Finite Group Databasebeta

← C2×#61676 #10577281

Subgroups — C2×#61676 #10577281

Order 512.

7536 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3551C211yesmaximal, characteristic, complemented
3#61676C2132yesmaximal, direct product factor
4C2×#3315C212yesmaximal, complemented
5C2×#3307C212yesmaximal, complemented
6C2×#3320C212yesmaximal, complemented
7C2×#3312C212yesmaximal, complemented
8C2×#3270C212yesmaximal, complemented
9C2×#3269C212yesmaximal, complemented
10C2×#3267C212yesmaximal, complemented
11C2×#3266C212yesmaximal, complemented
12C2×#3218C212yesmaximal, complemented
13C2×#3202C211yesmaximal, characteristic, complemented
14C2×#3201C212yesmaximal, complemented
15C2×#3200C211yesmaximal, characteristic, complemented
16C2×#3111C212yesmaximal, complemented
17C2×#3013C212yesmaximal, complemented
18C2×#3011C211yesmaximal, characteristic, complemented
19C2×#3010C211yesmaximal, characteristic, complemented
20C2×#2980C211yesmaximal, characteristic, complemented
21C22×2−1+4C2211yescharacteristic
22C22×2−1+4C2211yescharacteristic, complemented
23C22×#137C2212yes—
24C22×#137C2211yescharacteristic, complemented
25C22×AGL(1,ℤ/8)C2211yescharacteristic
26C22×#135C2212yes—
27C23×Q16C2211yescharacteristic, complemented
28C23×SD16C2211yescharacteristic
29#3551—28no—
30#3551C22116yescomplemented
31C2×#563—21no—
32C2×#560—21no—
33#3499—28no—
34#3499C22116yescomplemented
35C2×#555—21no—
36C2×#553C2212yes—
37C2×#552C2212yes—
38C2×#551—21no—
39C2×D4×Q8C2212yes—
40C2×D4×Q8C2212yescomplemented
41C2×#548C2212yes—
42C2×#547—22no—
43C2×#547—22no—
44C2×#547C2212yes—
45C2×#547C2212yescomplemented
46C2×#546C2212yes—
47C2×#540—22no—
48C2×#538—22no—
49C2×#537C2212yes—
50C2×#536—21no—
51C2×#536—21no—
52C2×#536C2211yescharacteristic
53C2×#536C2211yescharacteristic
54C2×#536C2211yescharacteristic, complemented
55C2×#535C2211yescharacteristic
56C2×#532—21no—
57C2×#532C2211yescharacteristic
58C22×C4⋊Q8—21no—
59C22×C4⋊Q8C2211yescharacteristic, complemented
60C2×#529C2212yes—
61C2×C4×#41C2211yescharacteristic, complemented
62#3320C22132yescomplemented
63#3315C22132yescomplemented
64#3312C22132yescomplemented
65#3307C22132yescomplemented
66#3270C22132yescomplemented
67#3269C22132yescomplemented
68#3267C22132yescomplemented
69#3266C22132yescomplemented
70#3218C22132yescomplemented
71#3202C22116yescomplemented
72#3201C22132yescomplemented
73#3200C22116yescomplemented
74C2×#497C2212yes—
75C2×#497C2212yes—
76C2×#491C2212yescomplemented
77C2×#491C2212yescomplemented
78#3111C22132yescomplemented
79C2×#484C2212yescomplemented
80C2×#485C2212yes—
81C2×#485C2212yescomplemented
82C2×#485C2212yescomplemented
83C2×#482C2212yes—
84C2×#483C2212yescomplemented
85C2×#479C2212yescomplemented
86C2×#478C2212yescomplemented
87C2×#470C2212yes—
88C2×#470C2212yescomplemented
89C2×#468C2212yes—
90C2×#468C2212yes—
91C2×#467C2212yes—
92C2×#467C2212yescomplemented
93C2×#465C2212yes—
94C2×#465C2212yes—
95C2×#464C2212yes—
96C2×#462C2212yescomplemented
97C2×#462C2212yescomplemented
98C2×#463C2212yes—
99C2×#461C2212yes—
100C2×#461C2212yes—
101#3013C22132yescomplemented
102#3011C22116yescomplemented
