Finite Group Databasebeta

← C2×#35302 #7628574

Subgroups — C2×#35302 #7628574

Order 512.

9310 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C23×#117C211yesmaximal, characteristic, complemented
3C2×#2855C211yesmaximal, characteristic, complemented
4C2×#2854C211yesmaximal, characteristic, complemented
5C2×#2848C211yesmaximal, characteristic, complemented
6C2×#2847C211yesmaximal, characteristic
7#35302C2132yesmaximal, direct product factor
8C2×#2609C214yesmaximal, complemented
9C2×#2601C214yesmaximal, complemented
10C2×#2579C212yesmaximal, complemented
11C2×#2534C212yesmaximal, complemented
12C2×#2413C212yesmaximal, complemented
13C2×#2411C212yesmaximal, complemented
14C2×#2629C212yesmaximal, complemented
15C2×#2620C212yesmaximal, complemented
16C2×#2324C212yesmaximal, complemented
17C2×#2323C212yesmaximal, complemented
18C2×#2285C211yesmaximal, characteristic, complemented
19C25×C4C2211yescharacteristic
20C2×#529—216no—
21C2×#529C22116yescomplemented
22C22×#126C2212yescomplemented
23C22×#125C2211yescharacteristic, complemented
24C22×#124C2211yescharacteristic, complemented
25C22×#123C2212yes—
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×#121C2211yescharacteristic
30C22×#121C2212yes—
31C22×#120C2212yes—
32C22×C4×Q8C2211yescharacteristic, complemented
33C22×C4×D4C2212yes—
34C22×C4×D4C2211yescharacteristic, complemented
35C22×#117—216no—
36C22×#117C2212yes—
37C22×#117C2212yes—
38C22×#117C2212yes—
39C22×#117C2212yes—
40C22×#117C2212yes—
41C22×#117C22116yescomplemented
42C22×#117C2212yescomplemented
43C23×C4⋊C4C2211yescharacteristic
44C23×C4⋊C4C2211yescharacteristic
45C23×C22⋊C4C2211yescharacteristic
46C23×C22⋊C4C2211yescharacteristic
47C23×C42C2211yescharacteristic
48C23×C42C2211yescharacteristic
49#2855C22116yescomplemented
50#2854C22116yescomplemented
51#2848C22116yescomplemented
52#2847C22116yes—
53#2629C22132yescomplemented
54#2620C22132yescomplemented
55#2609C22164yescomplemented
56#2601C22164yescomplemented
57#2579C22132yescomplemented
58#2534C22132yescomplemented
59#2413C22132yescomplemented
60#2411C22132yescomplemented
61C2×#398C2214yescomplemented
62C2×#398C2214yescomplemented
63C2×#396C2214yes—
64C2×#396C2214yes—
65C2×#396C2214yescomplemented
66C2×#396C2214yescomplemented
67C2×#394C2214yes—
68C2×#394C2214yes—
69#2324C22132yescomplemented
70#2323C22132yescomplemented
71C2×#391C2212yescomplemented
72C2×#390C2214yes—
73C2×#390C2212yescomplemented
74C2×#389C2212yescomplemented
75C2×#389C2212yescomplemented
76C2×#389C2214yescomplemented
77C2×#388C2214yes—
78C2×#388C2214yes—
79C2×#388C2214yescomplemented
80C2×#388C2214yescomplemented
81C2×#387C2214yescomplemented
82C2×#387C2214yescomplemented
83C2×#386C2214yes—
84C2×#386C2212yes—
85C2×#386C2214yes—
86C2×#386C2212yes—
87C2×#385C2212yes—
88C2×#385C2214yes—
89C2×#385C2212yes—
90C2×#385C2214yescomplemented
91#2285C22116yescomplemented
92C2×#384C2212yescomplemented
93C2×#382C2212yescomplemented
94C2×#381C2212yes—
95C2×#380C2212yes—
96C2×#380C2211yescharacteristic
97C2×#380C2212yes—
98C2×#380C2211yescharacteristic
99C2×#380C2212yes—
100C2×#379C2212yes—
101C2×C4×C4⋊C4C2212yescomplemented
102C2×C4×C4⋊C4C2212yescomplemented
103C26C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C23×D4C2314yes—
108C24×C4—28no—
