Finite Group Databasebeta

← C2×#61369 #10576216

Subgroups — C2×#61369 #10576216

Order 512.

6420 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic
2C22×#557C211yesmaximal, characteristic, complemented
3#61369C2132yesmaximal, direct product factor
4C2×#3390C214yesmaximal, complemented
5C2×#3388C214yesmaximal, complemented
6C2×#3387C212yesmaximal, complemented
7C2×#3386C212yesmaximal, complemented
8C2×#3383C212yesmaximal, complemented
9C2×#3381C212yesmaximal, complemented
10C2×#3166C212yesmaximal, complemented
11C2×#3165C211yesmaximal, characteristic, complemented
12C2×#3080C212yesmaximal
13C2×#3079C211yesmaximal, characteristic
14C2×#3078C211yesmaximal, characteristic, complemented
15C2×#3078C212yesmaximal, complemented
16C2×Q8×M16C211yesmaximal, characteristic, complemented
17C2×C4×#137C211yesmaximal, characteristic
18C2×C4×#137C212yesmaximal
19C22×#137C2211yescharacteristic
20Q8×#41—28no—
21Q8×#41C22116yes—
22C2×Q82C2211yescharacteristic
23C2×#557—21no—
24C2×#557—22no—
25C2×#557—21no—
26C2×#557—28no—
27C2×#557C2212yes—
28C2×#557C2211yescharacteristic
29C2×#557C2212yes—
30C2×#557C2214yes—
31C2×#557C2212yes—
32C2×#557C22116yescomplemented
33C2×#554—21no—
34C2×#554—22no—
35C2×#554C2211yescharacteristic
36C2×#554C2212yes—
37C2×D4×Q8—21no—
38C2×D4×Q8C2211yescharacteristic
39C2×#533—21no—
40C2×#533—22no—
41C2×#533C2211yescharacteristic
42C2×#533C2212yes—
43C22×C4⋊Q8—21no—
44C22×C4⋊Q8C2211yescharacteristic
45C22×#125—22no—
46C22×#125C2212yes—
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2212yes—
49C22×C4×Q8—21no—
50C22×C4×Q8—21no—
51C22×C4×Q8C2211yescharacteristic
52C22×C4×Q8C2212yes—
53C22×C4×Q8C2211yescharacteristic
54#3390C22164yescomplemented
55#3388C22164yescomplemented
56#3387C22132yescomplemented
57#3386C22132yescomplemented
58#3383C22132yescomplemented
59#3381C22132yescomplemented
60#3166C22132yescomplemented
61#3165C22116yescomplemented
62C2×#501C2214yes—
63C2×#501C2214yes—
64C2×#501C2214yes—
65C2×#500C2212yes—
66C2×#499C2214yes—
67C2×#499C2214yes—
68C2×#498C2212yes—
69#3080C22132yes—
70#3079C22116yes—
71#3078C22116yescomplemented
72#3078C22132yescomplemented
73C2×#479C2214yes—
74C2×#479C2214yes—
75C2×#479C2214yes—
76C2×#479C2214yes—
77C2×#479C2214yes—
78C2×#477C2212yes—
79C2×#477C2214yes—
80C2×#477C2212yes—
81C2×#475C2212yes—
82C2×#475C2214yes—
83C2×#475C2212yes—
84C2×#478C2214yes—
85C2×#478C2214yes—
86C2×#476C2212yes—
87C2×#474C2212yes—
88Q8×M16C22116yescomplemented
89C2×#446C2212yes—
90C2×#446C2214yes—
91C2×C8×Q8C2212yes—
92C4×#137C22116yes—
93C4×#137C22132yes—
94C2×#441C2214yes—
95C2×#441C2212yes—
96C2×#440C2214yes—
97C2×#440C2212yes—
98C2×C4×Q16C2212yes—
99C2×C4×Q16C2214yes—
100C2×C4×SD16C2212yes—
101C2×C4×SD16C2214yes—
102C2×#428C2212yes—
103C2×#428C2212yes—
104C2×#428C2212yes—
105C2×#428C2212yes—
106C2×#428C2211yescharacteristic
107C2×#423C2211yescharacteristic
108C2×#423C2212yes—
109C2×#417C2212yes—
110C2×#417C2211yescharacteristic
111C2×#419C2211yescharacteristic
