Finite Group Databasebeta

← C2×#61875 #10578273

Subgroups — C2×#61875 #10578273

Order 512.

5886 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic, complemented
2C2×#3555C211yesmaximal, characteristic
3#61875C2132yesmaximal, direct product factor
4C2×#3390C212yesmaximal, complemented
5C2×#3388C212yesmaximal, complemented
6C2×#3387C212yesmaximal, complemented
7C2×#3387C212yesmaximal, complemented
8C2×#3377C212yesmaximal, complemented
9C2×#3377C212yesmaximal, complemented
10C2×#3369C212yesmaximal, complemented
11C2×#3374C212yesmaximal, complemented
12C2×#3244C212yesmaximal
13C2×#3242C212yesmaximal, complemented
14C2×#3240C211yesmaximal, characteristic
15C2×#3237C211yesmaximal, characteristic, complemented
16C2×#3127C212yesmaximal, complemented
17C2×#3121C212yesmaximal
18C2×#3113C211yesmaximal, characteristic, complemented
19C2×#3117C211yesmaximal, characteristic
20C2×#2987C211yesmaximal, characteristic, complemented
21#3555—28no—
22#3555C22116yes—
23C2×#563—22no—
24#3502—28no—
25#3502C22116yescomplemented
26C2×Q82—21no—
27C2×Q82C2211yescharacteristic
28C2×Q82C2212yes—
29C2×#557—21no—
30C2×#557—22no—
31C2×#557C2211yescharacteristic
32C2×#557C2212yes—
33C2×#557C2212yes—
34C2×#557C2212yes—
35C2×#557C2212yes—
36C2×#556—21no—
37C2×#556C2212yes—
38C2×#556C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#552—21no—
41C2×#544—21no—
42C2×#544—21no—
43C2×#544—21no—
44C2×#544C2212yes—
45C2×#542C2212yes—
46C2×#541—21no—
47C2×#541—22no—
48C2×#541C2212yes—
49C2×#533—22no—
50C2×#533C2211yescharacteristic
51C2×#533C2211yescharacteristic
52C2×#533C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C2×#519C2212yes—
55C22×C4×Q8C2211yescharacteristic
56#3390C22132yescomplemented
57#3388C22132yescomplemented
58#3387C22132yescomplemented
59#3387C22132yescomplemented
60#3377C22132yescomplemented
61#3377C22132yescomplemented
62#3374C22132yescomplemented
63#3369C22132yescomplemented
64#3244C22132yes—
65#3242C22132yescomplemented
66#3240C22116yes—
67#3237C22116yescomplemented
68C2×#501C2211yescharacteristic
69C2×#501C2212yes—
70C2×#501C2212yes—
71C2×#501C2212yes—
72C2×#501C2211yescharacteristic
73C2×#499C2212yes—
74C2×#498C2212yes—
75C2×#491C2212yes—
76C2×#491C2212yes—
77C2×#489C2211yescharacteristic
78C2×#489C2212yes—
79C2×#489C2211yescharacteristic
80C2×#488C2212yes—
81C2×#487C2212yes—
82#3127C22132yescomplemented
83#3121C22132yes—
84#3117C22116yes—
85#3113C22116yescomplemented
86C2×#484C2211yescharacteristic
87C2×#481C2211yescharacteristic
88C2×#485C2212yes—
89C2×#485C2212yes—
90C2×#485C2212yes—
91C2×#482C2212yes—
92C2×#483C2212yes—
93C2×#479C2212yes—
94C2×#479C2212yes—
95C2×#479C2212yes—
96C2×#479C2212yes—
97C2×#479C2212yes—
98C2×#479C2212yes—
99C2×#479C2212yes—
100C2×#477C2212yes—
101C2×#477C2212yes—
102C2×#477C2212yes—
103C2×#475C2212yes—
104C2×#475C2212yes—
105C2×#475C2212yes—
106C2×#475C2212yes—
107C2×#475C2212yes—
108C2×#478C2212yes—
109C2×#478C2212yes—
110C2×#476C2212yes—
