Finite Group Databasebeta

← C2×#72217187 #72322278

Subgroups — C2×#72217187 #72322278

Order 2048.

2442 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#93996C211yesmaximal, characteristic, complemented
2C2×#93995C211yesmaximal, characteristic, complemented
3C2×#479958C211yesmaximal, characteristic
4C2×#151891C212yesmaximal
5C2×#149504C212yesmaximal, complemented
6#72217187C218yesmaximal, direct product factor
7C2×#33418C411yescharacteristic
8C23×#346C2211yescharacteristic
9C2×#17323C411yescharacteristic
10C2×#13553C414yes—
11C22×#1398C2212yes—
12C22×#1398C2212yes—
13#479958—24no—
14#479958C414yes—
15#479958C2214yes—
16C2×#11413—24no—
17C2×#11406C411yescharacteristic
18C2×#11406C411yescharacteristic
19C2×#11405C2211yescharacteristic
20C2×#11405C2211yescharacteristic
21#151891C418yes—
22#151891C2218yes—
23C2×#7466C414yes—
24#149504—24no—
25#149504C2218yescomplemented
26C2×#7333—24no—
27#93996C2214yescomplemented
28#93995C2214yescomplemented
29C24×C16C2×C412yes—
30C2×#2920—21no—
31C23×C4×C8C2×C411yescharacteristic
32C22×M64C2×C414yes—
33C22×M64C2×C414yes—
34#33418—22no—
35#33418—22no—
36#33418—22no—
37#33418C2×C414yes—
38C2×#2163—22no—
39C2×#2162—22no—
40C2×#2150—21no—
41C2×#2112—21no—
42C2×C4×M32C2×C411yescharacteristic
43C2×C4×M32C2×C411yescharacteristic
44C22×#346—22no—
45C22×#346—22no—
46C22×#346—21no—
47C22×#346—21no—
48C22×#346—21no—
49C22×#346—21no—
50C22×#346C2×C414yes—
51C22×#346C2×C412yes—
52C22×#346C2×C411yescharacteristic
53C22×#346C2×C412yes—
54C22×#346C2312yes—
55C22×#346C2311yescharacteristic
56#17323—22no—
57#17323—22no—
58#17323—22no—
59#17323C2×C414yes—
60C2×#1452—21no—
61C2×#1451—22no—
62C2×#1450C2×C411yescharacteristic
63C2×#1450C2×C411yescharacteristic
64C2×C8×M16—22no—
65#13553—28no—
66#13553C2×C4116yes—
67C2×C22⋊C32—28no—
68C2×#1398—22no—
69C2×#1398—22no—
70C2×#1398—22no—
71C2×#1398—22no—
72C2×#1398—22no—
73C2×#1398—22no—
74C2×#1398—22no—
75C2×#1398—22no—
76C2×#1398C2×C414yes—
77C2×#1398C2×C414yes—
78C2×#1398C2314yes—
79C2×#1398C2314yes—
80#11413—216no—
81#11413—216no—
82#11406—22no—
83#11406—22no—
84#11406C2×C414yes—
85#11406C2×C414yes—
86#11405—22no—
87#11405C2×C412yes—
88#11405C2×C412yes—
89#11405D414yes—
90#11405C2312yes—
91#11405C2312yes—
92C2×#1313—22no—
93C2×#1313—22no—
94C2×#1313—22no—
95C2×#1313D414yes—
96#7466C2×C4116yes—
97#7333—216no—
98C24×C8C4211yescharacteristic
99C24×C8M1611yescharacteristic
100C23×C42M1611yescharacteristic
101C22×M32—21no—
102C22×M32—21no—
103C23×C16—22no—
104C23×C16—22no—
105C23×C16—22no—
106C23×C16—22no—
107C23×C16—24no—
108C23×C16—24no—
109C23×C16—24no—
110C23×C16—24no—
111C23×C16C4214yes—
112C23×C16C4212yes—
113C23×C16C22×C414yes—
114C23×C16C22×C412yes—
115#2920—24no—
116#2920—24no—
117#2920—42no—
118#2920—42no—
119C2×#432—41no—
120C2×#432—41no—
121C2×#431—22no—
122C2×#431—21no—
123C2×#431—21no—
124C2×#423—41no—
125C2×#407—41no—
126C2×C4×M16—22no—
127C22×C4×C8—21no—
128C22×C4×C8—21no—
129C22×C4×C8—21no—
130C22×C4×C8—21no—
