Finite Group Databasebeta

← C2×#17514 #6343052

Subgroups — C2×#17514 #6343052

Order 512.

3008 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic
2C2×#2965C211yesmaximal, characteristic
3C2×#2925C211yesmaximal, characteristic
4#17514C2116yesmaximal, direct product factor
5C2×#1497C212yesmaximal, complemented
6C2×#1493C211yesmaximal, characteristic, complemented
7C2×#1485C212yesmaximal, complemented
8C2×#1481C211yesmaximal, characteristic, complemented
9C2×#1491C212yesmaximal, complemented
10C2×#1487C211yesmaximal, characteristic, complemented
11C2×#1479C212yesmaximal, complemented
12C22×Q8⋊C8C211yesmaximal, characteristic, complemented
13Q8×#41—24no—
14Q8×#41—24no—
15Q8×#41C418yes—
16Q8×#41C2218yes—
17C2×Q82C411yescharacteristic
18C2×#557—21no—
19C2×#557C411yescharacteristic
20C2×#554—22no—
21C2×#554—21no—
22C2×#554C412yes—
23C2×#554C411yescharacteristic
24C2×D4×Q8C411yescharacteristic
25C2×D4×Q8C412yes—
26C2×#533—21no—
27C2×#533—22no—
28C2×#533C2211yescharacteristic
29C2×#533C2212yes—
30C2×C4×#41—21no—
31C2×C4×#41C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2212yes—
34#2965—24no—
35#2965C2218yes—
36C2×#446—21no—
37C2×#436—21no—
38C2×#435—22no—
39#2925—24no—
40#2925C2218yes—
41C2×#433—22no—
42C2×#432C2212yes—
43C2×#431C2212yes—
44C2×#431C2212yes—
45C2×#431C2211yescharacteristic
46C2×#423C2211yescharacteristic
47C22×C4⋊C8C2211yescharacteristic
48C2×#408—21no—
49C2×#405—21no—
50C2×C4×M16C2212yes—
51C22×C4×C8C2211yescharacteristic
52#1497C22116yescomplemented
53#1493C2218yescomplemented
54#1491C22116yescomplemented
55#1487C2218yescomplemented
56#1485C22116yescomplemented
57#1481C2218yescomplemented
58#1479C22116yescomplemented
59C2×Q8⋊C8C2211yescharacteristic
60C2×Q8⋊C8C2211yescharacteristic
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×Q8⋊C8C2212yes—
64C2×Q8⋊C8C2212yes—
65C2×Q8⋊C8C2212yes—
66C2×Q8⋊C8C2212yes—
67C2×Q8⋊C8C2212yes—
68C2×Q8⋊C8C2212yes—
69C2×Q8⋊C8C2218yescomplemented
70C22×#41D411yescharacteristic
71C23×Q8C2×C411yescharacteristic
72C23×Q8C2×C412yes—
73C22×M16—22no—
74C22×M16—21no—
75C23×C8—21no—
76C23×C8—21no—
77Q82—24no—
78Q82C2×C418yes—
79#557—28no—
80#557—24no—
81#557—28no—
82#557C2×C418yes—
83#554—216no—
84#554—28no—
85#554—24no—
86#554—28no—
87#554—216no—
88#554—28no—
89#554C2×C4116yes—
90#554C2×C418yes—
91D4×Q8—28no—
92D4×Q8—24no—
93D4×Q8C2×C418yes—
94D4×Q8C2×C4116yes—
95#533—216no—
96#533—28no—
97#533—28no—
98#533—216no—
99#533—22no—
100#533—24no—
101#533—22no—
102#533—24no—
103#533C2×C414yes—
104#533C2×C418yes—
105#533C2314yes—
106#533C2318yes—
107C2×C4⋊Q8—22no—
108C2×C4⋊Q8—21no—
109C2×C4⋊Q8—22no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8C2×C411yescharacteristic
112C2×C4⋊Q8C2×C412yes—
113C2×C4⋊Q8C2×C411yescharacteristic
114C2×C4⋊Q8C2×C412yes—
115C2×#125—22no—
116C2×#125—21no—
117C2×#125—22no—
118C2×#125—21no—
119C2×#125—21no—