103#3010C22116yescomplemented
104C2×#452C2212yes—
105C2×#452C2212yes—
106C2×#452C2212yes—
107C2×#452C2212yescomplemented
108C2×#452C2212yescomplemented
109C2×#449C2212yes—
110C2×#449C2212yes—
111C2×#449C2212yes—
112C2×#451C2212yes—
113C2×#451C2212yescomplemented
114C2×#451C2212yescomplemented
115C2×#451C2212yescomplemented
116C2×#451C2212yescomplemented
117C2×#448C2212yes—
118C2×#448C2212yes—
119C2×#448C2212yes—
120C2×#448C2212yes—
121C2×#450C2212yes—
122#2980C22116yescomplemented
123C2×#442C2212yes—
124C2×#441C2212yescomplemented
125C2×#440C2212yes—
126C2×#440C2212yescomplemented
127C2×#435C2212yes—
128C2×#435C2212yes—
129C2×#435C2212yescomplemented
130C2×#435C2212yescomplemented
131C2×#432C2212yescomplemented
132C2×#417C2212yescomplemented
133C2×#419C2211yescharacteristic
134C2×#419C2211yescharacteristic, complemented
135C2×#416C2211yescharacteristic
136C2×#416C2211yescharacteristic, complemented
137C22×#103C2212yescomplemented
138C2×#408C2211yescharacteristic
139C2×#408C2211yescharacteristic
140C2×#408C2212yescomplemented
141C2×2−1+4—24no—
142C2×2−1+4—24no—
143C2×2−1+4—44no—
144C2×2−1+4—44no—
145C2×2−1+4—44no—
146C2×2−1+4—44no—
147C2×2−1+4C2318yes—
148C2×2−1+4C2318yescomplemented
149C22×#41—21no—
150C22×#41—21no—
151C22×#41—21no—
152C22×#41—21no—
153C22×#41—22no—
154C22×#41C2311yescharacteristic
155C22×#41C2311yescharacteristic
156C22×#41C2311yescharacteristic
157C22×#41C2312yes—
158C22×#41C2312yes—
159C22×#41C2311yescharacteristic
160C22×#41C2311yescharacteristic
161C23×Q8—21no—
162C23×Q8—21no—
163C23×Q8C2311yescharacteristic
164C23×Q8C2311yescharacteristic
165C23×Q8C2312yes—
166C23×Q8C2311yescharacteristic
167C23×Q8C2311yescharacteristic
168C23×Q8C2311yescharacteristic
169C23×D4C2311yescharacteristic
170C2×#137—44no—
171C2×#137—48no—
172C2×#137C23116yes—
173C2×#137C2318yescomplemented
174C2×AGL(1,ℤ/8)—44no—
175C2×AGL(1,ℤ/8)C2318yes—
176C2×#135—48no—
177C2×#135C23116yes—
178C22×Q16—44no—
179C22×Q16C2312yes—
180C22×Q16C2312yes—
181C22×Q16C2312yes—
182C22×Q16C2312yes—
183C22×Q16C2312yes—
184C22×Q16C2318yescomplemented
185C22×SD16—44no—
186C22×SD16C2312yes—
187C22×SD16C2312yes—
188C22×SD16C2312yes—
189C22×SD16C2312yes—
190C22×SD16C2312yes—
191C22×SD16C2312yes—
192C22×SD16C2318yes—
193C22×D8C2312yes—
194C22×M16C2311yescharacteristic
195C22×M16C2311yescharacteristic
196C22×M16C2312yes—
197C23×C8C2311yescharacteristic
198C23×C8C2311yescharacteristic
199C23×C8C2312yes—
200#563—216no—
201#560—216no—
202#555—216no—
203#553—28no—
204#553C23116yes—
205#552—28no—
206#552C23116yes—
207#551—216no—
208D4×Q8—28no—
209D4×Q8—28no—
210D4×Q8C23116yes—
211D4×Q8C23116yescomplemented
212#548—28no—
213#548C23116yes—
214#547—232no—
215#547—232no—
216#547—28no—
217#547—28no—
218#547C23116yes—
219#547C23116yescomplemented
220#546—28no—
221#546C23116yes—
222#540—232no—
223#538—232no—
224#537—28no—
225#537C23116yes—
226#536—24no—
227#536—24no—
228#536—24no—
229#536—216no—
230#536—216no—
231#536C2318yes—
232#536C2318yes—
233#536C2318yescomplemented
234#535—24no—
235#535C2318yes—
236#532—216no—
237#532D418yes—
238#532C2318yes—
239C2×C4⋊Q8—21no—
240C2×C4⋊Q8—21no—
