Finite Group Databasebeta

← C2×#11729868 #13355705

Subgroups — C2×#11729868 #13355705

Order 1792.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#575C211yesmaximal, characteristic
2C2×#41×Dic7C211yesmaximal, characteristic, complemented
3C2×#90012C211yesmaximal, characteristic, complemented
4C2×#90008C211yesmaximal, characteristic, complemented
5C22×#6411C211yesmaximal, characteristic, complemented
6#11729868C218yesmaximal, direct product factor
7C2×#89354C211yesmaximal, characteristic, complemented
8C2×#89350C211yesmaximal, characteristic, complemented
9C22×C7×#41C2211yescharacteristic
10C22×C7×#41C2211yescharacteristic
11C7×#575—22no—
12C7×#575—22no—
13C7×#575C414yescomplemented
14C7×#575C2214yes—
15C2×C7×#137—21no—
16C2×C7×#137C412yescomplemented
17C2×C7×AGL(1,ℤ/8)—21no—
18C2×C7×AGL(1,ℤ/8)C412yescomplemented
19C2×C7×#135—22no—
20C22×C7×M16C2211yescharacteristic
21#41×Dic7—22no—
22#41×Dic7—22no—
23#41×Dic7—22no—
24#41×Dic7C2214yescomplemented
25C2×Q8×Dic7—21no—
26C2×D4×Dic7—21no—
27C2×D4×Dic7—22no—
28C2×#6489—21no—
29C2×#6489C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C22×C4×Dic7—21no—
32C22×C4×Dic7C2211yescharacteristic
33C22×#1136C2211yescharacteristic
34#90012—22no—
35#90012C2214yescomplemented
36#90008—22no—
37#90008C2214yescomplemented
38C2×#6411—22no—
39C2×#6411—21no—
40C2×#6411—21no—
41C2×#6411—22no—
42C2×#6411C2214yescomplemented
43C2×#6408—22no—
44#89354C2214yescomplemented
45#89350C2214yescomplemented
46C2×#1906—71nomaximal, Sylow
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41—21no—
54C2×C7×#41—21no—
55C2×C7×#41—21no—
56C2×C7×#41—21no—
57C2×C7×#41—21no—
58C2×C7×#41—21no—
59C2×C7×#41—21no—
60C2×C7×#41—21no—
61C2×C7×#41—21no—
62C2×C7×#41—21no—
63C2×C7×#41C2×C412yes—
64C2×C7×#41C2×C412yes—
65C2×C7×#41C2×C412yescomplemented
66C2×C7×#41D412yes—
67C2×C7×#41D412yes—
68C2×C7×#41D412yes—
69C2×C7×#41C2312yes—
70C2×C7×#41C2312yes—
71C22×C7×Q8C2×C411yescharacteristic, complemented
72C22×C7×Q8D411yescharacteristic
73C22×C7×D4—21no—
74C22×C7×D4—21no—
75C22×C7×D4C2×C411yescharacteristic, complemented
76C22×C7×D4D411yescharacteristic
77C23×C4×C7—21no—
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C23×Dic7—22no—
81C23×Dic7—21no—
82C7×#137—24no—
83C7×#137—24no—
84C7×#137—24no—
85C7×#137C2×C418yescomplemented
86C7×AGL(1,ℤ/8)—24no—
87C7×AGL(1,ℤ/8)—24no—
88C7×AGL(1,ℤ/8)—24no—
89C7×AGL(1,ℤ/8)C2×C418yescomplemented
90C7×#135—28no—
91C7×#135—28no—
92C2×C7×Q16—22no—
93C2×C7×SD16—22no—
94C2×C7×SD16—22no—
95C2×C7×D8—22no—
96C2×C7×M16—21no—
97C2×C7×M16—21no—
98C2×C7×M16—21no—
99C2×C7×M16C2×C412yescomplemented
100C2×C7×M16C2×C412yescomplemented
101C2×C7×M16C2312yes—
102C22×C7×C8—21no—
103C2×C22⋊Dic7—22no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7D412yes—
106Q8×Dic7—24no—
107Q8×Dic7—24no—
108D4×Dic7—28no—
109D4×Dic7—24no—
110D4×Dic7—24no—
111D4×Dic7—28no—
112#6489—24no—
113#6489—21no—
114#6489—21no—
115#6489—21no—
116#6489—24no—
117#6489—21no—
118#6489—21no—
119#6489D412yes—
120#6489C2312yes—
