Finite Group Databasebeta

← #6583752

Subgroups — #6583752

Order 512.

1932 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3170C211yesmaximal, characteristic, complemented
2C2×#3165C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33255C211yesmaximal, characteristic, complemented
6#33207C211yesmaximal, characteristic, complemented
7#33176C211yesmaximal, characteristic, complemented
8#28656C211yesmaximal, characteristic, complemented
9#28653C211yesmaximal, characteristic, complemented
10#27797C214yesmaximal, complemented
11#26489C214yesmaximal, complemented
12#25904C211yesmaximal, characteristic, complemented
13#25902C211yesmaximal, characteristic, complemented
14#25674C211yesmaximal, characteristic, complemented
15#25672C211yesmaximal, characteristic, complemented
16#24791C214yesmaximal
17#23036C214yesmaximal, complemented
18#21726C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3170—28no—
25#3165—28no—
26C2×#501C2214yes—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#494C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#470C2214yes—
37C2×#467C2214yes—
38C2×C4×Q16C2214yes—
39C2×#435C2212yes—
40C2×#428C2214yes—
41C2×C4×M16C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2862C2211yescharacteristic
44#2862C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2550—21no—
50#2536—21no—
51#2492C2212yes—
52#2489—21no—
53#2489C2212yes—
54#2453—21no—
55#2453C2212yes—
56#2451C2212yes—
57#2446—21no—
58#2442—21no—
59#2439—21no—
60#2429—21no—
61#2421—21no—
62#2421—21no—
63#2417C2212yes—
64#2415—21no—
65#2415C2212yes—
66#2409—21no—
67#2362—21no—
68#2362C2212yes—
69#2360C2212yes—
70#2352—21no—
71#2351—21no—
72Q8×C22⋊C4—21no—
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C42×D4C2211yescharacteristic
76#2068C2214yes—
77#2066C2214yes—
78#2036C2214yes—
79#2035C2214yes—
80#2026C2214yes—
81#2024C2214yes—
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1971C2214yes—
87#1971C2214yes—
88#1971C2214yes—
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1943C2214yes—
92#1941C2214yes—
93#1928C2214yes—
94#1927C2214yes—
95#1873C2214yes—
96#1872C2214yes—
97#1865C2214yes—
98#1863C2214yes—
99#1844C2211yescharacteristic
100#1807C2214yes—
101#1776C2214yes—
102#1771C2212yes—
103C4×C4⋊C8C2211yescharacteristic
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C23×Q8—21no—
110C22×Q16C2314yes—
111C22×M16C2312yes—
112C23×C8C2312yes—
113#533—24no—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#533—42no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×#125—21no—
131C2×#125—21no—
132C2×#125C2312yes—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8C2312yes—
150C2×C4×Q8C2312yes—
151C2×C4×D4D411yescharacteristic
152C2×C4×D4D411yescharacteristic
153C2×C4×D4C2311yescharacteristic
154C2×#117—21no—
155C2×#117—21no—
156C2×#117C2312yes—
157C22×C4⋊C4—21no—
158C22×C4⋊C4C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#501—216no—
162#500—24no—
163#500D418yescomplemented
164#498—24no—
165#498—24no—
166#494—24no—
167#487—24no—
168#487—24no—
169#487—42no—
170#487—42no—
171#470—216no—
172#467—216no—
173C4×Q16—216no—
174#435—28no—
175#428—216no—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#106C2314yes—
179C2×#106C2314yes—
180C2×#106C2314yes—
181C2×C4⋊C8C2312yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C4×M16—24no—
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×C4×C8—24no—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200#400—22no—
201#400—22no—
202#400—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#397—22no—
207#397—22no—
208#396—22no—
209#395—22no—
210#394—22no—
211#393—22no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—22no—
221#391—22no—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#391C2312yes—
227#391C2312yes—
228#389—22no—
229#389—22no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—22no—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#386—22no—
253#385—22no—
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#382—21no—
257#382—21no—
258#382—21no—
259#382—21no—
260#382—22no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—22no—
268#380C2312yes—
269#380C2312yes—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—22no—
273C4×C4⋊C4D411yescharacteristic
274C4×C4⋊C4D411yescharacteristic
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C22⋊C4—22no—
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C43C2311yescharacteristic
