Finite Group Databasebeta

← C2×#72286610 #72320161

Subgroups — C2×#72286610 #72320161

Order 2048.

23078 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481074C212yesmaximal, complemented
2C2×#483585C213yesmaximal, complemented
3C2×#483583C213yesmaximal, complemented
4C2×#483603C213yesmaximal, complemented
5C2×#483581C216yesmaximal, complemented
6C2×#483602C216yesmaximal, complemented
7C2×D4×#504C212yesmaximal, complemented
8#72286610C2132yesmaximal, direct product factor
9C22×#12062C213yesmaximal, complemented
10C2×D8×#131C211yesmaximal, characteristic
11C2×#483325C211yesmaximal, characteristic, complemented
12C2×#479903C211yesmaximal, characteristic, complemented
13C23×#504—22no—
14C2×D8×#41C411yescharacteristic
15C2×D4×#131C2212yes—
16D4×#504—216no—
17D4×#504C22132yescomplemented
18C2×#33438C2216yescomplemented
19C2×D4×M32C2216yescomplemented
20C2×#33436—26no—
21C2×#33434C2216yescomplemented
22C2×#33432—26no—
23C22×D4×C16C2216yescomplemented
24C2×#33398C2212yes—
25C2×#33334—22no—
26C2×C4×#504C2211yescharacteristic
27C2×C4×#504C2211yescharacteristic
28D8×#131C4116yes—
29D8×#131C22116yes—
30C2×#18066C413yes—
31C2×M16×D8C413yes—
32C2×#17994C416yes—
33C2×#17956C2213yes—
34C2×#17900C2216yes—
35C22×C8×D8C2213yes—
36C2×#17828C411yescharacteristic
37C2×#17507C412yes—
38C2×C8×#131C2211yescharacteristic
39#483603C22148yescomplemented
40#483602C22196yescomplemented
41#483585C22148yescomplemented
42#483583C22148yescomplemented
43#483581C22196yescomplemented
44C2×#12064C2216yescomplemented
45C2×#12064C2216yescomplemented
46C2×#12063C22112yescomplemented
47C2×#12063C22112yescomplemented
48C2×#12062C2213yes—
49C2×#12062C2211yescharacteristic
50C2×#12062C22148yescomplemented
51C2×#12062C2216yescomplemented
52C2×#12062C2216yescomplemented
53C2×#12062C2216yescomplemented
54C2×#12062C2213yescomplemented
55C2×#12062C2213yescomplemented
56#483325C22116yescomplemented
57C2×#11997C2216yescomplemented
58C2×#11996C2213yescomplemented
59C22×#1367C2213yescomplemented
60#481074C22132yescomplemented
61C2×#11584C2216yescomplemented
62C2×#11582C2216yescomplemented
63C2×#11583C2216yescomplemented
64C22×D4⋊C16C2216yescomplemented
65#479903C22116yescomplemented
66C2×#11402C2213yescomplemented
67C2×#11401C2213yescomplemented
68C2×#11401C2213yescomplemented
69C22×#1312C2213yescomplemented
70C23×#131—22no—
71C2×D4×#41C2×C412yes—
72C22×#504—22no—
73C22×#504—21no—
74C22×#504—232no—
75C22×#504—26no—
76C22×#504—26no—
77C22×#504—432no—
78C22×#504D412yes—
79C23×M32—26no—
80C24×C16—26no—
81D8×#41C8116yes—
82D8×#41C2×C4116yes—
83C2×#3391C811yescharacteristic
84C2×Q8×D8C811yescharacteristic
85C2×#3358C812yes—
86C2×#3334C813yes—
87C2×#3294C816yes—
88C2×D4×D8C813yes—
89C2×#3169C2×C413yes—
90C2×#3100C2×C416yes—
91C2×C8×#41C2×C411yescharacteristic
92C2×C8×#41C2×C411yescharacteristic
93C22×C4×D8C2×C413yes—
94D4×#131—28no—
95D4×#131—28no—
96D4×#131C2×C4116yes—
97D4×#131C23116yes—
98C2×#2935C2×C416yes—
99C2×D4×M16C2×C416yes—
100C2×#2933—26no—
101C2×#2931C2316yes—
102C2×#2929—26no—
103C22×C8×D4C2316yes—
104C2×#2906C2×C412yes—
105C2×#2880—22no—
106C2×C4×#131C2311yescharacteristic
107#33438—224no—
108#33438C23148yescomplemented
109D4×M32—224no—
110D4×M32C23148yescomplemented
111#33436—296no—
112#33434—224no—
113#33434C23148yescomplemented
114#33432—296no—
115C2×#2169—26no—
116C2×#2169C23112yes—
117C2×#2168—212no—
118C2×#2168—212no—
119C2×D4×C16—26no—
120C2×D4×C16—26no—
121C2×D4×C16—224no—
122C2×D4×C16—26no—
123C2×D4×C16C2312yes—
124C2×D4×C16C2316yes—
125C2×D4×C16C2316yes—
126C2×D4×C16C2316yes—
127C2×D4×C16C23148yescomplemented
128#33398—28no—
129#33398C23116yes—
130C2×#2151—26no—
131C2×#2150C2316yes—
132C22×C4⋊C16C2316yes—
133#33334—232no—
134C2×#2113—26no—
135C2×#2113—26no—
136C2×#2112—26no—