109C24×C4—216no—
110C24×C4C2318yes—
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C24×C4C2312yes—
119C24×C4C2311yescharacteristic
120#529—2128no—
121C2×#126—216no—
122C2×#126C23116yescomplemented
123C2×#125—28no—
124C2×#125C2318yescomplemented
125C2×#124—28no—
126C2×#124C2318yescomplemented
127C2×#123—216no—
128C2×#123—48no—
129C2×#123C23116yes—
130C2×#123C23116yes—
131C2×C22⋊Q8—28no—
132C2×C22⋊Q8—216no—
133C2×C22⋊Q8C23116yes—
134C2×C22⋊Q8C2318yes—
135C2×#121—28no—
136C2×#121—216no—
137C2×#121C23116yes—
138C2×#121C2318yes—
139C2×#120—48no—
140C2×#120C23116yes—
141C2×C4×Q8—28no—
142C2×C4×Q8C2318yescomplemented
143C2×C4×D4—216no—
144C2×C4×D4—28no—
145C2×C4×D4C23116yes—
146C2×C4×D4C2318yescomplemented
147C2×#117—216no—
148C2×#117—216no—
149C2×#117—216no—
150C2×#117—216no—
151C2×#117—216no—
152C2×#117—2128no—
153C2×#117—48no—
154C2×#117C23116yes—
155C2×#117C23116yes—
156C2×#117C23116yes—
157C2×#117C23116yes—
158C2×#117C23116yes—
159C2×#117C23116yescomplemented
160C22×C4⋊C4—28no—
161C22×C4⋊C4—28no—
162C22×C4⋊C4C2318yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2314yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2318yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2314yes—
178C22×C4⋊C4C2314yes—
179C22×C4⋊C4C2314yes—
180C22×C4⋊C4C2314yes—
181C22×C22⋊C4—28no—
182C22×C22⋊C4—28no—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2318yes—
192C22×C22⋊C4C2318yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2314yes—
199C22×C22⋊C4C2314yes—
200C22×C22⋊C4C2314yes—
201C22×C22⋊C4C2314yes—
202C22×C42—28no—
203C22×C42D4116yescomplemented
204C22×C42C2318yes—
205C22×C42C2312yes—
206C22×C42C2312yes—
207C22×C42C2312yes—
208C22×C42C2314yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2318yes—
214#398C23132yescomplemented
215#398C23132yescomplemented
216#396C23132yes—
217#396C23132yes—
218#396C23132yescomplemented
219#396C23132yescomplemented
220#394C23132yes—
221#394C23132yes—
222#391C23116yescomplemented
223#390C23132yes—
224#390C23116yescomplemented
225#389C23116yescomplemented
226#389C23132yescomplemented
227#389C23116yescomplemented
228#388C23132yes—
229#388C23132yes—
230#388C23132yescomplemented
231#388C23132yescomplemented
232#387C23132yescomplemented
233#387C23132yescomplemented
234#386C23116yes—
235#386C23116yes—
236#386C23132yes—
237#386C23132yes—
238#385C23116yes—
239#385C23116yes—
240#385C23132yes—
241#385C23132yescomplemented
242#384C23116yescomplemented
243#382C23116yescomplemented
244#381C23116yes—
245#380C23116yes—
246#380C23116yes—
247#380C23116yes—
248#380C2318yes—
249#380C2318yes—
250#379C23116yes—
251C4×C4⋊C4C23116yescomplemented
252C4×C4⋊C4C23116yescomplemented
253C2×#95C2314yes—
254C2×#95C2314yes—
255C2×#95C2314yes—
256C2×#95C2314yes—
257C2×#95C2314yes—
258C2×#95C2314yes—
259C2×#95C2312yes—
260C2×#95C2314yes—
261C2×#95C2312yes—
262C25—24no—
263C25—28no—
264C25—24no—
265C25—24no—
266C25—44no—
267C25C2412yes—
268C25C2412yes—
269C25C2414yes—
270C25C2411yescharacteristic
271C22×Q8—24no—
272C22×Q8—28no—
273C22×Q8C2414yes—
274C22×D4—28no—
275C22×D4—28no—
276C22×D4—28no—
277C22×D4—216no—
278C22×D4—24no—
279C22×D4—28no—
280C22×D4—48no—
281C22×D4—48no—
282C22×D4C2418yes—
283C22×D4C2414yes—
284C22×D4C24116yes—
285C23×C4—2128no—
286C23×C4—24no—