131C22×C4×C8—21no—
132C22×C4×C8—21no—
133C22×C4×C8—21no—
134C22×C4×C8—21no—
135C22×C4×C8C4211yescharacteristic
136C22×C4×C8C4212yes—
137C22×C4×C8M1611yescharacteristic
138C22×C4×C8M1612yes—
139C22×C4×C8M1611yescharacteristic
140C22×C4×C8M1612yes—
141C22×C4×C8C22×C412yes—
142C22×C4×C8C22×C411yescharacteristic
143C2×M64—24no—
144C2×M64—24no—
145C2×M64—24no—
146C2×M64—24no—
147C2×M64—24no—
148C2×M64—24no—
149C2×M64—24no—
150C2×M64—24no—
151C2×M64—24no—
152C2×M64M1618yescomplemented
153C2×M64C22×C418yes—
154C2×M64C22×C418yes—
155C22×C32—24no—
156C22×C32M1618yescomplemented
157#2163—28no—
158#2163—28no—
159#2162—28no—
160#2162—28no—
161#2150—24no—
162#2150—24no—
163C2×C4⋊C16—24no—
164#2112—24no—
165#2112—24no—
166C2×C22⋊C16—24no—
167C4×M32—21no—
168C4×M32—21no—
169C4×M32—21no—
170C4×M32—21no—
171C4×M32C22⋊C412yes—
172C4×M32M1612yes—
173C4×M32C22×C412yes—
174C4×M32C22×C412yes—
175C2×#346—22no—
176C2×#346—22no—
177C2×#346—22no—
178C2×#346—22no—
179C2×#346—21no—
180C2×#346—21no—
181C2×#346—21no—
182C2×#346—21no—
183C2×#346—21no—
184C2×#346—24no—
185C2×#346—22no—
186C2×#346—22no—
187C2×#346—24no—
188C2×#346—24no—
189C2×#346—24no—
190C2×#346—24no—
191C2×#346—24no—
192C2×#346—22no—
193C2×#346—22no—
194C2×#346C4214yes—
195C2×#346C4212yes—
196C2×#346C22⋊C412yes—
197C2×#346C22×C414yes—
198C2×#346C22×C412yes—
199C2×#346C22×C411yescharacteristic
200C2×#346C22×C412yes—
201C2×#346C2×D412yes—
202C2×#346C2×D412yes—
203C2×#346#4111yescharacteristic
204C2×#346#4111yescharacteristic
205C2×#346#4111yescharacteristic
206C2×#346#4111yescharacteristic
207C2×#346C2411yescharacteristic
208C2×C4×C16—21no—
209C2×C4×C16M1612yes—
210#1452—24no—
211#1452—24no—
212#1451—28no—
213#1451—28no—
214#1450—21no—
215#1450—21no—
216#1450—21no—
217#1450—21no—
218#1450C22⋊C412yes—
219#1450M1612yes—
220#1450C22×C412yes—
221#1450C22×C412yes—
222C8×M16—28no—
223C8×M16—28no—
224C2×#322—24no—
225C2×#322—21no—
226C2×#322C22⋊C412yes—
227C2×C82—21no—
228C2×C82M1612yes—
229C22⋊C32—232no—
230#1398—24no—
231#1398—24no—
232#1398—24no—
233#1398—24no—
234#1398—24no—
235#1398—24no—
236#1398—24no—
237#1398—24no—
238#1313—24no—
239#1313—28no—
240#1313—24no—
241#1313—28no—
242#1313C22⋊C418yes—
243#1313C2×D418yes—
244C24×C4—21no—
245C24×C4#9711yescharacteristic
246C22×M16—42no—
247C23×C8—21no—
248C23×C8—21no—
249C23×C8—21no—
250C23×C8—21no—
251C23×C8—22no—
252C23×C8—22no—
253C23×C8—22no—
254C23×C8—22no—
255C23×C8—21no—
256C23×C8—21no—
257C23×C8—21no—
258C23×C8—21no—
259C23×C8—42no—
260C23×C8—42no—
261C23×C8#9711yescharacteristic
262C23×C8#9711yescharacteristic
263C23×C8#9712yes—
264C23×C8#9712yes—
265C23×C8C2×C4212yes—
266C23×C8C2×C4211yescharacteristic
267C23×C8C2×M1611yescharacteristic
268C23×C8C2×M1612yes—
269C22×C42—21no—
270C22×C42—22no—
271C22×C42—21no—
272C22×C42—21no—
273C22×C42—22no—
274C22×C42—21no—
275C22×C42—21no—
276C22×C42—21no—
277C22×C42—21no—
278C22×C42#9712yes—
279C22×C42#9711yescharacteristic
280C22×C42C2×M1612yes—
281C22×C42C2×M1611yescharacteristic