137C22×C22⋊C16—26no—
138C4×#504—24no—
139C4×#504D418yes—
140C4×#504C2318yes—
141C4×#504C2318yes—
142C2×#2108—23no—
143C2×#2108D416yes—
144C2×C4×M32C2313yes—
145C2×C4×M32C2313yes—
146C22×C4×C16C2313yes—
147C22×C4×C16C2313yes—
148#18066C2×C4148yes—
149M16×D8C2×C4148yes—
150#17994C2×C4196yes—
151#17956C2×C4124yes—
152#17956C23124yes—
153#17900C2×C4148yes—
154#17900C23148yes—
155C2×#1589C2×C416yes—
156C2×#1589C2×C416yes—
157C2×#1581C2×C4112yes—
158C2×#1581C2×C4112yes—
159C2×C8×D8C2×C413yes—
160C2×C8×D8C2×C4124yes—
161C2×C8×D8C2×C413yes—
162C2×C8×D8C2×C416yes—
163C2×C8×D8C23124yes—
164C2×C8×D8C2311yescharacteristic
165C2×C8×D8C2313yes—
166C2×C8×D8C2316yes—
167C2×C8×D8C2316yes—
168#17828C2×C4116yes—
169C2×#1571C2×C416yes—
170C2×#1567C2×C413yes—
171C22×#335C2×C413yes—
172#17507C2×C4132yes—
173C2×#1492C2×C416yes—
174C2×#1480C2×C416yes—
175C2×#1486C2×C416yes—
176C22×D4⋊C8C2×C416yes—
177C8×#131C2×C418yes—
178C8×#131C2318yes—
179C2×#1450C2313yes—
180C2×C8×M16C2×C413yes—
181C2×C8×M16C2×C413yes—
182C22×C82C2313yes—
183#12064C23148yescomplemented
184#12064C23148yescomplemented
185#12063C23196yescomplemented
186#12063C23196yescomplemented
187#12062C23124yes—
188#12062C2318yes—
189#12062C23124yescomplemented
190#12062C23148yescomplemented
191#12062C23148yescomplemented
192#12062C23124yescomplemented
193#12062C23148yescomplemented
194#11997C23148yescomplemented
195#11996C23124yescomplemented
196C2×#1367C2311yescharacteristic
197C2×#1367C2313yes—
198C2×#1367C2316yes—
199C2×#1367C2316yes—
200C2×#1367C23124yescomplemented
201#11584C23148yescomplemented
202#11583C23148yescomplemented
203#11582C23148yescomplemented
204C2×D4⋊C16C2312yes—
205C2×D4⋊C16C2316yes—
206C2×D4⋊C16C2316yes—
207C2×D4⋊C16C2316yes—
208C2×D4⋊C16C23112yes—
209C2×D4⋊C16C23148yescomplemented
210#11402C23124yescomplemented
211#11401C23124yescomplemented
212#11401C23124yescomplemented
213C2×#1312C2311yescharacteristic
214C2×#1312C2313yes—
215C2×#1312C2313yes—
216C2×#1312C2313yes—
217C2×#1312C2316yes—
218C2×#1312C23124yescomplemented
219C23×#41—22no—
220C23×D8C2×C813yes—
221C22×#131—22no—
222C22×#131—216no—
223C22×#131—216no—
224C22×#131—26no—
225C22×#131—26no—
226C22×#131—416no—
227C22×#131—416no—
228C22×#131C2×D411yescharacteristic
229C22×#131#4111yescharacteristic
230C23×M16—26no—
231C24×C8—26no—
232D4×#41—28no—
233D4×#41—28no—
234D4×#41C2×C8116yes—
235D4×#41C22×C4116yes—
236C2×#550C2×C812yes—
237C2×D4×Q8C2×C812yes—
238C2×#548—22no—
239C2×#547C2×C816yes—
240C2×#546—26no—
241C2×D42C2×C816yes—
242C2×#532C22×C416yes—
243C2×#525—26no—
244C2×C4×#41C22×C411yescharacteristic
245C22×C4×D4C22×C416yes—
246C2×#504—248no—
247C2×#504—248no—
248C2×#504—216no—
249C2×#504—216no—
250C2×#504—28no—
251C2×#504—48no—
252C2×#504—448no—
253C2×#504—448no—
254C2×#504—4256no—
255C2×#504—416no—
256C2×#504C2×D4116yes—
257C22×M32—248no—
258C22×M32—212no—
259C22×M32—26no—
260C22×M32—23no—
261C22×M32—448no—
262C22×M32C2×D416yes—
263C23×C16—22no—
264C23×C16—26no—
265C23×C16—26no—
266C23×C16—26no—
267C23×C16—248no—
268C23×C16—26no—
269C23×C16—23no—
270C23×C16—448no—
271C23×C16C2×D416yes—
272#3391C2×C8116yes—
273Q8×D8C2×C8116yes—
274#3358C2×C8132yes—
275#3334C2×C8148yes—
276#3294C2×C8196yes—
277D4×D8C2×C8148yes—
278#3169C2×C8124yes—
279#3169C22×C4124yes—
280C2×#500C2×C813yes—
281C2×#493C2×C813yes—
282C2×#486C2×C816yes—
283#3100C2×C8148yes—
284#3100C22×C4148yes—
285C2×#480C2×C8112yes—
286C2×#474C2×C816yes—
287C2×#474C2×C816yes—
288C2×#466C2×C816yes—
289C2×#466C2×C816yes—
290C2×#459C2×C816yes—
291C2×#459C2×C816yes—
292C2×#447C2×C8112yes—
293C8×#41—24no—
294C8×#41C2×C818yes—
295C8×#41C22×C418yes—
296C8×#41C22×C418yes—
297C2×C8×Q8—21no—
298C2×C8×Q8C2×C811yescharacteristic
299C2×C8×Q8C2×C811yescharacteristic
300C2×C4×D8C2×C813yes—
301C2×C4×D8C2×C813yes—