111C2×#464C2212yes—
112C2×#464C2212yes—
113C2×#464C2212yes—
114C2×#462C2212yes—
115C2×#462C2212yes—
116C2×#462C2212yes—
117C2×#451C2211yescharacteristic
118C2×#451C2212yes—
119C2×#448C2211yescharacteristic
120#2987C22116yescomplemented
121C2×#446C2212yes—
122C2×#446C2212yes—
123C2×#446C2212yes—
124C2×#446C2212yes—
125C2×#441C2212yes—
126C2×#441C2212yes—
127C2×#441C2212yes—
128C2×#441C2212yes—
129C2×#441C2212yes—
130C2×#441C2212yes—
131C2×#440C2212yes—
132C2×#440C2212yes—
133C2×C4×Q16C2212yes—
134C2×C4×Q16C2212yes—
135C2×C4×Q16C2212yes—
136C2×C4×SD16C2212yes—
137C2×#433C2212yes—
138C2×#433C2212yes—
139C2×#432C2211yescharacteristic
140C2×#432C2211yescharacteristic
141C23×Q8C2311yescharacteristic
142C22×Q16C2312yes—
143C22×Q16C2312yes—
144C22×Q16C2312yes—
145C22×SD16C2312yes—
146#563—232no—
147Q82—216no—
148Q82—28no—
149Q82—24no—
150Q82C23116yes—
151Q82C2318yes—
152#557—216no—
153#557—232no—
154#557—28no—
155#557—28no—
156#557—28no—
157#557—24no—
158#557—28no—
159#557C2318yes—
160#557C23116yes—
161#557C23116yes—
162#557C23116yes—
163#557C23116yes—
164#556—216no—
165#556—28no—
166#556—24no—
167#556C23116yes—
168#556C2318yes—
169#554—24no—
170#554C2318yes—
171#552—216no—
172#544—216no—
173#544—216no—
174#544—216no—
175#544—28no—
176#544C23116yes—
177#542—28no—
178#542C23116yes—
179#541—216no—
180#541—232no—
181#541—28no—
182#541C23116yes—
183#533—232no—
184#533—24no—
185#533—24no—
186#533D418yes—
187#533C2318yes—
188#533C2318yes—
189#533C2318yes—
190C2×C4⋊Q8—22no—
191C2×C4⋊Q8—22no—
192C2×C4⋊Q8—22no—
193C2×C4⋊Q8—22no—
194C2×C4⋊Q8—22no—
195C2×C4⋊Q8—22no—
196C2×C4⋊Q8—21no—
197C2×C4⋊Q8—22no—
198C2×C4⋊Q8—22no—
199C2×C4⋊Q8—22no—
200C2×C4⋊Q8D411yescharacteristic
201C2×C4⋊Q8D411yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210#529—24no—
211#529C2318yes—
212C2×#126—22no—
213C2×#126—22no—
214C2×#126—22no—
215C2×#126—22no—
216C2×#126—22no—
217C2×#126—22no—
218C2×#126—21no—
219C2×#125—22no—
220C2×#125—22no—
221C2×#125—22no—
222C2×#125—22no—
223C2×#125—22no—
224C2×#125—22no—
225C2×#125—22no—
226C2×#125—21no—
227C2×#125—22no—
228C2×#125—22no—
229C2×#125—22no—
230C2×#125—22no—
231C2×#125—22no—
232C2×#125—21no—
233C2×#125D412yes—
234C2×#125C2312yes—
235C2×#125C2312yes—
236C2×#125C2312yes—
237C2×#125C2312yes—
238C2×#125C2311yescharacteristic
239C2×#124—22no—
240C2×#124C2312yes—
241C2×#124C2311yescharacteristic
242C2×#123—21no—
243C2×#123—22no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—22no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—22no—
251C2×C22⋊Q8—22no—
252C2×C22⋊Q8—22no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8D412yes—
255C2×C22⋊Q8D411yescharacteristic
256C2×C22⋊Q8D411yescharacteristic
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×#121C2311yescharacteristic
260#519—28no—
261#519C23116yes—
262C2×C4×Q8—22no—
263C2×C4×Q8—21no—
264C2×C4×Q8—21no—
265C2×C4×Q8—22no—
266C2×C4×Q8—22no—
267C2×C4×Q8—22no—
268C2×C4×Q8—22no—
269C2×C4×Q8—22no—
270C2×C4×Q8—22no—
