Finite Group Databasebeta

← C2×#42819 #7641415

Subgroups — C2×#42819 #7641415

Order 512.

4686 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2805C212yesmaximal
2C2×#2802C212yesmaximal
3C2×#2792C212yesmaximal
4C2×#2791C212yesmaximal
5#42819C2132yesmaximal, direct product factor
6C2×#2843C212yesmaximal
7C2×#2582C211yesmaximal, characteristic
8C2×#2552C211yesmaximal, characteristic
9C2×#2581C211yesmaximal, characteristic
10C2×#2570C211yesmaximal, characteristic
11C2×#2584C211yesmaximal, characteristic
12C2×#2584C211yesmaximal, characteristic
13C2×#2606C212yesmaximal
14C2×#2509C211yesmaximal, characteristic
15C2×#2507C211yesmaximal, characteristic
16C2×#2453C211yesmaximal, characteristic
17C2×#2453C211yesmaximal, characteristic
18C2×#2647C212yesmaximal
19C2×#2647C211yesmaximal, characteristic
20C2×#2666C212yesmaximal
21C2×#2399C211yesmaximal, characteristic
22C2×#2356C211yesmaximal, characteristic
23C2×Q8×C4⋊C4C211yesmaximal, characteristic
24C2×#2320C211yesmaximal, characteristic
25C22×#125C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2843C22132yes—
33#2805C22132yes—
34#2802C22132yes—
35#2792C22132yes—
36#2791C22132yes—
37#2666C22132yes—
38#2647C22116yes—
39#2647C22132yes—
40#2606C22132yes—
41#2584C22116yes—
42#2584C22116yes—
43#2582C22116yes—
44#2581C22116yes—
45#2570C22116yes—
46#2552C22116yes—
47#2509C22116yes—
48#2507C22116yes—
49#2453C22116yes—
50#2453C22116yes—
51#2399C22116yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#400C2212yes—
55C2×#400C2212yes—
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#400C2212yes—
60C2×#398C2211yescharacteristic
61C2×#398C2212yes—
62C2×#398C2212yes—
63C2×#398C2212yes—
64C2×#398C2212yes—
65C2×#398C2212yes—
66C2×#398C2212yes—
67C2×#398C2212yes—
68C2×#398C2212yes—
69C2×#398C2212yes—
70C2×#398C2211yescharacteristic
71C2×#398C2212yes—
72C2×#398C2212yes—
73C2×#398C2211yescharacteristic
74C2×#398C2212yes—
75C2×#398C2212yes—
76C2×#398C2211yescharacteristic
77C2×#395C2211yescharacteristic
78C2×#395C2212yes—
79C2×#395C2212yes—
80C2×#395C2211yescharacteristic
81C2×#395C2212yes—
82C2×#395C2211yescharacteristic
83C2×#395C2211yescharacteristic
84#2356C22116yes—
85Q8×C4⋊C4C22116yes—
86#2320C22116yes—
87C2×#391C2211yescharacteristic
88C2×#391C2211yescharacteristic
89C2×#391C2212yes—
90C2×#391C2211yescharacteristic
91C2×#391C2211yescharacteristic
92C2×#389C2211yescharacteristic
93C2×#389C2211yescharacteristic
94C2×#389C2212yes—
95C2×#389C2212yes—
96C2×#389C2212yes—
97C2×#389C2212yes—
98C2×#389C2212yes—
99C2×#389C2212yes—
100C2×#389C2212yes—
101C2×#389C2212yes—
102C2×#389C2212yes—
103C2×#389C2212yes—
104C2×#389C2212yes—
105C2×#389C2212yes—
106C2×#389C2211yescharacteristic
107C2×#389C2211yescharacteristic
108C2×#389C2211yescharacteristic
109C2×#389C2211yescharacteristic
110C2×#389C2211yescharacteristic
111C2×#389C2211yescharacteristic
112C2×#389C2211yescharacteristic
113C2×#389C2211yescharacteristic
114C2×#389C2211yescharacteristic
115C2×#389C2211yescharacteristic
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×#384C2212yes—
129C2×#384C2212yes—
130C2×#384C2211yescharacteristic
131C2×#384C2211yescharacteristic
132C2×#383C2212yes—
133C2×#383C2212yes—
134C2×#382C2212yes—
135C2×#382C2211yescharacteristic
136C2×#382C2211yescharacteristic
137C2×C4×C4⋊C4C2211yescharacteristic
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×#376C2211yescharacteristic
146C2×#376C2212yes—
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2311yescharacteristic
150C2×#125—44no—
151C2×#125—44no—
152C2×#125C2318yes—
153C2×#125C2318yes—
154C2×C4×Q8—44no—
155C2×C4×Q8—44no—
156C2×C4×Q8—44no—
157C2×C4×Q8—44no—
158C2×C4×Q8Q8116yescomplemented
159C2×C4×Q8C2318yes—
160C2×C4×Q8C2318yes—
161C2×C4×Q8C2318yes—
162C2×C4×Q8C2318yes—
163C2×C4×Q8C2318yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2312yes—
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221#400C23116yes—
