteristic
187#1767C2211yescharacteristic
188#1767C2211yescharacteristic
189#1767C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1745C2211yescharacteristic
201#1745C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204#557—24no—
205#557—24no—
206#533—48no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8D411yescharacteristic
232C2×C4×Q8D411yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C22×C42—21no—
247#501—24no—
248#478—24no—
249#477—24no—
250#477—24no—
251#475—24no—
252#440—24no—
253#440Q818yescomplemented
254C4×SD16—24no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#399—21no—
305#399—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#395—21no—
315#395—21no—
316#393—21no—
317#393—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#385—21no—
377#385—21no—
378#384—21no—
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#382—21no—
384#382—21no—
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#380—21no—
388C4×C4⋊C4—21no—
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4D411yescharacteristic
412C4×C4⋊C4D411yescharacteristic
413C4×C4⋊C4D411yescharacteristic
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4D411yescharacteristic
416C4×C4⋊C4D411yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C43—21no—
440C43—21no—
441C43—21no—
442C43C2311yescharacteristic
443C43C2311yescharacteristic
444C43C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16C2×Q814yes—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—28no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—44no—
520C4⋊Q8—44no—
521#125—28no—
522#125—28no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—44no—
527#125—44no—
528#125#4114yes—
529C22⋊Q8—44no—
530C22⋊Q8—44no—
531C22⋊Q8—44no—
532C22⋊Q8—44no—
533C22⋊Q8—44no—
534C4×Q8—28no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—24no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—42no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—44no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8C2×Q814yes—
557C4×Q8#4114yes—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—41no—
563C4×D4C2×Q814yes—
564#117—44no—
565#117—44no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—44no—
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#107—22no—
681#107—22no—
682#107—22no—
683#107—22no—
684#107—22no—
685#107—22no—
686#107—22no—
687#107—22no—
688#107—41no—
689#107C2×Q814yes—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—22no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103C2×Q814yes—
711#103#4114yes—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718#102C2×Q814yes—
719#97—22no—
720#97—22no—
721#97—22no—
722#97—22no—
723#97—22no—
724#97C2×Q814yes—
725C4×C8—22no—
726C4×C8—41no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24—21no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8C22×Q812yes—
787C2×Q8C2×#4112yes—
788C2×Q8C2×#4112yes—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4C22×Q812yes—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—24no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—81no—
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C2511yescharacteristic
834SD16—28no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8C22×Q812yes—
857C2×C8C22×Q812yes—
858C2×C8C2×#4112yes—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—41no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4AGL(1,ℤ/8)14yes—
929C4⋊C4C22×Q812yes—
930C4⋊C4C22×Q812yes—
931C4⋊C4C2×#4112yes—
932C4⋊C4C2×#4112yes—
933C4⋊C4C2×#4112yes—
934C4⋊C4C2×#4112yes—
935C22⋊C4—24no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—41no—
969C42—41no—
970C42—41no—
971C42—41no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42C22×Q812yes—
990C42C2×#4112yes—
991C42C2×#4112yes—
992C422−1+412yes—
993C23—22no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23C23×D411yescharacteristic
1001Q8—22no—
1002Q8—22no—
1003Q8—22no—
1004Q8—44no—
1005Q8—48no—
1006Q8—84no—
1007Q8—84no—
1008Q8—84no—
1009Q8#53314yescomplemented
1010D4—22no—
1011D4—22no—
1012D4—41no—
1013D4—41no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—48no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—84no—
1095C2×C4—84no—
1096C2×C4#52512yes—
1097C2×C4#52512yes—
1098C2×C4D4×Q812yes—
1099C2×C4D4×Q812yes—
1100C2×C4C2×AGL(1,ℤ/8)12yes—
1101C2×C4C2×AGL(1,ℤ/8)12yes—
1102C2×C4C2×AGL(1,ℤ/8)12yes—
1103C2×C4#57512yes—
1104C2×C4C23×Q811yescharacteristic
1105C2×C4C22×#4111yescharacteristic
1106C2×C4C22×#4111yescharacteristic
1107C2×C4C22×#4111yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4#58511yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—22no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22C2×#52511yescharacteristic
1126C22C2×D4×Q811yescharacteristic
1127C22D4×#4111yescharacteristic
1128C22C22×AGL(1,ℤ/8)11yescharacteristic
1129C22C2×#57511yescharacteristic
1130C22#358611yescharacteristic
1131C22#358611yescharacteristic
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—24no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—42no—
1147C4—42no—
1148C4—41no—
1149C4—41no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4C2×#53311yescharacteristic
1162C4#346111yescharacteristic
1163C4Q8×#4111yescharacteristic
1164C4#348211yescharacteristic
1165C2—82no—
1166C2#3469111yescharacteristic
1167C2#6056111yescharacteristic
1168C2#6057711yescharacteristic
1169C2Q8×AGL(1,ℤ/8)11yescharacteristic
1170C2#6136911yescharacteristic
1171C2#6145211yescharacteristic
1172C2#6145811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#557C2semidirect
3. #27303C2semidirect
4. #27298C2semidirect
7. #26865C2semidirect
8. #26856C2semidirect
9. #26458C2semidirect
12. #26294C2semidirect
13. #26056C2semidirect
14. #25849C2semidirect
19. #23841C2semidirect
20. #23839C2semidirect
23. #21731C2semidirect
25. #21616C2semidirect
26. #21616C2semidirect
27. #21615C2semidirect
28. #21346C2semidirect
253. #440Q8semidirect
1009. Q8#533semidirect

Maximal subgroups

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

subgroupindex
#349292
C4×#5572
#273032
#272982
#270072
#269982
#268652
#268562
#264582
#263772
#263732
#262942
#260562
#258492
#254652
#250732
#248272
#243462
#238412
#238392
#237842
#237802
#217312
#216172
#216162
#216152
#213462
#211242
C4×#4402