Finite Group Databasebeta

← C2×#42689 #7641304

Subgroups — C2×#42689 #7641304

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2769C212yesmaximal
2C2×#2766C212yesmaximal
3C2×#2762C212yesmaximal
4C2×#2762C212yesmaximal
5#42689C2132yesmaximal, direct product factor
6C2×#2833C212yesmaximal
7C2×#2582C211yesmaximal, characteristic
8C2×#2581C211yesmaximal, characteristic
9C2×#2509C211yesmaximal, characteristic
10C2×#2514C211yesmaximal, characteristic
11C2×#2514C211yesmaximal, characteristic
12C2×#2514C211yesmaximal, characteristic
13C2×#2508C211yesmaximal, characteristic
14C2×#2508C211yesmaximal, characteristic
15C2×#2524C212yesmaximal
16C2×#2511C211yesmaximal, characteristic
17C2×#2507C211yesmaximal, characteristic
18C2×#2647C211yesmaximal, characteristic
19C2×#2666C212yesmaximal
20C2×#2655C212yesmaximal
21C2×#2399C211yesmaximal, characteristic
22C2×#2355C211yesmaximal, characteristic
23C2×#2355C211yesmaximal, characteristic
24C2×#2320C211yesmaximal, characteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#2833C22132yes—
29#2769C22132yes—
30#2766C22132yes—
31#2762C22132yes—
32#2762C22132yes—
33#2666C22132yes—
34#2655C22132yes—
35#2647C22116yes—
36#2582C22116yes—
37#2581C22116yes—
38#2524C22132yes—
39#2514C22116yes—
40#2514C22116yes—
41#2514C22116yes—
42#2511C22116yes—
43#2509C22116yes—
44#2508C22116yes—
45#2508C22116yes—
46#2507C22116yes—
47C2×#401C2212yes—
48C2×#401C2212yes—
49C2×#401C2212yes—
50#2399C22116yes—
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#400C2212yes—
55C2×#400C2212yes—
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#400C2212yes—
60C2×#400C2212yes—
61C2×#400C2212yes—
62C2×#400C2212yes—
63C2×#398C2211yescharacteristic
64C2×#398C2212yes—
65C2×#398C2212yes—
66C2×#398C2212yes—
67C2×#398C2212yes—
68C2×#398C2212yes—
69C2×#398C2212yes—
70C2×#398C2212yes—
71C2×#398C2212yes—
72C2×#398C2211yescharacteristic
73C2×#398C2211yescharacteristic
74C2×#398C2211yescharacteristic
75C2×#395C2211yescharacteristic
76C2×#395C2212yes—
77C2×#395C2211yescharacteristic
78C2×#395C2211yescharacteristic
79C2×#395C2211yescharacteristic
80#2355C22116yes—
81#2355C22116yes—
82#2320C22116yes—
83C2×#391C2211yescharacteristic
84C2×#391C2211yescharacteristic
85C2×#391C2212yes—
86C2×#391C2212yes—
87C2×#391C2211yescharacteristic
88C2×#391C2211yescharacteristic
89C2×#391C2211yescharacteristic
90C2×#391C2211yescharacteristic
91C2×#391C2212yes—
92C2×#389C2211yescharacteristic
93C2×#389C2211yescharacteristic
94C2×#389C2212yes—
95C2×#389C2212yes—
96C2×#389C2211yescharacteristic
97C2×#389C2211yescharacteristic
98C2×#389C2211yescharacteristic
99C2×#389C2211yescharacteristic
100C2×#389C2211yescharacteristic
101C2×#389C2211yescharacteristic
102C2×#389C2211yescharacteristic
103C2×#389C2211yescharacteristic
104C2×#389C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#387C2212yes—
110C2×#387C2212yes—
111C2×#387C2212yes—
112C2×#387C2212yes—
113C2×#387C2212yes—
114C2×#387C2212yes—
115C2×#387C2212yes—
116C2×#387C2212yes—
117C2×#387C2212yes—
118C2×#387C2212yes—
119C2×#387C2212yes—
120C2×#387C2212yes—
121C2×#387C2212yes—
122C2×#384C2211yescharacteristic
123C2×#384C2211yescharacteristic
124C2×#383C2212yes—
125C2×#383C2212yes—
126C2×#383C2212yes—
127C2×#383C2212yes—
128C2×#382C2212yes—
129C2×#382C2212yes—
130C2×#382C2211yescharacteristic
131C2×#382C2211yescharacteristic
132C2×#382C2211yescharacteristic
133C2×#382C2211yescharacteristic
134C2×#382C2212yes—
135C2×C4×C4⋊C4C2211yescharacteristic
136C2×C4×C4⋊C4C2212yes—
137C2×C4×C4⋊C4C2212yes—
138C2×C4×C4⋊C4C2211yescharacteristic
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