287C23×C4—28no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—28no—
291C23×C4—232no—
292C23×C4—28no—
293C23×C4—28no—
294C23×C4—28no—
295C23×C4—264no—
296C23×C4—28no—
297C23×C4—28no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—28no—
303C23×C4—44no—
304C23×C4—48no—
305C23×C4—44no—
306C23×C4C2×D418yes—
307C23×C4C2×D418yes—
308C23×C4C2×D418yes—
309C23×C4#41116yes—
310C23×C4C2414yes—
311C23×C4C2414yes—
312C23×C4C2418yes—
313C23×C4C2414yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2414yes—
320C23×C4C2414yes—
321C23×C4C2414yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2418yes—
328C23×C4C2412yes—
329C23×C4C2414yes—
330C23×C4C2418yes—
331C23×C4C2414yes—
332C23×C4C2411yescharacteristic
333#126—264no—
334#125—232no—
335#124—232no—
336#123—264no—
337#123—432no—
338C22⋊Q8—232no—
339C22⋊Q8—264no—
340#121—232no—
341#121—264no—
342#120—432no—
343C4×Q8—232no—
344C4×D4—264no—
345C4×D4—232no—
346#117—264no—
347#117—264no—
348#117—264no—
349#117—264no—
350#117—264no—
351#117—432no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—232no—
357C2×C4⋊C4—232no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—216no—
367C2×C4⋊C4—48no—
368C2×C4⋊C4—48no—
369C2×C4⋊C4—48no—
370C2×C4⋊C4—48no—
371C2×C4⋊C4C2418yes—
372C2×C4⋊C4C2418yes—
373C2×C4⋊C4C2418yes—
374C2×C4⋊C4C2418yes—
375C2×C4⋊C4C2418yes—
376C2×C4⋊C4C2418yes—
377C2×C4⋊C4C2418yes—
378C2×C4⋊C4C2414yes—
379C2×C4⋊C4C2414yes—
380C2×C4⋊C4C2418yes—
381C2×C4⋊C4C2418yes—
382C2×C4⋊C4C2418yes—
383C2×C4⋊C4C24116yes—
384C2×C4⋊C4C24116yes—
385C2×C4⋊C4C24116yes—
386C2×C4⋊C4C24116yes—
387C2×C4⋊C4C24116yes—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—216no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—232no—
397C2×C22⋊C4—232no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—216no—
403C2×C22⋊C4—48no—
404C2×C22⋊C4—48no—
405C2×C22⋊C4—48no—
406C2×C22⋊C4—48no—
407C2×C22⋊C4C2418yes—
408C2×C22⋊C4C2418yes—
409C2×C22⋊C4C2418yes—
410C2×C22⋊C4C2418yes—
411C2×C22⋊C4C2418yes—
412C2×C22⋊C4C2418yes—
413C2×C22⋊C4C2418yes—
414C2×C22⋊C4C2418yes—
415C2×C22⋊C4C2418yes—
416C2×C22⋊C4C2418yes—
417C2×C22⋊C4C2418yes—
418C2×C22⋊C4C24116yes—
419C2×C22⋊C4C24116yes—
420C2×C22⋊C4C24116yes—
421C2×C22⋊C4C24116yes—
422C2×C22⋊C4C24116yes—
423C2×C22⋊C4C24116yes—
424C2×C42—28no—
425C2×C42—232no—
426C2×C42—28no—
427C2×C42—28no—
428C2×C42—48no—
429C2×C42C2×D418yes—
430C2×C42C2×D418yes—
431C2×C42C2×D418yes—
432C2×C42C2×D418yes—
433C2×C42C2×D4164yescomplemented
434C2×C42C2418yes—
435C2×C42C2418yes—
436C2×C42C2418yes—
437C2×C42C24116yes—
438C2×C42C2414yes—
439C2×C42C2414yes—
440C2×C42C2414yes—
441C2×C42C2414yes—
442#95C2418yes—
443#95C24116yes—
444#95C2418yes—
445#95C24116yes—
446#95C24116yes—
447#95C24116yes—
448#95C24116yes—
449#95C24116yes—
450#95C24116yes—
451C24—24no—
452C24—24no—
453C24—232no—
454C24—28no—
455C24—24no—
456C24—216no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—28no—
464C24—24no—
465C24—28no—
466C24—24no—
467C24—28no—
468C24—28no—
469C24—48no—
470C24—432no—
471C24—432no—
472C24—416no—
473C24—416no—
474C24C22×D414yes—
475C24C2×#4118yes—
476C24H(5,𝔽2)14yes—
477C242−1+414yes—
478C24C2514yes—
479C24C2514yes—
480C24C2512yes—
481C24C2511yescharacteristic
482C2×Q8—28no—
483C2×Q8—216no—
484C2×Q8—416no—