282C2×M32—22no—
283C2×M32—22no—
284C2×M32—22no—
285C2×M32—22no—
286C2×M32—42no—
287C2×M32—42no—
288C2×M32—42no—
289C2×M32—42no—
290C22×C16—22no—
291C22×C16—22no—
292C22×C16—22no—
293C22×C16—22no—
294C22×C16—22no—
295C22×C16—22no—
296C22×C16—22no—
297C22×C16—22no—
298C22×C16—24no—
299C22×C16—24no—
300C22×C16—28no—
301C22×C16—28no—
302C22×C16—24no—
303C22×C16—24no—
304C22×C16—28no—
305C22×C16—28no—
306C22×C16—44no—
307C22×C16—44no—
308C22×C16—44no—
309C22×C16—44no—
310C22×C16—44no—
311C22×C16—44no—
312C22×C16—44no—
313C22×C16—44no—
314C22×C16C2×C4214yes—
315C22×C16C2×C4212yes—
316C22×C16C4×D412yes—
317C22×C16C4×D412yes—
318C22×C16C4×D412yes—
319C22×C16C4×D412yes—
320C22×C16C2×M1614yes—
321C22×C16C2×M1614yes—
322C22×C16#13114yes—
323C22×C16#13114yes—
324C22×C16C23×C412yes—
325#432—44no—
326#432—44no—
327#432—44no—
328#432—44no—
329#431—28no—
330#431—22no—
331#431—22no—
332#431—22no—
333#431—22no—
334#431—44no—
335#431—41no—
336#431—41no—
337#431—41no—
338#431—41no—
339#423—44no—
340#423—44no—
341C2×C4⋊C8—42no—
342C2×C4⋊C8—41no—
343C2×C4⋊C8—41no—
344#407—44no—
345#407—44no—
346C2×C22⋊C8—42no—
347C2×C22⋊C8—41no—
348C2×C22⋊C8—41no—
349C4×M16—28no—
350C4×M16—44no—
351C2×#97—42no—
352C2×C4×C8—21no—
353C2×C4×C8—21no—
354C2×C4×C8—21no—
355C2×C4×C8—21no—
356C2×C4×C8—21no—
357C2×C4×C8—21no—
358C2×C4×C8—21no—
359C2×C4×C8—21no—
360C2×C4×C8—21no—
361C2×C4×C8—21no—
362C2×C4×C8—21no—
363C2×C4×C8—21no—
364C2×C4×C8—22no—
365C2×C4×C8—22no—
366C2×C4×C8—22no—
367C2×C4×C8—22no—
368C2×C4×C8—22no—
369C2×C4×C8—22no—
370C2×C4×C8—22no—
371C2×C4×C8—22no—
372C2×C4×C8—22no—
373C2×C4×C8—22no—
374C2×C4×C8—22no—
375C2×C4×C8—22no—
376C2×C4×C8—22no—
377C2×C4×C8—22no—
378C2×C4×C8—22no—
379C2×C4×C8—22no—
380C2×C4×C8—22no—
381C2×C4×C8—22no—
382C2×C4×C8#9712yes—
383C2×C4×C8#9712yes—
384C2×C4×C8#9712yes—
385C2×C4×C8C2×C4212yes—
386C2×C4×C8C2×C4211yescharacteristic
387C2×C4×C8C2×C22⋊C411yescharacteristic
388C2×C4×C8C2×C22⋊C411yescharacteristic
389C2×C4×C8#11711yescharacteristic
390C2×C4×C8#11711yescharacteristic
391C2×C4×C8C2×M1612yes—
392C2×C4×C8C2×M1612yes—
393C2×C4×C8C2×M1611yescharacteristic
394C2×C4×C8C2×M1611yescharacteristic
395C2×C4×C8C2×M1611yescharacteristic
396C2×C4×C8C2×M1611yescharacteristic
397C2×C4×C8C2×M1611yescharacteristic
398C2×C4×C8C2×M1611yescharacteristic
399C2×C4×C8C23×C411yescharacteristic
400M64—28no—
401M64—28no—
402M64—28no—
403M64—28no—
404M64—28no—
405M64—28no—
406M64—44no—
407M64—44no—
408C2×C32—28no—
409C2×C32—28no—
410C2×C32—28no—
411C2×C32—44no—
412C2×C32—44no—
413C2×C32C2×M16116yescomplemented
414C4⋊C16—216no—
415C22⋊C16—216no—
416#346—24no—
417#346—24no—
418#346—24no—
419#346—24no—
420#346—22no—
421#346—22no—
422#346—22no—
423#346—22no—
424#346—22no—
425#346—22no—
426#346—22no—
427#346C2×C22⋊C414yes—
428#346C2×C22⋊C412yes—
429#346#11711yescharacteristic
430#346#11711yescharacteristic
431#346C4×D412yes—
432#346C4×D412yes—
433#346C4×D412yes—
434#346C4×D412yes—
435#346C22×D412yes—
436#346C2×#4111yescharacteristic