120C2×#125—22no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—22no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8C2×C412yes—
130C2×C22⋊Q8C2×C412yes—
131C2×C22⋊Q8C2×C412yes—
132C4×#41—28no—
133C4×#41—28no—
134C4×#41C2×C414yes—
135C4×#41D414yes—
136C4×#41D414yes—
137C4×#41C2314yes—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—22no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—22no—
144C2×C4×Q8—22no—
145C2×C4×Q8—24no—
146C2×C4×Q8—22no—
147C2×C4×Q8—24no—
148C2×C4×Q8—22no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2×C411yescharacteristic
151C2×C4×Q8C2×C412yes—
152C2×C4×Q8C2×C411yescharacteristic
153C2×C4×Q8C2×C412yes—
154C2×C4×Q8C2×C414yes—
155C2×C4×Q8C2×C418yes—
156C2×C4×Q8C2×C411yescharacteristic
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2314yes—
162C2×C4×Q8C2318yes—
163C2×C4×D4—22no—
164C2×C4×D4—21no—
165C2×C4×D4—22no—
166C2×C4×D4—21no—
167C2×C4×D4C2×C412yes—
168C2×C4×D4C2×C411yescharacteristic
169C2×C4×D4D412yes—
170C2×C4×D4D411yescharacteristic
171C2×#117—22no—
172C2×#117—21no—
173C2×#117D411yescharacteristic
174C2×#117D412yes—
175C22×C4⋊C4—21no—
176C22×C4⋊C4—22no—
177C22×C4⋊C4C2×C411yescharacteristic
178C22×C4⋊C4C2×C412yes—
179C22×C42—22no—
180C22×C42—21no—
181C22×C42C2311yescharacteristic
182C22×C42C2312yes—
183#446—28no—
184#436—28no—
185#435—216no—
186#433—216no—
187#432—24no—
188#432C2318yes—
189#431—24no—
190#431—24no—
191#431—22no—
192#431C2318yes—
193#431C2318yes—
194#431C2314yes—
195#423—22no—
196#423C2314yes—
197C2×C4⋊C8—21no—
198C2×C4⋊C8—22no—
199C2×C4⋊C8—21no—
200C2×C4⋊C8—22no—
201C2×C4⋊C8—21no—
202C2×C4⋊C8C2311yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2314yes—
205C2×C4⋊C8C2312yes—
206#408—28no—
207C2×C22⋊C8—22no—
208C2×C22⋊C8—22no—
209C2×C22⋊C8—21no—
210C2×C22⋊C8—22no—
211#405—28no—
212C4×M16—24no—
213C4×M16C2318yes—
214C2×#97—22no—
215C2×#97—22no—
216C2×C4×C8—21no—
217C2×C4×C8—22no—
218C2×C4×C8—22no—
219C2×C4×C8C2311yescharacteristic
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2314yes—
222C2×C4×C8C2312yes—
223Q8⋊C8C2314yes—
224Q8⋊C8C2314yes—
225Q8⋊C8C2314yes—
226Q8⋊C8C2314yes—
227Q8⋊C8C2318yes—
228Q8⋊C8C2318yes—
229Q8⋊C8C2318yes—
230Q8⋊C8C2318yes—
231Q8⋊C8C2318yes—
232Q8⋊C8C2318yes—
233C2×#41—24no—
234C2×#41—24no—
235C2×#41C22⋊C414yes—
236C2×#41C2×D414yes—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—21no—
243C22×Q8—24no—
244C22×Q8—28no—
245C22×Q8—42no—
246C22×Q8—44no—
247C22×Q8C22⋊C411yescharacteristic
248C22×Q8C22×C411yescharacteristic
249C22×Q8C22×C412yes—
250C22×Q8C22×C414yes—
251C22×Q8C22×C418yes—
252C22×Q8C22×C411yescharacteristic
253C22×D4C22⋊C412yes—
254C22×D4C22⋊C411yescharacteristic
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4C22×C412yes—
260C23×C4C22×C411yescharacteristic
261C23×C4C2×D412yes—
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D412yes—