271C2×C4×Q8—21no—
272C2×C4×Q8—21no—
273C2×C4×Q8—24no—
274C2×C4×Q8—21no—
275C2×C4×Q8—21no—
276C2×C4×Q8—21no—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2318yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×D4—21no—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×#117—21no—
296C2×#117—22no—
297C2×#117—21no—
298C2×#117—22no—
299C2×#117—22no—
300C2×#117—21no—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C22×C4⋊C4—21no—
304C22×C4⋊C4—21no—
305C22×C4⋊C4C2311yescharacteristic
306C22×C42—21no—
307C22×C42C2311yescharacteristic
308#501C2318yes—
309#501C23116yes—
310#501C23116yes—
311#501C23116yes—
312#501C2318yes—
313#499C23116yes—
314#498C23116yes—
315#491C23116yes—
316#491C23116yes—
317#489C2318yes—
318#489C23116yes—
319#489C2318yes—
320#488C23116yes—
321#487C23116yes—
322#485C23116yes—
323#485C23116yes—
324#485C23116yes—
325#484C2318yes—
326#483C23116yes—
327#482C23116yes—
328#481C2318yes—
329#479C23116yes—
330#479C23116yes—
331#479C23116yes—
332#479C23116yes—
333#479C23116yes—
334#479C23116yes—
335#479C23116yes—
336#478C23116yes—
337#478C23116yes—
338#477C23116yes—
339#477C23116yes—
340#477C23116yes—
341#476C23116yes—
342#475C23116yes—
343#475C23116yes—
344#475C23116yes—
345#475C23116yes—
346#475C23116yes—
347#464C23116yes—
348#464C23116yes—
349#464C23116yes—
350#462C23116yes—
351#462C23116yes—
352#462C23116yes—
353#451C23116yes—
354#451C2318yes—
355#448C2318yes—
356#446C23116yes—
357#446C23116yes—
358#446C23116yes—
359#446C23116yes—
360#441C23116yes—
361#441C23116yes—
362#441C23116yes—
363#441C23116yes—
364#441C23116yes—
365#441C23116yes—
366#440C23116yes—
367#440C23116yes—
368C4×Q16C23116yes—
369C4×Q16C23116yes—
370C4×Q16C23116yes—
371C4×SD16C23116yes—
372#433C23116yes—
373#433C23116yes—
374#432C2318yes—
375#432C2318yes—
376C2×#107C2312yes—
377C2×#107C2312yes—
378C2×#107C2312yes—
379C2×#107C2312yes—
380C2×#107C2312yes—
381C2×#106C2312yes—
382C2×#106C2312yes—
383C2×#106C2312yes—
384C2×#106C2312yes—
385C2×#106C2312yes—
386C2×#106C2312yes—
387C2×#106C2312yes—
388C2×C4⋊C8C2312yes—
389C2×C4⋊C8C2312yes—
390C2×C4⋊C8C2312yes—
391C2×C4⋊C8C2312yes—
392C2×C4⋊C8C2312yes—
393C2×C4⋊C8C2312yes—
394C2×#103C2312yes—
395C2×#103C2312yes—
396C2×#103C2312yes—
397C2×#103C2312yes—
398C2×#103C2312yes—
399C2×#103C2312yes—
400C2×#103C2312yes—
401C2×#103C2312yes—
402C2×#103C2312yes—
403C2×#103C2312yes—
404C2×#103C2312yes—
405C2×#103C2312yes—
406C2×#103C2312yes—
407C2×#102C2312yes—
408C2×#102C2312yes—
409C2×#102C2312yes—
410C2×C22⋊C8C2312yes—
411C2×C22⋊C8C2311yescharacteristic
412C2×C22⋊C8C2311yescharacteristic
413C2×#97C2311yescharacteristic
414C2×#97C2311yescharacteristic
415C2×#97C2312yes—
416C2×#97C2312yes—
417C2×#97C2312yes—
418C2×C4×C8C2312yes—
419C2×C4×C8C2312yes—
420C22×Q8—28no—
421C22×Q8—21no—
422C22×Q8—22no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—22no—
426C22×Q8—21no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8C2×D412yes—
430C22×Q8C2×D411yescharacteristic
