Finite Group Databasebeta

← C2×#13789 #513404

Subgroups — C2×#13789 #513404

Order 512.

5970 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×#388C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic
3C22×#385C211yesmaximal, characteristic
4C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊C4C211yesmaximal, characteristic
6#13789C2116yesmaximal, direct product factor
7C2×#1437C211yesmaximal, characteristic
8C2×#1437C211yesmaximal, characteristic
9C2×#1436C211yesmaximal, characteristic, complemented
10C2×#1436C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×C4⋊#95C211yesmaximal, characteristic, complemented
14C2×#1434C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C4×#95C211yesmaximal, characteristic, complemented
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#388C4116yescomplemented
35C2×#388C4116yescomplemented
36C2×#388C2218yes—
37C2×#388C2218yes—
38C2×#385C4116yescomplemented
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#1437C2218yes—
63#1437C2218yes—
64#1436C2218yescomplemented
65#1436C2218yescomplemented
66#1436C2218yescomplemented
67#1436C2218yescomplemented
68C4⋊#95C2218yescomplemented
69#1434C2218yescomplemented
70C22⋊#95C2218yes—
71C4×#95C2218yescomplemented
72C26C2311yescharacteristic
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—42no—
76C24×C4—42no—
77C24×C4—42no—
78C24×C4—42no—
79C24×C4C2×C418yes—
80C24×C4C2311yescharacteristic
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×C4C2314yes—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4C2×C418yes—
104C22×C4⋊C4C2×C418yes—
105C22×C4⋊C4C2×C418yescomplemented
106C22×C4⋊C4C2×C418yescomplemented
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—42no—
116C22×C22⋊C4—42no—
117C22×C22⋊C4—42no—
118C22×C22⋊C4—42no—
119C22×C22⋊C4—42no—
120C22×C22⋊C4—42no—
121C22×C22⋊C4C2×C418yes—
122C22×C22⋊C4C2×C418yes—
123C22×C22⋊C4C2×C418yes—
124C22×C22⋊C4C2×C418yes—
125C22×C22⋊C4C2×C418yes—
126C22×C22⋊C4C2×C418yes—
127C22×C22⋊C4C2×C418yes—
128C22×C22⋊C4C2×C418yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—24no—
139C22×C42—24no—
140C22×C42—42no—
141C22×C42—42no—
142C22×C42—42no—
143C22×C42—42no—
144C22×C42—42no—
145C22×C42—42no—
146C22×C42—42no—
147C22×C42—42no—
148C22×C42—42no—
149C22×C42—42no—
150C22×C42C2×C418yescomplemented
151C22×C42C2×C418yescomplemented
152C22×C42D418yes—
153C22×C42C2314yes—
154C22×C42C2314yes—
155C22×C42C2314yes—
156C22×C42C2314yes—
157C22×C42C2314yes—
158C22×C42C2314yes—
159#388C2×C4164yescomplemented
160#388C2×C4164yescomplemented
161#385C2×C4164yescomplemented
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—42no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95—42no—
176C2×#95C2×C418yes—
177C2×#95C2×C418yes—
178C2×#95C2×C418yescomplemented
179C2×#95C2×C418yescomplemented
180C2×#95C2×C418yescomplemented
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—
213C25C22×C414yes—
214C25C22×C414yes—
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—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—232no—
292C23×C4—28no—
293C23×C4—28no—
294C23×C4—416no—
295C23×C4—416no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4—416no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4C22×C414yes—
