Finite Group Databasebeta

← C2×#14222 #514728

Subgroups — C2×#14222 #514728

Order 512.

5658 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#396C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic
4C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊C4C211yesmaximal, characteristic
6#14222C2116yesmaximal, direct product factor
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic
10C2×#1437C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×C4⋊#95C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#396C4116yescomplemented
35C2×#396C2218yes—
36C2×#387—28no—
37C2×#387C2218yescomplemented
38C2×#385—28no—
39C2×#385C2218yes—
40C2×C4×C4⋊C4—28no—
41C2×C4×C4⋊C4C2218yescomplemented
42C2×C4×C22⋊C4—28no—
43C2×C4×C22⋊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
62#1441C2218yescomplemented
63#1441C2218yescomplemented
64#1439C2218yes—
65#1437C2218yes—
66#1437C2218yes—
67#1436C2218yescomplemented
68#1436C2218yescomplemented
69C4⋊#95C2218yescomplemented
70#1434C2218yescomplemented
71C22⋊#95C2218yes—
72C26C2311yescharacteristic
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—42no—
79C24×C4—42no—
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2314yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C22×C4⋊C4—24no—
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—42no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4C2×C418yescomplemented
110C22×C4⋊C4C2×C418yescomplemented
111C22×C4⋊C4C2×C418yescomplemented
112C22×C4⋊C4D418yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—42no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4C2×C418yes—
134C22×C22⋊C4C2×C418yes—
135C22×C22⋊C4C2×C418yes—
136C22×C22⋊C4Q818yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42—42no—
151C22×C42—42no—
152C22×C42—42no—
153C22×C42—42no—
154C22×C42D418yes—
155C22×C42C2314yes—
156C22×C42C2314yes—
157C22×C42C2314yes—
158C22×C42C2314yes—
159#396C2×C4164yescomplemented
160#387—232no—
161#385—232no—
162C4×C4⋊C4—232no—
163C4×C22⋊C4—232no—
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—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—42no—
179C2×#95—42no—
180C2×#95—42no—
181C2×#95C2×C418yescomplemented
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—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25C22×C414yes—
213C25C2×Q814yes—
214C25#4114yes—
215C25C2412yes—
216C25C2411yescharacteristic
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—232no—
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—28no—
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—28no—
284C23×C4—28no—
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×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—28no—
300C23×C4—28no—
301C23×C4—44no—
302C23×C4—44no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4—416no—
306C23×C4—416no—
307C23×C4—416no—
308C23×C4—416no—
309C23×C4C22×C414yes—
310C23×C4C22×C414yes—
311C23×C4C22×C414yes—
312C23×C4C22×C414yes—
313C23×C4C22×C414yes—
314C23×C4C22×C414yes—
315C23×C4C2×D414yes—
316C23×C4C2×D414yes—
317C23×C4C2×D414yes—
318C23×C4C2×D414yes—
319C23×C4C2×D414yes—
320C23×C4C2×D414yes—
321C23×C4C2×Q814yes—
322C23×C4C2×Q814yes—
323C23×C4#4114yes—
324C23×C4#4114yes—
325C23×C4#4114yes—
326C23×C4#4114yes—
327C23×C4#4114yes—
328C23×C4#4114yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C2×C4⋊C4—232no—
344C2×C4⋊C4—232no—
345C2×C4⋊C4—232no—
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—416no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—416no—
362C2×C4⋊C4—416no—
363C2×C4⋊C4C22×C4116yescomplemented
364C2×C4⋊C4C22×C4116yescomplemented
365C2×C4⋊C4C22×C4116yescomplemented
366C2×C4⋊C4C2×D4116yes—
367C2×C22⋊C4—232no—
368C2×C22⋊C4—232no—
369C2×C22⋊C4—232no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—416no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—416no—
