Finite Group Databasebeta

← C2×#42864 #7641456

Subgroups — C2×#42864 #7641456

Order 512.

4750 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2809C212yesmaximal
2C2×#2789C212yesmaximal
3C2×#2776C212yesmaximal
4C2×#2767C212yesmaximal
5#42864C2132yesmaximal, direct product factor
6C2×#2839C212yesmaximal
7C2×#2568C211yesmaximal, characteristic
8C2×#2546C211yesmaximal, characteristic
9C2×#2588C212yesmaximal
10C2×#2514C211yesmaximal, characteristic
11C2×#2508C211yesmaximal, characteristic
12C2×#2451C211yesmaximal, characteristic
13C2×#2451C211yesmaximal, characteristic
14C2×#2446C211yesmaximal, characteristic
15C2×#2446C211yesmaximal, characteristic
16C2×#2446C211yesmaximal, characteristic
17C2×#2446C211yesmaximal, characteristic
18C2×#2645C211yesmaximal, characteristic
19C2×#2666C212yesmaximal
20C2×#2655C212yesmaximal
21C2×#2402C211yesmaximal, characteristic
22C2×#2365C211yesmaximal, characteristic
23C2×#2351C211yesmaximal, characteristic
24C2×#2327C211yesmaximal, characteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34#2839C22132yes—
35#2809C22132yes—
36#2789C22132yes—
37#2776C22132yes—
38#2767C22132yes—
39#2666C22132yes—
40#2655C22132yes—
41#2645C22116yes—
42#2588C22132yes—
43#2568C22116yes—
44#2546C22116yes—
45#2514C22116yes—
46#2508C22116yes—
47#2451C22116yes—
48#2451C22116yes—
49#2446C22116yes—
50#2446C22116yes—
51#2446C22116yes—
52#2446C22116yes—
53#2402C22116yes—
54C2×#401C2212yes—
55C2×#401C2212yes—
56C2×#400C2211yescharacteristic
57C2×#400C2212yes—
58C2×#400C2211yescharacteristic
59C2×#400C2212yes—
60C2×#400C2212yes—
61C2×#400C2212yes—
62C2×#400C2212yes—
63C2×#400C2212yes—
64C2×#400C2212yes—
65C2×#400C2212yes—
66C2×#400C2211yescharacteristic
67C2×#400C2212yes—
68C2×#400C2212yes—
69C2×#400C2212yes—
70C2×#400C2211yescharacteristic
71C2×#398C2212yes—
72C2×#398C2212yes—
73C2×#398C2212yes—
74C2×#398C2212yes—
75C2×#398C2211yescharacteristic
76C2×#398C2211yescharacteristic
77C2×#398C2212yes—
78C2×#398C2212yes—
79C2×#398C2212yes—
80C2×#398C2211yescharacteristic
81C2×#398C2212yes—
82C2×#398C2212yes—
83C2×#398C2211yescharacteristic
84C2×#395C2212yes—
85C2×#395C2212yes—
86#2365C22116yes—
87#2351C22116yes—
88#2327C22116yes—
89C2×#391C2212yes—
90C2×#391C2212yes—
91C2×#391C2211yescharacteristic
92C2×#391C2211yescharacteristic
93C2×#391C2212yes—
94C2×#391C2212yes—
95C2×#391C2211yescharacteristic
96C2×#391C2211yescharacteristic
97C2×#391C2211yescharacteristic
98C2×#391C2211yescharacteristic
99C2×#391C2211yescharacteristic
100C2×#391C2211yescharacteristic
101C2×#391C2211yescharacteristic
102C2×#391C2211yescharacteristic
103C2×#389C2212yes—
104C2×#389C2212yes—
105C2×#389C2212yes—
106C2×#389C2212yes—
107C2×#389C2211yescharacteristic
108C2×#389C2211yescharacteristic
109C2×#389C2211yescharacteristic
110C2×#389C2211yescharacteristic
111C2×#389C2212yes—
112C2×#389C2211yescharacteristic
113C2×#389C2211yescharacteristic
114C2×#387C2212yes—
115C2×#387C2212yes—
116C2×#387C2212yes—
117C2×#387C2212yes—
118C2×#387C2212yes—
119C2×#387C2212yes—
120C2×#387C2212yes—
121C2×#387C2212yes—
122C2×#387C2212yes—
123C2×#387C2212yes—
124C2×#387C2212yes—
125C2×#387C2212yes—
126C2×#387C2212yes—
127C2×#387C2212yes—
128C2×#387C2212yes—
129C2×#387C2212yes—
130C2×#387C2212yes—
131C2×#387C2212yes—
132C2×#383C2212yes—
133C2×#382C2212yes—
134C2×#382C2211yescharacteristic
135C2×#382C2212yes—
136C2×#382C2211yescharacteristic
137C2×C4×C4⋊C4C2212yes—
138C2×C4×C4⋊C4C2212yes—
139C2×C4×C4⋊C4C2211yescharacteristic
140C2×C4×C4⋊C4C2211yescharacteristic
141C2×C4×C4⋊C4C2211yescharacteristic
142C2×C4×C4⋊C4C2211yescharacteristic
143C2×C4×C4⋊C4C2211yescharacteristic
144C2×C4×C4⋊C4C2211yescharacteristic
145C2×C4×C4⋊C4C2211yescharacteristic
146C2×#376C2211yescharacteristic
