Finite Group Databasebeta

← #190893

Subgroups — #190893

Order 512.

1015 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34129C211yesmaximal, characteristic
2#21924C211yesmaximal, characteristic, complemented
3C4×#433C211yesmaximal, characteristic, complemented
4#8710C211yesmaximal, characteristic, complemented
5#8709C211yesmaximal, characteristic, complemented
6#8569C211yesmaximal, characteristic, complemented
7#8567C211yesmaximal, characteristic, complemented
8#8566C211yesmaximal, characteristic, complemented
9#8564C211yesmaximal, characteristic, complemented
10#8312C211yesmaximal, characteristic
11#8312C211yesmaximal, characteristic
12#8181C211yesmaximal, characteristic, complemented
13#8177C211yesmaximal, characteristic, complemented
14#8173C211yesmaximal, characteristic, complemented
15C4×Q8⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×#41C2211yescharacteristic
17C2×#433—21no—
18#2354—21no—
19#2354—21no—
20#2354C411yescharacteristic
21#2354C411yescharacteristic
22Q8×C4⋊C4C411yescharacteristic
23Q8×C4⋊C4C411yescharacteristic
24#2346—21no—
25#2346—21no—
26#2346C411yescharacteristic
27#2346C411yescharacteristic
28#2341C411yescharacteristic
29#2341C411yescharacteristic
30#2293—21no—
31#2293—21no—
32#2293C2211yescharacteristic
33#2293C2211yescharacteristic
34#2285—21no—
35#2285C2211yescharacteristic
36C42×Q8C2211yescharacteristic
37C42×Q8C2211yescharacteristic
38C4×#117—21no—
39C4×#117C2211yescharacteristic
40#1924—21no—
41#1923—21no—
42#1917—21no—
43#1916—21no—
44#1842C2211yescharacteristic
45#1831C2211yescharacteristic
46#1797C2211yescharacteristic
47#1797C2211yescharacteristic
48#1768—21no—
49#1767C2211yescharacteristic
50C4×C4⋊C8C2211yescharacteristic
51C4×C4⋊C8C2211yescharacteristic
52C4×C4⋊C8C2211yescharacteristic
53#1750—21no—
54C4×C22⋊C8C2211yescharacteristic
55C4×C22⋊C8C2211yescharacteristic
56#1746—21no—
57C4×#97C2211yescharacteristic
58C42×C8C2211yescharacteristic
59C2×Q8⋊C8C2211yescharacteristic
60C2×Q8⋊C8C2211yescharacteristic
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic
64C2×D4⋊C8C2211yescharacteristic
65C2×D4⋊C8C2211yescharacteristic
66C2×D4⋊C8C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C22×#41C2×C411yescharacteristic
76C4×#41—22no—
77C4×#41—22no—
78C4×#41—22no—
79C4×#41—22no—
80C2×C4×Q8C2×C411yescharacteristic
81C2×C4×Q8C2×C411yescharacteristic
82C2×C4×Q8C2×C411yescharacteristic
83C2×C4×Q8C2×C411yescharacteristic
84C2×C4×Q8C2×C411yescharacteristic
85C2×C4×Q8C2311yescharacteristic
86C2×C4×D4—21no—
87C2×C4×D4—21no—
88C2×C4×D4C2×C411yescharacteristic
89C2×C4×D4C2311yescharacteristic
90C2×#117—21no—
91C2×#117—21no—
92C2×#117—21no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—21no—
96C2×#117C2×C411yescharacteristic
97C2×#117D411yescharacteristic
98C2×#117D411yescharacteristic
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101#433—28no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8C2311yescharacteristic
107C2×C4⋊C8C2311yescharacteristic
108C2×C4⋊C8C2311yescharacteristic
109C2×C4⋊C8C2311yescharacteristic
110C2×C22⋊C8—21no—
111C2×C22⋊C8—21no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—21no—
114C2×#97—21no—
115C2×#97—21no—
116C2×#97—21no—
117C2×C4×C8—21no—
118C2×C4×C8—21no—
119C2×C4×C8—21no—
120C2×C4×C8C2311yescharacteristic
121C2×C4×C8C2311yescharacteristic
122C2×C4×C8C2311yescharacteristic
123C2×C4×C8C2311yescharacteristic
124#390—21no—
125#390—21no—
126#390—21no—
127#390—21no—
128#390C2×C411yescharacteristic
129#390C2×C411yescharacteristic
130#390C2×C411yescharacteristic
131#390C2×C411yescharacteristic
132#389—21no—
133#389—21no—
134#389—21no—
135#389—21no—
136#389C2×C411yescharacteristic
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
139#389C2×C411yescharacteristic
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#388—21no—
149#388—21no—
150#388—21no—
151#388—21no—
152#384—21no—
153#384—21no—
154#384C2×C411yescharacteristic
155#384C2×C411yescharacteristic
156#382—21no—
157#382—21no—
158#382—21no—
159#380—21no—
160#380—21no—
161#380—21no—
162#380—21no—
163#380—21no—
164#380C2×C411yescharacteristic
165#380C2×C411yescharacteristic
166C4×C4⋊C4—21no—
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C4⋊C4C2311yescharacteristic
184C4×C4⋊C4C2311yescharacteristic
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4C2×C411yescharacteristic
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193#376—21no—
194#376—21no—
195#376D411yescharacteristic
196#376D411yescharacteristic
197C43—21no—
198C43—21no—
199C43C2311yescharacteristic
200C43C2311yescharacteristic
201#336—21no—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211Q8⋊C8—22no—
212Q8⋊C8—22no—
213Q8⋊C8—22no—
214Q8⋊C8—22no—
215D4⋊C8—22no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218D4⋊C8—22no—
219C2×#41—22no—
220C2×#41—22no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—41no—
224C2×#41—41no—
225C22×Q8C22×C411yescharacteristic
226C22×D4—21no—
227C22×D4C22×C411yescharacteristic
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4C22×C411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—22no—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—41no—