121#6489C2312yes—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—24no—
127C2×C4×Dic7—21no—
128C2×C4×Dic7—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C2×C4×Dic7—24no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7D411yescharacteristic
134C2×C4×Dic7D411yescharacteristic
135C2×C4×Dic7D412yes—
136C2×C4×Dic7C2312yes—
137C2×#1136—21no—
138C2×#1136—21no—
139C2×#1136—21no—
140C2×#1136—21no—
141C2×#1136—21no—
142C2×#1136C2312yes—
143C22×C7⋊C8—21no—
144#6411—28no—
145#6411—24no—
146#6411—24no—
147#6408—28no—
148C2×#575D711yescharacteristic
149C2×C4×#41—71no—
150C2×#421—71no—
151C22×#104—71no—
152C2×#410—71no—
153#1906—78no—
154C2×#344—71no—
155C2×#339—71no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7C2×D411yescharacteristic
159C7×#41—22no—
160C7×#41—22no—
161C7×#41—22no—
162C7×#41—22no—
163C7×#41—22no—
164C7×#41—22no—
165C7×#41—22no—
166C7×#41—22no—
167C7×#41—22no—
168C7×#41—22no—
169C7×#41—22no—
170C7×#41—22no—
171C7×#41—22no—
172C7×#41—22no—
173C7×#41—22no—
174C7×#41—22no—
175C7×#41—22no—
176C7×#41—22no—
177C7×#41—22no—
178C7×#41—22no—
179C7×#41—41no—
180C7×#41—41no—
181C7×#41—41no—
182C7×#41—41no—
183C7×#41—41no—
184C7×#41—41no—
185C7×#41—41no—
186C7×#41—41no—
187C7×#41C22⋊C414yes—
188C7×#41C22⋊C414yes—
189C7×#41C22×C414yes—
190C7×#41C2×D414yes—
191C2×C7×Q8—21no—
192C2×C7×Q8—21no—
193C2×C7×Q8—21no—
194C2×C7×Q8—21no—
195C2×C7×Q8—21no—
196C2×C7×Q8—21no—
197C2×C7×Q8—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8C22⋊C412yes—
200C2×C7×Q8C22⋊C412yes—
201C2×C7×Q8C22×C412yescomplemented
202C2×C7×Q8C2×D412yes—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—21no—
212C2×C7×D4—21no—
213C2×C7×D4—21no—
214C2×C7×D4—21no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—21no—
218C2×C7×D4—21no—
219C2×C7×D4—41no—
220C2×C7×D4—41no—
221C2×C7×D4—41no—
222C2×C7×D4—41no—
223C2×C7×D4C22⋊C412yes—
224C2×C7×D4C22⋊C412yes—
225C2×C7×D4C22×C412yescomplemented
226C2×C7×D4C2×D412yes—
227C22×C4×C7—21no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—21no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—41no—
238C22×C4×C7—41no—
239C22×C4×C7—41no—
240C22×C4×C7—41no—
241C22×C4×C7C22×C411yescharacteristic
242C22×C4×C7C22×C411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7#4111yescharacteristic
251C22×C4×C7#4111yescharacteristic
252C22×C4×C7#4111yescharacteristic
253C22×C4×C7#4111yescharacteristic
254C22×C4×C7C2411yescharacteristic
255C22×Dic7—21no—
256C22×Dic7—28no—
257C22×Dic7—22no—
258C22×Dic7—21no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—44no—
262C22×Dic7—48no—
263C22×Dic7—41no—
264C7×Q16—28no—
265C7×SD16—28no—
266C7×SD16—28no—
267C7×D8—28no—
268C7×M16—22no—
269C7×M16—22no—
270C7×M16—22no—
271C7×M16C22×C414yescomplemented
272C2×C7×C8—22no—
273C2×C7×C8—22no—
274C2×C7×C8—22no—
275C22⋊Dic7—28no—
276C22⋊Dic7—22no—
277C22⋊Dic7—22no—
278C22⋊Dic7—41no—
279C22⋊Dic7C2×D414yes—
280C4⋊Dic7—28no—
281C4⋊Dic7—22no—
282C4⋊Dic7—22no—
283C4⋊Dic7—22no—
284C4⋊Dic7—41no—
285C4×Dic7—28no—
286C4×Dic7—21no—
287C4×Dic7—22no—