386C2×C22⋊C4—416no—
387C2×C22⋊C4C22×C4116yes—
388C2×C22⋊C4C22×C4116yes—
389C2×C22⋊C4C22×C4116yes—
390C2×C22⋊C4C2×Q8116yes—
391C2×C42—232no—
392C2×C42—28no—
393C2×C42—28no—
394C2×C42—28no—
395C2×C42—28no—
396C2×C42—28no—
397C2×C42—28no—
398C2×C42—28no—
399C2×C42—416no—
400C2×C42—44no—
401C2×C42—44no—
402C2×C42—44no—
403C2×C42—44no—
404C2×C42—416no—
405C2×C42—416no—
406C2×C42C2×D4116yes—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95C22×C4116yescomplemented
425C24—28no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—28no—
441C24—28no—
442C24—28no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—44no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24C4×Q8116yes—
472C24C23×C414yes—
473C24C23×C412yes—
474C24C22×D412yes—
475C24C22×D412yes—
476C24C22×Q814yes—
477C24C22×Q812yes—
478C24C2×#4114yes—
479C24C2×#4112yes—
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24C2×#4112yes—
483C24C2×#4112yes—
484C24C2×#4112yes—
485C24C2×#4112yes—
486C24H(5,𝔽2)12yes—
487C24H(5,𝔽2)12yes—
488C24H(5,𝔽2)12yes—
489C242−1+412yes—
490C24C2511yescharacteristic
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—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
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—232no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
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—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—416no—
619C22×C4—416no—
620C22×C4—416no—
621C22×C4—416no—
622C22×C4—416no—
623C22×C4—4128no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—416no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4C4×D4116yes—
672C22×C4C4×D4116yes—
673C22×C4#121116yes—
674C22×C4C22⋊Q8116yes—
675C22×C4C23×C414yes—
676C22×C4C23×C414yes—
677C22×C4C23×C414yes—
678C22×C4C23×C414yes—
679C22×C4C23×C414yes—
680C22×C4C23×C414yes—
681C22×C4C22×D414yes—
682C22×C4C22×D414yes—
683C22×C4C22×D414yes—
684C22×C4C22×D414yes—
685C22×C4C22×D414yes—
686C22×C4C22×D414yes—
687C22×C4C22×Q814yes—
688C22×C4C22×Q814yes—
689C22×C4C2×#4114yes—
690C22×C4C2×#4114yes—
691C22×C4C2×#4114yes—
692C22×C4C2×#4114yes—
693C22×C4C2×#4114yes—
694C22×C4C2×#4114yes—
695C4⋊C4—232no—
696C4⋊C4—232no—
697C4⋊C4—232no—
698C4⋊C4—416no—
699C4⋊C4—416no—
700C4⋊C4—416no—
701C22⋊C4—232no—
702C22⋊C4—232no—
703C22⋊C4—232no—
704C22⋊C4—416no—
705C22⋊C4—416no—
706C22⋊C4—416no—
707C42—232no—
708C42—416no—
709C42—416no—
710C42—416no—
711C23—232no—
712C23—232no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—232no—
732C23—416no—
733C23—416no—
734C23—416no—
735C23—416no—
736C23—416no—
737C23—416no—
738C23—416no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—416no—
759C23—416no—
760C23C2×C4×D414yes—
761C23C2×C4×D414yes—
762C23C2×C4×Q818yes—
763C23C2×C4×Q814yes—
764C23C4×#4114yes—
765C23C4×#4114yes—
766C23#51814yes—
767C23#52014yes—
768C23C2×#12114yes—
769C23C2×C22⋊Q814yes—
770C23#52514yes—
771C23#52514yes—
772C23#52914yes—
773C23#52914yes—
774C23#53214yes—
775C23#53314yes—
776C23#53414yes—
777C23#53714yes—
778C23#53814yes—
779C23#53914yes—
780C23#54614yes—
781C23#54614yes—
782C23D4×Q814yes—
783C23#55014yes—
784C23#55114yes—
785C23#55114yes—
786C23#55114yes—
787C23#55214yes—
788C23#55214yes—
789C23#55314yes—
790C23#55314yes—
791C23#55414yes—
792C23#55414yes—
793C23#55414yes—
794C23#55514yes—
795C23#55614yes—
796C23C24×C411yescharacteristic
797C23C23×D411yescharacteristic
798C23C23×D411yescharacteristic
799C23C23×Q811yescharacteristic
800C23C22×#4111yescharacteristic
801C23C22×#4111yescharacteristic
802C23C22×#4111yescharacteristic
803C23C22×#4111yescharacteristic
804C23C22×#4111yescharacteristic
805C23C22×#4111yescharacteristic
806C23C22×#4111yescharacteristic
807C23C2×H(5,𝔽2)11yescharacteristic
808C23C2×H(5,𝔽2)11yescharacteristic