302C2×C4×D8C2×C816yes—
303C2×C4×D8C2×C8124yes—
304C2×C4×D8C22×C416yes—
305C2×C4×D8C22×C416yes—
306C2×C4×D8C22×C4124yes—
307C2×C4×D8C22×C411yescharacteristic
308C2×C4×D8C22×C413yes—
309#2935—224no—
310#2935C22×C4148yes—
311D4×M16—224no—
312D4×M16C22×C4148yes—
313#2933—248no—
314#2933—248no—
315#2931—212no—
316#2931—212no—
317#2931C22×C4124yes—
318#2931C24124yes—
319#2929—248no—
320#2929—248no—
321C2×#436—26no—
322C2×#436C22×C4112yes—
323C2×#435—212no—
324C2×#435—212no—
325C2×C8×D4—26no—
326C2×C8×D4—212no—
327C2×C8×D4—26no—
328C2×C8×D4—26no—
329C2×C8×D4—212no—
330C2×C8×D4—23no—
331C2×C8×D4C2×C813yes—
332C2×C8×D4C2×C813yes—
333C2×C8×D4C22×C416yes—
334C2×C8×D4C22×C416yes—
335C2×C8×D4C22×C4124yes—
336C2×C8×D4C2412yes—
337C2×C8×D4C2416yes—
338C2×C8×D4C24124yes—
339C2×#431C22×C413yes—
340C2×#431C22×C413yes—
341C22×#107C2×C813yes—
342#2906—28no—
343#2906C22×C4116yes—
344C2×#424—26no—
345C2×#423C22×C416yes—
346C22×C4⋊C8C22×C416yes—
347C22×#102C2×C816yes—
348#2880—216no—
349#2880—216no—
350C2×#408—26no—
351C2×#408—26no—
352C2×#407—26no—
353C22×C22⋊C8—26no—
354C4×#131C22×C414yes—
355C4×#131C2×D414yes—
356C4×#131#4114yes—
357C4×#131C2414yes—
358C2×#405C2×D413yes—
359C2×#405#4113yes—
360C2×C4×M16C22×C413yes—
361C22×C4×C8C22×C413yes—
362C22×C4×C8C22×C413yes—
363C22×C4×C8C2413yes—
364#2169—248no—
365#2169—224no—
366#2169C24148yes—
367#2168—296no—
368#2168—296no—
369D4×C16—24no—
370D4×C16—212no—
371D4×C16—212no—
372D4×C16—212no—
373D4×C16—248no—
374D4×C16—248no—
375D4×C16—248no—
376D4×C16C2418yes—
377D4×C16C24124yes—
378D4×C16C24124yes—
379D4×C16C24124yes—
380#2151—248no—
381#2150—212no—
382#2150C24124yes—
383C2×C4⋊C16—26no—
384C2×C4⋊C16—212no—
385C2×C4⋊C16—26no—
386C2×C4⋊C16C2412yes—
387C2×C4⋊C16C2416yes—
388C2×C4⋊C16C24124yes—
389#2113—248no—
390#2113—248no—
391#2112—248no—
392C2×C22⋊C16—22no—
393C2×C22⋊C16—26no—
394C2×C22⋊C16—26no—
395C2×C22⋊C16—26no—
396C2×C22⋊C16—248no—
397C2×C22⋊C16—212no—
398#2108—224no—
399#2108C2×D4148yes—
400C4×M32—26no—
401C4×M32C2×D4112yes—
402C4×M32C24112yes—
403C4×M32C24112yes—
404C2×#346—23no—
405C2×#346C2×D416yes—
406C2×C4×C16—23no—
407C2×C4×C16—26no—
408C2×C4×C16C2×D416yes—
409C2×C4×C16C2×D4112yes—
410C2×C4×C16C2411yescharacteristic
411C2×C4×C16C2413yes—
412C2×C4×C16C24112yes—
413C2×C4×C16C2411yescharacteristic
414C2×C4×C16C2413yes—
415C2×C4×C16C24112yes—
416#1589C22×C4148yes—
417#1589C22×C4148yes—
418#1581C22×C4196yes—
419#1581C22×C4196yes—
420C8×D8C22×C4112yes—
421C8×D8C22×C4124yes—
422C8×D8C22×C4148yes—
423C8×D8C22×C4124yes—
424C8×D8C22×C4124yes—
425C8×D8C22×C414yes—
426C8×D8C22×C4124yes—
427C8×D8C2414yes—
428C8×D8C24124yes—
429C8×D8C24112yes—
430C8×D8C24124yes—
431#1571C22×C4148yes—
432#1567C22×C4124yes—
433C2×#335C22×C411yescharacteristic
434C2×#335C22×C413yes—
435C2×#335C22×C416yes—
436C2×#335C22×C4124yes—
437C2×#335C22×C416yes—
438#1492C22×C4148yes—
439#1486C22×C4148yes—
440#1480C22×C4148yes—
441C2×D4⋊C8C22×C412yes—
442C2×D4⋊C8C22×C416yes—
443C2×D4⋊C8C22×C416yes—
444C2×D4⋊C8C22×C416yes—
445C2×D4⋊C8C22×C4148yes—
446C2×D4⋊C8C22×C4112yes—
447#1450C22×C4112yes—
448#1450C24112yes—
449C8×M16C22×C4124yes—
450C8×M16C22×C4124yes—
451C2×#322C22×C416yes—
452C2×C82C22×C4112yes—
453C2×C82C22×C413yes—
454C2×C82C22×C413yes—
455C2×C82C24112yes—
456C2×C82C2411yescharacteristic
457C2×C82C2413yes—
458#1367C2414yes—
459#1367C24112yes—
460#1367C24124yes—
461#1367C24124yes—
462D4⋊C16C2418yes—
463D4⋊C16C24124yes—
464D4⋊C16C24124yes—
465D4⋊C16C24124yes—
466D4⋊C16C24148yes—
467#1312C2414yes—
468#1312C24112yes—
469#1312C24112yes—
470#1312C24112yes—
471#1312C24124yes—
472C22×#41—216no—
473C22×#41—216no—
474C22×#41—22no—
475C22×#41—26no—
476C22×#41—26no—
477C22×#41—416no—
478C22×#41—416no—
479C22×#41C4×D411yescharacteristic
480C23×Q8—22no—
481C23×D4—26no—