264C23×C4C2×D411yescharacteristic
265C2×M16—28no—
266C2×M16—24no—
267C2×M16—48no—
268C2×M16—44no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—24no—
272C22×C8—24no—
273C22×C8—22no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—22no—
277C22×C8—44no—
278C22×C8—44no—
279C4⋊Q8—216no—
280C4⋊Q8—28no—
281C4⋊Q8—216no—
282C4⋊Q8—28no—
283C4⋊Q8—24no—
284C4⋊Q8—22no—
285C4⋊Q8—24no—
286C4⋊Q8—22no—
287C4⋊Q8C22×C414yes—
288C4⋊Q8C22×C418yes—
289C4⋊Q8C22×C414yes—
290C4⋊Q8C22×C418yes—
291#125—216no—
292#125—28no—
293#125—216no—
294#125—28no—
295#125—28no—
296#125—24no—
297#125—24no—
298#125—28no—
299C22⋊Q8—28no—
300C22⋊Q8—24no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—28no—
306C22⋊Q8—216no—
307C22⋊Q8—216no—
308C22⋊Q8—216no—
309C22⋊Q8—216no—
310C22⋊Q8—216no—
311C22⋊Q8—216no—
312C22⋊Q8C22×C418yes—
313C22⋊Q8C22×C418yes—
314C22⋊Q8C22×C418yes—
315C4×Q8—28no—
316C4×Q8—28no—
317C4×Q8—24no—
318C4×Q8—28no—
319C4×Q8—24no—
320C4×Q8—22no—
321C4×Q8—24no—
322C4×Q8—22no—
323C4×Q8—28no—
324C4×Q8—24no—
325C4×Q8—24no—
326C4×Q8—28no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—22no—
331C4×Q8—28no—
332C4×Q8—24no—
333C4×Q8—21no—
334C4×Q8—22no—
335C4×Q8—24no—
336C4×Q8—28no—
337C4×Q8—28no—
338C4×Q8—24no—
339C4×Q8C22⋊C414yes—
340C4×Q8C22⋊C414yes—
341C4×Q8C22×C412yes—
342C4×Q8C22×C412yes—
343C4×Q8C22×C414yes—
344C4×Q8C22×C414yes—
345C4×Q8C22×C418yes—
346C4×Q8C22×C414yes—
347C4×Q8C22×C418yes—
348C4×Q8C22×C414yes—
349C4×Q8C2×D414yes—
350C4×Q8C2412yes—
351C4×Q8C2412yes—
352C4×Q8C2414yes—
353C4×D4—216no—
354C4×D4—28no—
355C4×D4—216no—
356C4×D4—28no—
357C4×D4C22⋊C418yes—
358C4×D4C22⋊C414yes—
359C4×D4C22⋊C418yes—
360C4×D4C22⋊C414yes—
361C4×D4C22×C418yes—
362C4×D4C22×C414yes—
363C4×D4C2×D418yes—
364C4×D4C2×D414yes—
365#117—28no—
366#117—24no—
367#117—28no—
368#117—24no—
369#117C22⋊C418yes—
370#117C22⋊C414yes—
371#117C2×D414yes—
372#117C2×D418yes—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4C22⋊C412yes—
398C2×C4⋊C4C22⋊C411yescharacteristic
399C2×C4⋊C4C22⋊C412yes—
400C2×C4⋊C4C22⋊C411yescharacteristic
401C2×C4⋊C4C22×C411yescharacteristic
402C2×C4⋊C4C22×C411yescharacteristic
403C2×C4⋊C4C22×C412yes—
404C2×C4⋊C4C22×C414yes—
405C2×C4⋊C4C22×C418yes—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4C22⋊C412yes—
410C2×C22⋊C4C22⋊C412yes—
411C2×C22⋊C4C22⋊C412yes—
412C2×C42—22no—
413C2×C42—21no—
414C2×C42—22no—
415C2×C42—21no—
416C2×C42—28no—
417C2×C42—24no—
418C2×C42—28no—
419C2×C42—24no—
420C2×C42—21no—
421C2×C42—22no—
422C2×C42—21no—
423C2×C42C22×C412yes—
424C2×C42C22×C411yescharacteristic
425C2×C42C22×C414yes—
426C2×C42C22×C412yes—
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D412yes—
429C2×C42C2×D412yes—
430C2×C42C2×D414yes—
431C2×C42C2×D412yes—
432C2×C42C2×D414yes—
433C2×C42C2×D412yes—
434C2×C42C2×D411yescharacteristic
435C2×C42C2412yes—
436C2×C42C2414yes—
