Finite Group Databasebeta

← #6374459

Subgroups — #6374459

Order 512.

3226 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3461C211yesmaximal, characteristic
2C2×#2925C211yesmaximal, characteristic, complemented
3#34183C211yesmaximal, characteristic, complemented
4#21873C214yesmaximal, complemented
5#21871C214yesmaximal, complemented
6#21870C212yesmaximal, complemented
7#21867C212yesmaximal, complemented
8#21862C212yesmaximal, complemented
9#21860C212yesmaximal, complemented
10#21326C212yesmaximal, complemented
11#21205C212yesmaximal, complemented
12#20915C212yesmaximal
13#20913C212yesmaximal, complemented
14#20648C211yesmaximal, characteristic, complemented
15#20647C211yesmaximal, characteristic, complemented
16#20645C211yesmaximal, characteristic, complemented
17C2×#1803C211yesmaximal, characteristic, complemented
18#3461—28no—
19#3461C4116yescomplemented
20C2×#544C2211yescharacteristic
21C2×#542—21no—
22C2×#542C2212yes—
23C2×#541—21no—
24C2×#541C2212yes—
25C2×#539—22no—
26C2×#537C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533—21no—
30C2×#533C2212yes—
31C2×#529—21no—
32C2×#529—22no—
33C2×#529C2212yes—
34C2×#520C2212yes—
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2925—28no—
39C2×#433C2214yes—
40C2×#432C2212yes—
41C2×#431C2212yes—
42C2×#423C2211yescharacteristic
43C22×C4⋊C8C2211yescharacteristic
44C2×#417C2212yes—
45C2×#419C2212yes—
46C2×#416C2212yes—
47C22×#103C2212yes—
48C2×#408C2212yes—
49C2×#405C2212yes—
50Q8×C4⋊C4—21no—
51Q8×C4⋊C4—21no—
52D4×C4⋊C4—21no—
53D4×C4⋊C4—22no—
54D4×C4⋊C4—22no—
55D4×C4⋊C4—21no—
56#2317C2212yes—
57#2317C2214yes—
58#2285C2212yes—
59#2285C2211yescharacteristic
60C2×#384C2212yes—
61C2×#384C2211yescharacteristic
62#1993C2214yes—
63#1992C2214yes—
64#1991C2214yes—
65#1990C2214yes—
66#1960C2214yes—
67#1959C2214yes—
68#1958C2214yes—
69#1956C2214yes—
70#1875C2214yes—
71#1874C2214yes—
72#1873C2214yes—
73#1873C2214yes—
74#1873C2214yes—
75#1872C2214yes—
76#1872C2214yes—
77#1872C2214yes—
78#1805C2214yes—
79#1805C2212yes—
80#1804C2212yes—
81#1803C2211yescharacteristic
82#1803C2212yes—
83#1803C2212yes—
84#1803C2212yes—
85#1803C2212yes—
86#1803C2212yes—
87#1803C2211yescharacteristic
88#1803C2214yes—
89#1803C2212yes—
90#1802C2211yescharacteristic
91#1802C2212yes—
92#1802C2211yescharacteristic
93#1802C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1735C2212yes—
97C2×#340C2212yes—
98C22×#41C2311yescharacteristic
99C22×#41C2311yescharacteristic
100C23×Q8C2311yescharacteristic
101C22×M16C2312yes—
102C23×C8C2312yes—
103#544—24no—
104#544C2×C418yescomplemented
105#542—216no—
106#542—28no—
107#542C2×C4116yescomplemented
108#541—216no—
109#541—28no—
110#541C2×C4116yescomplemented
111#539—232no—
112#537—24no—
113#537C2×C418yes—
114#536—24no—
115#536—24no—
116#536C2×C418yes—
117#536C2×C418yescomplemented
118#533—216no—
119#533—28no—
120#533C2×C4116yescomplemented
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8C2312yes—
124C2×C4⋊Q8C2312yes—
125#529—232no—
126#529—216no—
127#529—28no—
128#529C2×C4116yescomplemented
129C2×#126—22no—
130C2×#126—22no—
131C2×#126—22no—
132C2×#126—22no—
133C2×#125—22no—
134C2×#125—21no—
135C2×#125—22no—
136C2×#125—22no—
137C2×#125C2312yes—
138C2×#124—21no—
139C2×#124—22no—
140C2×#124C2312yes—
141C2×#123—22no—
142C2×#123—22no—
143C2×#123—22no—
144C2×#123—22no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2312yes—
153C2×C22⋊Q8C2312yes—
154C2×#121—22no—
155C2×#121—21no—
