Finite Group Databasebeta

← C2×#14388 #520689

Subgroups — C2×#14388 #520689

Order 512.

3594 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic
3C22×#383C211yesmaximal, characteristic
4#14388C2116yesmaximal, direct product factor
5C2×#1445C211yesmaximal, characteristic
6C2×#1445C211yesmaximal, characteristic
7C2×#1443C211yesmaximal, characteristic
8C2×#1442C211yesmaximal, characteristic
9C2×#1441C211yesmaximal, characteristic
10C2×#1441C211yesmaximal, characteristic
11C2×#1436C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic
14C2×C4⋊#95C211yesmaximal, characteristic
15C2×#1434C211yesmaximal, characteristic
16C2×#1434C211yesmaximal, characteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#389C4116yescomplemented
27C2×#389C2218yes—
28C2×#387—28no—
29C2×#387C2218yes—
30C2×#383—28no—
31C2×#383C2218yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
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
58#1445C2218yes—
59#1445C2218yes—
60#1443C2218yes—
61#1442C2218yes—
62#1441C2218yes—
63#1441C2218yes—
64#1436C2218yes—
65#1436C2218yes—
66#1436C2218yes—
67C4⋊#95C2218yes—
68#1434C2218yes—
69#1434C2218yes—
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×C4⋊C4—24no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—42no—
93C22×C4⋊C4—42no—
94C22×C4⋊C4—42no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4C2×C418yes—
100C22×C4⋊C4C2×C418yes—
101C22×C4⋊C4C2×C418yes—
102C22×C4⋊C4C2×C418yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C42—24no—
110C22×C42—24no—
111C22×C42—24no—
112C22×C42—24no—
113C22×C42—24no—
114C22×C42—42no—
115C22×C42—42no—
116C22×C42—42no—
117C22×C42C2×C418yes—
118C22×C42C2314yes—
119C22×C42C2314yes—
120C22×C42C2314yes—
121#389C2×C4164yescomplemented
122#387—232no—
123#383—232no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95C2×C418yes—
148C2×#95C2×C418yes—
149C2×#95D418yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C25C2411yescharacteristic
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
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×C4C22×C414yes—
268C23×C4C22×C414yes—
269C23×C4C22×C414yes—
270C23×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4#4114yes—
278C23×C4#4114yes—
279C23×C4#4114yes—
280C23×C4#4114yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C2×C4⋊C4—232no—
298C2×C4⋊C4—232no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—416no—
307C2×C4⋊C4—416no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—416no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4C22×C4116yes—
318C2×C4⋊C4C22×C4116yes—
319C2×C4⋊C4C22×C4116yes—
320C2×C4⋊C4C22×C4116yes—
321C2×C42—232no—
322C2×C42—28no—
323C2×C42—28no—
324C2×C42—28no—
325C2×C42—28no—
326C2×C42—28no—
327C2×C42—44no—
328C2×C42—44no—
329C2×C42—44no—
330C2×C42—416no—
331C2×C42—416no—
332C2×C42C22×C4116yes—
333#95—28no—
334#95—28no—
335#95—28no—
336#95—28no—
337#95—28no—
338#95—28no—
339#95—28no—
340#95—28no—
341#95—28no—
342#95—28no—
343#95—28no—
344#95—28no—
345#95—28no—
346#95—28no—
347#95—28no—
348#95—44no—
349#95—44no—
350#95—44no—
351#95—44no—
352#95—44no—
353#95—44no—
354#95—44no—
355#95—44no—
356#95C22×C4116yes—
357#95C22×C4116yes—
358#95C2×D4116yes—
359C24C23×C412yes—
360C24C22×D412yes—
361C24C2×#4112yes—
362C24C2×#4112yes—
363C24C2×#4112yes—
364C24C2×#4112yes—
365C24C2×#4112yes—
366C24H(5,𝔽2)12yes—
367C24H(5,𝔽2)12yes—
368C24H(5,𝔽2)12yes—
369C242−1+412yes—
370C242−1+412yes—
371C242−1+412yes—
372C242−1+412yes—
373C242−1+412yes—
374C24C2511yescharacteristic
375C22×C4—28no—
376C22×C4—28no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4—28no—
382C22×C4—28no—
383C22×C4—28no—
384C22×C4—28no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—28no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—28no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
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—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4#117116yes—
569C22×C4C4×D4116yes—
570C22×C4C23×C414yes—
571C22×C4C23×C414yes—
572C22×C4C23×C414yes—
573C22×C4C23×C414yes—
574C22×C4C23×C414yes—
575C22×C4C23×C414yes—
576C22×C4C23×C414yes—
577C22×C4C22×D414yes—
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C2×#4114yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C4⋊C4—232no—