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—22no—
298C22×Q8—44no—
299C22×Q8—44no—
300C22×Q8—82no—
301C22×Q8C2412yes—
302C22×Q8C2412yes—
303C22×D4C2×D411yescharacteristic
304C23×C4—22no—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C2×Q16—28no—
312C2×Q16—28no—
313C2×Q16—28no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16#4118yes—
317C22×C8—24no—
318C22×C8—24no—
319C22×C8—24no—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C4⋊Q8—24no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—42no—
336C4⋊Q8—44no—
337C4⋊Q8—44no—
338C4⋊Q8C2×D414yes—
339C4⋊Q8C2×D414yes—
340#125—24no—
341#125—42no—
342#125—44no—
343#125—44no—
344C22⋊Q8—28no—
345C22⋊Q8—28no—
346C22⋊Q8—24no—
347C22⋊Q8—24no—
348C22⋊Q8—42no—
349C22⋊Q8—42no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—82no—
356C4×Q8—24no—
357C4×Q8—24no—
358C4×Q8—42no—
359C4×Q8—42no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×Q8—44no—
364C4×Q8—44no—
365C4×Q8—82no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—42no—
369#117—24no—
370#117—42no—
371#117—44no—
372#117—44no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446#107—28no—
447#107C2×D4116yes—
448#106—28no—
449#106—28no—
450#106—28no—
451C4⋊C8—24no—
452#103—28no—
453#103—28no—
454#103—28no—
455#103—28no—
456#103—44no—
457#103—44no—
458C22⋊C8—24no—
459C22⋊C8—24no—
460#97—24no—
461#97—24no—
462#97—24no—
463C4×C8—24no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8C2×D414yes—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494C24C22×D411yescharacteristic
495C24C22×D411yescharacteristic
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—82no—
519C2×Q8—816no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—82no—
552C22×C4#13714yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C2×#4114yes—
566C22×C4C2511yescharacteristic
567Q16—416no—
568M16—216no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—48no—
578C2×C8C22×D414yes—
579C2×C8C2×#4114yes—
580C2×C8C2×#4114yes—
581C2×C82−1+414yes—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—44no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4C22×D414yes—
620C4⋊C4C22×D414yes—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—82no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—22no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—82no—
653C42C22×D412yes—
654C42H(5,𝔽2)12yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23#53212yes—
668C23C2×#13712yes—
669C23C23×D411yescharacteristic
670Q8—48no—
671Q8—48no—
672Q8—44no—
673Q8—44no—
674Q8—44no—
675Q8—44no—
676Q8—88no—
677Q8—84no—
678Q8—84no—
679D4—44no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—28no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—88no—
741C2×C4#53212yes—
742C2×C4D4212yes—
743C2×C4D4212yes—
744C2×C4C2×#13712yes—
745C2×C4C2×#13712yes—
746C2×C4#57512yes—
747C2×C4#57712yes—
748C2×C4#57812yes—
749C2×C4C23×D411yescharacteristic
750C2×C4C22×#4112yes—
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C2×C4C2×2−1+412yes—
753C8—24no—
754C8—42no—
755C8—42no—
756C8#54818yes—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C2×#53211yescharacteristic
772C22C2×D4211yescharacteristic
773C22#349911yescharacteristic
774C22C22×#13711yescharacteristic
775C22C2×#57511yescharacteristic
776C22C2×#57711yescharacteristic
777C22C2×#57811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—44no—
788C4—44no—
789C4—41no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4#326714yes—
797C4#327014yes—
798C4C2×#54812yes—
799C4#351112yes—
800C2—42no—
801C2—42no—
802C2#3612211yescharacteristic
803C2#6070111yescharacteristic
804C2#6072311yescharacteristic
805C2C2×#326711yescharacteristic
806C2C2×#327011yescharacteristic
807C2#6247811yescharacteristic
808C2#6248211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3170C2semidirect
2. C2×#3165C2semidirect
5. #33255C2semidirect
6. #33207C2semidirect
7. #33176C2semidirect
8. #28656C2semidirect
9. #28653C2semidirect
10. #27797C2semidirect
11. #26489C2semidirect
12. #25904C2semidirect
13. #25902C2semidirect
14. #25674C2semidirect
15. #25672C2semidirect
17. #23036C2semidirect
18. #21726C2semidirect
163. #500D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31702
C2×#31652
#361512
#361292
#332552
#332072
#331762
#286562
#286532
#277972
#264892
#259042
#259022
#256742
#256722
#247912
#230362
#217262
C4×#4352