288C4×Dic7—21no—
289C4×Dic7—22no—
290C4×Dic7—22no—
291C4×Dic7—22no—
292C4×Dic7—22no—
293C4×Dic7—41no—
294C4×Dic7C2×D412yes—
295C4×Dic7C2×D412yes—
296#1136—22no—
297#1136—22no—
298#1136—41no—
299#1136—41no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—41no—
302C2×C7⋊C8—41no—
303C22×#41C2×D711yescharacteristic
304C22×#41C2×D711yescharacteristic
305#575—22no—
306#575—22no—
307#575Dic714yescomplemented
308#575C2×D714yes—
309C2×#137—21no—
310C2×#137Dic712yescomplemented
311C2×AGL(1,ℤ/8)—21no—
312C2×AGL(1,ℤ/8)Dic712yescomplemented
313C2×#135—22no—
314C22×M16—71no—
315C22×M16C2×D711yescharacteristic
316C4×#41—74no—
317C4×#41—142no—
318C4×#41—142no—
319C4×#41—142no—
320C2×C4×Q8—141no—
321C2×C4×D4—142no—
322C2×C4×D4—141no—
323C2×#117—71no—
324C2×#117—71no—
325C2×#117—141no—
326C22×C42—71no—
327C22×C42—141no—
328#421—74no—
329#421—142no—
330C2×#104—74no—
331C2×#104—141no—
332C2×#104—142no—
333C2×#104—141no—
334C2×#104—142no—
335#410—74no—
336#410—142no—
337C2×#99—142no—
338#344—74no—
339#339—74no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—42no—
345C23×C7—44no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—82no—
349C23×C7C4×D411yescharacteristic
350C23×C7C4×D411yescharacteristic
351C23×C7#12011yescharacteristic
352C23×C7#12011yescharacteristic
353C23×C7#12111yescharacteristic
354C23×C7#12111yescharacteristic
355C23×C7C22×D411yescharacteristic
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—22no—
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—41no—
362C7×Q8—41no—
363C7×Q8C2×C22⋊C414yes—
364C7×D4—24no—
365C7×D4—24no—
366C7×D4—24no—
367C7×D4—24no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—22no—
373C7×D4—42no—
374C7×D4—42no—
375C7×D4—42no—
376C7×D4—42no—
377C7×D4—41no—
378C7×D4—41no—
379C7×D4C2×C22⋊C414yes—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—24no—
385C2×C4×C7—24no—
386C2×C4×C7—24no—
387C2×C4×C7—22no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7C2×C22⋊C411yescharacteristic
395C2×C4×C7C2×C22⋊C411yescharacteristic
396C2×C4×C7C2×C22⋊C411yescharacteristic
397C2×C4×C7C2×C22⋊C411yescharacteristic
398C2×C4×C7C4×D411yescharacteristic
399C2×C4×C7C4×D411yescharacteristic
400C2×C4×C7C4×D411yescharacteristic
401C2×C4×C7C4×D411yescharacteristic
402C2×C4×C7C4×D411yescharacteristic
403C2×C4×C7C4×D411yescharacteristic
404C2×C4×C7#12011yescharacteristic
405C2×C4×C7#12011yescharacteristic
406C2×C4×C7#12111yescharacteristic
407C2×C4×C7#12111yescharacteristic
408C2×C4×C7#12111yescharacteristic
409C2×C4×C7#12111yescharacteristic
410C2×C4×C7#12111yescharacteristic
411C2×C4×C7#12111yescharacteristic
412C2×C4×C7#12311yescharacteristic
413C2×C4×C7#12311yescharacteristic
414C2×C4×C7#12311yescharacteristic
415C2×C4×C7#12311yescharacteristic
416C2×C4×C7C23×C411yescharacteristic
417C2×C4×C7C22×D411yescharacteristic
418C2×C4×C7C22×D411yescharacteristic
419C2×C4×C7C22×D411yescharacteristic
420C2×C4×C7C2×#4111yescharacteristic
421C2×C4×C7C2×#4111yescharacteristic
422C2×Dic7—24no—
423C2×Dic7—22no—
424C2×Dic7—24no—
