Finite Group Databasebeta

← #6585619

Subgroups — #6585619

Order 512.

1901 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3185C211yesmaximal, characteristic, complemented
2C2×#3170C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic
4#36134C211yesmaximal, characteristic
5#33314C211yesmaximal, characteristic, complemented
6#33212C211yesmaximal, characteristic, complemented
7#33207C211yesmaximal, characteristic, complemented
8#28719C211yesmaximal, characteristic, complemented
9#28717C211yesmaximal, characteristic, complemented
10#28238C214yesmaximal
11#25674C211yesmaximal, characteristic, complemented
12#25674C211yesmaximal, characteristic, complemented
13#25672C211yesmaximal, characteristic, complemented
14#25672C211yesmaximal, characteristic, complemented
15#25043C214yesmaximal, complemented
16#25039C214yesmaximal, complemented
17#22679C214yesmaximal, complemented
18#21691C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#533C2211yescharacteristic
24#3185—28no—
25#3170—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#494C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#470C2214yes—
36C2×#467C2214yes—
37C2×#441C2214yes—
38C2×#441C2214yes—
39C2×C4×Q16C2214yes—
40C2×#435C2212yes—
41C2×C4×M16C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2868C2211yescharacteristic
44#2862C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2552—21no—
50#2542—21no—
51#2538C2212yes—
52#2536C2212yes—
53#2489—21no—
54#2489—21no—
55#2453—21no—
56#2453—21no—
57#2441—21no—
58#2441—21no—
59#2429—21no—
60#2429—21no—
61#2423C2212yes—
62#2423C2212yes—
63#2421C2212yes—
64#2421C2212yes—
65#2415—21no—
66#2415—21no—
67#2365—21no—
68#2362—21no—
69#2362—21no—
70#2354—21no—
71#2351C2212yes—
72Q8×C4⋊C4C2212yes—
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C42×D4C2211yescharacteristic
76#2074C2214yes—
77#2072C2214yes—
78#2036C2214yes—
79#2036C2214yes—
80#2035C2214yes—
81#2035C2214yes—
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1971C2214yes—
87#1956C2211yescharacteristic
88#1956C2211yescharacteristic
89#1944C2214yes—
90#1941C2214yes—
91#1865C2214yes—
92#1865C2214yes—
93#1863C2214yes—
94#1863C2214yes—
95#1847C2214yes—
96#1847C2214yes—
97#1844C2211yescharacteristic
98#1809C2214yes—
99#1807C2214yes—
100#1805C2214yes—
101#1803C2214yes—
102#1771C2212yes—
103C4×C4⋊C8C2211yescharacteristic
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×Q16C2314yes—
110C22×M16C2312yes—
111C23×C8C2312yes—
112#533—24no—
113#533—24no—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#533—42no—
119#533—42no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×#125—21no—
129C2×#125—21no—
130C2×#125—21no—
131C2×#125—21no—
132C2×C22⋊Q8—21no—
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⋊Q8—21no—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2312yes—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D411yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×#117—21no—
158C2×#117—21no—
159C2×#117—21no—
160C2×#117—21no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#500—24no—
164#500—42no—
165#498—24no—
166#498—42no—
167#494D418yescomplemented
168#487—24no—
169#487—24no—
170#487—24no—
171#487—24no—
172#470—216no—
173#467—216no—
174#441—216no—
175#441—216no—
176C4×Q16—216no—
177#435—28no—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#106C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8C2312yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C4×M16—24no—
193C2×#97C2312yes—
194C2×#97C2312yes—
195C2×#97C2312yes—
196C2×C4×C8—24no—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202#400—22no—
203#400—22no—
204#399—22no—
205#399—22no—
206#398—22no—
207#398—22no—
208#398—22no—
209#397—22no—
210#397—22no—
211#396—22no—
212#396—22no—
213#394—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391C2312yes—
223#391C2312yes—
224#390—22no—
225#389—22no—
226#389—22no—
227#389—22no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—22no—
237#389—22no—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#388—22no—
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#384—22no—
253#384—21no—
254#384—21no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#384C2312yes—
258#384C2312yes—
259#382—22no—
260#382C2312yes—
261#382C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270C4×C4⋊C4—22no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4D411yescharacteristic