482C23×D4C22×C816yes—
483C24×C4—26no—
484C22×D8—224no—
485C22×D8C22×C813yes—
486C22×D8C22×C816yes—
487C22×D8C22×C8124yes—
488C22×D8C22×C816yes—
489C22×D8C22×C811yescharacteristic
490C2×#131—28no—
491C2×#131—216no—
492C2×#131—248no—
493C2×#131—224no—
494C2×#131—224no—
495C2×#131—416no—
496C2×#131—464no—
497C2×#131—464no—
498C2×#131—4128no—
499C2×#131—448no—
500C2×#131—424no—
501C2×#131—424no—
502C2×#131C4×D414yes—
503C2×#131C4×D414yes—
504C2×#131AGL(1,ℤ/8)116yes—
505C2×#131C22×D414yes—
506C2×#131C2×#4114yes—
507C22×M16—26no—
508C22×M16—248no—
509C22×M16—212no—
510C22×M16—448no—
511C22×M16C4×D413yes—
512C22×M16C4×D413yes—
513C23×C8—26no—
514C23×C8—23no—
515C23×C8—26no—
516C23×C8—26no—
517C23×C8—224no—
518C23×C8—224no—
519C23×C8—22no—
520C23×C8—26no—
521C23×C8—424no—
522C23×C8—424no—
523C23×C8C22×C813yes—
524C23×C8C22×C813yes—
525C23×C8C22×D413yes—
526C23×C8C2×#4113yes—
527#550—28no—
528#550C22×C8116yes—
529D4×Q8—28no—
530D4×Q8C22×C8116yes—
531#548—216no—
532#548—216no—
533#547—224no—
534#547C22×C8148yes—
535#546—248no—
536#546—248no—
537D42—224no—
538D42C22×C8148yes—
539#532—212no—
540#532—212no—
541#532C22×C8124yes—
542#532C23×C4124yes—
543C2×C4⋊Q8C22×C816yes—
544C2×#127C22×C816yes—
545C2×#124—26no—
546#525—248no—
547#525—248no—
548C2×#123—212no—
549C2×C22⋊Q8—26no—
550C2×C22⋊Q8—26no—
551C2×#121—26no—
552C2×#121—26no—
553C2×#121—26no—
554C2×#121C22×C8112yes—
555C2×#120—212no—
556C4×#41C4×D414yes—
557C4×#41C22×C814yes—
558C4×#41#13114yes—
559C4×#41C23×C414yes—
560C2×C4×Q8C22×C811yescharacteristic
561C2×C4×Q8#13111yescharacteristic
562C2×C4×D4—26no—
563C2×C4×D4—212no—
564C2×C4×D4—26no—
565C2×C4×D4—26no—
566C2×C4×D4—212no—
567C2×C4×D4C22×C8124yes—
568C2×C4×D4C22×C816yes—
569C2×C4×D4C22×C816yes—
570C2×C4×D4C22×C813yes—
571C2×C4×D4#13113yes—
572C2×C4×D4C23×C4124yes—
573C2×C4×D4C23×C412yes—
574C2×C4×D4C23×C416yes—
575C2×#117C4×D413yes—
576C22×C4⋊C4C22×C816yes—
577C22×C22⋊C4—26no—
578C22×C42C23×C413yes—
579#504—264no—
580#504—4192no—
581#504—4192no—
582#504—432no—
583#504—464no—
584C2×M32—224no—
585C2×M32—224no—
586C2×M32—212no—
587C2×M32—248no—
588C2×M32—448no—
589C2×M32—4192no—
590C2×M32—412no—
591C2×M32—424no—
592C2×M32C22×D4124yes—
593C22×C16—224no—
594C22×C16—224no—
595C22×C16—22no—
596C22×C16—26no—
597C22×C16—21no—
598C22×C16—23no—
599C22×C16—212no—
600C22×C16—28no—
601C22×C16—224no—
602C22×C16—224no—
603C22×C16—224no—
604C22×C16—48no—
605C22×C16—424no—
606C22×C16—424no—
607C22×C16—424no—
608C22×C16—4192no—
609C22×C16—412no—
610C22×C16—424no—
611C22×C16C22×D4124yes—
612C22×C16C22×D412yes—
613C22×C16C22×D416yes—
614#500C22×C8124yes—
615#493C22×C8124yes—
616#486C22×C8148yes—
617#480C22×C8196yes—
618#474C22×C8148yes—
619#474C22×C8148yes—
620#466C22×C8148yes—
621#466C22×C8148yes—
622#459C22×C8148yes—
623#459C22×C8148yes—
624#447C22×C8196yes—
625C8×Q8—28no—
626C8×Q8C22×C818yes—
627C8×Q8C22×C818yes—
628C4×D8C22×C8124yes—
629C4×D8C22×C8124yes—
630C4×D8C22×C8124yes—
631C4×D8C22×C8148yes—
632C4×D8C22×C8124yes—
633C4×D8C22×C8112yes—
634C4×D8C22×C814yes—
635C4×D8C23×C4124yes—
636C4×D8C23×C4124yes—
637C4×D8C23×C414yes—
638C4×D8C23×C4112yes—
639#436—224no—
640#436—224no—
641#436—224no—
642#436C23×C4148yes—
643#435—296no—
644#435—296no—
645C8×D4—224no—
646C8×D4—224no—
647C8×D4—224no—
648C8×D4—212no—
649C8×D4—212no—
650C8×D4—224no—
651C8×D4—22no—
652C8×D4—224no—
653C8×D4—26no—
654C8×D4—224no—
655C8×D4—22no—
656C8×D4—26no—
657C8×D4—224no—
658C8×D4C22×C8124yes—
659C8×D4C22×C8124yes—
660C8×D4C23×C414yes—
661C8×D4C23×C4112yes—
662C8×D4C23×C4124yes—
663C8×D4C23×C4124yes—
664C8×D4C2514yes—
665C8×D4C25112yes—
666#431—26no—
667#431C22×C8112yes—
668#431C23×C4112yes—
669#431C23×C4112yes—
670C2×#107C22×C8124yes—
671C2×#107C22×C816yes—
672C2×#107C22×C816yes—
673C2×#107C22×C813yes—