425C2×Dic7—22no—
426C2×Dic7—44no—
427C2×Dic7—44no—
428C2×Dic7—416no—
429C2×Dic7—44no—
430C2×Dic7—42no—
431C2×Dic7—42no—
432C2×Dic7—82no—
433C7×C8—24no—
434C7⋊C8—42no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41C2×Dic712yes—
452C2×#41C2×Dic712yes—
453C2×#41C2×Dic712yescomplemented
454C2×#41C22⋊D712yes—
455C2×#41C22⋊D712yes—
456C2×#41C22⋊D712yes—
457C2×#41C22×D712yes—
458C2×#41C22×D712yes—
459C22×Q8C2×Dic711yescharacteristic, complemented
460C22×Q8C22⋊D711yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C2×Dic711yescharacteristic, complemented
464C22×D4C22⋊D711yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—142no—
468C23×C4—141no—
469C23×C4C22×D711yescharacteristic
470#137—24no—
471#137—24no—
472#137—24no—
473#137C2×Dic718yescomplemented
474AGL(1,ℤ/8)—24no—
475AGL(1,ℤ/8)—24no—
476AGL(1,ℤ/8)—24no—
477AGL(1,ℤ/8)C2×Dic718yescomplemented
478#135—28no—
479#135—28no—
480C2×Q16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×D8—22no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—72no—
488C2×M16—141no—
489C2×M16—141no—
490C2×M16—141no—
491C2×M16—141no—
492C2×M16—141no—
493C2×M16C2×Dic712yescomplemented
494C2×M16C2×Dic712yescomplemented
495C2×M16C22×D712yes—
496C22×C8—21no—
497C22×C8—141no—
498C4×Q8—144no—
499C4×Q8—144no—
500C4×D4—148no—
501C4×D4—148no—
502C4×D4—144no—
503C4×D4—144no—
504#117—72no—
505#117—72no—
506#117—72no—
507#117—144no—
508#117—144no—
509#117—141no—
510#117—141no—
511#117—141no—
512#117—141no—
513#117—141no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C22⋊C4—72no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—141no—
520C2×C42—71no—
521C2×C42—72no—
522C2×C42—71no—
523C2×C42—72no—
524C2×C42—144no—
525C2×C42—142no—
526C2×C42—144no—
527C2×C42—141no—
528C2×C42—141no—
529C2×C42—141no—
530C2×C42—141no—
531C2×C42—141no—
532#104—144no—
533#104—144no—
534#104—148no—
535#99—148no—
536C22×C7—22no—
537C22×C7—22no—
538C22×C7—22no—
539C22×C7—24no—
540C22×C7—41no—
541C22×C7—41no—
542C22×C7—41no—
543C22×C7—41no—
544C22×C7—44no—
545C22×C7—44no—
546C22×C7—44no—
547C22×C7—42no—
548C22×C7—82no—
549C22×C7—82no—
550C22×C7—82no—
551C22×C7#38611yescharacteristic
552C22×C7#38611yescharacteristic
553C22×C7#38611yescharacteristic
554C22×C7#38611yescharacteristic
555C22×C7C2×C4×D411yescharacteristic
556C22×C7C2×#12011yescharacteristic
557C22×C7C2×#12111yescharacteristic
558C4×C7—24no—
559C4×C7—42no—
560C4×C7#38611yescharacteristic
561C4×C7#38611yescharacteristic
562C4×C7#38611yescharacteristic
563C4×C7#38611yescharacteristic
564C4×C7C22×C22⋊C411yescharacteristic
565C4×C7C2×C4×D411yescharacteristic
566C4×C7C2×#12111yescharacteristic
567C4×C7C2×#12311yescharacteristic
568Dic7—24no—
569Dic7—44no—
570Dic7—42no—
571Dic7—82no—
572C24—21no—
573C24—21no—
574C24D4×D711yescharacteristic
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—22no—
580#41—22no—
581#41—22no—
582#41—22no—
583#41—22no—
584#41—22no—
585#41—22no—
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—22no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—41no—