156C2×#121C2312yes—
157#520—44no—
158#520—44no—
159C4×#41—24no—
160C4×#41C2×C418yes—
161C4×#41C2×C418yescomplemented
162C4×#41D418yes—
163C2×C4×Q8—22no—
164C2×C4×Q8—21no—
165C2×C4×Q8—21no—
166C2×C4×Q8—24no—
167C2×C4×Q8—22no—
168C2×C4×Q8C2×C418yescomplemented
169C2×C4×Q8D411yescharacteristic
170C2×C4×Q8D411yescharacteristic
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2311yescharacteristic
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×D4—21no—
176C2×C4×D4—21no—
177C2×C4×D4—22no—
178C2×C4×D4—24no—
179C2×C4×D4—22no—
180C2×C4×D4D412yes—
181C2×C4×D4D411yescharacteristic
182C2×C4×D4D412yes—
183C2×C4×D4D411yescharacteristic
184C2×C4×D4C2311yescharacteristic
185C2×C4×D4C2311yescharacteristic
186C2×#117—22no—
187C2×#117—21no—
188C2×#117—22no—
189C2×#117C2312yes—
190C2×#117C2311yescharacteristic
191C2×#117C2314yes—
192C2×#117C2311yescharacteristic
193C2×#117C2312yes—
194C22×C4⋊C4—21no—
195C22×C4⋊C4—22no—
196C22×C4⋊C4—21no—
197C22×C4⋊C4—21no—
198C22×C4⋊C4—22no—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2314yes—
202C22×C42—21no—
203C22×C42—21no—
204C22×C42C2311yescharacteristic
205C22×C42C2312yes—
206#433—216no—
207#432—28no—
208#431—28no—
209#423—24no—
210C2×C4⋊C8—24no—
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2312yes—
214C2×C4⋊C8C2312yes—
215C2×C4⋊C8C2312yes—
216#419—44no—
217#417—44no—
218#416—44no—
219C2×#103—44no—
220C2×#103C2314yes—
221C2×#103C2314yes—
222C2×#103C2314yes—
223C2×#103C2312yes—
224C2×#103C2312yes—
225C2×#103C2314yes—
226C2×#103C2314yes—
227C2×#102C2314yes—
228C2×#102C2312yes—
229C2×#102C2312yes—
230#408—28no—
231C2×C22⋊C8C2314yes—
232C2×C22⋊C8C2314yes—
233#405—28no—
234C2×#97C2314yes—
235C2×C4×C8C2314yes—
236#389—22no—
237#389—24no—
238#389—22no—
239#389—24no—
240#385—24no—
241#385—24no—
242#385—24no—
243#384—22no—
244#384—21no—
245#384—21no—
246#384—22no—
247#384C2312yes—
248#384C2312yes—
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2314yes—
252#382C2312yes—
253#382C2314yes—
254#380—22no—
255#380—21no—
256#380—21no—
257#380—22no—
258C4×C4⋊C4—22no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—22no—
262#340C2314yes—
263#340C2314yes—
264#340C2312yes—
265#340C2312yes—
266#340C2314yes—
267#340C2314yes—
268#340C2312yes—
269#340C2312yes—
270#340C2314yes—
271#340C2314yes—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41C22×C414yes—
282C2×#41C22×C414yes—
283C2×#41C2×D414yes—
284C22×Q8—21no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8C22×C414yes—
292C22×Q8C2×D411yescharacteristic
293C22×Q8C2412yes—
294C22×Q8C2411yescharacteristic
295C22×D4—21no—
296C22×D4—22no—
297C22×D4C2×D412yes—
298C22×D4C2×D411yescharacteristic
299C22×D4C2411yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—24no—
306C23×C4—22no—
307C23×C4C2×D412yes—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C22×C8—24no—
317C22×C8—24no—
318C22×C8—24no—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2414yes—
322C4⋊Q8—28no—
323C4⋊Q8—28no—
324C4⋊Q8—24no—
325C4⋊Q8—24no—
326C4⋊Q8C22×C418yes—
327C4⋊Q8C22×C418yes—
328#126—216no—
329#126—216no—
330#126—216no—
331#126—216no—
332#125—216no—
333#125—28no—
334#125—216no—
335#125—216no—
336#125—24no—
337#125C22×C418yes—
338#124—28no—
339#124—216no—
340#124—24no—
341#124C22×C418yes—
342#123—216no—
343#123—216no—
344#123—216no—
345#123—216no—
346C22⋊Q8—28no—
347C22⋊Q8—216no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8—28no—
352C22⋊Q8—28no—
353C22⋊Q8—216no—
354C22⋊Q8—216no—