437C2×C42C2411yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—24no—
441C4⋊C8—24no—
442C4⋊C8—28no—
443C4⋊C8—24no—
444C4⋊C8—22no—
445C4⋊C8C2412yes—
446C4⋊C8C2412yes—
447C4⋊C8C2414yes—
448C22⋊C8—28no—
449C22⋊C8—28no—
450C22⋊C8—24no—
451C22⋊C8—28no—
452#97—28no—
453#97—28no—
454C4×C8—21no—
455C4×C8—21no—
456C4×C8—24no—
457C4×C8—28no—
458C4×C8—22no—
459C4×C8C2412yes—
460C4×C8C2412yes—
461C4×C8C2414yes—
462C24C2×C22⋊C412yes—
463C24C2×C22⋊C411yescharacteristic
464#41—28no—
465#41—28no—
466#41—216no—
467C2×Q8—21no—
468C2×Q8—28no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—28no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—28no—
477C2×Q8—216no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—24no—
482C2×Q8—44no—
483C2×Q8—48no—
484C2×Q8—44no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—416no—
488C2×Q8—82no—
489C2×Q8—84no—
490C2×Q8C2×C22⋊C414yes—
491C2×Q8#13114yes—
492C2×Q8C23×C412yes—
493C2×Q8C23×C414yes—
494C2×Q8C23×C412yes—
495C2×D4—28no—
496C2×D4—24no—
497C2×D4C2×C22⋊C418yes—
498C2×D4C2×C22⋊C414yes—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—28no—
512C22×C4—24no—
513C22×C4—28no—
514C22×C4—24no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—82no—
520C22×C4—84no—
521C22×C4C2×C22⋊C412yes—
522C22×C4C2×C22⋊C414yes—
523C22×C4C2×C22⋊C412yes—
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C412yes—
527C22×C4C2×C22⋊C414yes—
528C22×C4C2×C22⋊C412yes—
529C22×C4C2×C22⋊C414yes—
530C22×C4C2×C22⋊C412yes—
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C412yes—
533C22×C4#13714yes—
534C22×C4#13714yes—
535C22×C4C23×C414yes—
536C22×C4C23×C412yes—
537C22×C4C23×C411yescharacteristic
538C22×C4C22×D414yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D412yes—
541C22×C4C22×D414yes—
542C22×C4C22×D412yes—
543C22×C4C22×D411yescharacteristic
544M16—416no—
545M16—48no—
546C2×C8—24no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—24no—
551C2×C8—24no—
552C2×C8—22no—
553C2×C8—48no—
554C2×C8—42no—
555C2×C8—44no—
556C2×C8—42no—
557C2×C8—42no—
558C2×C8—48no—
559C2×C8—44no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—28no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—28no—
567C4⋊C4—24no—
568C4⋊C4—28no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—28no—
573C4⋊C4—24no—
574C4⋊C4—28no—
575C4⋊C4—24no—
576C4⋊C4—28no—
577C4⋊C4—24no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4C2×C22⋊C418yes—
585C4⋊C4C2×C22⋊C414yes—
586C4⋊C4C2×C22⋊C418yes—
587C4⋊C4C2×C22⋊C414yes—
588C4⋊C4C23×C412yes—
589C4⋊C4C23×C412yes—
590C4⋊C4C23×C414yes—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4C2×C22⋊C418yes—
595C22⋊C4C2×C22⋊C418yes—
596C22⋊C4C2×C22⋊C418yes—
597C42—22no—
598C42—24no—
599C42—22no—
600C42—28no—
601C42—24no—
602C42—28no—
603C42—24no—
604C42—22no—
605C42—24no—
606C42—22no—
607C42C2×C22⋊C412yes—
608C42C2×C22⋊C414yes—
609C42C2×C22⋊C414yes—
610C42C2×C22⋊C412yes—