222#400C23116yes—
223#400C23116yes—
224#400C23116yes—
225#400C23116yes—
226#400C23116yes—
227#400C23116yes—
228#400C23116yes—
229#398C23116yes—
230#398C23116yes—
231#398C23116yes—
232#398C23116yes—
233#398C23116yes—
234#398C23116yes—
235#398C23116yes—
236#398C23116yes—
237#398C23116yes—
238#398C2318yes—
239#398C23116yes—
240#398C2318yes—
241#398C23116yes—
242#398C23116yes—
243#398C2318yes—
244#398C2318yes—
245#398C23116yes—
246#395C23116yes—
247#395C23116yes—
248#395C23116yes—
249#395C2318yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#391C2318yes—
254#391C2318yes—
255#391C2318yes—
256#391C2318yes—
257#391C23116yes—
258#389C2318yes—
259#389C2318yes—
260#389C2318yes—
261#389C2318yes—
262#389C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C23116yes—
266#389C2318yes—
267#389C2318yes—
268#389C2318yes—
269#389C23116yes—
270#389C23116yes—
271#389C23116yes—
272#389C23116yes—
273#389C23116yes—
274#389C23116yes—
275#389C23116yes—
276#389C2318yes—
277#389C2318yes—
278#389C23116yes—
279#389C23116yes—
280#389C23116yes—
281#389C23116yes—
282#387C23116yes—
283#387C23116yes—
284#387C23116yes—
285#387C23116yes—
286#387C23116yes—
287#387C23116yes—
288#387C23116yes—
289#387C23116yes—
290#387C23116yes—
291#387C23116yes—
292#387C23116yes—
293#387C23116yes—
294#384C2318yes—
295#384C23116yes—
296#384C2318yes—
297#384C23116yes—
298#383C23116yes—
299#383C23116yes—
300#382C2318yes—
301#382C2318yes—
302#382C23116yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2318yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C2318yes—
307C4×C4⋊C4C23116yes—
308C4×C4⋊C4C2318yes—
309C4×C4⋊C4C2318yes—
310C4×C4⋊C4C2318yes—
311#376C2318yes—
312#376C23116yes—
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2312yes—
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2312yes—
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2312yes—
326C2×#95C2312yes—
327C2×#95C2312yes—
328C2×#95C2312yes—
329C2×#95C2312yes—
330C2×#95C2311yescharacteristic
331C2×#95C2312yes—
332C2×#95C2312yes—
333C2×#95C2311yescharacteristic
334C2×#95C2312yes—
335C2×#95C2312yes—
336C2×#95C2312yes—
337C2×#95C2312yes—
338C2×#95C2312yes—
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2312yes—
342C2×#95C2312yes—
343C2×#95C2312yes—
344C2×#95C2312yes—
345C2×#95C2312yes—
346C2×#95C2312yes—
347C2×#95C2312yes—
348C2×#95C2312yes—
349C2×#95C2312yes—
350C2×#95C2312yes—
351C2×#95C2312yes—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—24no—
355C22×Q8—42no—
356C22×Q8—42no—
357C22×Q8—42no—
358C22×Q8—42no—
359C22×Q8—42no—
360C22×Q8C2×Q818yes—
361C22×Q8C2414yes—
362C22×Q8C2414yes—
363C22×Q8C2414yes—
364C23×C4C2411yescharacteristic
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2412yes—
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2412yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387#125—416no—
388#125—416no—
389C4×Q8—416no—
390C4×Q8—416no—
391C4×Q8—416no—
392C4×Q8—416no—
393C4×Q8C2×Q8164yescomplemented
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—42no—
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—44no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4—44no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—44no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4C2×Q8116yes—
437C2×C4⋊C4C2×Q818yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2418yes—
482C2×C42—24no—
483C2×C42—24no—
484C2×C42—24no—
485C2×C42—24no—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—44no—
489C2×C42—44no—
490C2×C42—44no—
491C2×C42—44no—
492C2×C42—44no—
493C2×C42C2×Q8116yes—
494C2×C42C2×Q818yes—
495C2×C42C2414yes—
496C2×C42C2414yes—
497C2×C42C2414yes—
498C2×C42C2414yes—
499C2×C42C2414yes—
500C2×C42C2414yes—
501C2×C42C2418yes—
502C2×C42C2418yes—
503C2×C42C2418yes—
504C2×C42C2418yes—
505C2×C42C2418yes—
506C2×C42C2414yes—
507C2×C42C2418yes—
508#95C2414yes—
509#95C2414yes—
510#95C2418yes—
511#95C2414yes—
512#95C2418yes—