355C22⋊Q8C22×C418yes—
356C22⋊Q8C22×C418yes—
357C22⋊Q8C22×C418yes—
358#121—216no—
359#121—28no—
360#121—24no—
361#121C22×C418yes—
362C4×Q8—28no—
363C4×Q8—28no—
364C4×Q8—216no—
365C4×Q8—24no—
366C4×Q8—24no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—48no—
370C4×Q8C22⋊C418yes—
371C4×Q8C22⋊C418yes—
372C4×Q8C22×C418yes—
373C4×Q8C22×C418yes—
374C4×Q8C22×C414yes—
375C4×Q8C22×C414yes—
376C4×D4—28no—
377C4×D4—28no—
378C4×D4—216no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—416no—
382C4×D4—48no—
383C4×D4C22⋊C418yes—
384C4×D4C22⋊C4116yes—
385C4×D4C22⋊C4116yes—
386C4×D4C22⋊C418yes—
387C4×D4C22×C414yes—
388C4×D4C22×C414yes—
389#117—216no—
390#117—22no—
391#117—28no—
392#117—216no—
393#117—24no—
394#117—24no—
395#117—44no—
396#117—44no—
397#117C22×C414yes—
398#117C22×C414yes—
399#117C22×C418yes—
400#117C2×D414yes—
401#117C2×D418yes—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—82no—
434C2×C4⋊C4—84no—
435C2×C4⋊C4—82no—
436C2×C4⋊C4—84no—
437C2×C4⋊C4C22×C414yes—
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—28no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—28no—
469C2×C42—24no—
470C2×C42—22no—
471C2×C42C22×C414yes—
472C2×C42C22×C418yes—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D412yes—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D412yes—
477C2×C42C2×D414yes—
478C2×C42C2×D418yes—
479C2×C42C2411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C4⋊C8—22no—
483C4⋊C8—22no—
484C4⋊C8—24no—
485C4⋊C8—24no—
486C4⋊C8—24no—
487#103—44no—
488#103—44no—
489#103—42no—
490#103—42no—
491#103—44no—
492#103—44no—
493#103—44no—
494#102—42no—
495#102—42no—
496#102—44no—
497C22⋊C8—28no—
498C22⋊C8—28no—
499#97—28no—
500C4×C8—28no—
501#95—22no—
502#95—22no—
503#95—24no—
504#95—24no—
505C24—21no—
506C24C22×D412yes—
507C24C22×D411yescharacteristic
508#41—28no—
509#41—28no—
510#41—28no—
511#41—28no—
512#41—28no—
513#41—28no—
514#41—44no—
515#41—44no—
516C2×Q8—24no—
517C2×Q8—28no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—21no—
522C2×Q8—28no—
523C2×Q8—28no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—82no—
537C2×Q8—82no—
538C2×Q8C2×C22⋊C414yes—
539C2×Q8C23×C414yes—
540C2×Q8C23×C412yes—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—28no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4C2×C22⋊C418yes—
557C2×D4C2×C22⋊C414yes—
558C2×D4C23×C412yes—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—41no—
581C22×C4—42no—
582C22×C4—41no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—82no—
597C22×C4—84no—
598C22×C4—82no—
599C22×C4—84no—
600C22×C4C2×C22⋊C414yes—
601C22×C4C2×C22⋊C418yes—
602C22×C4C2×C22⋊C414yes—
603C22×C4C2×C22⋊C418yes—
604C22×C4C23×C414yes—
605C22×C4C23×C412yes—
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D414yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C42−1+412yes—
619C22×C42−1+412yes—
620C22×C4C2511yescharacteristic
621M16—48no—
622C2×C8—22no—
623C2×C8—24no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—24no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—24no—
631C2×C8—48no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—42no—
655C4⋊C4—48no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—82no—
663C4⋊C4—84no—
664C4⋊C4—82no—
665C4⋊C4—84no—
666C4⋊C4C2×C22⋊C418yes—
667C4⋊C4C2×C22⋊C414yes—
668C4⋊C4C2×C22⋊C414yes—
669C4⋊C4C2×C22⋊C418yes—
670C4⋊C4C23×C414yes—
671C4⋊C4C23×C412yes—
672C4⋊C4C23×C412yes—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—24no—