241C2×C4⋊Q8—21no—
242C2×C4⋊Q8—216no—
243C2×C4⋊Q8—22no—
244C2×C4⋊Q8—22no—
245C2×C4⋊Q8—21no—
246C2×C4⋊Q8—21no—
247C2×C4⋊Q8—24no—
248C2×C4⋊Q8D411yescharacteristic
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2318yescomplemented
252C2×#127—21no—
253C2×#127D411yescharacteristic
254#529—28no—
255#529C23116yes—
256C2×#126—22no—
257C2×#126—22no—
258C2×#126—22no—
259C2×#125—22no—
260C2×#125C2312yes—
261C2×#124—21no—
262C2×#124—21no—
263C2×#124—21no—
264C2×#124—21no—
265C2×#124—22no—
266C2×#124D411yescharacteristic
267C2×#124D411yescharacteristic
268C2×#124C2312yes—
269C2×#123—21no—
270C2×#123—21no—
271C2×#123—21no—
272C2×#123—21no—
273C2×#123—22no—
274C2×#123—22no—
275C2×#123—22no—
276C2×#123—22no—
277C2×#123—22no—
278C2×#123—22no—
279C2×#123—22no—
280C2×#123—22no—
281C2×#123—22no—
282C2×C22⋊Q8—22no—
283C2×C22⋊Q8—22no—
284C2×C22⋊Q8—22no—
285C2×C22⋊Q8—22no—
286C2×C22⋊Q8—22no—
287C2×C22⋊Q8—22no—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×#121—22no—
296C2×#121—22no—
297C2×#121—22no—
298C2×#121—22no—
299C2×#121—22no—
300C2×#121—22no—
301C2×#121—22no—
302C2×#121—22no—
303C2×#121D412yes—
304C2×#121D412yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#120—21no—
309C2×#120—21no—
310C2×#120—22no—
311C4×#41—24no—
312C4×#41C2318yescomplemented
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4—22no—
316C2×C4×D4—22no—
317C2×C4×D4—22no—
318C2×C4×D4—22no—
319C2×C4×D4—22no—
320C2×C4×D4—22no—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×#117—22no—
326C2×#117—21no—
327C2×#117—22no—
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C22×C4⋊C4—22no—
332C22×C4⋊C4—22no—
333C22×C4⋊C4—22no—
334C22×C4⋊C4C2312yes—
335C22×C22⋊C4—22no—
336C22×C42—21no—
337C22×C42C2311yescharacteristic
338#497C23116yes—
339#497C23116yes—
340#491C23116yescomplemented
341#491C23116yescomplemented
342#485C23116yes—
343#485C23116yescomplemented
344#485C23116yescomplemented
345#484C23116yescomplemented
346#483C23116yescomplemented
347#482C23116yes—
348#479C23116yescomplemented
349#478C23116yescomplemented
350#470C23116yes—
351#470C23116yescomplemented
352#468C23116yes—
353#468C23116yes—
354#467C23116yes—
355#467C23116yescomplemented
356#465C23116yes—
357#465C23116yes—
358#464C23116yes—
359#463C23116yes—
360#462C23116yescomplemented
361#462C23116yescomplemented
362#461C23116yes—
363#461C23116yes—
364#452C23116yes—
365#452C23116yes—
366#452C23116yes—
367#452C23116yescomplemented
368#452C23116yescomplemented
369#451C23116yes—
370#451C23116yescomplemented
371#451C23116yescomplemented
372#451C23116yescomplemented
373#451C23116yescomplemented
374#450C23116yes—
375#449C23116yes—
376#449C23116yes—
377#449C23116yes—
378#448C23116yes—
379#448C23116yes—
380#448C23116yes—
381#448C23116yes—
382#442C23116yes—
383#441C23116yescomplemented
384#440C23116yes—
385#440C23116yescomplemented
386#435C23116yes—
387#435C23116yes—
388#435C23116yescomplemented
389#435C23116yescomplemented
390#432C23116yescomplemented
391C2×#107C2312yes—
392C2×#107C2312yes—
393C2×#106C2312yes—
394C2×#106C2312yes—
395C2×C4⋊C8C2312yes—
396C2×C4⋊C8C2312yes—
397#419C2318yes—
398#419C2318yescomplemented