431C22×Q8C2×D411yescharacteristic
432C22×Q8C2412yes—
433C22×Q8C2411yescharacteristic
434C22×Q8C2414yes—
435C22×Q8C2412yes—
436C22×D4—21no—
437C22×D4C2411yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—22no—
442C23×C4C2×D411yescharacteristic
443C23×C4C2×D411yescharacteristic
444C23×C4C2411yescharacteristic
445C2×Q16—28no—
446C2×Q16—28no—
447C2×Q16—28no—
448C2×Q16C2418yes—
449C2×Q16C2418yes—
450C2×Q16C2418yes—
451C2×SD16—28no—
452C2×SD16C2418yes—
453C22×C8C2412yes—
454C22×C8C2412yes—
455C22×C8C2412yes—
456C22×C8C2412yes—
457C4⋊Q8—216no—
458C4⋊Q8—216no—
459C4⋊Q8—216no—
460C4⋊Q8—216no—
461C4⋊Q8—216no—
462C4⋊Q8—216no—
463C4⋊Q8—28no—
464C4⋊Q8—216no—
465C4⋊Q8—216no—
466C4⋊Q8—216no—
467C4⋊Q8—22no—
468C4⋊Q8—22no—
469C4⋊Q8—22no—
470C4⋊Q8—22no—
471C4⋊Q8—24no—
472C4⋊Q8—24no—
473C4⋊Q8—24no—
474C4⋊Q8—24no—
475C4⋊Q8C2×D418yes—
476C4⋊Q8C2×D418yes—
477C4⋊Q8C2414yes—
478C4⋊Q8C2418yes—
479C4⋊Q8C2414yes—
480C4⋊Q8C2414yes—
481C4⋊Q8C2414yes—
482C4⋊Q8C2418yes—
483C4⋊Q8C2418yes—
484C4⋊Q8C2418yes—
485#126—216no—
486#126—216no—
487#126—216no—
488#126—216no—
489#126—216no—
490#126—216no—
491#126—28no—
492#125—216no—
493#125—216no—
494#125—216no—
495#125—216no—
496#125—216no—
497#125—216no—
498#125—216no—
499#125—28no—
500#125—216no—
501#125—216no—
502#125—216no—
503#125—216no—
504#125—216no—
505#125—28no—
506#125—22no—
507#125—24no—
508#125—24no—
509#125—24no—
510#125—24no—
511#125C2×D4116yes—
512#125C2414yes—
513#125C2418yes—
514#125C2418yes—
515#125C2418yes—
516#125C2418yes—
517#124—216no—
518#124—22no—
519#124—24no—
520#124C2414yes—
521#124C2418yes—
522#123—28no—
523#123—216no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—28no—
528C22⋊Q8—28no—
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—24no—
532C22⋊Q8—216no—
533C22⋊Q8—216no—
534C22⋊Q8—216no—
535C22⋊Q8—216no—
536C22⋊Q8C2×D4116yes—
537C22⋊Q8C2×D418yes—
538C22⋊Q8C2×D418yes—
539C22⋊Q8C2414yes—
540C22⋊Q8C2418yes—
541#121—22no—
542#121C2414yes—
543C4×Q8—216no—
544C4×Q8—28no—
545C4×Q8—28no—
546C4×Q8—216no—
547C4×Q8—216no—
548C4×Q8—216no—
549C4×Q8—216no—
550C4×Q8—216no—
551C4×Q8—216no—
552C4×Q8—24no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—24no—
556C4×Q8—28no—
557C4×Q8—28no—
558C4×Q8—28no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—24no—
562C4×Q8—24no—
563C4×Q8—22no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8C2×D414yes—
569C4×Q8C2×D414yes—
570C4×Q8C2×D418yes—
571C4×Q8C2418yes—
572C4×Q8C2418yes—
573C4×Q8C2418yes—
574C4×Q8C2418yes—
575C4×Q8C2418yes—
576C4×Q8C2418yes—
577C4×Q8C2414yes—
578C4×Q8C2418yes—
579C4×Q8C2418yes—
580C4×Q8C2418yes—
581C4×Q8C2418yes—
582C4×Q8C2414yes—
583C4×Q8C2418yes—
584C4×Q8C2414yes—
585C4×D4—28no—
586C4×D4—22no—
587C4×D4—24no—
588C4×D4C2414yes—
589C4×D4C2418yes—
590#117—28no—
591#117—24no—
592#117—216no—
593#117—28no—
594#117—216no—
595#117—216no—
596#117—28no—
597#117C2×D418yes—
598#117C2418yes—
599#117C2418yes—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—28no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—28no—
