Finite Group Databasebeta

← C2×#14816 #607758

Subgroups — C2×#14816 #607758

Order 512.

4774 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic
2C22×#395C211yesmaximal, characteristic
3C22×#395C211yesmaximal, characteristic
4C22×#391C211yesmaximal, characteristic
5C22×#389C211yesmaximal, characteristic
6C22×C4×C4⋊C4C211yesmaximal, characteristic
7#14816C2116yesmaximal, direct product factor
8C2×#1444C211yesmaximal, characteristic
9C2×#1444C211yesmaximal, characteristic
10C2×#1441C211yesmaximal, characteristic
11C2×#1441C211yesmaximal, characteristic
12C2×#1441C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic
14C2×#1436C211yesmaximal, characteristic
15C2×C4⋊#95C211yesmaximal, characteristic
16C2×#1434C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C2×#398—28no—
33C2×#398C2218yes—
34C2×#395—28no—
35C2×#395—28no—
36C2×#395C2218yes—
37C2×#395C2218yes—
38C2×#391—28no—
39C2×#391C2218yes—
40C2×#389—28no—
41C2×#389C2218yes—
42C2×C4×C4⋊C4—28no—
43C2×C4×C4⋊C4C2218yes—
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1444C2218yes—
65#1444C2218yes—
66#1441C2218yes—
67#1441C2218yes—
68#1441C2218yes—
69#1436C2218yes—
70#1436C2218yes—
71C4⋊#95C2218yes—
72#1434C2218yes—
73C23×Q8—24no—
74C23×Q8—24no—
75C23×Q8—24no—
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—42no—
79C23×Q8—42no—
80C23×Q8C2314yes—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4—42no—
127C22×C4⋊C4D418yes—
128C22×C4⋊C4Q818yescomplemented
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—42no—
147C22×C42—42no—
148C22×C42Q818yescomplemented
149C22×C42C2314yes—
150C22×C42C2314yes—
151C22×C42C2314yes—
152#398—232no—
153#395—232no—
154#395—232no—
155#391—232no—
156#389—232no—
157C4×C4⋊C4—232no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—42no—
175C2×#95D418yes—
176C2×#95D418yes—
177C2×#95Q818yescomplemented
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C25C2411yescharacteristic
199C22×Q8—232no—
200C22×Q8—28no—
201C22×Q8—28no—
202C22×Q8—28no—
203C22×Q8—28no—
204C22×Q8—28no—
205C22×Q8—44no—
206C22×Q8—44no—
207C22×Q8—416no—
208C22×Q8—416no—
209C22×Q8—416no—
210C22×Q8—416no—
211C22×Q8—416no—
212C22×Q8—416no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×Q814yes—
305C23×C4C2×Q814yes—
306C23×C4C2×Q814yes—
307C23×C4C2×Q814yes—
308C23×C4C2×Q814yes—
309C23×C4C2×Q814yes—
310C23×C4C2×Q814yes—
311C23×C4C2×Q814yes—
312C23×C4C2×Q814yes—
313C23×C4#4114yes—
314C23×C4#4114yes—
315C23×C4#4114yes—
316C23×C4#4114yes—
317C23×C4#4114yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C2×C4⋊C4—232no—
334C2×C4⋊C4—232no—
335C2×C4⋊C4—232no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—416no—
368C2×C4⋊C4—416no—
369C2×C4⋊C4—416no—
370C2×C4⋊C4—416no—
371C2×C4⋊C4—416no—
372C2×C4⋊C4—416no—
373C2×C4⋊C4—416no—
374C2×C4⋊C4—416no—
375C2×C4⋊C4C2×D4116yes—
376C2×C4⋊C4C2×Q8116yescomplemented
377C2×C42—232no—
378C2×C42—28no—
379C2×C42—28no—
380C2×C42—28no—
381C2×C42—28no—
382C2×C42—28no—
383C2×C42—28no—