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—216no—
488C2×D4—232no—
489C2×D4—28no—
490C2×D4—216no—
491C2×D4—416no—
492C2×D4—416no—
493C2×D4—432no—
494C2×D4—416no—
495C2×D4—832no—
496C22×C4—264no—
497C22×C4—232no—
498C22×C4—2256no—
499C22×C4—232no—
500C22×C4—28no—
501C22×C4—24no—
502C22×C4—216no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—232no—
514C22×C4—264no—
515C22×C4—216no—
516C22×C4—216no—
517C22×C4—216no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—28no—
540C22×C4—24no—
541C22×C4—28no—
542C22×C4—24no—
543C22×C4—28no—
544C22×C4—216no—
545C22×C4—416no—
546C22×C4—48no—
547C22×C4—416no—
548C22×C4—48no—
549C22×C4—432no—
550C22×C4—416no—
551C22×C4—416no—
552C22×C4C22×D414yes—
553C22×C4C22×D414yes—
554C22×C4C22×D4116yes—
555C22×C4C22×D414yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D4116yes—
559C22×C4C22×D4116yes—
560C22×C4C22×D414yes—
561C22×C4C2×#4118yes—
562C22×C4C2×#41132yes—
563C22×C4C2×#4118yes—
564C22×C4C2518yes—
565C22×C4C2514yes—
566C22×C4C2514yes—
567C22×C4C2518yes—
568C22×C4C2514yes—
569C22×C4C2514yes—
570C22×C4C2514yes—
571C22×C4C2512yes—
572C22×C4C2512yes—
573C22×C4C2512yes—
574C22×C4C2512yes—
575C22×C4C2512yes—
576C22×C4C2514yes—
577C22×C4C2512yes—
578C4⋊C4—216no—
579C4⋊C4—216no—
580C4⋊C4—216no—
581C4⋊C4—216no—
582C4⋊C4—216no—
583C4⋊C4—216no—
584C4⋊C4—28no—
585C4⋊C4—216no—
586C4⋊C4—28no—
587C4⋊C4—216no—
588C4⋊C4—216no—
589C4⋊C4—216no—
590C4⋊C4—232no—
591C4⋊C4—416no—
592C4⋊C4—416no—
593C4⋊C4—416no—
594C4⋊C4—416no—
595C22⋊C4—216no—
596C22⋊C4—232no—
597C22⋊C4—216no—
598C22⋊C4—216no—
599C22⋊C4—216no—
600C22⋊C4—216no—
601C22⋊C4—216no—
602C22⋊C4—216no—
603C22⋊C4—216no—
604C22⋊C4—216no—
605C22⋊C4—216no—
606C22⋊C4—216no—
607C22⋊C4—232no—
608C22⋊C4—416no—
609C22⋊C4—416no—
610C22⋊C4—416no—
611C22⋊C4—416no—
612C42—216no—
613C42—216no—
614C42—216no—
615C42—416no—
616C42C22×D4116yes—
617C42C22×D4116yes—
618C42C22×D4116yes—
619C42C22×D4116yes—
620C23—24no—
621C23—24no—
622C23—28no—
623C23—28no—
624C23—216no—
625C23—216no—
626C23—232no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—216no—
634C23—216no—
635C23—216no—
636C23—24no—
637C23—28no—
638C23—24no—
639C23—24no—
640C23—28no—
641C23—432no—
642C23—432no—
643C23—416no—
644C23—4128no—
645C23—416no—
646C23—48no—
647C23—48no—
648C23—48no—
649C23—48no—
650C23—48no—
651C23—48no—
652C23—48no—
653C23—416no—
654C23—416no—
655C23#537116yes—
656C23C23×D414yes—
657C23C23×D412yes—
658C23C22×#4118yes—
659C23C22×#4114yes—
660C23C2×H(5,𝔽2)14yes—
661C23C2×H(5,𝔽2)12yes—
662C23C2×2−1+414yes—
663C23C2×2−1+412yes—
664C23#58514yes—
665C23C2611yescharacteristic
666Q8—416no—
667D4—432no—
668D4—416no—
669D4—832no—
670C2×C4—264no—
671C2×C4—232no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—28no—
682C2×C4—216no—
683C2×C4—232no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—232no—
689C2×C4—264no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—416no—
710C2×C4—432no—
711C2×C4—416no—
712C2×C4—48no—
713C2×C4—416no—
714C2×C4—48no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4#525116yes—
721C2×C4C23×D414yes—
722C2×C4C23×D414yes—
723C2×C4C23×D414yes—
724C2×C4C23×D414yes—
725C2×C4C23×D414yes—
726C2×C4C23×D414yes—
727C2×C4C22×#4118yes—
728C2×C4C22×#4118yes—
729C22—28no—
730C22—28no—
731C22—24no—
732C22—24no—