437#346C2×#4111yescharacteristic
438C4×C16—22no—
439C4×C16—22no—
440C4×C16—22no—
441C4×C16C2×M1614yes—
442#322—216no—
443#322—22no—
444#322—22no—
445#322—22no—
446#322C2×C22⋊C414yes—
447C82—22no—
448C82—22no—
449C82—22no—
450C82C2×M1614yes—
451C25#34711yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—84no—
471C23×C4#34711yescharacteristic
472C23×C4#34712yes—
473C23×C4C2×#9712yes—
474C23×C4C2×#9711yescharacteristic
475C2×M16—48no—
476C2×M16—88no—
477C22×C8—22no—
478C22×C8—22no—
479C22×C8—22no—
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—22no—
488C22×C8—24no—
489C22×C8—24no—
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—24no—
493C22×C8—24no—
494C22×C8—22no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—44no—
500C22×C8—44no—
501C22×C8—42no—
502C22×C8—42no—
503C22×C8—44no—
504C22×C8—42no—
505C22×C8—42no—
506C22×C8—44no—
507C22×C8—42no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—42no—
512C22×C8—41no—
513C22×C8—42no—
514C22×C8—42no—
515C22×C8—42no—
516C22×C8—42no—
517C22×C8—42no—
518C22×C8—42no—
519C22×C8C4×C22⋊C411yescharacteristic
520C22×C8C4×C22⋊C411yescharacteristic
521C22×C8C2×#9712yes—
522C22×C8C2×#9712yes—
523C22×C8C2×#9711yescharacteristic
524C22×C8C2×#9711yescharacteristic
525C22×C8C4×M1612yes—
526C22×C8C4×M1612yes—
527C22×C8C4×M1611yescharacteristic
528C22×C8C4×M1611yescharacteristic
529C22×C8#40512yes—
530C22×C8#40512yes—
531C22×C8#40711yescharacteristic
532C22×C8#40711yescharacteristic
533C22×C8#43211yescharacteristic
534C22×C8#43211yescharacteristic
535C22×C8C22×C4211yescharacteristic
536C22×C8C22×M1611yescharacteristic
537C2×C42—21no—
538C2×C42—22no—
539C2×C42—21no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—21no—
552C2×C42—21no—
553C2×C42—21no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42#34711yescharacteristic
568C2×C42#34711yescharacteristic
569C2×C42#34712yes—
570C2×C42C2×#9712yes—
571C2×C42C2×#9711yescharacteristic
572C2×C42#40711yescharacteristic
573C2×C42#40711yescharacteristic
574C2×C42#43211yescharacteristic
575C2×C42#43211yescharacteristic
576C2×C42C22×M1611yescharacteristic
577M32—44no—
578M32—44no—
579M32—44no—
580M32—44no—
581C2×C16—24no—
582C2×C16—24no—
583C2×C16—24no—
584C2×C16—24no—
585C2×C16—24no—
586C2×C16—42no—
587C2×C16—42no—
588C2×C16—42no—
589C2×C16—42no—
590C2×C16—42no—
591C2×C16—42no—
592C2×C16—42no—
593C2×C16—42no—
594C2×C16—48no—
595C2×C16—48no—
596C2×C16—48no—
597C2×C16—48no—
598C2×C16C4×C22⋊C412yes—
599C2×C16C4×C22⋊C412yes—
600C2×C16C4×M1614yes—
601C2×C16#40514yes—
602C2×C16#43514yes—
603C2×C16#43514yes—
604C2×C16#43514yes—
605C2×C16#43514yes—
606C2×C16#43614yes—
607C2×C16#43614yes—
608C2×C16#43614yes—
609C2×C16#43614yes—
610C2×C16C2×C4×D412yes—
611C2×C16C2×C4×D412yes—
612C2×C16C22×M1614yes—
613C2×C16C2×#13114yes—
614C4⋊C8—48no—
615C4⋊C8—42no—
616C4⋊C8—42no—
617C4⋊C8—42no—
618C4⋊C8—42no—
619C22⋊C8—48no—
620C22⋊C8—42no—
621C22⋊C8—42no—
622C22⋊C8—42no—
623C22⋊C8—42no—
624#97—48no—
625C4×C8—22no—