305C23×C4C22×C414yes—
306C23×C4C22×C414yes—
307C23×C4C22×C414yes—
308C23×C4C22×C414yes—
309C23×C4C22×C414yes—
310C23×C4C22×C414yes—
311C23×C4C22×C414yes—
312C23×C4C22×C414yes—
313C23×C4C22×C414yes—
314C23×C4C22×C414yes—
315C23×C4C22×C414yes—
316C23×C4C22×C414yes—
317C23×C4C22×C414yes—
318C23×C4C22×C414yes—
319C23×C4C22×C414yes—
320C23×C4C22×C414yes—
321C23×C4C22×C414yes—
322C23×C4C22×C4116yes—
323C23×C4C2×D414yes—
324C23×C4C2×D414yes—
325C23×C4C2×D414yes—
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—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—416no—
350C2×C4⋊C4—416no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4C22×C4116yes—
356C2×C4⋊C4C22×C4116yes—
357C2×C4⋊C4C22×C4116yescomplemented
358C2×C4⋊C4C22×C4116yescomplemented
359C2×C22⋊C4—232no—
360C2×C22⋊C4—232no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—416no—
366C2×C22⋊C4—416no—
367C2×C22⋊C4—416no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4C42164yescomplemented
375C2×C22⋊C4C22×C4116yes—
376C2×C22⋊C4C22×C4116yes—
377C2×C22⋊C4C22×C4116yes—
378C2×C22⋊C4C22×C4116yes—
379C2×C22⋊C4C22×C4116yes—
380C2×C22⋊C4C22×C4116yes—
381C2×C22⋊C4C22×C4116yes—
382C2×C22⋊C4C22×C4116yes—
383C2×C42—232no—
384C2×C42—28no—
385C2×C42—28no—
386C2×C42—28no—
387C2×C42—28no—
388C2×C42—28no—
389C2×C42—416no—
390C2×C42—416no—
391C2×C42—44no—
392C2×C42—44no—
393C2×C42—44no—
394C2×C42—44no—
395C2×C42—44no—
396C2×C42—44no—
397C2×C42—44no—
398C2×C42—44no—
399C2×C42—44no—
400C2×C42—44no—
401C2×C42—416no—
402C2×C42—416no—
403C2×C42—416no—
404C2×C42C22×C4116yescomplemented
405C2×C42C22×C4116yescomplemented
406C2×C42C2×D4116yes—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95C22×C4116yes—
420#95C22×C4116yes—
421#95C22×C4116yescomplemented
422#95C22×C4116yescomplemented
423#95C22×C4116yescomplemented
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—
471C24C2×C42116yes—
472C24C23×C414yes—
473C24C23×C414yes—
474C24C23×C414yes—
475C24C23×C412yes—
476C24C23×C412yes—
477C24C23×C412yes—
478C24C22×D412yes—
479C24C2×#4112yes—
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24H(5,𝔽2)12yes—
483C24H(5,𝔽2)12yes—
484C24H(5,𝔽2)12yes—
485C24H(5,𝔽2)12yes—
486C24H(5,𝔽2)12yes—
487C242−1+412yes—
488C242−1+412yes—
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—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
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—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—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
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—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—232no—
623C22×C4—416no—
624C22×C4—416no—
625C22×C4—4128no—
626C22×C4—416no—
627C22×C4—416no—
628C22×C4—416no—
629C22×C4—416no—
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—44no—
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×C4C2×C42116yes—
667C22×C4C2×C42116yes—
668C22×C4C4×D4116yes—
669C22×C4C4×D4116yes—
670C22×C4C4×D4116yes—
671C22×C4C23×C414yes—
672C22×C4C23×C414yes—
673C22×C4C23×C414yes—
674C22×C4C23×C414yes—
675C22×C4C23×C414yes—
676C22×C4C23×C414yes—
677C22×C4C23×C414yes—
678C22×C4C23×C414yes—
679C22×C4C23×C414yes—