676C22⋊C4—28no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—48no—
683C22⋊C4—44no—
684C22⋊C4C2×C22⋊C418yes—
685C22⋊C4C2×C22⋊C418yes—
686C22⋊C4C2×C22⋊C418yes—
687C42—28no—
688C42—24no—
689C42—24no—
690C42—24no—
691C42—28no—
692C42—48no—
693C42—44no—
694C42C2×C22⋊C414yes—
695C42C2×C22⋊C414yes—
696C42C2×C22⋊C418yes—
697C42C2×C22⋊C418yes—
698C42C23×C412yes—
699C42C23×C412yes—
700C42C23×C414yes—
701C42C22×D414yes—
702C42C22×D412yes—
703C42C22×D412yes—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23C22×C22⋊C414yes—
722C23C22×C22⋊C412yes—
723C23#53512yes—
724C23#53612yes—
725C23C23×D411yescharacteristic
726Q8—28no—
727Q8—24no—
728Q8—24no—
729Q8—22no—
730Q8—22no—
731Q8—48no—
732Q8—42no—
733Q8—42no—
734Q8—41no—
735Q8—41no—
736Q8—88no—
737D4—216no—
738D4—28no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—88no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—28no—
758C2×C4—216no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—44no—
769C2×C4—48no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—48no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4—164no—
795C2×C4—168no—
796C2×C4C22×C22⋊C412yes—
797C2×C4C22×C22⋊C412yes—
798C2×C4C22×C22⋊C412yes—
799C2×C4C22×C22⋊C414yes—
800C2×C4C22×C22⋊C414yes—
801C2×C4C22×C22⋊C414yes—
802C2×C4C22×C22⋊C412yes—
803C2×C4C22×C22⋊C412yes—
804C2×C4#52014yes—
805C2×C4#52014yes—
806C2×C4#53512yes—
807C2×C4#53612yes—
808C2×C4#53714yes—
809C2×C4#53714yes—
810C2×C4#57712yes—
811C2×C4#57812yes—
812C2×C4C24×C411yescharacteristic
813C2×C4C23×D411yescharacteristic
814C2×C4C2×H(5,𝔽2)11yescharacteristic
815C2×C4C2×H(5,𝔽2)11yescharacteristic
816C2×C4C2×2−1+411yescharacteristic
817C2×C4C2×2−1+411yescharacteristic
818C8—42no—
819C8—42no—
820C8—44no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22#231114yes—
842C22C23×C22⋊C411yescharacteristic
843C22C2×#53511yescharacteristic
844C22C2×#53611yescharacteristic
845C22C2×#57711yescharacteristic
846C22C2×#57811yescharacteristic
847C22#358511yescharacteristic
848C22#358611yescharacteristic
849C4—22no—
850C4—24no—
851C4—22no—
852C4—22no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—84no—
861C4—82no—
862C4—82no—
863C4#231114yes—
864C4#289814yes—
865C4C2×#52011yescharacteristic
866C4C2×#52011yescharacteristic
867C4C2×#53711yescharacteristic
868C4C2×#53711yescharacteristic
869C2—24no—
870C2—44no—
871C2—82no—
872C2C2×#231111yescharacteristic
873C2C2×#289811yescharacteristic
874C2#6008911yescharacteristic
875C2#6083311yescharacteristic
876C2#6083711yescharacteristic
877C2#6088911yescharacteristic
878C2#6089311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#537C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2925C2semidirect
3. #34183C2semidirect
4. #21873C2semidirect
5. #21871C2semidirect
6. #21870C2semidirect
7. #21867C2semidirect
8. #21862C2semidirect
9. #21860C2semidirect
10. #21326C2semidirect
11. #21205C2semidirect
13. #20913C2semidirect
14. #20648C2semidirect
15. #20647C2semidirect
16. #20645C2semidirect
17. C2×#1803C2semidirect
19. #3461C4semidirect
104. #544C2×C4semidirect
107. #542C2×C4semidirect
110. #541C2×C4semidirect
117. #536C2×C4semidirect
120. #533C2×C4semidirect
128. #529C2×C4semidirect
161. C4×#41C2×C4semidirect
168. C2×C4×Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34612
C2×#29252
#341832
#218732
#218712
#218702
#218672
#218622
#218602
#213262
#212052
#209152
#209132
#206482
#206472
#206452
C2×#18032