399#417C23116yescomplemented
400#416C2318yes—
401#416C2318yescomplemented
402C2×#103C2312yes—
403C2×#103C2312yes—
404C2×#103C2312yes—
405C2×#103C2312yes—
406C2×#103C2312yes—
407C2×#103C2312yes—
408C2×#103C2312yes—
409C2×#103C2312yes—
410C2×#103C2312yes—
411C2×#103C2312yes—
412C2×#103C2312yes—
413C2×#103C2312yes—
414C2×#103C23116yescomplemented
415C2×#102C2312yes—
416C2×#102C2312yes—
417C2×#102C2312yes—
418C2×#102C2312yes—
419#408C2318yes—
420#408C2318yes—
421#408C23116yescomplemented
422C2×C22⋊C8C2312yes—
423C2×C22⋊C8C2312yes—
424C2×C22⋊C8C2312yes—
425C2×C22⋊C8C2312yes—
426C2×C22⋊C8C2312yes—
427C2×C22⋊C8C2312yes—
428C2×#97C2312yes—
429C2×#97C2312yes—
430C25—21no—
4312−1+4—416no—
4322−1+4—416no—
4332−1+4—416no—
4342−1+4—416no—
4352−1+4—432no—
4362−1+4—432no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—216no—
443C2×#41—24no—
444C2×#41—22no—
445C2×#41—24no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—24no—
449C2×#41—28no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—42no—
453C2×#41—42no—
454C2×#41—42no—
455C2×#41—42no—
456C2×#41—42no—
457C2×#41—42no—
458C2×#41—44no—
459C2×#41—48no—
460C2×#41—48no—
461C2×#41—44no—
462C2×#41—44no—
463C2×#41—48no—
464C2×#41—48no—
465C2×#41—416no—
466C2×#41C2×D414yes—
467C2×#41C2×D414yes—
468C2×#41C2414yes—
469C2×#41C2414yes—
470C2×#41C2418yes—
471C2×#41C2414yes—
472C2×#41C2418yes—
473C2×#41C2414yes—
474C2×#41C2414yes—
475C22×Q8—28no—
476C22×Q8—28no—
477C22×Q8—21no—
478C22×Q8—21no—
479C22×Q8—22no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—24no—
485C22×Q8—22no—
486C22×Q8—22no—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—24no—
491C22×Q8—28no—
492C22×Q8—44no—
493C22×Q8—42no—
494C22×Q8—42no—
495C22×Q8—42no—
496C22×Q8—42no—
497C22×Q8—42no—
498C22×Q8—42no—
499C22×Q8—48no—
500C22×Q8—48no—
501C22×Q8—42no—
502C22×Q8—42no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2412yes—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2412yes—
509C22×Q8C2414yes—
510C22×Q8C2418yes—
511C22×Q8C2414yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2414yes—
514C22×Q8C2414yes—
515C22×Q8C2414yes—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4C2×D412yes—
529C22×D4C2×D412yes—
530C22×D4C2×D411yescharacteristic
531C22×D4C2×D411yescharacteristic
532C22×D4C2×D412yes—
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—22no—
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—21no—
546C23×C4—22no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—22no—
552C23×C4C2×D412yes—
553C23×C4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557#137—416no—
558#137—432no—
559AGL(1,ℤ/8)—416no—
560#135—432no—
561C2×Q16—28no—
562C2×Q16—44no—
563C2×Q16—44no—
564C2×Q16—44no—
565C2×Q16—44no—
566C2×Q16—416no—
567C2×Q16C2418yes—
568C2×Q16C2418yes—
569C2×Q16C2418yes—
570C2×Q16C2418yes—
571C2×Q16C2418yes—
572C2×SD16—28no—
573C2×SD16—28no—
574C2×SD16—44no—
575C2×SD16—44no—
576C2×SD16—44no—
577C2×SD16—44no—
578C2×SD16—416no—
579C2×SD16C2418yes—
580C2×SD16C2418yes—
581C2×SD16C2418yes—
582C2×SD16C2418yes—
583C2×SD16C2418yes—
584C2×SD16C2418yes—
585C2×D8—28no—
586C2×D8C2418yes—
587C2×M16—42no—