680C22×C4C23×C414yes—
681C22×C4C23×C414yes—
682C22×C4C23×C414yes—
683C22×C4C23×C414yes—
684C22×C4C23×C414yes—
685C22×C4C23×C414yes—
686C22×C4C23×C414yes—
687C22×C4C23×C414yes—
688C22×C4C23×C414yes—
689C22×C4C22×D414yes—
690C22×C4C22×D414yes—
691C22×C4C22×D414yes—
692C22×C4C2×#4114yes—
693C22×C4C2×#4114yes—
694C22×C4C2×#4114yes—
695C4⋊C4—232no—
696C4⋊C4—232no—
697C4⋊C4—416no—
698C4⋊C4—416no—
699C22⋊C4—232no—
700C22⋊C4—232no—
701C22⋊C4—416no—
702C22⋊C4—416no—
703C22⋊C4—416no—
704C22⋊C4C2×C42164yescomplemented
705C42—232no—
706C42—416no—
707C42—416no—
708C42—416no—
709C42—416no—
710C42—416no—
711C23—24no—
712C23—24no—
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—232no—
730C23—232no—
731C23—232no—
732C23—416no—
733C23—416no—
734C23—416no—
735C23—416no—
736C23—416no—
737C23—416no—
738C23—416no—
739C23—416no—
740C23—416no—
741C23—416no—
742C23—416no—
743C23—416no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23C22×C4218yes—
761C23C22×C4214yes—
762C23C2×C4×D414yes—
763C23C2×C4×D414yes—
764C23C2×C4×D414yes—
765C23C4×#4114yes—
766C23C4×#4114yes—
767C23C4×#4114yes—
768C23#51814yes—
769C23#51814yes—
770C23#51814yes—
771C23#51814yes—
772C23#51914yes—
773C23#52014yes—
774C23#52014yes—
775C23#52014yes—
776C23#52014yes—
777C23#52014yes—
778C23#52014yes—
779C23#52014yes—
780C23#53414yes—
781C23#53514yes—
782C23#53614yes—
783C23#53714yes—
784C23#53814yes—
785C23#53814yes—
786C23#53814yes—
787C23#53914yes—
788C23#53914yes—
789C23#53914yes—
790C23#54014yes—
791C23#54114yes—
792C23#54214yes—
793C23#54214yes—
794C23#54214yes—
795C23#54214yes—
796C23C24×C411yescharacteristic
797C23C24×C411yescharacteristic
798C23C24×C411yescharacteristic
799C23C23×D411yescharacteristic
800C23C22×#4111yescharacteristic
801C23C22×#4111yescharacteristic
802C23C22×#4111yescharacteristic
803C23C2×H(5,𝔽2)11yescharacteristic
804C23C2×H(5,𝔽2)11yescharacteristic
805C23C2×H(5,𝔽2)11yescharacteristic
806C23C2×H(5,𝔽2)11yescharacteristic
807C23C2×H(5,𝔽2)11yescharacteristic
808C23C2×2−1+411yescharacteristic
809C23C2×2−1+411yescharacteristic
810C23C2×2−1+411yescharacteristic
811C2×C4—232no—
812C2×C4—232no—
813C2×C4—232no—
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—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—232no—
845C2×C4—232no—
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—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—464no—
874C2×C4—416no—
875C2×C4—416no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—416no—
880C2×C4—416no—
881C2×C4—416no—
882C2×C4—416no—
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—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
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—42no—
919C2×C4C22×C4218yes—
920C2×C4C22×C4218yes—
921C2×C4C2×C4×D418yes—
922C2×C4C2×C4×D418yes—
923C2×C4C2×C4×D418yes—
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—44no—
939C22—464no—
940C22C42×D418yes—
941C22#227418yes—
942C22#227518yes—
943C22#232118yes—
944C22#232218yes—
945C22#232318yes—
946C22#232418yes—
947C22#232518yes—
948C22#232618yes—
949C22#233218yes—
950C22#233418yes—
951C22#233418yes—
952C22#233518yes—
953C22#233518yes—
954C22#233718yes—
955C22C23×C4211yescharacteristic