112C2×#419C2212yes—
113C2×C4×M16C2211yescharacteristic
114C2×C4×M16C2212yes—
115C22×#41C2311yescharacteristic
116C23×Q8—21no—
117C23×Q8—21no—
118C23×Q8D411yescharacteristic
119C23×Q8C2311yescharacteristic
120C2×#137Q8116yescomplemented
121C2×#137C2318yes—
122C22×Q16C2312yes—
123C22×SD16C2312yes—
124C22×M16C2311yescharacteristic
125C22×M16C2312yes—
126C22×M16C2311yescharacteristic
127Q82—24no—
128Q82C2318yes—
129#557—28no—
130#557—28no—
131#557—216no—
132#557—216no—
133#557—232no—
134#557—216no—
135#557—24no—
136#557—28no—
137#557C23116yes—
138#557C2318yes—
139#557C23116yes—
140#557C23132yes—
141#557C23116yes—
142#554—24no—
143#554—28no—
144#554—216no—
145#554—232no—
146#554C2318yes—
147#554C23116yes—
148D4×Q8—216no—
149D4×Q8—24no—
150D4×Q8C2318yes—
151#533—232no—
152#533—216no—
153#533—28no—
154#533—24no—
155#533C2318yes—
156#533C23116yes—
157C2×C4⋊Q8—22no—
158C2×C4⋊Q8—22no—
159C2×C4⋊Q8—24no—
160C2×C4⋊Q8—216no—
161C2×C4⋊Q8—21no—
162C2×C4⋊Q8—22no—
163C2×C4⋊Q8—21no—
164C2×C4⋊Q8—22no—
165C2×C4⋊Q8—21no—
166C2×C4⋊Q8—21no—
167C2×C4⋊Q8—24no—
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2318yes—
175C2×#125—24no—
176C2×#125—24no—
177C2×#125—24no—
178C2×#125—24no—
179C2×#125—232no—
180C2×#125—22no—
181C2×#125—22no—
182C2×#125—22no—
183C2×#125—22no—
184C2×#125—22no—
185C2×#125—28no—
186C2×#125C2314yes—
187C2×#125C2314yes—
188C2×#125C2312yes—
189C2×#125C2312yes—
190C2×#125C2312yes—
191C2×#125C23116yes—
192C2×C22⋊Q8—21no—
193C2×C22⋊Q8—22no—
194C2×C22⋊Q8—21no—
195C2×C22⋊Q8—22no—
196C2×C22⋊Q8—21no—
197C2×C22⋊Q8—22no—
198C2×C22⋊Q8—21no—
199C2×C22⋊Q8—22no—
200C2×C22⋊Q8—22no—
201C2×C22⋊Q8—22no—
202C2×C22⋊Q8—22no—
203C4×#41—28no—
204C4×#41—24no—
205C4×#41C2318yes—
206C4×#41C23116yes—
207C2×C4×Q8—21no—
208C2×C4×Q8—216no—
209C2×C4×Q8—21no—
210C2×C4×Q8—22no—
211C2×C4×Q8—22no—
212C2×C4×Q8—24no—
213C2×C4×Q8—22no—
214C2×C4×Q8—216no—
215C2×C4×Q8—22no—
216C2×C4×Q8—21no—
217C2×C4×Q8—22no—
218C2×C4×Q8—22no—
219C2×C4×Q8—28no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8—24no—
223C2×C4×Q8—22no—
224C2×C4×Q8—21no—
225C2×C4×Q8D411yescharacteristic
226C2×C4×Q8D411yescharacteristic
227C2×C4×Q8D412yes—
228C2×C4×Q8D418yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C23116yes—
238C2×C4×Q8C2318yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2318yes—
243C2×C4×D4—21no—
244C2×C4×D4—22no—
245C2×C4×D4—21no—
246C2×C4×D4—22no—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—22no—
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C22×C4⋊C4—22no—
256C22×C4⋊C4—21no—
257C22×C4⋊C4—22no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4—22no—
260C22×C4⋊C4—21no—
261C22×C4⋊C4—22no—
262C22×C4⋊C4D411yescharacteristic
263C22×C4⋊C4D412yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C42—22no—
267C22×C42—21no—
268C22×C42—22no—
269C22×C42—21no—
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272#501C23132yes—
273#501C23132yes—
274#501C23132yes—
275#500C23116yes—
276#499C23132yes—
277#499C23132yes—