626C4×C8—22no—
627C4×C8—22no—
628C4×C8—22no—
629C4×C8—22no—
630C4×C8—22no—
631C4×C8—22no—
632C4×C8—22no—
633C4×C8—22no—
634C4×C8—24no—
635C4×C8—24no—
636C4×C8—22no—
637C4×C8—22no—
638C4×C8—22no—
639C4×C8—42no—
640C4×C8—42no—
641C4×C8C4×C22⋊C411yescharacteristic
642C4×C8C4×C22⋊C411yescharacteristic
643C4×C8C4×M1611yescharacteristic
644C4×C8C4×M1611yescharacteristic
645C4×C8#40711yescharacteristic
646C4×C8#40711yescharacteristic
647C4×C8#40711yescharacteristic
648C4×C8#40711yescharacteristic
649C4×C8#43211yescharacteristic
650C4×C8#43211yescharacteristic
651C4×C8#43211yescharacteristic
652C4×C8#43211yescharacteristic
653C4×C8C22×C22⋊C411yescharacteristic
654C4×C8C2×#11711yescharacteristic
655C4×C8C22×M1611yescharacteristic
656C4×C8C22×M1611yescharacteristic
657C32—216no—
658C32—48no—
659C24—21no—
660C24—22no—
661C24—21no—
662C24—22no—
663C24—44no—
664C24C2×#34712yes—
665C24C2×#34711yescharacteristic
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—24no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—24no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—41no—
699C22×C4—42no—
700C22×C4—41no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—41no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—82no—
709C22×C4—82no—
710C22×C4—84no—
711C22×C4—84no—
712C22×C4—82no—
713C22×C4—84no—
714C22×C4—82no—
715C22×C4—84no—
716C22×C4#145112yes—
717C22×C4#145112yes—
718C22×C4#174911yescharacteristic
719C22×C4#174911yescharacteristic
720C22×C4C2×#34712yes—
721C22×C4C2×#34711yescharacteristic
722C22×C4C2×#34711yescharacteristic
723C22×C4C2×#34711yescharacteristic
724C22×C4#211012yes—
725C22×C4#211012yes—
726C22×C4C22×#9711yescharacteristic
727M16—816no—
728C2×C8—22no—
729C2×C8—22no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—22no—
733C2×C8—22no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—24no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—24no—
740C2×C8—44no—
741C2×C8—44no—
742C2×C8—44no—
743C2×C8—44no—
744C2×C8—41no—
745C2×C8—42no—
746C2×C8—41no—
747C2×C8—41no—
748C2×C8—42no—
749C2×C8—41no—
750C2×C8—44no—
751C2×C8—42no—
752C2×C8—42no—
753C2×C8—42no—
754C2×C8—44no—
755C2×C8—42no—
756C2×C8—44no—
757C2×C8—44no—
758C2×C8—84no—
759C2×C8—84no—
760C2×C8#145112yes—
761C2×C8#145112yes—
762C2×C8#145312yes—
763C2×C8#145311yescharacteristic
764C2×C8#145311yescharacteristic
765C2×C8#145511yescharacteristic
766C2×C8#145512yes—
767C2×C8#145511yescharacteristic
768C2×C8#174911yescharacteristic
769C2×C8#174911yescharacteristic
770C2×C8#174911yescharacteristic
771C2×C8#174911yescharacteristic
772C2×C8#175312yes—
773C2×C8#175312yes—
774C2×C8#175312yes—
775C2×C8#175312yes—
776C2×C8C2×C4×C22⋊C411yescharacteristic
777C2×C8C2×C4×M1612yes—
778C2×C8C2×C4×M1611yescharacteristic
779C2×C8C2×#40512yes—
780C2×C8C2×#40711yescharacteristic
781C2×C8C2×#43211yescharacteristic
782C42—22no—
783C42—22no—
784C42—22no—
785C42—22no—
786C42—22no—
787C42—22no—
788C42—22no—
789C42—22no—
790C42—21no—
791C42—21no—