601#41—41no—
602#41—41no—
603#41C22⋊Dic714yes—
604#41C22⋊Dic714yes—
605#41C22×Dic714yes—
606#41C2×C22⋊D714yes—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C22⋊Dic712yes—
616C2×Q8C22⋊Dic712yes—
617C2×Q8C22×Dic712yescomplemented
618C2×Q8C2×C22⋊D712yes—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—41no—
639C2×D4C22⋊Dic712yes—
640C2×D4C22⋊Dic712yes—
641C2×D4C22×Dic712yescomplemented
642C2×D4C2×C22⋊D712yes—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—141no—
658C22×C4—148no—
659C22×C4—141no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—284no—
664C22×C4—288no—
665C22×C4—281no—
666C22×C4D4×D711yescharacteristic
667C22×C4D4×D711yescharacteristic
668C22×C4D4×D711yescharacteristic
669C22×C4#115911yescharacteristic
670C22×C4#115911yescharacteristic
671C22×C4#115911yescharacteristic
672C22×C4#115911yescharacteristic
673C22×C4C22×Dic711yescharacteristic
674C22×C4C22×Dic711yescharacteristic
675C22×C4C2×C22⋊D711yescharacteristic
676C22×C4C2×C22⋊D711yescharacteristic
677C22×C4C2×C22⋊D711yescharacteristic
678C22×C4C2×C22⋊D711yescharacteristic
679C22×C4C23×D711yescharacteristic
680Q16—28no—
681SD16—28no—
682SD16—28no—
683D8—28no—
684M16—22no—
685M16—22no—
686M16—22no—
687M16—142no—
688M16—142no—
689M16—281no—
690M16—281no—
691M16C22×Dic714yescomplemented
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—142no—
696C2×C8—281no—
697C2×C8—281no—
698C4⋊C4—148no—
699C4⋊C4—142no—
700C4⋊C4—142no—
701C4⋊C4—142no—
702C4⋊C4—281no—
703C22⋊C4—74no—
704C22⋊C4—148no—
705C22⋊C4—142no—
706C22⋊C4—142no—
707C22⋊C4—281no—
708C42—72no—
709C42—72no—
710C42—148no—
711C42—141no—
712C42—141no—
713C42—142no—
714C42—142no—
715C42—142no—
716C42—142no—
717C42—142no—
718C42—281no—
719C2×C7—21no—
720C2×C7—21no—
721C2×C7—21no—
722C2×C7—21no—
723C2×C7—21no—
724C2×C7—21no—
725C2×C7—44no—
726C2×C7—82no—
727C2×C7#190612yescomplemented
728C2×C7C2×#38611yescharacteristic
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—44no—
735C23—41no—
736C23—41no—
737C23—82no—
738C23D4×Dic711yescharacteristic
739C23D4×Dic711yescharacteristic
740C23#650011yescharacteristic
741C23#650011yescharacteristic
742C23#650211yescharacteristic
743C23#650211yescharacteristic
744C23C2×D4×D711yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—41no—
751Q8—41no—
752Q8C2×C22⋊Dic714yes—
753D4—24no—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—41no—
767D4—41no—
768D4C2×C22⋊Dic714yes—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—144no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—144no—
787C2×C4—284no—
788C2×C4—284no—
789C2×C4—2816no—
790C2×C4—282no—
791C2×C4—284no—
792C2×C4—282no—
793C2×C4—562no—
794C2×C4D4×Dic711yescharacteristic
795C2×C4D4×Dic711yescharacteristic
796C2×C4D4×Dic711yescharacteristic
797C2×C4D4×Dic711yescharacteristic
798C2×C4D4×Dic711yescharacteristic
799C2×C4D4×Dic711yescharacteristic
800C2×C4#649811yescharacteristic
801C2×C4#649811yescharacteristic
802C2×C4#649811yescharacteristic
803C2×C4#649811yescharacteristic