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2311yescharacteristic
150C23×Q8C2312yes—
151C2×C4⋊Q8—28no—
152C2×C4⋊Q8—28no—
153C2×C4⋊Q8—44no—
154C2×C4⋊Q8—44no—
155C2×C4⋊Q8C2318yes—
156C2×C4⋊Q8C2318yes—
157C2×C4⋊Q8C2318yes—
158C2×C4⋊Q8C2318yes—
159C2×C4×Q8—28no—
160C2×C4×Q8—44no—
161C2×C4×Q8—44no—
162C2×C4×Q8—44no—
163C2×C4×Q8—44no—
164C2×C4×Q8C2318yes—
165C2×C4×Q8C2318yes—
166C2×C4×Q8C2318yes—
167C2×C4×Q8C2318yes—
168C2×C4×Q8C2318yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2312yes—
217#401C23116yes—
218#401C23116yes—
219#400C23116yes—
220#400C23116yes—
221#400C2318yes—
222#400C23116yes—
223#400C23116yes—
224#400C23116yes—
225#400C23116yes—
226#400C23116yes—
227#400C23116yes—
228#400C23116yes—
229#400C23116yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C23116yes—
234#398C23116yes—
235#398C23116yes—
236#398C23116yes—
237#398C23116yes—
238#398C23116yes—
239#398C2318yes—
240#398C23116yes—
241#398C23116yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C23116yes—
246#398C23116yes—
247#395C23116yes—
248#395C23116yes—
249#391C23116yes—
250#391C2318yes—
251#391C23116yes—
252#391C2318yes—
253#391C2318yes—
254#391C2318yes—
255#391C23116yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2318yes—
260#391C2318yes—
261#391C2318yes—
262#391C23116yes—
263#389C23116yes—
264#389C23116yes—
265#389C2318yes—
266#389C2318yes—
267#389C23116yes—
268#389C23116yes—
269#389C2318yes—
270#389C2318yes—
271#389C23116yes—
272#389C2318yes—
273#389C2318yes—
274#387C23116yes—
275#387C23116yes—
276#387C23116yes—
277#387C23116yes—
278#387C23116yes—
279#387C23116yes—
280#387C23116yes—
281#387C23116yes—
282#387C23116yes—
283#387C23116yes—
284#387C23116yes—
285#387C23116yes—
286#387C23116yes—
287#387C23116yes—
288#387C23116yes—
289#387C23116yes—
290#387C23116yes—
291#387C23116yes—
292#383C23116yes—
293#382C2318yes—
294#382C2318yes—
295#382C23116yes—
296#382C23116yes—
297C4×C4⋊C4C2318yes—
298C4×C4⋊C4C23116yes—
299C4×C4⋊C4C23116yes—
300C4×C4⋊C4C2318yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2318yes—
305C4×C4⋊C4C2318yes—
306#376C2318yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C2×#95C2311yescharacteristic
323C2×#95C2312yes—
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C2×#95C2312yes—
333C2×#95C2312yes—
334C2×#95C2312yes—
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2312yes—
338C2×#95C2312yes—
339C2×#95C2312yes—
340C2×#95C2312yes—
341C2×#95C2311yescharacteristic
342C2×#95C2312yes—
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2312yes—
346C2×#95C2312yes—
347C2×#95C2312yes—
348C2×#95C2312yes—
349C2×#95C2312yes—
350C2×#95C2312yes—
351C2×#95C2312yes—
352C2×#95C2312yes—
353C2×#95C2312yes—
354C22×Q8—24no—
355C22×Q8—24no—
356C22×Q8—24no—
357C22×Q8—24no—
358C22×Q8—24no—
359C22×Q8—24no—
360C22×Q8—24no—
361C22×Q8—24no—
362C22×Q8—28no—
363C22×Q8—44no—
364C22×Q8—44no—
365C22×Q8#4118yes—
366C22×Q8C2414yes—
367C22×Q8C2414yes—
368C22×Q8C2414yes—
369C22×Q8C2418yes—
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C4⋊Q8—232no—
394C4⋊Q8—232no—
395C4⋊Q8—416no—
396C4⋊Q8—416no—
397C4×Q8—232no—
398C4×Q8—416no—
399C4×Q8—416no—
400C4×Q8—416no—
401C4×Q8—416no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4—44no—
429C2×C4⋊C4—44no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—44no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2414yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C42—28no—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—24no—
479C2×C42—28no—
480C2×C42—24no—
481C2×C42—44no—
482C2×C42—44no—
483C2×C42—44no—
484C2×C42—44no—
485C2×C42C2414yes—
486C2×C42C2414yes—
487C2×C42C2414yes—
488C2×C42C2414yes—
489C2×C42C2418yes—
490C2×C42C2414yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2418yes—