513#95C2418yes—
514#95C2414yes—
515#95C2414yes—
516#95C2418yes—
517#95C2414yes—
518#95C2418yes—
519#95C2418yes—
520#95C2414yes—
521#95C2414yes—
522#95C2414yes—
523#95C2414yes—
524#95C2418yes—
525#95C2418yes—
526#95C2414yes—
527#95C2414yes—
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—
545#95C2418yes—
546#95C2418yes—
547C24C2511yescharacteristic
548C2×Q8—232no—
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—416no—
558C2×Q8—416no—
559C2×Q8C22×Q8116yes—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
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—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—24no—
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×C4C22×Q814yes—
622C22×C4C22×Q814yes—
623C22×C4C22×Q818yes—
624C22×C4C22×Q818yes—
625C22×C4C22×Q814yes—
626C22×C4H(5,𝔽2)14yes—
627C22×C42−1+414yes—
628C22×C42−1+414yes—
629C22×C4C2512yes—
630C22×C4C2514yes—
631C22×C4C2512yes—
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C22×C4C2512yes—
637C22×C4C2512yes—
638C22×C4C2514yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2512yes—
642C22×C4C2512yes—
643C22×C4C2512yes—
644C22×C4C2514yes—
645C22×C4C2514yes—
646C22×C4C2512yes—
647C22×C4C2514yes—
648C22×C4C2512yes—
649C22×C4C2514yes—
650C22×C4C2512yes—
651C22×C4C2512yes—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—216no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—44no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—44no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—48no—
681C4⋊C4—48no—
682C4⋊C4—44no—
683C4⋊C4—48no—
684C4⋊C4—48no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4C22×Q8132yes—
695C4⋊C4C22×Q8116yes—
696C42—28no—
697C42—28no—
698C42—28no—
699C42—28no—
700C42—28no—
701C42—28no—
702C42—48no—
703C42—48no—
704C42—48no—
705C42—48no—
706C42—48no—
707C42C22×Q8132yes—
708C42C22×Q8116yes—
709C23C23×Q812yes—
710C23C2×H(5,𝔽2)12yes—
711C23C2×2−1+412yes—
712C23C2×2−1+412yes—
713C23#58512yes—
714C23#58512yes—
715C23#58512yes—
716C23C2611yescharacteristic
717Q8—232no—
718Q8—416no—
719Q8—416no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—216no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—216no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—48no—
789C2×C4—48no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—48no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—44no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4#544116yes—
804C2×C4C23×Q814yes—
805C2×C4C23×Q814yes—
806C2×C4C23×Q818yes—
807C2×C4C23×Q818yes—
808C2×C4C23×Q814yes—
809C2×C4C2×H(5,𝔽2)14yes—
810C2×C4C2×2−1+414yes—
811C2×C4C2×2−1+414yes—
812C22C2×#54414yes—
813C22#350214yes—
814C22#350414yes—
815C22#353914yes—
816C22#354114yes—
817C22#355514yes—
818C22#355714yes—
819C22C24×Q811yescharacteristic
820C22C22×H(5,𝔽2)11yescharacteristic
821C22C22×2−1+411yescharacteristic
822C22C22×2−1+411yescharacteristic
823C22C2×#58511yescharacteristic
824C22C2×#58511yescharacteristic
825C22C2×#58511yescharacteristic
826C4—24no—
827C4—24no—
828C4—24no—
829C4—28no—
830C4—28no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—44no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—44no—
845C4—44no—
846C4—42no—
847C4—44no—
848C4C2×#54418yes—
849C2#4281918yesdirect product factor
850C2C22×#54411yescharacteristic
851C2C2×#354111yescharacteristic
852C2C2×#353911yescharacteristic
853C2C2×#355711yescharacteristic
854C2C2×#355511yescharacteristic
855C2C2×#350211yescharacteristic
856C2C2×#350411yescharacteristic
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. #42819C2direct (N × H)
158. C2×C4×Q8Q8semidirect
393. C4×Q8C2×Q8semidirect
849. C2#42819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28052
C2×#28022
C2×#27922
C2×#27912
#428192
C2×#28432
C2×#25822
C2×#25522
C2×#25812
C2×#25702
C2×#25842
C2×#26062
C2×#25092
C2×#25072
C2×#24532
C2×#26472
C2×#26662
C2×#23992
C2×#23562
C2×Q8×C4⋊C42
C2×#23202