674C2×#107C22×C811yescharacteristic
675#424—248no—
676#423—212no—
677#423C23×C4124yes—
678C2×C4⋊C8—26no—
679C2×C4⋊C8—212no—
680C2×C4⋊C8—26no—
681C2×C4⋊C8—23no—
682C2×C4⋊C8C22×C813yes—
683C2×C4⋊C8C22×C813yes—
684C2×C4⋊C8C23×C412yes—
685C2×C4⋊C8C23×C416yes—
686C2×C4⋊C8C23×C4124yes—
687C2×#102C22×C816yes—
688C2×#102C22×C8112yes—
689C2×#102C22×C816yes—
690C2×#102C22×C812yes—
691C2×#102C22×C816yes—
692C2×#102C22×C8148yes—
693#408—248no—
694#408—224no—
695#408—224no—
696#407—248no—
697C2×C22⋊C8—23no—
698C2×C22⋊C8—26no—
699C2×C22⋊C8—26no—
700C2×C22⋊C8—224no—
701C2×C22⋊C8—212no—
702C2×C22⋊C8—22no—
703C2×C22⋊C8—26no—
704C2×C22⋊C8—224no—
705C2×C22⋊C8C22×C816yes—
706#405C4×D4112yes—
707#405C4×D4112yes—
708#405C22×D4112yes—
709#405C2×#41112yes—
710C4×M16C4×D4112yes—
711C4×M16C23×C4112yes—
712C2×#97C4×D416yes—
713C2×C4×C8—23no—
714C2×C4×C8—26no—
715C2×C4×C8C22×C813yes—
716C2×C4×C8C22×C813yes—
717C2×C4×C8C22×C8112yes—
718C2×C4×C8C23×C411yescharacteristic
719C2×C4×C8C23×C413yes—
720C2×C4×C8C23×C4112yes—
721C2×C4×C8C23×C413yes—
722C2×C4×C8C23×C416yes—
723C2×C4×C8C23×C411yescharacteristic
724C2×C4×C8C23×C413yes—
725C2×C4×C8C23×C4112yes—
726C2×C4×C8C22×D416yes—
727C2×C4×C8C22×D413yes—
728C2×C4×C8C2×#4113yes—
729C2×C4×C8C2×#4116yes—
730C2×C4×C8C2516yes—
731C2×C4×C8C2511yescharacteristic
732C4⋊C16—22no—
733C4⋊C16—26no—
734C4⋊C16—224no—
735C4⋊C16—224no—
736C4⋊C16C2514yes—
737C4⋊C16C25112yes—
738C22⋊C16—28no—
739C22⋊C16—224no—
740C22⋊C16—224no—
741C22⋊C16—224no—
742C22⋊C16—248no—
743#346—212no—
744#346C22×D4124yes—
745C4×C16—21no—
746C4×C16—23no—
747C4×C16—212no—
748C4×C16C22×D412yes—
749C4×C16C22×D416yes—
750C4×C16C22×D4124yes—
751C4×C16C2512yes—
752C4×C16C2516yes—
753C4×C16C2512yes—
754C4×C16C2516yes—
755#335C23×C414yes—
756#335C23×C4112yes—
757#335C23×C4124yes—
758#335C23×C4124yes—
759D4⋊C8C23×C418yes—
760D4⋊C8C23×C4124yes—
761D4⋊C8C23×C4124yes—
762D4⋊C8C23×C4124yes—
763D4⋊C8C23×C4148yes—
764#322C23×C4124yes—
765C82C23×C412yes—
766C82C23×C416yes—
767C82C23×C4112yes—
768C82C23×C4112yes—
769C82C2512yes—
770C82C2516yes—
771C25—26no—
772C2×#41—216no—
773C2×#41—248no—
774C2×#41—224no—
775C2×#41—224no—
776C2×#41—4128no—
777C2×#41—464no—
778C2×#41—464no—
779C2×#41—416no—
780C2×#41—448no—
781C2×#41—424no—
782C2×#41—424no—
783C2×#41C8×D414yes—
784C2×#41#44218yes—
785C2×#41#44418yes—
786C2×#41C2×C4×D414yes—
787C22×Q8—216no—
788C22×Q8—26no—
789C22×Q8—416no—
790C22×Q8C8×D411yescharacteristic
791C22×D4—224no—
792C22×D4—212no—
793C22×D4—248no—
794C22×D4—26no—
795C22×D4—212no—
796C22×D4—26no—
797C22×D4—26no—
798C22×D4—412no—
799C22×D4—448no—
800C22×D4C8×D413yes—
801C22×D4C23×C816yes—
802C22×D4C23×C8124yes—
803C22×D4C23×C812yes—
804C23×C4—26no—
805C23×C4—22no—
806C23×C4—26no—
807C23×C4—224no—
808C23×C4—26no—
809C23×C4—26no—
810C23×C4—224no—
811C23×C4—424no—
812C23×C4—424no—
813C23×C4C2×C4×D413yes—
814C23×C4C23×C813yes—
815C23×C4C2×#13113yes—
816C2×D8—224no—
817C2×D8—296no—
818C2×D8—212no—
819C2×D8—412no—
820C2×D8#50418yescomplemented
821C2×D8C23×C8124yes—
822C2×D8C23×C8112yes—
823C2×D8C23×C8124yes—
824C2×D8C23×C814yes—
825#131—216no—
826#131—216no—
827#131—464no—
828#131—4192no—
829#131—496no—
830#131—448no—
831#131—448no—
832#131#442132yes—
833#131C2×AGL(1,ℤ/8)132yes—
834C2×M16—212no—
835C2×M16—224no—
836C2×M16—248no—
837C2×M16—424no—
838C2×M16—4192no—
839C2×M16—448no—
840C2×M16#442124yes—
841C2×M16C2×C4×D4112yes—
842C2×M16C2×C4×D4112yes—
843C22×C8—212no—
844C22×C8—212no—
845C22×C8—22no—
846C22×C8—26no—
847C22×C8—224no—
848C22×C8—21no—
849C22×C8—23no—
850C22×C8—212no—
851C22×C8—24no—
852C22×C8—212no—
853C22×C8—24no—
854C22×C8—224no—
855C22×C8—212no—
856C22×C8—224no—
857C22×C8—46no—
858C22×C8—424no—
859C22×C8—424no—
860C22×C8—424no—
861C22×C8—496no—
862C22×C8—44no—
863C22×C8—44no—
864C22×C8—412no—