804C2×C4#650011yescharacteristic
805C2×C4#650011yescharacteristic
806C2×C4#650211yescharacteristic
807C2×C4#650211yescharacteristic
808C2×C4#650211yescharacteristic
809C2×C4#650211yescharacteristic
810C2×C4#650211yescharacteristic
811C2×C4#650211yescharacteristic
812C2×C4C2×C22⋊Dic711yescharacteristic
813C2×C4C2×C22⋊Dic711yescharacteristic
814C2×C4C2×C22⋊Dic711yescharacteristic
815C2×C4C2×C22⋊Dic711yescharacteristic
816C2×C4C2×D4×D711yescharacteristic
817C2×C4C2×#115911yescharacteristic
818C2×C4C2×#115911yescharacteristic
819C2×C4C23×Dic711yescharacteristic
820C2×C4C22×C22⋊D711yescharacteristic
821C2×C4C22×C22⋊D711yescharacteristic
822C8—24no—
823C8—282no—
824C7C2×#190611yescharacteristic, complemented, Sylow
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22#8999211yescharacteristic
841C22#8999211yescharacteristic
842C22#8999211yescharacteristic
843C22#8999211yescharacteristic
844C22C2×D4×Dic711yescharacteristic
845C22C2×#650011yescharacteristic
846C22C2×#650211yescharacteristic
847C4—24no—
848C4—42no—
849C4—144no—
850C4—282no—
851C4—284no—
852C4—562no—
853C4#8999211yescharacteristic
854C4#8999211yescharacteristic
855C4#8999211yescharacteristic
856C4#8999211yescharacteristic
857C4C2×D4×Dic711yescharacteristic
858C4C2×#649811yescharacteristic
859C4C2×#650211yescharacteristic
860C4C22×C22⋊Dic711yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—44no—
868C2—82no—
869C2#1172986812yesdirect product factor
870C2C2×#8999211yescharacteristic
subgroupG/H
centerC2×C4#6502
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#575C2
socleC22×C7#386
cosocleC22×C4×C7C24
hypercenterC2×#575D7
hypocenterC7C2×#1906
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. C2×#41×Dic7C2semidirect
3. C2×#90012C2semidirect
4. C2×#90008C2semidirect
5. C22×#6411C2semidirect
6. #11729868C2direct (N × H)
7. C2×#89354C2semidirect
8. C2×#89350C2semidirect
13. C7×#575C4semidirect
16. C2×C7×#137C4semidirect
18. C2×C7×AGL(1,ℤ/8)C4semidirect
24. #41×Dic7C22semidirect
35. #90012C22semidirect
37. #90008C22semidirect
42. C2×#6411C22semidirect
44. #89354C22semidirect
45. #89350C22semidirect
65. C2×C7×#41C2×C4semidirect
71. C22×C7×Q8C2×C4semidirect
75. C22×C7×D4C2×C4semidirect
85. C7×#137C2×C4semidirect
89. C7×AGL(1,ℤ/8)C2×C4semidirect
99. C2×C7×M16C2×C4semidirect
100. C2×C7×M16C2×C4semidirect
201. C2×C7×Q8C22×C4semidirect
225. C2×C7×D4C22×C4semidirect
271. C7×M16C22×C4semidirect
307. #575Dic7semidirect
310. C2×#137Dic7semidirect
312. C2×AGL(1,ℤ/8)Dic7semidirect
453. C2×#41C2×Dic7semidirect
459. C22×Q8C2×Dic7semidirect
463. C22×D4C2×Dic7semidirect
473. #137C2×Dic7semidirect
477. AGL(1,ℤ/8)C2×Dic7semidirect
493. C2×M16C2×Dic7semidirect
494. C2×M16C2×Dic7semidirect
617. C2×Q8C22×Dic7semidirect
641. C2×D4C22×Dic7semidirect
691. M16C22×Dic7semidirect
727. C2×C7#1906semidirect
824. C7C2×#1906semidirect
869. C2#11729868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5752
C2×#41×Dic72
C2×#900122
C2×#900082
C22×#64112
#117298682
C2×#893542
C2×#893502
C2×#19067