384C2×C42—44no—
385C2×C42—44no—
386C2×C42—416no—
387C2×C42—416no—
388C2×C42C2×Q8116yescomplemented
389#95—28no—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—44no—
406#95C2×D4116yes—
407#95C2×D4116yes—
408#95C2×Q8116yescomplemented
409C24C22×D412yes—
410C24C22×D412yes—
411C24C22×D412yes—
412C24C22×Q812yes—
413C24C22×Q812yes—
414C24C22×Q812yes—
415C24C2×#4112yes—
416C24C2×#4112yes—
417C24C2×#4112yes—
418C24C2×#4112yes—
419C24C2×#4112yes—
420C24H(5,𝔽2)12yes—
421C24H(5,𝔽2)12yes—
422C242−1+412yes—
423C242−1+412yes—
424C24C2511yescharacteristic
425C2×Q8—232no—
426C2×Q8—416no—
427C2×Q8—416no—
428C2×Q8—416no—
429C2×Q8—416no—
430C2×Q8—4128no—
431C2×Q8—416no—
432C2×Q8—416no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4#121116yes—
616C22×C4C22⋊Q8116yes—
617C22×C4C22⋊Q8116yes—
618C22×C4C4⋊Q8116yes—
619C22×C4C4⋊Q8116yes—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D414yes—
624C22×C4C22×D414yes—
625C22×C4C22×D414yes—
626C22×C4C22×D414yes—
627C22×C4C22×D414yes—
628C22×C4C22×D414yes—
629C22×C4C22×Q814yes—
630C22×C4C22×Q814yes—
631C22×C4C22×Q814yes—
632C22×C4C22×Q814yes—
633C22×C4C22×Q814yes—
634C22×C4C22×Q814yes—
635C22×C4C22×Q814yes—
636C22×C4C22×Q814yes—
637C22×C4C22×Q814yes—
638C22×C4C2×#4114yes—
639C22×C4C2×#4114yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4114yes—
642C22×C4C2×#4114yes—
643C4⋊C4—232no—
644C4⋊C4—232no—
645C4⋊C4—232no—
646C4⋊C4—416no—
647C4⋊C4—416no—
648C4⋊C4—416no—
649C4⋊C4—416no—
650C4⋊C4—416no—
651C4⋊C4—416no—
652C4⋊C4—416no—
653C4⋊C4—416no—
654C42—232no—
655C42—416no—
656C42—416no—
657C23C2×#12114yes—
658C23C2×C22⋊Q814yes—
659C23C2×C22⋊Q814yes—
660C23#52514yes—
661C23#52514yes—
662C23C2×C4⋊Q814yes—
663C23C2×C4⋊Q814yes—
664C23#53214yes—
665C23#53314yes—
666C23#53314yes—
667C23#53314yes—
668C23#53314yes—
669C23#53314yes—
670C23#53814yes—
671C23#53914yes—
672C23#54114yes—
673C23#54214yes—
674C23#54414yes—
675C23#54414yes—
676C23D4214yes—
677C23D4214yes—
678C23#54614yes—
679C23#54614yes—
680C23#54714yes—
681C23#54714yes—
682C23#54814yes—
683C23D4×Q814yes—
684C23D4×Q814yes—
685C23D4×Q814yes—
686C23#55114yes—
687C23#55214yes—
688C23#55414yes—
689C23#55414yes—
690C23#55714yes—
691C23Q8214yes—
692C23C23×D411yescharacteristic
693C23C23×D411yescharacteristic
694C23C23×D411yescharacteristic
695C23C23×Q811yescharacteristic
696C23C23×Q811yescharacteristic
697C23C23×Q811yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4111yescharacteristic
700C23C22×#4111yescharacteristic
701C23C22×#4111yescharacteristic
702C23C22×#4111yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23C2×2−1+411yescharacteristic
707Q8—464no—
708C2×C4—232no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—232no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—232no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—232no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—232no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—416no—
776C2×C4—416no—