586C4⋊C4—232no—
587C4⋊C4—416no—
588C4⋊C4—416no—
589C4⋊C4—416no—
590C4⋊C4—416no—
591C42—232no—
592C42—416no—
593C42—416no—
594C23C2×#11714yes—
595C23C2×C4×D414yes—
596C23C4×#4114yes—
597C23#51814yes—
598C23#51914yes—
599C23#51914yes—
600C23#52014yes—
601C23#53514yes—
602C23#53714yes—
603C23#53914yes—
604C23#53914yes—
605C23#54014yes—
606C23#54114yes—
607C23#54114yes—
608C23#54114yes—
609C23#54114yes—
610C23#54214yes—
611C23#54214yes—
612C23#54214yes—
613C23#54714yes—
614C23#54714yes—
615C23#54714yes—
616C23#54814yes—
617C23#55114yes—
618C23#55114yes—
619C23#55214yes—
620C23#55214yes—
621C23#55214yes—
622C23#55314yes—
623C23#55314yes—
624C23#55614yes—
625C23#56314yes—
626C23#56314yes—
627C23#56314yes—
628C23#56314yes—
629C23C24×C411yescharacteristic
630C23C23×D411yescharacteristic
631C23C22×#4111yescharacteristic
632C23C22×#4111yescharacteristic
633C23C22×#4111yescharacteristic
634C23C22×#4111yescharacteristic
635C23C22×#4111yescharacteristic
636C23C2×H(5,𝔽2)11yescharacteristic
637C23C2×H(5,𝔽2)11yescharacteristic
638C23C2×H(5,𝔽2)11yescharacteristic
639C23C2×2−1+411yescharacteristic
640C23C2×2−1+411yescharacteristic
641C23C2×2−1+411yescharacteristic
642C23C2×2−1+411yescharacteristic
643C23C2×2−1+411yescharacteristic
644C2×C4—232no—
645C2×C4—232no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—416no—
686C2×C4—416no—
687C2×C4—416no—
688C2×C4—416no—
689C2×C4—416no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
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—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—416no—
725C2×C4—416no—
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—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—88no—
759C2×C4—88no—
760C2×C4—88no—
761C2×C4—88no—
762C2×C4C2×#11718yes—
763C2×C4C2×C4×D418yes—
764C22#232018yes—
765C22#232418yes—
766C22#233618yes—
767C22#234418yes—
768C22#235318yes—
769C22#236218yes—
770C22#238118yes—
771C22#271818yes—
772C22#272218yes—
773C22#272318yes—
774C22#272518yes—
775C22#273818yes—
776C22#275818yes—
777C22#276618yes—
778C22#277718yes—
779C22C22×#11711yescharacteristic
780C22C22×C4×D411yescharacteristic
781C22C2×C4×#4111yescharacteristic
782C22C2×#51811yescharacteristic
783C22C2×#51911yescharacteristic
784C22C2×#51911yescharacteristic
785C22C2×#52011yescharacteristic
786C22C2×#53511yescharacteristic
787C22C2×#53711yescharacteristic
788C22C2×#53911yescharacteristic
789C22C2×#53911yescharacteristic
790C22C2×#54011yescharacteristic
791C22C2×#54111yescharacteristic
792C22C2×#54111yescharacteristic
793C22C2×#54111yescharacteristic
794C22C2×#54111yescharacteristic
795C22C2×#54211yescharacteristic
796C22C2×#54211yescharacteristic
797C22C2×#54211yescharacteristic
798C22C2×#54711yescharacteristic
799C22C2×#54711yescharacteristic
800C22C2×#54711yescharacteristic
801C22C2×#54811yescharacteristic
802C22C2×#55111yescharacteristic
803C22C2×#55111yescharacteristic
804C22C2×#55211yescharacteristic
805C22C2×#55211yescharacteristic
806C22C2×#55211yescharacteristic
807C22C2×#55311yescharacteristic
808C22C2×#55311yescharacteristic
809C22C2×#55611yescharacteristic
810C22C2×#56311yescharacteristic
811C22C2×#56311yescharacteristic
812C22C2×#56311yescharacteristic
813C22C2×#56311yescharacteristic
814C4—28no—
815C4—28no—
816C4—44no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C2#14388116yesdirect product factor
830C2C2×#232011yescharacteristic
831C2C2×#232411yescharacteristic
832C2C2×#233611yescharacteristic
833C2C2×#234411yescharacteristic
834C2C2×#235311yescharacteristic
835C2C2×#236211yescharacteristic
836C2C2×#238111yescharacteristic
837C2C2×#271811yescharacteristic
838C2C2×#272211yescharacteristic
839C2C2×#272311yescharacteristic
840C2C2×#272511yescharacteristic
841C2C2×#273811yescharacteristic
842C2C2×#275811yescharacteristic
843C2C2×#276611yescharacteristic
844C2C2×#277711yescharacteristic
subgroupG/H
center, socle, prime radicalC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #14388C2direct (N × H)
26. C2×#389C4semidirect
121. #389C2×C4semidirect
829. C2#14388direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3892
C22×#3872
C22×#3832
#143882
C2×#14452
C2×#14432
C2×#14422
C2×#14412
C2×#14362
C2×C4⋊#952
C2×#14342