792C42—21no—
793C42—21no—
794C42—22no—
795C42—21no—
796C42—21no—
797C42—21no—
798C42—21no—
799C42—22no—
800C42#174911yescharacteristic
801C42#174911yescharacteristic
802C42C2×#34712yes—
803C42C2×#34712yes—
804C42C2×#40711yescharacteristic
805C42C2×#43211yescharacteristic
806C16—44no—
807C16—44no—
808C16—44no—
809C16#175314yes—
810C16#175314yes—
811C16C2×#43514yes—
812C16C2×#43614yes—
813C23—24no—
814C23—28no—
815C23—22no—
816C23—24no—
817C23—42no—
818C23—44no—
819C23—42no—
820C23—44no—
821C23—44no—
822C23—48no—
823C23—41no—
824C23—42no—
825C23—41no—
826C23#1141312yes—
827C23#1141312yes—
828C23#1260511yescharacteristic
829C23#1260511yescharacteristic
830C23C22×#34711yescharacteristic
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—24no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—81no—
861C2×C4—82no—
862C2×C4—81no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#814711yescharacteristic
867C2×C4#814712yes—
868C2×C4#814711yescharacteristic
869C2×C4#1141312yes—
870C2×C4#1141312yes—
871C2×C4#1141412yes—
872C2×C4#1141412yes—
873C2×C4#1141412yes—
874C2×C4#1141412yes—
875C2×C4#1260511yescharacteristic
876C2×C4#1260511yescharacteristic
877C2×C4#1260611yescharacteristic
878C2×C4#1260612yes—
879C2×C4#1260611yescharacteristic
880C2×C4C2×#145112yes—
881C2×C4C2×#174911yescharacteristic
882C2×C4C22×#34711yescharacteristic
883C2×C4C2×#211012yes—
884C8—21no—
885C8—21no—
886C8—21no—
887C8—21no—
888C8—42no—
889C8—42no—
890C8—84no—
891C8—84no—
892C8#814711yescharacteristic
893C8#814712yes—
894C8#814711yescharacteristic
895C8C2×#145311yescharacteristic
896C8C2×#145511yescharacteristic
897C8C2×#175312yes—
898C22—22no—
899C22—24no—
900C22—24no—
901C22—28no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—44no—
907C22—44no—
908C22—48no—
909C22—42no—
910C22—44no—
911C22#12827811yescharacteristic
912C22#12827812yes—
913C22#12827811yescharacteristic
914C22C2×#1141312yes—
915C22C2×#1260511yescharacteristic
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—42no—
923C4#12827811yescharacteristic
924C4#12827812yes—
925C4#12827811yescharacteristic
926C4C2×#814711yescharacteristic
927C4C2×#1141412yes—
928C4C2×#1260611yescharacteristic
929C2—21no—
930C2—22no—
931C2—21no—
932C2—22no—
933C2—44no—
934C2#7221718712yesdirect product factor
935C2C2×#12827811yescharacteristic
subgroupG/H
centerC2×C8#1455
commutatorC22×C8C22×C42
Frattini, cosocleC2×#346C24
socleC22#128278
prime radicalC25#347
LCSG ▷ C22×C8 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C22×#346 ◁ G
LECSG ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#93996C2semidirect
2. C2×#93995C2semidirect
5. C2×#149504C2semidirect
6. #72217187C2direct (N × H)
25. #149504C22semidirect
27. #93996C22semidirect
28. #93995C22semidirect
152. C2×M64M16semidirect
156. C22×C32M16semidirect
413. C2×C32C2×M16semidirect
934. C2#72217187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#939962
C2×#939952
C2×#4799582
C2×#1518912
C2×#1495042
#722171872