777C2×C4—416no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—416no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—416no—
804C2×C4—416no—
805C2×C4—416no—
806C2×C4—416no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—88no—
822C2×C4—88no—
823C2×C4C2×#12118yes—
824C2×C4C2×C22⋊Q818yes—
825C2×C4C2×C22⋊Q818yes—
826C2×C4C2×C4⋊Q818yes—
827C2×C4C2×C4⋊Q818yes—
828C22#239918yes—
829C22#242418yes—
830C22#242918yes—
831C22#243818yes—
832C22#244018yes—
833C22#244918yes—
834C22#245118yes—
835C22#246118yes—
836C22#246218yes—
837C22#255018yes—
838C22#255118yes—
839C22#255618yes—
840C22#258618yes—
841C22#266618yes—
842C22#285718yes—
843C22C22×#12111yescharacteristic
844C22C22×C22⋊Q811yescharacteristic
845C22C22×C22⋊Q811yescharacteristic
846C22C2×#52511yescharacteristic
847C22C2×#52511yescharacteristic
848C22C22×C4⋊Q811yescharacteristic
849C22C22×C4⋊Q811yescharacteristic
850C22C2×#53211yescharacteristic
851C22C2×#53311yescharacteristic
852C22C2×#53311yescharacteristic
853C22C2×#53311yescharacteristic
854C22C2×#53311yescharacteristic
855C22C2×#53311yescharacteristic
856C22C2×#53811yescharacteristic
857C22C2×#53911yescharacteristic
858C22C2×#54111yescharacteristic
859C22C2×#54211yescharacteristic
860C22C2×#54411yescharacteristic
861C22C2×#54411yescharacteristic
862C22C2×D4211yescharacteristic
863C22C2×D4211yescharacteristic
864C22C2×#54611yescharacteristic
865C22C2×#54611yescharacteristic
866C22C2×#54711yescharacteristic
867C22C2×#54711yescharacteristic
868C22C2×#54811yescharacteristic
869C22C2×D4×Q811yescharacteristic
870C22C2×D4×Q811yescharacteristic
871C22C2×D4×Q811yescharacteristic
872C22C2×#55111yescharacteristic
873C22C2×#55211yescharacteristic
874C22C2×#55411yescharacteristic
875C22C2×#55411yescharacteristic
876C22C2×#55711yescharacteristic
877C22C2×Q8211yescharacteristic
878C4—28no—
879C4—28no—
880C4—28no—
881C4—28no—
882C4—28no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—82no—
892C4—82no—
893C2#14816116yesdirect product factor
894C2C2×#239911yescharacteristic
895C2C2×#266611yescharacteristic
896C2C2×#242411yescharacteristic
897C2C2×#244911yescharacteristic
898C2C2×#244011yescharacteristic
899C2C2×#246111yescharacteristic
900C2C2×#246211yescharacteristic
901C2C2×#242911yescharacteristic
902C2C2×#245111yescharacteristic
903C2C2×#243811yescharacteristic
904C2C2×#255611yescharacteristic
905C2C2×#258611yescharacteristic
906C2C2×#255011yescharacteristic
907C2C2×#255111yescharacteristic
908C2C2×#285711yescharacteristic
subgroupG/H
center, socle, prime radicalC25C24
commutator, Frattini, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #14816C2direct (N × H)
128. C22×C4⋊C4Q8semidirect
148. C22×C42Q8semidirect
177. C2×#95Q8semidirect
376. C2×C4⋊C4C2×Q8semidirect
388. C2×C42C2×Q8semidirect
408. #95C2×Q8semidirect
893. C2#14816direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3982
C22×#3952
C22×#3912
C22×#3892
C22×C4×C4⋊C42
#148162
C2×#14442
C2×#14412
C2×#14362
C2×C4⋊#952
C2×#14342