809C23C2×H(5,𝔽2)11yescharacteristic
810C23C2×2−1+411yescharacteristic
811C2×C4—232no—
812C2×C4—232no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—232no—
838C2×C4—232no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—464no—
864C2×C4—416no—
865C2×C4—416no—
866C2×C4—416no—
867C2×C4—416no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—416no—
901C2×C4—416no—
902C2×C4—416no—
903C2×C4—416no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—88no—
919C2×C4—88no—
920C2×C4C2×C4×D418yes—
921C2×C4C2×C4×D418yes—
922C2×C4C2×#12118yes—
923C2×C4C2×C22⋊Q818yes—
924C22—28no—
925C22—28no—
926C22—28no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—464no—
939C22—44no—
940C22C4×#12118yes—
941C22C4×C22⋊Q818yes—
942C22#232518yes—
943C22#236018yes—
944C22#236318yes—
945C22#236818yes—
946C22#237318yes—
947C22#253418yes—
948C22#253818yes—
949C22#255418yes—
950C22#255618yes—
951C22#257318yes—
952C22#257418yes—
953C22#257918yes—
954C22#260918yes—
955C22C22×C4×D411yescharacteristic
956C22C22×C4×D411yescharacteristic
957C22C22×C4×Q811yescharacteristic
958C22C2×C4×#4111yescharacteristic
959C22C2×C4×#4111yescharacteristic
960C22C2×#51811yescharacteristic
961C22C2×#52011yescharacteristic
962C22C22×#12111yescharacteristic
963C22C22×C22⋊Q811yescharacteristic
964C22C2×#52511yescharacteristic
965C22C2×#52511yescharacteristic
966C22C2×#52911yescharacteristic
967C22C2×#52911yescharacteristic
968C22C2×#53211yescharacteristic
969C22C2×#53311yescharacteristic
970C22C2×#53411yescharacteristic
971C22C2×#53711yescharacteristic
972C22C2×#53811yescharacteristic
973C22C2×#53911yescharacteristic
974C22C2×#54611yescharacteristic
975C22C2×#54611yescharacteristic
976C22C2×D4×Q811yescharacteristic
977C22C2×#55011yescharacteristic
978C22C2×#55111yescharacteristic
979C22C2×#55111yescharacteristic
980C22C2×#55111yescharacteristic
981C22C2×#55211yescharacteristic
982C22C2×#55211yescharacteristic
983C22C2×#55311yescharacteristic
984C22C2×#55311yescharacteristic
985C22C2×#55411yescharacteristic
986C22C2×#55411yescharacteristic
987C22C2×#55411yescharacteristic
988C22C2×#55511yescharacteristic
989C22C2×#55611yescharacteristic
990C4—28no—
991C4—28no—
992C4—28no—
993C4—28no—
994C4—44no—
995C4—44no—
996C4—44no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—82no—
1003C4—82no—
1004C2—48no—
1005C2#14222116yesdirect product factor
1006C2C2×C4×#12111yescharacteristic
1007C2C2×C4×C22⋊Q811yescharacteristic
1008C2C2×#232511yescharacteristic
1009C2C2×#236011yescharacteristic
1010C2C2×#236311yescharacteristic
1011C2C2×#236811yescharacteristic
1012C2C2×#237311yescharacteristic
1013C2C2×#253411yescharacteristic
1014C2C2×#255411yescharacteristic
1015C2C2×#255611yescharacteristic
1016C2C2×#257911yescharacteristic
1017C2C2×#257411yescharacteristic
1018C2C2×#257311yescharacteristic
1019C2C2×#260911yescharacteristic
1020C2C2×#253811yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#387C2semidirect
4. C22×C4×C4⋊C4C2semidirect
6. #14222C2direct (N × H)
7. C2×#1441C2semidirect
8. C2×#1441C2semidirect
12. C2×#1436C2semidirect
13. C2×#1436C2semidirect
14. C2×C4⋊#95C2semidirect
15. C2×#1434C2semidirect
34. C2×#396C4semidirect
37. C2×#387C22semidirect
41. C2×C4×C4⋊C4C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. C4⋊#95C22semidirect
70. #1434C22semidirect
109. C22×C4⋊C4C2×C4semidirect
110. C22×C4⋊C4C2×C4semidirect
111. C22×C4⋊C4C2×C4semidirect
159. #396C2×C4semidirect
181. C2×#95C2×C4semidirect
363. C2×C4⋊C4C22×C4semidirect
364. C2×C4⋊C4C22×C4semidirect
365. C2×C4⋊C4C22×C4semidirect
424. #95C22×C4semidirect
1005. C2#14222direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3962
C22×#3872
C22×#3852
C22×C4×C4⋊C42
C22×C4×C22⋊C42
#142222
C2×#14412
C2×#14392
C2×#14372
C2×#14362
C2×C4⋊#952
C2×#14342
C2×C22⋊#952