251C4×Q8—41no—
252C4×Q8—41no—
253C4×Q8—41no—
254C4×Q8#4112yes—
255C4×Q8#4112yes—
256C4×D4—24no—
257C4×D4—24no—
258C4×D4—24no—
259C4×D4—24no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4#4112yes—
265C4×D4#4112yes—
266#117—24no—
267#117—24no—
268#117—24no—
269#117—22no—
270#117—22no—
271#117—42no—
272#117—44no—
273#117—44no—
274#117—81no—
275#117—81no—
276#117—81no—
277#117—81no—
278#117—81no—
279#117—81no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4C22⋊C411yescharacteristic
297C2×C4⋊C4C22⋊C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4C22⋊C411yescharacteristic
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C42—24no—
322C2×C42—24no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42C22×C411yescharacteristic
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2411yescharacteristic
356C4⋊C8—24no—
357C4⋊C8—24no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—81no—
367C4⋊C8—81no—
368C22⋊C8—24no—
369C22⋊C8—24no—
370C22⋊C8—81no—
371C22⋊C8—81no—
372#97—24no—
373#97—42no—
374#97—81no—
375C4×C8—24no—
376C4×C8—21no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—42no—
385C4×C8—81no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406C24—21no—
407C24C2×C22⋊C411yescharacteristic
408#41—44no—
409#41—44no—
410#41—44no—
411#41—44no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8#11712yes—
416C2×Q8#13112yes—
417C2×Q8#13112yes—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4#11712yes—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—42no—
462C22×C4C2×C22⋊C411yescharacteristic
463C22×C4C2×C22⋊C411yescharacteristic
464C22×C4C2×C22⋊C411yescharacteristic
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4C2×C22⋊C411yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C23×C411yescharacteristic
474C22×C4C22×D411yescharacteristic
475C22×C4C22×D411yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4—81no—
525C4⋊C4—81no—
526C4⋊C4—81no—
527C4⋊C4—81no—
528C4⋊C4#10414yes—
529C4⋊C4#11712yes—
530C4⋊C4#11712yes—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C42—24no—
550C42—24no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—22no—
556C42—22no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—41no—
579C42—42no—
580C42—42no—
581C42—42no—
582C42—42no—
583C42—42no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—42no—
589C42—42no—
590C42—42no—
591C42C2×#4111yescharacteristic
592C42C2×#4111yescharacteristic
593C42C2×#4111yescharacteristic
594C42C2×#4111yescharacteristic
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C22×C22⋊C411yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8#43314yescomplemented
614D4—22no—
615D4—22no—
616D4—48no—
617D4—41no—
618D4—41no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—48no—
658C2×C4—48no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4C2×#10412yes—
688C2×C4C2×#10412yes—
689C2×C4C2×#10412yes—
690C2×C4#42112yes—
691C2×C4C2×#11711yescharacteristic
692C2×C4C2×#11711yescharacteristic
693C2×C4#52511yescharacteristic
694C2×C4#52511yescharacteristic
695C2×C4#52511yescharacteristic
696C2×C4#52511yescharacteristic
697C2×C4C2×#13111yescharacteristic
698C2×C4C2×#13111yescharacteristic
699C2×C4#56811yescharacteristic
700C2×C4#56811yescharacteristic
701C2×C4#57611yescharacteristic
702C2×C4#57711yescharacteristic
703C2×C4#57711yescharacteristic
704C2×C4#57811yescharacteristic
705C8—42no—
706C8—42no—
707C8—42no—
708C8—42no—
709C8—81no—
710C8—81no—
711C8—81no—
712C8—81no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—42no—
722C22—41no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22#228011yescharacteristic
728C22#288011yescharacteristic
729C22#288011yescharacteristic
730C22#289711yescharacteristic
731C22#289811yescharacteristic
732C22C22×#10411yescharacteristic
733C22C2×#42111yescharacteristic
734C4—21no—
735C4—21no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—24no—
741C4—41no—
742C4—42no—
743C4—42no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4C2×#43311yescharacteristic
755C4#292111yescharacteristic
756C4#292411yescharacteristic
757C4#292411yescharacteristic
758C4#311911yescharacteristic
759C4#312011yescharacteristic
760C4#312411yescharacteristic
761C4#312511yescharacteristic
762C2—81no—
763C2—82no—
764C2#1751911yescharacteristic
765C2#1752011yescharacteristic
766C2#1752411yescharacteristic
767C2#1752611yescharacteristic
768C2#2071611yescharacteristic
769C2#2074611yescharacteristic
770C2#2074711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×#41C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×#117 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21924C2semidirect
3. C4×#433C2semidirect
4. #8710C2semidirect
5. #8709C2semidirect
6. #8569C2semidirect
7. #8567C2semidirect
8. #8566C2semidirect
9. #8564C2semidirect
12. #8181C2semidirect
13. #8177C2semidirect
14. #8173C2semidirect
15. C4×Q8⋊C8C2semidirect
613. Q8#433semidirect

Maximal subgroups

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

subgroupindex
#341292
#219242
C4×#4332
#87102
#87092
#85692
#85672
#85662
#85642
#83122
#81812
#81772
#81732
C4×Q8⋊C82