865C22×C8—448no—
866C22×C8—412no—
867C22×C8—448no—
868C22×C8—86no—
869C22×C8C2×C4×D413yes—
870C22×C8C2×C4×D416yes—
871C22×C8C2×C4×D413yes—
872C22×C8C2×C4×D416yes—
873C22×C8C23×C811yescharacteristic
874C22×C8C23×C813yes—
875C22×C8C23×C813yes—
876C22×C8C23×C8112yes—
877C22×C8C23×C8112yes—
878C22×C8C23×C811yescharacteristic
879C22×C8C2×AGL(1,ℤ/8)124yes—
880C22×C8C23×D416yes—
881C22×C8C23×D411yescharacteristic
882C22×C8C22×#4111yescharacteristic
883C22×C8C22×#4116yes—
884C4⋊Q8—212no—
885C4⋊Q8C23×C8124yes—
886#127—212no—
887#127C23×C8124yes—
888#124—224no—
889#124—224no—
890#123—296no—
891C22⋊Q8—248no—
892C22⋊Q8—248no—
893#121—224no—
894#121—224no—
895#121—224no—
896#121—248no—
897#121—248no—
898#121C23×C8148yes—
899#120—296no—
900C4×Q8C8×D414yes—
901C4×Q8C8×D414yes—
902C4×Q8C23×C814yes—
903C4×Q8C2×#13114yes—
904C4×D4—22no—
905C4×D4—224no—
906C4×D4—26no—
907C4×D4—224no—
908C4×D4—224no—
909C4×D4—212no—
910C4×D4—224no—
911C4×D4—212no—
912C4×D4—224no—
913C4×D4—22no—
914C4×D4—26no—
915C4×D4—224no—
916C4×D4C8×D4112yes—
917C4×D4C8×D4112yes—
918C4×D4C23×C814yes—
919C4×D4C23×C8112yes—
920C4×D4C23×C8124yes—
921C4×D4C23×C8124yes—
922C4×D4C23×C8112yes—
923C4×D4C2×#131112yes—
924C4×D4C24×C414yes—
925C4×D4C24×C4112yes—
926#117C8×D4112yes—
927#117C2×C4×D4112yes—
928C2×C4⋊C4—26no—
929C2×C4⋊C4—212no—
930C2×C4⋊C4—26no—
931C2×C4⋊C4C8×D413yes—
932C2×C4⋊C4C8×D413yes—
933C2×C4⋊C4C23×C812yes—
934C2×C4⋊C4C23×C816yes—
935C2×C4⋊C4C23×C8124yes—
936C2×C22⋊C4—26no—
937C2×C22⋊C4—26no—
938C2×C22⋊C4—224no—
939C2×C22⋊C4—212no—
940C2×C22⋊C4—22no—
941C2×C22⋊C4—26no—
942C2×C22⋊C4—224no—
943C2×C22⋊C4C8×D416yes—
944C2×C42C2×C4×D413yes—
945C2×C42C2×C4×D416yes—
946C2×C42C23×C813yes—
947C2×C42C23×C816yes—
948C2×C42C2×#13113yes—
949C2×C42C2×#13116yes—
950C2×C42C24×C411yescharacteristic
951C2×C42C24×C416yes—
952M32—248no—
953M32—496no—
954M32—424no—
955M32—448no—
956C2×C16—24no—
957C2×C16—212no—
958C2×C16—248no—
959C2×C16—24no—
960C2×C16—212no—
961C2×C16—22no—
962C2×C16—26no—
963C2×C16—416no—
964C2×C16—448no—
965C2×C16—448no—
966C2×C16—448no—
967C2×C16—42no—
968C2×C16—46no—
969C2×C16—424no—
970C2×C16—44no—
971C2×C16—412no—
972C2×C16—448no—
973C2×C16C23×D414yes—
974C2×C16C23×D4112yes—
975#107C23×C814yes—
976#107C23×C8112yes—
977#107C23×C8124yes—
978#107C23×C8124yes—
979C4⋊C8—22no—
980C4⋊C8—26no—
981C4⋊C8—224no—
982C4⋊C8—224no—
983C4⋊C8—212no—
984C4⋊C8C23×C8112yes—
985C4⋊C8C23×C8112yes—
986C4⋊C8C24×C414yes—
987C4⋊C8C24×C4112yes—
988#102C23×C818yes—
989#102C23×C8124yes—
990#102C23×C8124yes—
991#102C23×C8124yes—
992#102C23×C8148yes—
993C22⋊C8—212no—
994C22⋊C8—24no—
995C22⋊C8—212no—
996C22⋊C8—24no—
997C22⋊C8—224no—
998C22⋊C8—224no—
999C22⋊C8—212no—
1000C22⋊C8—248no—
1001C22⋊C8C23×C8124yes—
1002#97C2×C4×D4124yes—
1003C4×C8—21no—
1004C4×C8—23no—
1005C4×C8—212no—
1006C4×C8C2×C4×D416yes—
1007C4×C8C2×C4×D416yes—
1008C4×C8C2×C4×D416yes—
1009C4×C8C23×C812yes—
1010C4×C8C23×C816yes—
1011C4×C8C23×C8112yes—
1012C4×C8C23×C8112yes—
1013C4×C8C24×C412yes—
1014C4×C8C24×C416yes—
1015C4×C8C24×C411yescharacteristic
1016C4×C8C24×C416yes—
1017C4×C8C24×C412yes—
1018C4×C8C24×C416yes—
1019C4×C8C23×D411yescharacteristic
1020C4×C8C23×D416yes—
1021C4×C8C22×#4111yescharacteristic
1022C4×C8C22×#4116yes—
1023C4×C8C2611yescharacteristic
1024C24—22no—
1025C24—26no—
1026C24—224no—
1027C24—424no—
1028C24—424no—
1029C24—812no—
1030C24C2×C8×D413yes—
1031#41—464no—
1032#41—4192no—
1033#41—448no—
1034#41—496no—
1035#41—448no—
1036#41#1580132yes—
1037#41C2×#442116yes—
1038#41C2×#444116yes—
1039C2×Q8—224no—
1040C2×Q8—464no—
1041C2×Q8—424no—
1042C2×Q8#158018yes—
1043C2×Q8C2×C8×D414yes—
1044C2×D4—248no—
1045C2×D4—248no—
1046C2×D4—212no—
1047C2×D4—24no—
1048C2×D4—212no—
1049C2×D4—22no—
1050C2×D4—224no—
1051C2×D4—26no—
1052C2×D4—224no—
1053C2×D4—224no—