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D412yes—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D412yes—
641C2×C4⋊C4C2×D412yes—
642C2×C4⋊C4C2×D412yes—
643C2×C4⋊C4C2×D412yes—
644C2×C4⋊C4C2×D412yes—
645C2×C4⋊C4C2×D412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4C2×D412yes—
664C2×C22⋊C4C2×D412yes—
665C2×C42—22no—
666C2×C42—21no—
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—28no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D414yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2414yes—
686#107C2418yes—
687#107C2418yes—
688#107C2418yes—
689#107C2418yes—
690#107C2418yes—
691#106C2418yes—
692#106C2418yes—
693#106C2418yes—
694#106C2418yes—
695#106C2418yes—
696#106C2418yes—
697#106C2418yes—
698C4⋊C8C2418yes—
699C4⋊C8C2418yes—
700C4⋊C8C2418yes—
701C4⋊C8C2418yes—
702C4⋊C8C2418yes—
703C4⋊C8C2418yes—
704#103C2418yes—
705#103C2418yes—
706#103C2418yes—
707#103C2418yes—
708#103C2418yes—
709#103C2418yes—
710#103C2418yes—
711#103C2418yes—
712#103C2418yes—
713#103C2418yes—
714#103C2418yes—
715#103C2418yes—
716#103C2418yes—
717#102C2418yes—
718#102C2418yes—
719#102C2418yes—
720C22⋊C8C2414yes—
721C22⋊C8C2414yes—
722C22⋊C8C2418yes—
723#97C2418yes—
724#97C2414yes—
725#97C2414yes—
726#97C2418yes—
727#97C2418yes—
728C4×C8C2418yes—
729C4×C8C2418yes—
730C24—21no—
731C24C22×D411yescharacteristic
732C2×Q8—216no—
733C2×Q8—28no—
734C2×Q8—216no—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—21no—
738C2×Q8—22no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—28no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—82no—
754C2×Q8—82no—
755C2×Q8—84no—
756C2×Q8—84no—
757C2×Q8—84no—
758C2×Q8C22×D418yes—
759C2×Q8C22×D414yes—
760C2×Q8C22×D414yes—
761C2×Q82−1+418yes—
762C2×Q8C2514yes—
763C2×Q8C2512yes—
764C2×Q8C2514yes—
765C2×D4—24no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—82no—
769C2×D4C2512yes—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—84no—
789C22×C4—82no—
790C22×C4C22×D412yes—
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D412yes—
796C22×C4C22×D412yes—
797C22×C4C22×D412yes—
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D412yes—
800C22×C4C22×D414yes—
801C22×C4C22×D414yes—
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804Q16—216no—
805Q16—216no—
806Q16—216no—
807SD16—216no—
808C2×C8—24no—
809C2×C8—24no—
810C2×C8—24no—
811C2×C8—24no—
812C2×C8C2514yes—
813C2×C8C2514yes—
814C2×C8C2514yes—
815C2×C8C2514yes—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—21no—
854C4⋊C4—22no—
855C4⋊C4—21no—
856C4⋊C4C22×D414yes—
857C4⋊C4C22×D418yes—
858C4⋊C4C22×D414yes—
859C4⋊C4C22×D418yes—
860C4⋊C4C22×D418yes—
861C4⋊C4C22×D418yes—
862C4⋊C4C22×D418yes—
863C4⋊C4C22×D418yes—
864C4⋊C4C22×D418yes—
865C4⋊C4C2514yes—
866C4⋊C4C2514yes—
867C4⋊C4C2514yes—
868C4⋊C4C2514yes—
869C4⋊C4C2512yes—
870C4⋊C4C2512yes—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—24no—
880C22⋊C4—28no—
881C22⋊C4C22×D418yes—