588C2×M16—42no—
589C2×M16—44no—
590C2×M16C2414yes—
591C2×M16C2418yes—
592C2×M16C2414yes—
593C22×C8—42no—
594C22×C8—42no—
595C22×C8—44no—
596C22×C8C2412yes—
597C22×C8C2412yes—
598C22×C8C2412yes—
599C22×C8C2412yes—
600C22×C8C2414yes—
601C22×C8C2414yes—
602C22×C8C2418yes—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—216no—
607C4⋊Q8—216no—
608C4⋊Q8—28no—
609C4⋊Q8—24no—
610C4⋊Q8—24no—
611C4⋊Q8—28no—
612C4⋊Q8C2×D418yes—
613C4⋊Q8C2418yes—
614C4⋊Q8C2418yes—
615#127—28no—
616#127C2×D418yes—
617#126—216no—
618#126—216no—
619#126—216no—
620#125—216no—
621#125—24no—
622#125C2418yes—
623#124—28no—
624#124—28no—
625#124—28no—
626#124—28no—
627#124—216no—
628#124—24no—
629#124C2×D418yes—
630#124C2×D418yes—
631#124C2418yes—
632#123—28no—
633#123—28no—
634#123—28no—
635#123—28no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—216no—
645C22⋊Q8—216no—
646C22⋊Q8—24no—
647C22⋊Q8—24no—
648C22⋊Q8—24no—
649C22⋊Q8—24no—
650C22⋊Q8—24no—
651C22⋊Q8—24no—
652C22⋊Q8—24no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8C2418yes—
659C22⋊Q8C2418yes—
660C22⋊Q8C2418yes—
661C22⋊Q8C2418yes—
662C22⋊Q8C2418yes—
663C22⋊Q8C2418yes—
664C22⋊Q8C2418yes—
665#121—216no—
666#121—216no—
667#121—216no—
668#121—216no—
669#121—216no—
670#121—216no—
671#121—216no—
672#121—24no—
673#121—24no—
674#121—24no—
675#121—216no—
676#121C2×D4116yes—
677#121C2×D4116yes—
678#121C2418yes—
679#121C2418yes—
680#121C2418yes—
681#120—28no—
682#120—28no—
683#120—216no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8C2418yes—
687C4×Q8C2418yes—
688C4×D4—216no—
689C4×D4—216no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—216no—
694C4×D4—24no—
695C4×D4—24no—
696C4×D4C2×D418yes—
697C4×D4C2×D418yes—
698C4×D4C2418yes—
699C4×D4C2418yes—
700C4×D4C2418yes—
701C4×D4C2418yes—
702#117—22no—
703#117—22no—
704#117—22no—
705#117—216no—
706#117—28no—
707#117—216no—
708#117C2414yes—
709#117C2414yes—
710#117C2414yes—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—216no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—24no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—22no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4—22no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—216no—
730C2×C4⋊C4—216no—
731C2×C4⋊C4C2×D412yes—
732C2×C4⋊C4C2×D412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2412yes—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—216no—
755C2×C22⋊C4C2×D412yes—
756C2×C22⋊C4C2×D412yes—
757C2×C22⋊C4C2×D412yes—
758C2×C22⋊C4C2×D412yes—
759C2×C42—21no—
760C2×C42—22no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—22no—
764C2×C42—28no—
765C2×C42C2×D411yescharacteristic
766C2×C42C2×D414yes—
767C2×C42C2×D411yescharacteristic
768C2×C42C2412yes—
769C2×C42C2414yes—
770#107C2418yes—
771#107C2418yes—
772#106C2418yes—
773#106C2418yes—
774C4⋊C8C2418yes—
775C4⋊C8C2418yes—
776#103C2418yes—
777#103C2418yes—
778#103C2418yes—
779#103C2418yes—
780#103C2418yes—
781#103C2418yes—
782#103C2418yes—
783#103C2418yes—
784#103C2418yes—
785#103C2418yes—
786#103C2418yes—
787#103C2418yes—
788#102C2418yes—
789#102C2418yes—
790#102C2418yes—
791#102C2418yes—
792C22⋊C8C2418yes—