278#498C23116yes—
279#479C23132yes—
280#479C23132yes—
281#479C23132yes—
282#479C23132yes—
283#479C23132yes—
284#478C23132yes—
285#478C23132yes—
286#477C23116yes—
287#477C23132yes—
288#477C23116yes—
289#476C23116yes—
290#475C23116yes—
291#475C23132yes—
292#475C23116yes—
293#474C23116yes—
294#446C23116yes—
295#446C23132yes—
296C8×Q8C23116yes—
297#441C23132yes—
298#441C23116yes—
299#440C23132yes—
300#440C23116yes—
301C4×Q16C23116yes—
302C4×Q16C23132yes—
303C4×SD16C23116yes—
304C4×SD16C23132yes—
305#428C23116yes—
306#428C23116yes—
307#428C23116yes—
308#428C23116yes—
309#428C2318yes—
310C2×#107C2314yes—
311C2×#107C2314yes—
312C2×#107C2314yes—
313C2×#107C2312yes—
314C2×#107C2314yes—
315C2×#106C2314yes—
316C2×#106C2314yes—
317C2×#106C2314yes—
318C2×#106C2314yes—
319C2×#106C2312yes—
320#423C2318yes—
321#423C23116yes—
322C2×C4⋊C8C2314yes—
323C2×C4⋊C8C2314yes—
324C2×C4⋊C8C2312yes—
325C2×C4⋊C8C2312yes—
326#419C23116yes—
327#419C2318yes—
328#417C23116yes—
329#417C2318yes—
330C2×#103C2312yes—
331C2×#103C2314yes—
332C2×#103C2314yes—
333C2×#103C2314yes—
334C2×#103C2312yes—
335C2×#103C2312yes—
336C2×#102C2312yes—
337C2×#102C2314yes—
338C4×M16C2318yes—
339C4×M16C23116yes—
340C2×#97C2312yes—
341C2×#97C2314yes—
342C2×C4×C8C2312yes—
343C2×C4×C8C2314yes—
344C2×#41—22no—
345C2×#41—24no—
346C2×#41C2×Q818yes—
347C2×#41C2414yes—
348C22×Q8—28no—
349C22×Q8—22no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8—28no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—21no—
358C22×Q8—24no—
359C22×Q8—44no—
360C22×Q8—48no—
361C22×Q8—48no—
362C22×Q8C2×D411yescharacteristic
363C22×Q8C2×D411yescharacteristic
364C22×Q8C2×D412yes—
365C22×Q8C2×D418yes—
366C22×Q8C2×Q818yescomplemented
367C22×Q8C2412yes—
368C22×Q8C2411yescharacteristic
369C22×Q8C2414yes—
370C22×D4—21no—
371C22×D4C2411yescharacteristic
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—21no—
378C23×C4—22no—
379C23×C4—21no—
380C23×C4C2×D411yescharacteristic
381C23×C4C2×D411yescharacteristic
382C23×C4C2×D412yes—
383C23×C4C2×D412yes—
384C23×C4C2411yescharacteristic
385#137C2×Q8164yescomplemented
386C2×Q16C2×Q8116yescomplemented
387C2×Q16C2418yes—
388C2×SD16C2×Q8116yescomplemented
389C2×SD16C2418yes—
390C2×M16—24no—
391C2×M16—28no—
392C2×M16C2×Q818yescomplemented
393C2×M16C2414yes—
394C2×M16C2418yes—
395C2×M16C2414yes—
396C22×C8C2412yes—
397C22×C8C2414yes—
398C22×C8C2412yes—
399C4⋊Q8—216no—
400C4⋊Q8—216no—
401C4⋊Q8—232no—
402C4⋊Q8—28no—
403C4⋊Q8—216no—
404C4⋊Q8—28no—
405C4⋊Q8—216no—
406C4⋊Q8—28no—
407C4⋊Q8—28no—
408C4⋊Q8—24no—
409C4⋊Q8—24no—
410C4⋊Q8—24no—
411C4⋊Q8—22no—
412C4⋊Q8—24no—
413C4⋊Q8—22no—
414C4⋊Q8C2418yes—
415C4⋊Q8C2418yes—
416C4⋊Q8C2414yes—
417C4⋊Q8C2418yes—
418C4⋊Q8C2418yes—
419C4⋊Q8C2414yes—
420#125—232no—
421#125—232no—
422#125—232no—
423#125—232no—
424#125—216no—
425#125—216no—
426#125—216no—
427#125—216no—
428#125—216no—
429#125—28no—
430#125—28no—
431#125—24no—
432#125—24no—
433#125—24no—
434#125C24116yes—
435#125C24116yes—
