Finite Group Databasebeta

← C2×#45044 #7669517

Subgroups — C2×#45044 #7669517

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2805C212yesmaximal
2C2×#2774C212yesmaximal
3C2×#2713C212yesmaximal
4C2×#2713C212yesmaximal
5#45044C2132yesmaximal, direct product factor
6C2×#2552C211yesmaximal, characteristic
7C2×#2546C212yesmaximal
8C2×#2551C211yesmaximal, characteristic
9C2×#2551C211yesmaximal, characteristic
10C2×#2551C211yesmaximal, characteristic
11C2×#2550C212yesmaximal
12C2×#2585C212yesmaximal
13C2×#2509C211yesmaximal, characteristic
14C2×#2508C211yesmaximal, characteristic
15C2×#2507C211yesmaximal, characteristic
16C2×#2506C211yesmaximal, characteristic
17C2×#2462C212yesmaximal
18C2×#2402C211yesmaximal, characteristic
19C2×#2370C211yesmaximal, characteristic
20C2×#2370C211yesmaximal, characteristic
21C2×#2369C211yesmaximal, characteristic
22C2×#2365C211yesmaximal, characteristic
23C2×#2331C211yesmaximal, characteristic
24C2×#2330C211yesmaximal, characteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×C4⋊Q8C2212yes—
29C22×C4⋊Q8C2212yes—
30C22×C4⋊Q8C2212yes—
31C22×#125C2212yes—
32C22×#125C2212yes—
33C22×#125C2211yescharacteristic
34C22×C4×Q8C2212yes—
35#2805C22132yes—
36#2774C22132yes—
37#2713C22132yes—
38#2713C22132yes—
39#2585C22132yes—
40#2552C22116yes—
41#2551C22116yes—
42#2551C22116yes—
43#2551C22116yes—
44#2550C22132yes—
45#2546C22132yes—
46#2509C22116yes—
47#2508C22116yes—
48#2507C22116yes—
49#2506C22116yes—
50#2462C22132yes—
51#2402C22116yes—
52C2×#400C2212yes—
53C2×#400C2211yescharacteristic
54C2×#400C2212yes—
55C2×#400C2212yes—
56C2×#400C2211yescharacteristic
57C2×#400C2211yescharacteristic
58C2×#400C2212yes—
59C2×#400C2211yescharacteristic
60C2×#398C2211yescharacteristic
61C2×#398C2212yes—
62C2×#398C2212yes—
63C2×#398C2211yescharacteristic
64C2×#398C2211yescharacteristic
65C2×#398C2212yes—
66C2×#398C2212yes—
67C2×#398C2212yes—
68C2×#398C2211yescharacteristic
69C2×#398C2212yes—
70C2×#395C2212yes—
71C2×#395C2212yes—
72C2×#395C2212yes—
73C2×#395C2212yes—
74C2×#395C2212yes—
75C2×#395C2212yes—
76#2370C22116yes—
77#2370C22116yes—
78#2369C22116yes—
79#2365C22116yes—
80#2331C22116yes—
81#2330C22116yes—
82C2×#391C2212yes—
83C2×#391C2212yes—
84C2×#391C2212yes—
85C2×#391C2212yes—
86C2×#391C2212yes—
87C2×#389C2212yes—
88C2×#389C2212yes—
89C2×#389C2212yes—
90C2×#389C2212yes—
91C2×#389C2211yescharacteristic
92C2×#389C2211yescharacteristic
93C2×#389C2212yes—
94C2×#389C2211yescharacteristic
95C2×#389C2211yescharacteristic
96C2×#389C2212yes—
97C2×#389C2212yes—
98C2×#389C2212yes—
99C2×#389C2212yes—
100C2×#389C2211yescharacteristic
101C2×#389C2211yescharacteristic
102C2×#389C2212yes—
103C2×#389C2211yescharacteristic
104C2×#389C2211yescharacteristic
105C2×#389C2212yes—
106C2×#389C2211yescharacteristic
107C2×#389C2211yescharacteristic
108C2×#389C2211yescharacteristic
109C2×#389C2211yescharacteristic
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×#387C2212yes—
123C2×#387C2212yes—