793C22⋊C8C2418yes—
794C22⋊C8C2418yes—
795C22⋊C8C2418yes—
796C22⋊C8C2418yes—
797C22⋊C8C2418yes—
798#97C2418yes—
799#97C2418yes—
800C24—21no—
801C24—22no—
802C24—24no—
803C24—82no—
804C24—84no—
805C24C22×D411yescharacteristic
806C24C22×D412yes—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809#41—216no—
810#41—28no—
811#41—28no—
812#41—216no—
813#41—28no—
814#41—28no—
815#41—48no—
816#41—48no—
817#41—44no—
818#41—44no—
819#41—44no—
820#41—44no—
821#41—44no—
822#41—44no—
823#41—48no—
824#41—48no—
825#41—48no—
826#41—416no—
827#41—432no—
828#41—432no—
829#41—48no—
830#41—48no—
831#41—432no—
832#41—432no—
833#41—464no—
834#41—88no—
835C2×Q8—21no—
836C2×Q8—22no—
837C2×Q8—24no—
838C2×Q8—24no—
839C2×Q8—28no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—22no—
843C2×Q8—24no—
844C2×Q8—24no—
845C2×Q8—24no—
846C2×Q8—22no—
847C2×Q8—28no—
848C2×Q8—28no—
849C2×Q8—216no—
850C2×Q8—24no—
851C2×Q8—22no—
852C2×Q8—22no—
853C2×Q8—24no—
854C2×Q8—24no—
855C2×Q8—24no—
856C2×Q8—22no—
857C2×Q8—22no—
858C2×Q8—42no—
859C2×Q8—42no—
860C2×Q8—48no—
861C2×Q8—44no—
862C2×Q8—44no—
863C2×Q8—48no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×Q8—44no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—48no—
871C2×Q8—48no—
872C2×Q8—416no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—432no—
876C2×Q8—432no—
877C2×Q8—48no—
878C2×Q8—48no—
879C2×Q8—44no—
880C2×Q8—44no—
881C2×Q8—82no—
882C2×Q8—84no—
883C2×Q8C22×D414yes—
884C2×Q8C22×D414yes—
885C2×Q8H(5,𝔽2)14yes—
886C2×Q8C2512yes—
887C2×Q8C2512yes—
888C2×Q8C2514yes—
889C2×Q8C2514yes—
890C2×Q8C2512yes—
891C2×D4—28no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—28no—
895C2×D4—24no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—21no—
901C2×D4—22no—
902C2×D4—24no—
903C2×D4—22no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—44no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—44no—
916C2×D4—48no—
917C2×D4—44no—
918C2×D4—84no—
919C2×D4—82no—
920C2×D4—84no—
921C2×D4—84no—
922C2×D4—84no—
923C2×D4—84no—
924C2×D4C22×D418yes—
925C2×D4C22×D418yes—
926C2×D4C22×D414yes—
927C2×D4C22×D414yes—
928C2×D4C22×D418yes—
929C2×D4C22×D414yes—
930C2×D4C22×D414yes—
931C2×D4H(5,𝔽2)14yes—
932C2×D4C2514yes—
933C2×D4C2512yes—
934C22×C4—28no—
935C22×C4—21no—
936C22×C4—24no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—24no—
940C22×C4—22no—
941C22×C4—24no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—22no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—28no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—48no—
968C22×C4—44no—
969C22×C4—48no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—48no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—84no—
976C22×C4—84no—
977C22×C4—84no—
978C22×C4—82no—
979C22×C4C22×D412yes—
980C22×C4C22×D414yes—
981C22×C4C22×D412yes—
982C22×C4C22×D412yes—
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D412yes—
985C22×C4C22×D412yes—
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D412yes—
989C22×C4C22×D418yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2511yescharacteristic
995Q16—216no—
996Q16—48no—
997Q16—48no—
998Q16—48no—
999Q16—48no—