150C2×C4×Q8—28no—
151C2×C4×Q8—28no—
152C2×C4×Q8—28no—
153C2×C4×Q8C2318yes—
154C2×C4×Q8C2318yes—
155C2×C4×Q8C2318yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204C22×C42C2311yescharacteristic
205#401C23116yes—
206#401C23116yes—
207#401C23116yes—
208#400C23116yes—
209#400C23116yes—
210#400C23116yes—
211#400C23116yes—
212#400C23116yes—
213#400C23116yes—
214#400C23116yes—
215#400C23116yes—
216#400C23116yes—
217#400C23116yes—
218#400C23116yes—
219#400C23116yes—
220#398C23116yes—
221#398C23116yes—
222#398C23116yes—
223#398C23116yes—
224#398C23116yes—
225#398C23116yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C23116yes—
231#398C23116yes—
232#395C2318yes—
233#395C23116yes—
234#395C2318yes—
235#395C2318yes—
236#395C2318yes—
237#391C2318yes—
238#391C2318yes—
239#391C23116yes—
240#391C2318yes—
241#391C2318yes—
242#391C23116yes—
243#391C2318yes—
244#391C2318yes—
245#391C23116yes—
246#389C2318yes—
247#389C2318yes—
248#389C2318yes—
249#389C2318yes—
250#389C2318yes—
251#389C2318yes—
252#389C23116yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#389C23116yes—
258#389C23116yes—
259#387C23116yes—
260#387C23116yes—
261#387C23116yes—
262#387C23116yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#387C23116yes—
267#387C23116yes—
268#387C23116yes—
269#387C23116yes—
270#387C23116yes—
271#387C23116yes—
272#387C23116yes—
273#387C23116yes—
274#387C23116yes—
275#387C23116yes—
276#384C2318yes—
277#384C2318yes—
278#383C23116yes—
279#383C23116yes—
280#383C23116yes—
281#383C23116yes—
282#382C23116yes—
283#382C2318yes—
284#382C2318yes—
285#382C2318yes—
286#382C2318yes—
287#382C23116yes—
288#382C23116yes—
289C4×C4⋊C4C2318yes—
290C4×C4⋊C4C23116yes—
291C4×C4⋊C4C23116yes—
292C4×C4⋊C4C2318yes—
293C4×C4⋊C4C2318yes—
294C4×C4⋊C4C2318yes—
295C4×C4⋊C4C2318yes—
296C4×C4⋊C4C2318yes—
297C4×C4⋊C4C2318yes—
298C4×C4⋊C4C2318yes—
299C4×C4⋊C4C2318yes—
300#376C2318yes—
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2311yescharacteristic
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C2×#95C2312yes—
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2312yes—
326C2×#95C2312yes—
327C2×#95C2312yes—
328C2×#95C2312yes—
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C2×#95C2312yes—
333C2×#95C2312yes—
334C2×#95C2312yes—
335C2×#95C2312yes—
336C2×#95C2312yes—
337C2×#95C2312yes—
338C2×#95C2312yes—
339C2×#95C2312yes—
340C2×#95C2312yes—
341C2×#95C2312yes—
342C2×#95C2312yes—
343C2×#95C2312yes—
344C2×#95C2312yes—
345C2×#95C2312yes—
346C2×#95C2312yes—
347C2×#95C2312yes—
348C22×Q8—24no—
349C22×Q8—24no—
350C22×Q8—24no—
351C22×Q8—24no—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—42no—
355C22×Q8—42no—
356C22×Q8—42no—
357C22×Q8C2414yes—
358C22×Q8C2414yes—
359C22×Q8C2414yes—
360C23×C4C2411yescharacteristic
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C4×Q8—232no—
384C4×Q8—232no—
385C4×Q8—232no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4C2414yes—
423C2×C4⋊C4C2414yes—
424C2×C4⋊C4C2414yes—
425C2×C4⋊C4C2414yes—
426C2×C4⋊C4C2414yes—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2414yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2418yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2418yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C42—24no—
459C2×C42—28no—
460C2×C42—24no—
461C2×C42—24no—
462C2×C42—24no—
463C2×C42—28no—
464C2×C42—24no—
465C2×C42—24no—
466C2×C42—44no—
467C2×C42—44no—
468C2×C42—44no—
469C2×C42—44no—
470C2×C42#4118yes—
471C2×C42C2414yes—
472C2×C42C2414yes—
473C2×C42C2414yes—
474C2×C42C2414yes—
475C2×C42C2418yes—
476C2×C42C2414yes—
477C2×C42C2414yes—