882C22⋊C4C22×D418yes—
883C42—28no—
884C42—28no—
885C42—28no—
886C42—24no—
887C42—28no—
888C42—28no—
889C42—28no—
890C42—28no—
891C42—28no—
892C42—28no—
893C42—28no—
894C42—28no—
895C42C22×D414yes—
896C42C22×D412yes—
897C42C22×D414yes—
898C42C22×D412yes—
899C42C22×D414yes—
900C42C22×D414yes—
901C42C2514yes—
902C42C2514yes—
903C42C2512yes—
904C42C2512yes—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23C23×D412yes—
913C23C23×D411yescharacteristic
914Q8—216no—
915Q8—24no—
916Q8—28no—
917Q8—24no—
918Q8—24no—
919Q8—24no—
920Q8—44no—
921Q8—44no—
922Q8—48no—
923Q8—48no—
924Q8—42no—
925Q8—44no—
926Q8—84no—
927Q8—84no—
928Q8—88no—
929Q8—88no—
930Q8—88no—
931Q8C2×2−1+418yes—
932D4—24no—
933D4—42no—
934D4—84no—
935C2×C4—216no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—48no—
960C2×C4—42no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—42no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—42no—
968C2×C4—88no—
969C2×C4—84no—
970C2×C4C23×D412yes—
971C2×C4C23×D412yes—
972C2×C4C23×D412yes—
973C2×C4C23×D412yes—
974C2×C4C23×D414yes—
975C2×C4C23×D414yes—
976C2×C4C23×D414yes—
977C2×C4C23×D412yes—
978C2×C4C23×D414yes—
979C2×C4C23×D411yescharacteristic
980C2×C4C2×2−1+414yes—
981C2×C4C2611yescharacteristic
982C8—24no—
983C8—24no—
984C8—24no—
985C8—24no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—44no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—84no—
994C22#348612yes—
995C22#358612yes—
996C22#358612yes—
997C22C24×D411yescharacteristic
998C4—28no—
999C4—22no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—24no—
1005C4—24no—
1006C4—24no—
1007C4—24no—
1008C4—44no—
1009C4—42no—
1010C4—42no—
1011C4—44no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4—44no—
1016C4#348612yes—
1017C4C22×2−1+412yes—
1018C2—42no—
1019C2—82no—
1020C2#6187514yesdirect product factor
1021C2C2×#348611yescharacteristic
1022C2C2×#358611yescharacteristic
1023C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#121C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3502C2semidirect
3. #61875C2direct (N × H)
4. C2×#3390C2semidirect
5. C2×#3388C2semidirect
6. C2×#3387C2semidirect
7. C2×#3387C2semidirect
8. C2×#3377C2semidirect
9. C2×#3377C2semidirect
10. C2×#3369C2semidirect
11. C2×#3374C2semidirect
13. C2×#3242C2semidirect
15. C2×#3237C2semidirect
16. C2×#3127C2semidirect
18. C2×#3113C2semidirect
20. C2×#2987C2semidirect
25. #3502C22semidirect
56. #3390C22semidirect
57. #3388C22semidirect
58. #3387C22semidirect
59. #3387C22semidirect
60. #3377C22semidirect
61. #3377C22semidirect
62. #3374C22semidirect
63. #3369C22semidirect
65. #3242C22semidirect
67. #3237C22semidirect
82. #3127C22semidirect
85. #3113C22semidirect
120. #2987C22semidirect
1020. C2#61875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35022
C2×#35552
#618752
C2×#33902
C2×#33882
C2×#33872
C2×#33772
C2×#33692
C2×#33742
C2×#32442
C2×#32422
C2×#32402
C2×#32372
C2×#31272
C2×#31212
C2×#31132
C2×#31172
C2×#29872