733C22—232no—
734C22—28no—
735C22—28no—
736C22—28no—
737C22—464no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—432no—
743C22—48no—
744C22—48no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—816no—
749C22C2×#52514yes—
750C22C2×#53718yes—
751C22C2×#53714yes—
752C22#344914yes—
753C22#349418yes—
754C22#349518yes—
755C22C24×D411yescharacteristic
756C22C23×#4112yes—
757C22C22×H(5,𝔽2)11yescharacteristic
758C22C22×2−1+411yescharacteristic
759C22C2×#58512yes—
760C4—24no—
761C4—28no—
762C4—24no—
763C4—24no—
764C4—24no—
765C4—24no—
766C4—48no—
767C4—48no—
768C4—44no—
769C4—44no—
770C4—44no—
771C4—44no—
772C4—44no—
773C4C2×#52518yes—
774C2—28no—
775C2—48no—
776C2—84no—
777C2#3530218yesdirect product factor
778C2C22×#52511yescharacteristic
779C2C22×#53711yescharacteristic
780C2C2×#344911yescharacteristic
781C2C2×#349412yes—
782C2C2×#349512yes—
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2847C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C23×#117C2semidirect
3. C2×#2855C2semidirect
4. C2×#2854C2semidirect
5. C2×#2848C2semidirect
7. #35302C2direct (N × H)
8. C2×#2609C2semidirect
9. C2×#2601C2semidirect
10. C2×#2579C2semidirect
11. C2×#2534C2semidirect
12. C2×#2413C2semidirect
13. C2×#2411C2semidirect
14. C2×#2629C2semidirect
15. C2×#2620C2semidirect
16. C2×#2324C2semidirect
17. C2×#2323C2semidirect
18. C2×#2285C2semidirect
21. C2×#529C22semidirect
22. C22×#126C22semidirect
23. C22×#125C22semidirect
24. C22×#124C22semidirect
32. C22×C4×Q8C22semidirect
34. C22×C4×D4C22semidirect
41. C22×#117C22semidirect
42. C22×#117C22semidirect
49. #2855C22semidirect
50. #2854C22semidirect
51. #2848C22semidirect
53. #2629C22semidirect
54. #2620C22semidirect
55. #2609C22semidirect
56. #2601C22semidirect
57. #2579C22semidirect
58. #2534C22semidirect
59. #2413C22semidirect
60. #2411C22semidirect
61. C2×#398C22semidirect
62. C2×#398C22semidirect
65. C2×#396C22semidirect
66. C2×#396C22semidirect
69. #2324C22semidirect
70. #2323C22semidirect
71. C2×#391C22semidirect
73. C2×#390C22semidirect
74. C2×#389C22semidirect
75. C2×#389C22semidirect
76. C2×#389C22semidirect
79. C2×#388C22semidirect
80. C2×#388C22semidirect
81. C2×#387C22semidirect
82. C2×#387C22semidirect
90. C2×#385C22semidirect
91. #2285C22semidirect
92. C2×#384C22semidirect
93. C2×#382C22semidirect
101. C2×C4×C4⋊C4C22semidirect
102. C2×C4×C4⋊C4C22semidirect
122. C2×#126C23semidirect
124. C2×#125C23semidirect
126. C2×#124C23semidirect
142. C2×C4×Q8C23semidirect
146. C2×C4×D4C23semidirect
159. C2×#117C23semidirect
203. C22×C42D4semidirect
214. #398C23semidirect
215. #398C23semidirect
218. #396C23semidirect
219. #396C23semidirect
222. #391C23semidirect
224. #390C23semidirect
225. #389C23semidirect
226. #389C23semidirect
227. #389C23semidirect
230. #388C23semidirect
231. #388C23semidirect
232. #387C23semidirect
233. #387C23semidirect
241. #385C23semidirect
242. #384C23semidirect
243. #382C23semidirect
251. C4×C4⋊C4C23semidirect
252. C4×C4⋊C4C23semidirect
433. C2×C42C2×D4semidirect
777. C2#35302direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5292
C23×#1172
C2×#28552
C2×#28542
C2×#28482
C2×#28472
#353022
C2×#26092
C2×#26012
C2×#25792
C2×#25342
C2×#24132
C2×#24112
C2×#26292
C2×#26202
C2×#23242
C2×#23232
C2×#22852