436#125C2418yes—
437#125C2418yes—
438#125C2418yes—
439C22⋊Q8—28no—
440C22⋊Q8—216no—
441C22⋊Q8—28no—
442C22⋊Q8—216no—
443C22⋊Q8—216no—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8—216no—
447C22⋊Q8—216no—
448C22⋊Q8—216no—
449C22⋊Q8—216no—
450C4×Q8—28no—
451C4×Q8—28no—
452C4×Q8—216no—
453C4×Q8—216no—
454C4×Q8—232no—
455C4×Q8—216no—
456C4×Q8—216no—
457C4×Q8—28no—
458C4×Q8—216no—
459C4×Q8—216no—
460C4×Q8—28no—
461C4×Q8—28no—
462C4×Q8—28no—
463C4×Q8—28no—
464C4×Q8—24no—
465C4×Q8—24no—
466C4×Q8—216no—
467C4×Q8—28no—
468C4×Q8—24no—
469C4×Q8—22no—
470C4×Q8—24no—
471C4×Q8—22no—
472C4×Q8C2×D418yes—
473C4×Q8C2×D4116yes—
474C4×Q8C2×D418yes—
475C4×Q8C2×D414yes—
476C4×Q8C2×D414yes—
477C4×Q8C2×D418yes—
478C4×Q8C2418yes—
479C4×Q8C24116yes—
480C4×Q8C24116yes—
481C4×Q8C2418yes—
482C4×Q8C2418yes—
483C4×Q8C2414yes—
484C4×Q8C2414yes—
485C4×Q8C2418yes—
486C4×Q8C2414yes—
487C4×Q8C2414yes—
488C4×Q8C2418yes—
489C4×D4—28no—
490C4×D4—216no—
491C4×D4—216no—
492C4×D4—28no—
493C4×D4—24no—
494C4×D4—22no—
495C4×D4—24no—
496C4×D4—22no—
497C4×D4C2414yes—
498C4×D4C2418yes—
499C4×D4C2418yes—
500C4×D4C2414yes—
501#117—22no—
502#117—24no—
503#117—216no—
504#117—28no—
505#117C2414yes—
506#117C2418yes—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—216no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—216no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—216no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—216no—
542C2×C4⋊C4C2×D411yescharacteristic
543C2×C4⋊C4C2×D412yes—
544C2×C4⋊C4C2×D412yes—
545C2×C4⋊C4C2×D411yescharacteristic
546C2×C4⋊C4C2×D418yes—
547C2×C4⋊C4C2×D412yes—
548C2×C4⋊C4C2×D412yes—
549C2×C4⋊C4C2×D412yes—
550C2×C4⋊C4C2×D4116yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2411yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—22no—
568C2×C42—21no—
569C2×C42—22no—
570C2×C42—21no—
571C2×C42—216no—
572C2×C42—24no—
573C2×C42—24no—
574C2×C42—28no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—216no—
578C2×C42—28no—
579C2×C42C2×D412yes—
580C2×C42C2×D411yescharacteristic
581C2×C42C2×D412yes—
582C2×C42C2×D411yescharacteristic
583C2×C42C2×D418yes—
584C2×C42C2×D414yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2411yescharacteristic
588C2×C42C2411yescharacteristic
589C2×C42C2418yes—
590C2×C42C2414yes—
591#107C2418yes—
592#107C24116yes—
593#107C24116yes—
594#107C24116yes—
595#107C24116yes—
596#106C24116yes—
597#106C2418yes—
598#106C24116yes—
599#106C24116yes—
600#106C24116yes—
601C4⋊C8C2418yes—
602C4⋊C8C24116yes—
603C4⋊C8C24116yes—
604C4⋊C8C2418yes—
605#103C24116yes—
606#103C2418yes—
607#103C24116yes—
608#103C2418yes—
609#103C2418yes—
610#103C24116yes—
611#102C24116yes—
612#102C2418yes—
613#97C2418yes—
614#97C24116yes—
615C4×C8C2418yes—
616C4×C8C24116yes—
617C24—21no—
618C24C22×D411yescharacteristic
619#41—216no—
620#41—28no—
621#41C22×Q8116yes—
622C2×Q8—28no—
623C2×Q8—216no—
624C2×Q8—24no—
625C2×Q8—24no—
626C2×Q8—24no—
627C2×Q8—22no—
628C2×Q8—21no—
629C2×Q8—28no—
630C2×Q8—24no—