494C2×C42C2418yes—
495C2×C42C2418yes—
496C2×C42C2418yes—
497C2×C42C2418yes—
498#95C2414yes—
499#95C2414yes—
500#95C2414yes—
501#95C2414yes—
502#95C2414yes—
503#95C2414yes—
504#95C2418yes—
505#95C2414yes—
506#95C2414yes—
507#95C2418yes—
508#95C2414yes—
509#95C2414yes—
510#95C2414yes—
511#95C2418yes—
512#95C2414yes—
513#95C2414yes—
514#95C2418yes—
515#95C2414yes—
516#95C2414yes—
517#95C2414yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545C24C2511yescharacteristic
546C2×Q8—232no—
547C2×Q8—28no—
548C2×Q8—28no—
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—28no—
554C2×Q8—28no—
555C2×Q8—216no—
556C2×Q8—48no—
557C2×Q8—48no—
558C2×Q8—416no—
559C2×Q8—416no—
560C2×Q8—816no—
561C2×Q8C2×#41116yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4C2×#4118yes—
625C22×C4C2×#4114yes—
626C22×C4H(5,𝔽2)14yes—
627C22×C42−1+414yes—
628C22×C42−1+414yes—
629C22×C42−1+414yes—
630C22×C42−1+414yes—
631C22×C4C2512yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C22×C4C2512yes—
635C22×C4C2514yes—
636C22×C4C2512yes—
637C22×C4C2514yes—
638C22×C4C2512yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2514yes—
642C22×C4C2512yes—
643C22×C4C2514yes—
644C22×C4C2514yes—
645C22×C4C2514yes—
646C22×C4C2514yes—
647C22×C4C2512yes—
648C22×C4C2512yes—
649C22×C4C2514yes—
650C22×C4C2512yes—
651C22×C4C2512yes—
652C22×C4C2512yes—
653C22×C4C2512yes—
654C4⋊C4—216no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—216no—
658C4⋊C4—216no—
659C4⋊C4—216no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—216no—
668C4⋊C4—28no—
669C4⋊C4—28no—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—48no—
682C4⋊C4—48no—
683C4⋊C4—48no—
684C4⋊C4—48no—
685C4⋊C4—48no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—48no—
689C42—216no—
690C42—28no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—28no—
696C42—216no—
697C42—28no—
698C42—48no—
699C42—48no—
700C42—48no—
701C42—48no—
702C23C22×#4112yes—
703C23C2×H(5,𝔽2)12yes—
704C23C2×2−1+412yes—
705C23C2×2−1+412yes—
706C23C2×2−1+412yes—
707C23C2×2−1+412yes—
708C23#58512yes—
709C23C2611yescharacteristic
710Q8—232no—
711Q8—416no—
712Q8—416no—
713Q8—816no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—216no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—48no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4#539116yes—
799C2×C4C22×#4118yes—
800C2×C4C22×#4114yes—
801C2×C4C2×H(5,𝔽2)14yes—
802C2×C4C2×2−1+414yes—
803C2×C4C2×2−1+414yes—
804C2×C4C2×2−1+414yes—
805C2×C4C2×2−1+414yes—
806C22C2×#53914yes—
807C22#351814yes—
808C22#352314yes—
809C22#355214yes—
810C22#355514yes—
811C22#355614yes—
812C22#356114yes—
813C22C23×#4111yescharacteristic
814C22C22×H(5,𝔽2)11yescharacteristic
815C22C22×2−1+411yescharacteristic
816C22C22×2−1+411yescharacteristic
817C22C22×2−1+411yescharacteristic
818C22C22×2−1+411yescharacteristic
819C22C2×#58511yescharacteristic
820C4—24no—
821C4—24no—
822C4—24no—
823C4—28no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—44no—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—44no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—44no—
841C4—44no—
842C4C2×#53918yes—
843C2#4286418yesdirect product factor
844C2C22×#53911yescharacteristic
845C2C2×#356111yescharacteristic
846C2C2×#355211yescharacteristic
847C2C2×#355511yescharacteristic
848C2C2×#355611yescharacteristic
849C2C2×#352311yescharacteristic
850C2C2×#351811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #42864C2direct (N × H)
843. C2#42864direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28092
C2×#27892
C2×#27762
C2×#27672
#428642
C2×#28392
C2×#25682
C2×#25462
C2×#25882
C2×#25142
C2×#25082
C2×#24512
C2×#24462
C2×#26452
C2×#26662
C2×#26552
C2×#24022
C2×#23652
C2×#23512
C2×#23272