124C2×#384C2211yescharacteristic
125C2×#384C2211yescharacteristic
126C2×#384C2211yescharacteristic
127C2×#382C2211yescharacteristic
128C2×#382C2212yes—
129C2×C4×C4⋊C4C2212yes—
130C2×C4×C4⋊C4C2212yes—
131C2×C4×C4⋊C4C2211yescharacteristic
132C2×C4×C4⋊C4C2211yescharacteristic
133C2×C4×C4⋊C4C2211yescharacteristic
134C2×C4×C4⋊C4C2211yescharacteristic
135C2×C4×C4⋊C4C2212yes—
136C2×C4×C4⋊C4C2211yescharacteristic
137C2×C4×C4⋊C4C2211yescharacteristic
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×Q8C2312yes—
148C23×Q8C2312yes—
149C23×Q8C2312yes—
150C2×C4⋊Q8—28no—
151C2×C4⋊Q8—28no—
152C2×C4⋊Q8—28no—
153C2×C4⋊Q8—48no—
154C2×C4⋊Q8—48no—
155C2×C4⋊Q8—48no—
156C2×C4⋊Q8C2318yes—
157C2×C4⋊Q8C2318yes—
158C2×C4⋊Q8C2318yes—
159C2×C4⋊Q8C23116yes—
160C2×C4⋊Q8C23116yes—
161C2×C4⋊Q8C23116yes—
162C2×#125—48no—
163C2×#125—48no—
164C2×#125Q8116yescomplemented
165C2×#125C23116yes—
166C2×#125C23116yes—
167C2×#125C2318yes—
168C2×C4×Q8—48no—
169C2×C4×Q8C23116yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
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⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2312yes—
226C22×C42C2312yes—
227C22×C42C2311yescharacteristic
228#400C23116yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C23116yes—
234#400C23116yes—
235#400C23116yes—
236#398C2318yes—
237#398C23116yes—
238#398C23116yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C23116yes—
243#398C23116yes—
244#398C23116yes—
245#398C23116yes—
246#395C23116yes—
247#395C23116yes—
248#395C23116yes—
249#395C23116yes—
250#395C23116yes—
251#395C23116yes—
252#391C23116yes—
253#391C23116yes—
254#391C23116yes—
255#391C23116yes—
256#391C23116yes—
257#389C23116yes—
258#389C23116yes—
259#389C23116yes—
260#389C23116yes—
261#389C2318yes—
262#389C2318yes—
263#389C23116yes—
264#389C2318yes—
265#389C2318yes—
266#389C2318yes—
267#389C23116yes—
268#389C2318yes—
269#389C23116yes—
270#389C2318yes—
271#389C2318yes—
272#389C2318yes—
273#389C2318yes—
274#389C23116yes—
275#389C2318yes—
276#389C2318yes—
277#389C23116yes—
278#389C23116yes—
279#389C23116yes—
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#387C23116yes—
293#387C23116yes—
294#384C2318yes—
295#384C2318yes—
296#384C2318yes—
297#382C2318yes—
298#382C23116yes—
299C4×C4⋊C4C23116yes—
300C4×C4⋊C4C23116yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2318yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C2318yes—
307C4×C4⋊C4C2318yes—
308C4×C4⋊C4C2318yes—
309C4×C4⋊C4C2318yes—
310C4×C4⋊C4C2318yes—
311C4×C4⋊C4C2318yes—
312C4×C4⋊C4C2318yes—
313C4×C4⋊C4C23116yes—
314C4×C4⋊C4C2318yes—
315C4×C4⋊C4C2318yes—
316#376C2318yes—
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2312yes—
326C2×#95C2312yes—
327C2×#95C2312yes—
328C2×#95C2312yes—
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2312yes—
336C2×#95C2312yes—
337C2×#95C2312yes—
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2312yes—
344C2×#95C2312yes—
345C2×#95C2312yes—
346C2×#95C2311yescharacteristic
347C2×#95C2312yes—