956C22C22×C4×D411yescharacteristic
957C22C22×C4×D411yescharacteristic
958C22C22×C4×D411yescharacteristic
959C22C2×C4×#4111yescharacteristic
960C22C2×C4×#4111yescharacteristic
961C22C2×C4×#4111yescharacteristic
962C22C2×#51811yescharacteristic
963C22C2×#51811yescharacteristic
964C22C2×#51811yescharacteristic
965C22C2×#51811yescharacteristic
966C22C2×#51911yescharacteristic
967C22C2×#52011yescharacteristic
968C22C2×#52011yescharacteristic
969C22C2×#52011yescharacteristic
970C22C2×#52011yescharacteristic
971C22C2×#52011yescharacteristic
972C22C2×#52011yescharacteristic
973C22C2×#52011yescharacteristic
974C22C2×#53411yescharacteristic
975C22C2×#53511yescharacteristic
976C22C2×#53611yescharacteristic
977C22C2×#53711yescharacteristic
978C22C2×#53811yescharacteristic
979C22C2×#53811yescharacteristic
980C22C2×#53811yescharacteristic
981C22C2×#53911yescharacteristic
982C22C2×#53911yescharacteristic
983C22C2×#53911yescharacteristic
984C22C2×#54011yescharacteristic
985C22C2×#54111yescharacteristic
986C22C2×#54211yescharacteristic
987C22C2×#54211yescharacteristic
988C22C2×#54211yescharacteristic
989C22C2×#54211yescharacteristic
990C4—28no—
991C4—28no—
992C4—28no—
993C4—28no—
994C4—28no—
995C4—44no—
996C4—44no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4—44no—
1004C2—48no—
1005C2#13789116yesdirect product factor
1006C2C2×C42×D411yescharacteristic
1007C2C2×#227411yescharacteristic
1008C2C2×#227511yescharacteristic
1009C2C2×#232111yescharacteristic
1010C2C2×#232211yescharacteristic
1011C2C2×#232311yescharacteristic
1012C2C2×#232411yescharacteristic
1013C2C2×#232511yescharacteristic
1014C2C2×#232611yescharacteristic
1015C2C2×#233211yescharacteristic
1016C2C2×#233411yescharacteristic
1017C2C2×#233411yescharacteristic
1018C2C2×#233511yescharacteristic
1019C2C2×#233511yescharacteristic
1020C2C2×#233711yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC22C23×C42
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×C4×C4⋊C4C2semidirect
6. #13789C2direct (N × H)
9. C2×#1436C2semidirect
10. C2×#1436C2semidirect
11. C2×#1436C2semidirect
12. C2×#1436C2semidirect
13. C2×C4⋊#95C2semidirect
14. C2×#1434C2semidirect
16. C2×C4×#95C2semidirect
34. C2×#388C4semidirect
35. C2×#388C4semidirect
38. C2×#385C4semidirect
41. C2×C4×C4⋊C4C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. #1436C22semidirect
67. #1436C22semidirect
68. C4⋊#95C22semidirect
69. #1434C22semidirect
71. C4×#95C22semidirect
105. C22×C4⋊C4C2×C4semidirect
106. C22×C4⋊C4C2×C4semidirect
150. C22×C42C2×C4semidirect
151. C22×C42C2×C4semidirect
159. #388C2×C4semidirect
160. #388C2×C4semidirect
161. #385C2×C4semidirect
178. C2×#95C2×C4semidirect
179. C2×#95C2×C4semidirect
180. C2×#95C2×C4semidirect
181. C2×#95C2×C4semidirect
357. C2×C4⋊C4C22×C4semidirect
358. C2×C4⋊C4C22×C4semidirect
374. C2×C22⋊C4C42semidirect
404. C2×C42C22×C4semidirect
405. C2×C42C22×C4semidirect
421. #95C22×C4semidirect
422. #95C22×C4semidirect
423. #95C22×C4semidirect
424. #95C22×C4semidirect
704. C22⋊C4C2×C42semidirect
1005. C2#13789direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3882
C22×#3852
C22×C4×C4⋊C42
C22×C4×C22⋊C42
#137892
C2×#14372
C2×#14362
C2×C4⋊#952
C2×#14342
C2×C22⋊#952
C2×C4×#952