478C2×C42C2418yes—
479C2×C42C2418yes—
480C2×C42C2418yes—
481C2×C42C2418yes—
482C2×C42C2418yes—
483C2×C42C2414yes—
484#95C2414yes—
485#95C2414yes—
486#95C2414yes—
487#95C2414yes—
488#95C2414yes—
489#95C2418yes—
490#95C2414yes—
491#95C2418yes—
492#95C2418yes—
493#95C2418yes—
494#95C2418yes—
495#95C2414yes—
496#95C2414yes—
497#95C2414yes—
498#95C2418yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2414yes—
503#95C2414yes—
504#95C2414yes—
505#95C2418yes—
506#95C2418yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
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—
531C24C2511yescharacteristic
532C2×Q8—28no—
533C2×Q8—28no—
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—28no—
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—416no—
542C2×Q8—416no—
543C2×Q8—416no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4C2×#4114yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C42−1+414yes—
611C22×C42−1+414yes—
612C22×C42−1+414yes—
613C22×C4C2514yes—
614C22×C4C2514yes—
615C22×C4C2512yes—
616C22×C4C2512yes—
617C22×C4C2514yes—
618C22×C4C2512yes—
619C22×C4C2512yes—
620C22×C4C2512yes—
621C22×C4C2514yes—
622C22×C4C2512yes—
623C22×C4C2512yes—
624C22×C4C2514yes—
625C22×C4C2514yes—
626C22×C4C2514yes—
627C22×C4C2512yes—
628C22×C4C2512yes—
629C22×C4C2512yes—
630C22×C4C2512yes—
631C22×C4C2514yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—216no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—48no—
672C42—28no—
673C42—216no—
674C42—28no—
675C42—28no—
676C42—28no—
677C42—216no—
678C42—28no—
679C42—28no—
680C42—48no—
681C42—48no—
682C42—48no—
683C42—48no—
684C42C2×#41116yes—
685C23C22×#4112yes—
686C23C2×2−1+412yes—
687C23C2×2−1+412yes—
688C23C2×2−1+412yes—
689C23#58512yes—
690C23#58512yes—
691C23#58512yes—
692C23C2611yescharacteristic
693Q8—416no—
694Q8—416no—
695Q8—416no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
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—48no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—48no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—48no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—48no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—48no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—48no—
781C2×C4#541116yes—
782C2×C4C22×#4114yes—
783C2×C4C22×#4114yes—
784C2×C4C22×#4114yes—
785C2×C4C2×2−1+414yes—
786C2×C4C2×2−1+414yes—
787C2×C4C2×2−1+414yes—
788C22C2×#54114yes—
789C22#349314yes—
790C22#349514yes—
791C22#355514yes—
792C22#355514yes—
793C22#355714yes—
794C22#355714yes—
795C22C23×#4111yescharacteristic
796C22C22×2−1+411yescharacteristic
797C22C22×2−1+411yescharacteristic
798C22C22×2−1+411yescharacteristic
799C22C2×#58511yescharacteristic
800C22C2×#58511yescharacteristic
801C22C2×#58511yescharacteristic
802C4—24no—
803C4—24no—
804C4—24no—
805C4—42no—
806C4—42no—
807C4—44no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—44no—
815C4—42no—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—44no—
824C4C2×#54118yes—
825C2#4268918yesdirect product factor
826C2C22×#54111yescharacteristic
827C2C2×#355711yescharacteristic
828C2C2×#355711yescharacteristic
829C2C2×#355511yescharacteristic
830C2C2×#355511yescharacteristic
831C2C2×#349311yescharacteristic
832C2C2×#349511yescharacteristic
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. #42689C2direct (N × H)
825. C2#42689direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27692
C2×#27662
C2×#27622
#426892
C2×#28332
C2×#25822
C2×#25812
C2×#25092
C2×#25142
C2×#25082
C2×#25242
C2×#25112
C2×#25072
C2×#26472
C2×#26662
C2×#26552
C2×#23992
C2×#23552
C2×#23202