348C2×#95C2312yes—
349C2×#95C2312yes—
350C2×#95C2312yes—
351C2×#95C2311yescharacteristic
352C2×#95C2312yes—
353C2×#95C2312yes—
354C2×#95C2312yes—
355C22×Q8—28no—
356C22×Q8—28no—
357C22×Q8—28no—
358C22×Q8—28no—
359C22×Q8—44no—
360C22×Q8—44no—
361C22×Q8—44no—
362C22×Q8—44no—
363C22×Q8—44no—
364C22×Q8C2418yes—
365C22×Q8C2418yes—
366C22×Q8C2418yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2412yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C4⋊Q8—232no—
391C4⋊Q8—232no—
392C4⋊Q8—232no—
393C4⋊Q8—432no—
394C4⋊Q8—432no—
395C4⋊Q8—432no—
396#125—432no—
397#125—432no—
398#125C2×Q8164yescomplemented
399C4×Q8—432no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—28no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—28no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
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⋊C4—44no—
438C2×C4⋊C4C2×Q8116yes—
439C2×C4⋊C4C2×Q8116yes—
440C2×C4⋊C4C2×Q818yes—
441C2×C4⋊C4C2×Q818yes—
442C2×C4⋊C4#4118yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2414yes—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—28no—
490C2×C42—28no—
491C2×C42—24no—
492C2×C42—24no—
493C2×C42—24no—
494C2×C42—44no—
495C2×C42—44no—
496C2×C42—44no—
497C2×C42—44no—
498C2×C42—44no—
499C2×C42—44no—
500C2×C42C2×Q818yes—
501C2×C42C2418yes—
502C2×C42C2414yes—
503C2×C42C2414yes—
504C2×C42C2414yes—
505C2×C42C2414yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508C2×C42C2418yes—
509C2×C42C2418yes—
510C2×C42C2418yes—
511C2×C42C2418yes—
512C2×C42C2418yes—
513C2×C42C2418yes—
514C2×C42C2418yes—
515C2×C42C2414yes—
516#95C2414yes—
517#95C2414yes—
518#95C2414yes—
519#95C2414yes—
520#95C2414yes—
521#95C2414yes—
522#95C2414yes—
523#95C2414yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2414yes—
534#95C2414yes—
535#95C2414yes—
536#95C2414yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2414yes—
541#95C2414yes—
542#95C2414yes—
543#95C2414yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2418yes—
552#95C2418yes—
553#95C2418yes—
554C24C2511yescharacteristic
555C2×Q8—216no—
556C2×Q8—216no—
557C2×Q8—216no—
558C2×Q8—216no—
559C2×Q8—48no—
560C2×Q8—48no—
561C2×Q8—48no—
562C2×Q8—48no—
563C2×Q8—48no—
564C2×Q8—432no—
565C2×Q8—816no—
566C2×Q8—816no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—24no—
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—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4C22×Q814yes—
625C22×C4C22×Q814yes—
626C22×C4C22×Q818yes—
627C22×C4C22×Q818yes—
628C22×C4C22×Q814yes—
629C22×C4C2×#4118yes—
630C22×C4C2×#4114yes—
631C22×C4H(5,𝔽2)14yes—
632C22×C4H(5,𝔽2)14yes—
633C22×C42−1+414yes—
634C22×C42−1+414yes—
635C22×C42−1+414yes—
636C22×C4C2512yes—
637C22×C4C2512yes—
638C22×C4C2512yes—
639C22×C4C2512yes—
640C22×C4C2514yes—
641C22×C4C2514yes—
642C22×C4C2512yes—
643C22×C4C2512yes—
644C22×C4C2512yes—
645C22×C4C2512yes—
646C22×C4C2514yes—
647C22×C4C2514yes—
648C22×C4C2514yes—
649C22×C4C2514yes—
650C22×C4C2514yes—
651C22×C4C2512yes—
652C22×C4C2512yes—