277C4×C4⋊C4D411yescharacteristic
278C4×C4⋊C4C2311yescharacteristic
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×Q8C2412yes—
298C22×Q8C2412yes—
299C22×D4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×Q16—28no—
307C2×Q16—28no—
308C2×Q16C2×D4116yes—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C22×C8—24no—
313C22×C8—24no—
314C22×C8—24no—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—44no—
330C4⋊Q8—82no—
331C4⋊Q8C2×D414yes—
332C4⋊Q8C2×D414yes—
333#125—44no—
334#125—44no—
335#125—44no—
336#125—44no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—42no—
342C22⋊Q8—42no—
343C22⋊Q8—42no—
344C22⋊Q8—42no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—82no—
352C22⋊Q8—82no—
353C4×Q8—24no—
354C4×Q8—24no—
355C4×Q8—24no—
356C4×Q8—24no—
357C4×Q8—28no—
358C4×Q8—28no—
359C4×Q8—42no—
360C4×Q8—42no—
361C4×Q8—42no—
362C4×Q8—42no—
363C4×Q8—44no—
364C4×Q8—44no—
365C4×Q8—44no—
366C4×Q8—44no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—42no—
370#117—44no—
371#117—44no—
372#117—44no—
373#117—44no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450#107—28no—
451#107—44no—
452#106—28no—
453#106—28no—
454#106—44no—
455C4⋊C8—24no—
456#103—28no—
457#103—28no—
458#103—28no—
459#103—28no—
460#103—28no—
461#103—28no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464#97—24no—
465#97—24no—
466#97#4118yes—
467C4×C8—24no—
468C4×C8—22no—
469C4×C8—22no—
470C4×C8—22no—
471C4×C8C2×D414yes—
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—22no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8C22×D414yes—
515C2×Q8C22×D414yes—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4#13714yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C2511yescharacteristic
560Q16—232no—
561M16—48no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—48no—
571C2×C8C22×D414yes—
572C2×C8C2×#4114yes—
573C2×C8C2×#4114yes—
574C2×C82−1+414yes—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—41no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
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—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—22no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42C22×D412yes—
652C42C2×#4114yes—
653C42H(5,𝔽2)12yes—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23C2×#13712yes—
668C23C23×D411yescharacteristic
669Q8—28no—
670Q8—28no—
671Q8—44no—
672Q8—44no—
673Q8—84no—
674Q8—84no—
675Q8—84no—
676Q8—84no—
677D4—44no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—28no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—21no—
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—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
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#53212yes—
738C2×C4#53212yes—
739C2×C4D4212yes—
740C2×C4D4212yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4#57512yes—
744C2×C4#57712yes—
745C2×C4#57812yes—
746C2×C4C23×D411yescharacteristic
747C2×C4C22×#4112yes—
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4C2×2−1+412yes—
750C8—24no—
751C8—42no—
752C8—42no—
753C8#54718yes—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22C2×#53211yescharacteristic
769C22C2×D4211yescharacteristic
770C22#349911yescharacteristic
771C22C22×#13711yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57711yescharacteristic
774C22C2×#57811yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—44no—
783C4—44no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4#327014yes—
794C4#327114yes—
795C4C2×#54712yes—
796C4#351112yes—
797C2—42no—
798C2—81no—
799C2#3612711yescharacteristic
800C2#6070111yescharacteristic
801C2#6072311yescharacteristic
802C2C2×#327011yescharacteristic
803C2C2×#327111yescharacteristic
804C2#6247811yescharacteristic
805C2#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×#3185C2semidirect
2. C2×#3170C2semidirect
5. #33314C2semidirect
6. #33212C2semidirect
7. #33207C2semidirect
8. #28719C2semidirect
9. #28717C2semidirect
11. #25674C2semidirect
12. #25674C2semidirect
13. #25672C2semidirect
14. #25672C2semidirect
15. #25043C2semidirect
16. #25039C2semidirect
17. #22679C2semidirect
18. #21691C2semidirect
167. #494D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31852
C2×#31702
#361512
#361342
#333142
#332122
#332072
#287192
#287172
#282382
#256742
#256722
#250432
#250392
#226792
#216912
C4×#4352