611C42C2×C22⋊C414yes—
612C42C2×C22⋊C412yes—
613C42C23×C411yescharacteristic
614C42C23×C414yes—
615C42C23×C412yes—
616C42C22×D411yescharacteristic
617C42C22×D414yes—
618C42C22×D412yes—
619C42C22×D414yes—
620C42C22×D411yescharacteristic
621C42C22×D412yes—
622C42C2511yescharacteristic
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23#41914yes—
629C23C22×C22⋊C414yes—
630C23C22×C22⋊C412yes—
631C23C22×C22⋊C411yescharacteristic
632Q8—24no—
633Q8—28no—
634Q8—22no—
635Q8—22no—
636Q8—24no—
637Q8—22no—
638Q8—24no—
639Q8—48no—
640Q8—416no—
641Q8—42no—
642Q8—44no—
643Q8—84no—
644Q8—88no—
645Q8C2×#13114yes—
646D4—216no—
647D4—28no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—44no—
674C2×C4—48no—
675C2×C4—416no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—84no—
682C2×C4—88no—
683C2×C4#41914yes—
684C2×C4#41918yes—
685C2×C4C22×C22⋊C414yes—
686C2×C4C22×C22⋊C411yescharacteristic
687C2×C4C22×C22⋊C414yes—
688C2×C4C22×C22⋊C412yes—
689C2×C4C22×C22⋊C414yes—
690C2×C4C22×C22⋊C412yes—
691C2×C4C22×C22⋊C411yescharacteristic
692C2×C4C22×C22⋊C411yescharacteristic
693C2×C4C22×C22⋊C412yes—
694C2×C4C2×#13112yes—
695C2×C4#56812yes—
696C2×C4C2×#13712yes—
697C2×C4C2×#13712yes—
698C2×C4C2×#13714yes—
699C2×C4C2×#13714yes—
700C2×C4C24×C411yescharacteristic
701C2×C4C23×D411yescharacteristic
702C2×C4C23×D411yescharacteristic
703C8—24no—
704C8—42no—
705C8—44no—
706C8—42no—
707C8—42no—
708C8—44no—
709C22—28no—
710C22—22no—
711C22—22no—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—48no—
716C22#288012yes—
717C22C2×#41914yes—
718C22C2×#41912yes—
719C22#290112yes—
720C22C23×C22⋊C411yescharacteristic
721C4—22no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—21no—
726C4—21no—
727C4—22no—
728C4—24no—
729C4—42no—
730C4—44no—
731C4—42no—
732C4—42no—
733C4—44no—
734C4#288012yes—
735C4C2×#41912yes—
736C4C2×#41914yes—
737C4C22×#13111yescharacteristic
738C4C2×#56811yescharacteristic
739C4C22×#13711yescharacteristic
740C4C22×#13711yescharacteristic
741C2—24no—
742C2—44no—
743C2#1751414yesdirect product factor
744C2C2×#288011yescharacteristic
745C2C22×#41911yescharacteristic
746C2C2×#290111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC23C22×C22⋊C4
prime radicalC22×#41D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #17514C2direct (N × H)
5. C2×#1497C2semidirect
6. C2×#1493C2semidirect
7. C2×#1485C2semidirect
8. C2×#1481C2semidirect
9. C2×#1491C2semidirect
10. C2×#1487C2semidirect
11. C2×#1479C2semidirect
12. C22×Q8⋊C8C2semidirect
52. #1497C22semidirect
53. #1493C22semidirect
54. #1491C22semidirect
55. #1487C22semidirect
56. #1485C22semidirect
57. #1481C22semidirect
58. #1479C22semidirect
69. C2×Q8⋊C8C22semidirect
743. C2#17514direct (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
C2×#29652
C2×#29252
#175142
C2×#14972
C2×#14932
C2×#14852
C2×#14812
C2×#14912
C2×#14872
C2×#14792
C22×Q8⋊C82