1000SD16—216no—
1001SD16—216no—
1002SD16—48no—
1003SD16—48no—
1004SD16—48no—
1005SD16—48no—
1006D8—216no—
1007M16—44no—
1008M16—44no—
1009M16—48no—
1010C2×C8—24no—
1011C2×C8—24no—
1012C2×C8—24no—
1013C2×C8—24no—
1014C2×C8—44no—
1015C2×C8—44no—
1016C2×C8—48no—
1017C2×C8C2514yes—
1018C2×C8C2514yes—
1019C2×C8C2514yes—
1020C2×C8C2514yes—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—22no—
1040C4⋊C4C22×D418yes—
1041C4⋊C4C22×D418yes—
1042C4⋊C4C2514yes—
1043C4⋊C4C2514yes—
1044C4⋊C4C2514yes—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4C22×D418yes—
1063C22⋊C4C22×D418yes—
1064C22⋊C4C22×D418yes—
1065C22⋊C4C22×D418yes—
1066C42—24no—
1067C42—28no—
1068C42—24no—
1069C42—28no—
1070C42—24no—
1071C42C22×D414yes—
1072C42C22×D414yes—
1073C42C22×D414yes—
1074C42C2514yes—
1075C23—24no—
1076C23—24no—
1077C23—24no—
1078C23—24no—
1079C23—24no—
1080C23—22no—
1081C23—22no—
1082C23—24no—
1083C23—22no—
1084C23—24no—
1085C23—22no—
1086C23—24no—
1087C23—44no—
1088C23—44no—
1089C23—44no—
1090C23—44no—
1091C23—84no—
1092C23—88no—
1093C23—168no—
1094C23C23×D412yes—
1095C23C23×D412yes—
1096C23C23×D414yes—
1097C23C23×D412yes—
1098C23C23×D411yescharacteristic
1099Q8—22no—
1100Q8—24no—
1101Q8—24no—
1102Q8—22no—
1103Q8—22no—
1104Q8—24no—
1105Q8—24no—
1106Q8—24no—
1107Q8—22no—
1108Q8—22no—
1109Q8—44no—
1110Q8—44no—
1111Q8—416no—
1112Q8—48no—
1113Q8—48no—
1114Q8—48no—
1115Q8—48no—
1116Q8—42no—
1117Q8—42no—
1118Q8—44no—
1119Q8—44no—
1120Q8—84no—
1121Q8C2×H(5,𝔽2)14yes—
1122D4—216no—
1123D4—22no—
1124D4—24no—
1125D4—24no—
1126D4—24no—
1127D4—48no—
1128D4—48no—
1129D4—44no—
1130D4—44no—
1131D4—48no—
1132D4—44no—
1133D4—44no—
1134D4—48no—
1135D4—416no—
1136D4—48no—
1137D4—44no—
1138D4—84no—
1139D4—88no—
1140D4—88no—
1141D4—88no—
1142D4—88no—
1143D4C2×H(5,𝔽2)14yes—
1144C2×C4—216no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—416no—
1175C2×C4—48no—
1176C2×C4—416no—
1177C2×C4—48no—
1178C2×C4—48no—
1179C2×C4—416no—
1180C2×C4—48no—
1181C2×C4—48no—
1182C2×C4—44no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—88no—
1190C2×C4—88no—
1191C2×C4—88no—
1192C2×C4—84no—
1193C2×C4C23×D412yes—
1194C2×C4C23×D414yes—
1195C2×C4C23×D414yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D412yes—
1198C2×C4C23×D414yes—
1199C2×C4C23×D411yescharacteristic
1200C2×C4C2×H(5,𝔽2)12yes—
1201C2×C4C2×H(5,𝔽2)12yes—
1202C2×C4C2611yescharacteristic
1203C8—24no—
1204C8—24no—
1205C8—24no—
1206C8—24no—
1207C22—22no—
1208C22—24no—
1209C22—22no—
1210C22—24no—
1211C22—22no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—44no—
1218C22—44no—
1219C22—48no—
1220C22—44no—
1221C22—44no—
1222C22—48no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—88no—
1227C22—168no—
1228C22#348412yes—
1229C22#358614yes—
1230C22C24×D411yescharacteristic
1231C4—22no—
1232C4—24no—
1233C4—24no—
1234C4—22no—
1235C4—22no—
1236C4—24no—
1237C4—24no—
1238C4—42no—
1239C4—42no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C4—44no—
1244C4—44no—
1245C4#348412yes—
1246C4C22×H(5,𝔽2)11yescharacteristic
1247C4C22×H(5,𝔽2)11yescharacteristic
1248C2—42no—
1249C2—42no—
1250C2—44no—
1251C2—42no—
1252C2—44no—
1253C2—84no—