1054C2×D4—424no—
1055C2×D4—448no—
1056C2×D4—424no—
1057C2×D4—448no—
1058C2×D4—4192no—
1059C2×D4—424no—
1060C2×D4—812no—
1061C2×D4#1580124yes—
1062C2×D4C2×C8×D4112yes—
1063C2×D4C2×#50418yescomplemented
1064C2×D4C24×C8112yes—
1065C2×D4C24×C814yes—
1066C22×C4—26no—
1067C22×C4—26no—
1068C22×C4—22no—
1069C22×C4—26no—
1070C22×C4—224no—
1071C22×C4—24no—
1072C22×C4—212no—
1073C22×C4—24no—
1074C22×C4—212no—
1075C22×C4—224no—
1076C22×C4—224no—
1077C22×C4—46no—
1078C22×C4—424no—
1079C22×C4—44no—
1080C22×C4—412no—
1081C22×C4—448no—
1082C22×C4—424no—
1083C22×C4—424no—
1084C22×C4—496no—
1085C22×C4—44no—
1086C22×C4—412no—
1087C22×C4—448no—
1088C22×C4C2×C8×D413yes—
1089C22×C4C2×C8×D413yes—
1090C22×C4C2×C8×D416yes—
1091C22×C4C2×C8×D416yes—
1092C22×C4C2×C8×D413yes—
1093C22×C4C2×C8×D416yes—
1094C22×C4C2×#442112yes—
1095C22×C4C2×#444112yes—
1096C22×C4C22×C4×D411yescharacteristic
1097C22×C4C22×C4×D416yes—
1098C22×C4C24×C816yes—
1099C22×C4C24×C811yescharacteristic
1100C22×C4C22×#13111yescharacteristic
1101C22×C4C22×#13116yes—
1102D8—248no—
1103D8—224no—
1104D8—424no—
1105D8C2×#504116yescomplemented
1106M16—224no—
1107M16—448no—
1108M16—496no—
1109M16C2×#442148yes—
1110C2×C8—22no—
1111C2×C8—212no—
1112C2×C8—26no—
1113C2×C8—212no—
1114C2×C8—26no—
1115C2×C8—22no—
1116C2×C8—26no—
1117C2×C8—224no—
1118C2×C8—22no—
1119C2×C8—26no—
1120C2×C8—24no—
1121C2×C8—212no—
1122C2×C8—412no—
1123C2×C8—46no—
1124C2×C8—42no—
1125C2×C8—44no—
1126C2×C8—412no—
1127C2×C8—448no—
1128C2×C8—44no—
1129C2×C8—412no—
1130C2×C8—44no—
1131C2×C8—412no—
1132C2×C8—48no—
1133C2×C8—448no—
1134C2×C8—448no—
1135C2×C8—424no—
1136C2×C8—812no—
1137C2×C8C2×#442112yes—
1138C2×C8C2×#442124yes—
1139C2×C8C2×#50414yescomplemented
1140C2×C8C22×C4×D411yescharacteristic
1141C2×C8C22×C4×D416yes—
1142C2×C8C22×C4×D411yescharacteristic
1143C2×C8C22×C4×D416yes—
1144C2×C8C24×C812yes—
1145C2×C8C24×C816yes—
1146C2×C8C24×C816yes—
1147C2×C8C24×C812yes—
1148C2×C8C22×AGL(1,ℤ/8)14yes—
1149C2×C8C22×AGL(1,ℤ/8)124yes—
1150C2×C8C24×D411yescharacteristic
1151C2×C8C23×#4111yescharacteristic
1152C4⋊C4—22no—
1153C4⋊C4—26no—
1154C4⋊C4—224no—
1155C4⋊C4—224no—
1156C4⋊C4C2×C8×D4112yes—
1157C4⋊C4C2×C8×D4112yes—
1158C4⋊C4C24×C814yes—
1159C4⋊C4C24×C8112yes—
1160C22⋊C4—24no—
1161C22⋊C4—212no—
1162C22⋊C4—24no—
1163C22⋊C4—224no—
1164C22⋊C4—224no—
1165C22⋊C4—212no—
1166C22⋊C4—248no—
1167C22⋊C4C2×C8×D4124yes—
1168C42C2×C8×D416yes—
1169C42C2×C8×D416yes—
1170C42C2×C8×D416yes—
1171C42C22×C4×D411yescharacteristic
1172C42C22×C4×D416yes—
1173C42C24×C811yescharacteristic
1174C42C24×C816yes—
1175C42C22×#13111yescharacteristic
1176C42C22×#13116yes—
1177C42C25×C411yescharacteristic
1178C16—24no—
1179C16—212no—
1180C16—42no—
1181C16—46no—
1182C16—44no—
1183C16—412no—
1184C23—26no—
1185C23—26no—
1186C23—24no—
1187C23—28no—
1188C23—212no—
1189C23—448no—
1190C23—44no—
1191C23—44no—
1192C23—448no—
1193C23—412no—
1194C23—412no—
1195C23—412no—
1196C23—824no—
1197C23—896no—
1198C23C2×#1580112yes—
1199C23C22×C8×D416yes—
1200C23C22×C8×D411yescharacteristic
1201Q8—448no—
1202Q8C2×#1580116yes—
1203D4—28no—
1204D4—212no—
1205D4—24no—
1206D4—212no—
1207D4—448no—
1208D4—496no—
1209D4—448no—
1210D4—412no—
1211D4—824no—
1212D4C2×#1580148yes—
1213D4C22×#50418yescomplemented
1214C2×C4—22no—
1215C2×C4—26no—
1216C2×C4—26no—
1217C2×C4—212no—
1218C2×C4—26no—
1219C2×C4—26no—
1220C2×C4—24no—
1221C2×C4—212no—
1222C2×C4—46no—
1223C2×C4—46no—
1224C2×C4—44no—
1225C2×C4—412no—
1226C2×C4—448no—
1227C2×C4—44no—
1228C2×C4—412no—
1229C2×C4—44no—
1230C2×C4—412no—
1231C2×C4—48no—
1232C2×C4—448no—
1233C2×C4—448no—
1234C2×C4—424no—
1235C2×C4C2×#1580112yes—
1236C2×C4C2×#1580124yes—
1237C2×C4C22×C8×D411yescharacteristic
1238C2×C4C22×C8×D416yes—
1239C2×C4C22×C8×D416yes—
1240C2×C4C22×C8×D411yescharacteristic