631C2×Q8—28no—
632C2×Q8—28no—
633C2×Q8—28no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—28no—
637C2×Q8—22no—
638C2×Q8—44no—
639C2×Q8—416no—
640C2×Q8—48no—
641C2×Q8—48no—
642C2×Q8—432no—
643C2×Q8—432no—
644C2×Q8—44no—
645C2×Q8—48no—
646C2×Q8—84no—
647C2×Q8—82no—
648C2×Q8C22×D414yes—
649C2×Q8C22×D414yes—
650C2×Q8C22×D418yes—
651C2×Q8C22×Q818yes—
652C2×Q8C22×Q814yes—
653C2×Q8C22×Q8116yescomplemented
654C2×Q8C2514yes—
655C2×Q8C2512yes—
656C2×D4—28no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—22no—
660C2×D4C22×Q814yes—
661C2×D4C2512yes—
662C22×C4—28no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—22no—
666C22×C4—28no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—28no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—24no—
677C22×C4—28no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—24no—
681C22×C4—42no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—48no—
685C22×C4—44no—
686C22×C4—48no—
687C22×C4—44no—
688C22×C4—84no—
689C22×C4—82no—
690C22×C4C22×D414yes—
691C22×C4C22×D412yes—
692C22×C4C22×D412yes—
693C22×C4C22×D411yescharacteristic
694C22×C4C22×D411yescharacteristic
695C22×C4C22×D412yes—
696C22×C4C22×D412yes—
697C22×C4C22×D411yescharacteristic
698C22×C4C22×D418yes—
699C22×C4C22×D414yes—
700C22×C4C22×D418yes—
701C22×C4C22×D412yes—
702C22×C4C22×D411yescharacteristic
703C22×C4C22×D411yescharacteristic
704C22×C4C22×Q814yes—
705C22×C42−1+414yes—
706C22×C4C2512yes—
707C22×C4C2511yescharacteristic
708Q16C22×Q8132yescomplemented
709SD16C22×Q8132yescomplemented
710M16—28no—
711M16—216no—
712M16C22×Q8116yescomplemented
713C2×C8—24no—
714C2×C8—28no—
715C2×C8C22×Q818yes—
716C2×C8C2514yes—
717C2×C8C2518yes—
718C2×C8C2514yes—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—24no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—216no—
729C4⋊C4—216no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—216no—
733C4⋊C4—216no—
734C4⋊C4—24no—
735C4⋊C4—22no—
736C4⋊C4—28no—
737C4⋊C4—24no—
738C4⋊C4—28no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—24no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—22no—
748C4⋊C4—21no—
749C4⋊C4—22no—
750C4⋊C4—21no—
751C4⋊C4C22×D414yes—
752C4⋊C4C22×D418yes—
753C4⋊C4C22×D418yes—
754C4⋊C4C22×D414yes—
755C4⋊C4C22×D418yes—
756C4⋊C4C22×D418yes—
757C4⋊C4C22×D418yes—
758C4⋊C4C2514yes—
759C4⋊C4C2518yes—
760C4⋊C4C2514yes—
761C4⋊C4C2512yes—
762C4⋊C4C2512yes—
763C4⋊C4C2514yes—
764C22⋊C4—24no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—24no—
768C22⋊C4—28no—
769C22⋊C4—24no—
770C42—28no—
771C42—24no—
772C42—28no—
773C42—24no—
774C42—28no—
775C42—24no—
776C42—216no—
777C42—216no—
778C42—28no—
779C42—28no—
780C42C22×D418yes—
781C42C22×D414yes—
782C42C22×D418yes—
783C42C22×D414yes—
784C42C22×D414yes—
785C42C22×D414yes—
786C42C22×D412yes—
787C42C22×D412yes—
788C42C2514yes—
789C42C2512yes—
790C42C2514yes—
791C42C2512yes—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—42no—
797C23—42no—
798C23D4×Q814yes—