653C22×C4C2514yes—
654C22×C4C2512yes—
655C22×C4C2512yes—
656C22×C4C2512yes—
657C22×C4C2512yes—
658C22×C4C2512yes—
659C4⋊C4—216no—
660C4⋊C4—216no—
661C4⋊C4—216no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—216no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—216no—
670C4⋊C4—216no—
671C4⋊C4—216no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—216no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—48no—
685C4⋊C4—48no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—48no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4C22×Q8132yes—
698C4⋊C4C22×Q8132yes—
699C4⋊C4C22×Q8116yes—
700C4⋊C4C22×Q8116yes—
701C4⋊C4C2×#41116yes—
702C42—28no—
703C42—28no—
704C42—28no—
705C42—216no—
706C42—216no—
707C42—28no—
708C42—28no—
709C42—28no—
710C42—48no—
711C42—48no—
712C42—48no—
713C42—48no—
714C42—48no—
715C42—48no—
716C42C22×Q8116yes—
717C23C23×Q812yes—
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×H(5,𝔽2)12yes—
721C23C2×2−1+412yes—
722C23C2×2−1+412yes—
723C23C2×2−1+412yes—
724C23C2611yescharacteristic
725Q8—432no—
726Q8—816no—
727Q8—816no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—216no—
747C2×C4—216no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—216no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—48no—
795C2×C4—48no—
796C2×C4—48no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—48no—
806C2×C4—44no—
807C2×C4#557116yes—
808C2×C4C23×Q814yes—
809C2×C4C23×Q814yes—
810C2×C4C23×Q818yes—
811C2×C4C23×Q818yes—
812C2×C4C23×Q814yes—
813C2×C4C22×#4118yes—
814C2×C4C22×#4114yes—
815C2×C4C2×H(5,𝔽2)14yes—
816C2×C4C2×H(5,𝔽2)14yes—
817C2×C4C2×2−1+414yes—
818C2×C4C2×2−1+414yes—
819C2×C4C2×2−1+414yes—
820C22C2×#55714yes—
821C22#350314yes—
822C22#350314yes—
823C22#351914yes—
824C22#352314yes—
825C22#354414yes—
826C22#355214yes—
827C22C24×Q811yescharacteristic
828C22C23×#4111yescharacteristic
829C22C22×H(5,𝔽2)11yescharacteristic
830C22C22×H(5,𝔽2)11yescharacteristic
831C22C22×2−1+411yescharacteristic
832C22C22×2−1+411yescharacteristic
833C22C22×2−1+411yescharacteristic
834C4—24no—
835C4—24no—
836C4—28no—
837C4—24no—
838C4—24no—
839C4—28no—
840C4—28no—
841C4—24no—
842C4—24no—
843C4—42no—
844C4—44no—
845C4—42no—
846C4—42no—
847C4—44no—
848C4—42no—
849C4—44no—
850C4—44no—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4C2×#55718yes—
857C2#4504418yesdirect product factor
858C2C22×#55711yescharacteristic
859C2C2×#355211yescharacteristic
860C2C2×#354411yescharacteristic
861C2C2×#351911yescharacteristic
862C2C2×#352311yescharacteristic
863C2C2×#350311yescharacteristic
864C2C2×#350311yescharacteristic
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. #45044C2direct (N × H)
164. C2×#125Q8semidirect
398. #125C2×Q8semidirect
857. C2#45044direct (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×#27742
C2×#27132
#450442
C2×#25522
C2×#25462
C2×#25512
C2×#25502
C2×#25852
C2×#25092
C2×#25082
C2×#25072
C2×#25062
C2×#24622
C2×#24022
C2×#23702
C2×#23692
C2×#23652
C2×#23312
C2×#23302