1241C2×C4C22×C8×D416yes—
1242C2×C4C22×C8×D411yescharacteristic
1243C2×C4C22×#44212yes—
1244C2×C4C22×#442112yes—
1245C2×C4C22×#44412yes—
1246C2×C4C22×#444112yes—
1247C2×C4C22×#50412yes—
1248C2×C4#6262412yes—
1249C2×C4C23×C4×D411yescharacteristic
1250C2×C4C25×C811yescharacteristic
1251C2×C4C23×#13111yescharacteristic
1252C8—21no—
1253C8—21no—
1254C8—26no—
1255C8—26no—
1256C8—22no—
1257C8—26no—
1258C8—46no—
1259C8—42no—
1260C8—44no—
1261C8—412no—
1262C8C22×#44212yes—
1263C8C22×#442112yes—
1264C8C22×#50414yescomplemented
1265C8C23×AGL(1,ℤ/8)12yes—
1266C22—26no—
1267C22—26no—
1268C22—224no—
1269C22—28no—
1270C22—44no—
1271C22—416no—
1272C22—44no—
1273C22—412no—
1274C22—412no—
1275C22—412no—
1276C22—896no—
1277C22—824no—
1278C22C22×#1580112yes—
1279C22C22×#158012yes—
1280C22#762258812yes—
1281C22D4×#50412yes—
1282C22C23×C8×D411yescharacteristic
1283C4—26no—
1284C4—21no—
1285C4—21no—
1286C4—26no—
1287C4—44no—
1288C4—412no—
1289C4C22×#158012yes—
1290C4C22×#1580112yes—
1291C4D4×#50412yes—
1292C4C23×#44411yescharacteristic
1293C4C23×#44211yescharacteristic
1294C4C23×#50411yescharacteristic
1295C4C2×#6262411yescharacteristic
1296C2—212no—
1297C2—48no—
1298C2—812no—
1299C2C23×#158011yescharacteristic
1300C2#7228661014yesdirect product factor
1301C2C2×#762258811yescharacteristic
1302C2C2×D4×#50411yescharacteristic
subgroupG/H
centerC22×C8C23×D4
commutatorC2×C4C25×C8
Frattini, cosocleC4×C8C26
socleC23C22×C8×D4
prime radicalC2×D8×#41C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C8 ◁ C2×C4×#504 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#481074C2semidirect
2. C2×#483585C2semidirect
3. C2×#483583C2semidirect
4. C2×#483603C2semidirect
5. C2×#483581C2semidirect
6. C2×#483602C2semidirect
7. C2×D4×#504C2semidirect
8. #72286610C2direct (N × H)
9. C22×#12062C2semidirect
11. C2×#483325C2semidirect
12. C2×#479903C2semidirect
17. D4×#504C22semidirect
18. C2×#33438C22semidirect
19. C2×D4×M32C22semidirect
21. C2×#33434C22semidirect
23. C22×D4×C16C22semidirect
39. #483603C22semidirect
40. #483602C22semidirect
41. #483585C22semidirect
42. #483583C22semidirect
43. #483581C22semidirect
44. C2×#12064C22semidirect
45. C2×#12064C22semidirect
46. C2×#12063C22semidirect
47. C2×#12063C22semidirect
50. C2×#12062C22semidirect
51. C2×#12062C22semidirect
52. C2×#12062C22semidirect
53. C2×#12062C22semidirect
54. C2×#12062C22semidirect
55. C2×#12062C22semidirect
56. #483325C22semidirect
57. C2×#11997C22semidirect
58. C2×#11996C22semidirect
59. C22×#1367C22semidirect
60. #481074C22semidirect
61. C2×#11584C22semidirect
62. C2×#11582C22semidirect
63. C2×#11583C22semidirect
64. C22×D4⋊C16C22semidirect
65. #479903C22semidirect
66. C2×#11402C22semidirect
67. C2×#11401C22semidirect
68. C2×#11401C22semidirect
69. C22×#1312C22semidirect
108. #33438C23semidirect
110. D4×M32C23semidirect
113. #33434C23semidirect
127. C2×D4×C16C23semidirect
183. #12064C23semidirect
184. #12064C23semidirect
185. #12063C23semidirect
186. #12063C23semidirect
189. #12062C23semidirect
190. #12062C23semidirect
191. #12062C23semidirect
192. #12062C23semidirect
193. #12062C23semidirect
194. #11997C23semidirect
195. #11996C23semidirect
200. C2×#1367C23semidirect
201. #11584C23semidirect
202. #11583C23semidirect
203. #11582C23semidirect
209. C2×D4⋊C16C23semidirect
210. #11402C23semidirect
211. #11401C23semidirect
212. #11401C23semidirect
218. C2×#1312C23semidirect
820. C2×D8#504semidirect
1063. C2×D4C2×#504semidirect
1105. D8C2×#504semidirect
1139. C2×C8C2×#504semidirect
1213. D4C22×#504semidirect
1264. C8C22×#504semidirect
1300. C2#72286610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4810742
C2×#4835852
C2×#4835832
C2×#4836032
C2×#4835812
C2×#4836022
C2×D4×#5042
#722866102
C22×#120622
C2×D8×#1312
C2×#4833252
C2×#4799032