799C23C23×D412yes—
800C23C23×D411yescharacteristic
801Q8—24no—
802Q8—22no—
803Q8—28no—
804Q8—216no—
805Q8—24no—
806Q8—28no—
807Q8—28no—
808Q8—48no—
809Q8—416no—
810Q8—416no—
811Q8—48no—
812Q8—416no—
813Q8—88no—
814Q8—84no—
815Q8C23×Q818yes—
816Q8C23×Q814yes—
817D4—216no—
818D4—22no—
819D4—24no—
820D4C23×Q814yes—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—216no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—216no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—48no—
842C2×C4—44no—
843C2×C4—48no—
844C2×C4—416no—
845C2×C4—48no—
846C2×C4—416no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—48no—
853C2×C4—48no—
854C2×C4—88no—
855C2×C4—84no—
856C2×C4D4×Q814yes—
857C2×C4D4×Q818yes—
858C2×C4#57514yes—
859C2×C4C23×D414yes—
860C2×C4C23×D414yes—
861C2×C4C23×D412yes—
862C2×C4C23×D412yes—
863C2×C4C23×D414yes—
864C2×C4C23×D414yes—
865C2×C4C23×D412yes—
866C2×C4C23×D412yes—
867C2×C4C23×D411yescharacteristic
868C2×C4C23×D412yes—
869C2×C4C23×Q812yes—
870C2×C4C23×Q814yes—
871C2×C4C2×2−1+412yes—
872C2×C4C2×2−1+414yes—
873C2×C4C2611yescharacteristic
874C8—24no—
875C8—28no—
876C8C23×Q818yes—
877C22—22no—
878C22—22no—
879C22—28no—
880C22—24no—
881C22—42no—
882C22—42no—
883C22—48no—
884C22C2×D4×Q814yes—
885C22C2×D4×Q812yes—
886C22C2×#57512yes—
887C22#358612yes—
888C22C24×D411yescharacteristic
889C4—22no—
890C4—24no—
891C4—24no—
892C4—24no—
893C4—22no—
894C4—24no—
895C4—22no—
896C4—24no—
897C4—28no—
898C4—44no—
899C4—42no—
900C4—48no—
901C4—44no—
902C4—44no—
903C4—42no—
904C4C2×D4×Q814yes—
905C4C2×D4×Q812yes—
906C4C2×#57514yes—
907C4C24×Q811yescharacteristic
908C4C22×2−1+411yescharacteristic
909C2—24no—
910C2—44no—
911C2#6136914yesdirect product factor
912C2C22×D4×Q811yescharacteristic
913C2C22×#57511yescharacteristic
914C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC22×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#557C2semidirect
3. #61369C2direct (N × H)
4. C2×#3390C2semidirect
5. C2×#3388C2semidirect
6. C2×#3387C2semidirect
7. C2×#3386C2semidirect
8. C2×#3383C2semidirect
9. C2×#3381C2semidirect
10. C2×#3166C2semidirect
11. C2×#3165C2semidirect
14. C2×#3078C2semidirect
15. C2×#3078C2semidirect
16. C2×Q8×M16C2semidirect
32. C2×#557C22semidirect
54. #3390C22semidirect
55. #3388C22semidirect
56. #3387C22semidirect
57. #3386C22semidirect
58. #3383C22semidirect
59. #3381C22semidirect
60. #3166C22semidirect
61. #3165C22semidirect
71. #3078C22semidirect
72. #3078C22semidirect
88. Q8×M16C22semidirect
120. C2×#137Q8semidirect
366. C22×Q8C2×Q8semidirect
385. #137C2×Q8semidirect
386. C2×Q16C2×Q8semidirect
388. C2×SD16C2×Q8semidirect
392. C2×M16C2×Q8semidirect
653. C2×Q8C22×Q8semidirect
708. Q16C22×Q8semidirect
709. SD16C22×Q8semidirect
712. M16C22×Q8semidirect
911. C2#61369direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#412
C22×#5572
#613692
C2×#33902
C2×#33882
C2×#33872
C2×#33862
C2×#33832
C2×#33812
C2×#31662
C2×#31652
C2×#30802
C2×#30792
C2×#30782
C2×Q8×M162
C2×C4×#1372