1254C2#6167614yesdirect product factor
1255C2C2×#348411yescharacteristic
1256C2C2×#358612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3499C2semidirect
2. C2×#3551C2semidirect
3. #61676C2direct (N × H)
4. C2×#3315C2semidirect
5. C2×#3307C2semidirect
6. C2×#3320C2semidirect
7. C2×#3312C2semidirect
8. C2×#3270C2semidirect
9. C2×#3269C2semidirect
10. C2×#3267C2semidirect
11. C2×#3266C2semidirect
12. C2×#3218C2semidirect
13. C2×#3202C2semidirect
14. C2×#3201C2semidirect
15. C2×#3200C2semidirect
16. C2×#3111C2semidirect
17. C2×#3013C2semidirect
18. C2×#3011C2semidirect
19. C2×#3010C2semidirect
20. C2×#2980C2semidirect
22. C22×2−1+4C22semidirect
24. C22×#137C22semidirect
27. C23×Q16C22semidirect
30. #3551C22semidirect
34. #3499C22semidirect
40. C2×D4×Q8C22semidirect
45. C2×#547C22semidirect
54. C2×#536C22semidirect
59. C22×C4⋊Q8C22semidirect
61. C2×C4×#41C22semidirect
62. #3320C22semidirect
63. #3315C22semidirect
64. #3312C22semidirect
65. #3307C22semidirect
66. #3270C22semidirect
67. #3269C22semidirect
68. #3267C22semidirect
69. #3266C22semidirect
70. #3218C22semidirect
71. #3202C22semidirect
72. #3201C22semidirect
73. #3200C22semidirect
76. C2×#491C22semidirect
77. C2×#491C22semidirect
78. #3111C22semidirect
79. C2×#484C22semidirect
81. C2×#485C22semidirect
82. C2×#485C22semidirect
84. C2×#483C22semidirect
85. C2×#479C22semidirect
86. C2×#478C22semidirect
88. C2×#470C22semidirect
92. C2×#467C22semidirect
96. C2×#462C22semidirect
97. C2×#462C22semidirect
101. #3013C22semidirect
102. #3011C22semidirect
103. #3010C22semidirect
107. C2×#452C22semidirect
108. C2×#452C22semidirect
113. C2×#451C22semidirect
114. C2×#451C22semidirect
115. C2×#451C22semidirect
116. C2×#451C22semidirect
122. #2980C22semidirect
124. C2×#441C22semidirect
126. C2×#440C22semidirect
129. C2×#435C22semidirect
130. C2×#435C22semidirect
131. C2×#432C22semidirect
132. C2×#417C22semidirect
134. C2×#419C22semidirect
136. C2×#416C22semidirect
137. C22×#103C22semidirect
140. C2×#408C22semidirect
148. C2×2−1+4C23semidirect
173. C2×#137C23semidirect
184. C22×Q16C23semidirect
211. D4×Q8C23semidirect
219. #547C23semidirect
233. #536C23semidirect
251. C2×C4⋊Q8C23semidirect
312. C4×#41C23semidirect
340. #491C23semidirect
341. #491C23semidirect
343. #485C23semidirect
344. #485C23semidirect
345. #484C23semidirect
346. #483C23semidirect
348. #479C23semidirect
349. #478C23semidirect
351. #470C23semidirect
355. #467C23semidirect
360. #462C23semidirect
361. #462C23semidirect
367. #452C23semidirect
368. #452C23semidirect
370. #451C23semidirect
371. #451C23semidirect
372. #451C23semidirect
373. #451C23semidirect
383. #441C23semidirect
385. #440C23semidirect
388. #435C23semidirect
389. #435C23semidirect
390. #432C23semidirect
398. #419C23semidirect
399. #417C23semidirect
401. #416C23semidirect
414. C2×#103C23semidirect
421. #408C23semidirect
1254. C2#61676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#35512
#616762
C2×#33152
C2×#33072
C2×#33202
C2×#33122
C2×#32702
C2×#32692
C2×#32672
C2×#32662
C2×#32182
C2×#32022
C2×#32012
C2×#32002
C2×#31112
C2×#30132
C2×#30112
C2×#30102
C2×#29802