Finite Group Databasebeta

← #13355810

Subgroups — #13355810

Order 1792.

1748 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11744336C211yesmaximal, characteristic
2#11742799C211yesmaximal, characteristic, complemented
3C2×C7×#410C211yesmaximal, characteristic, complemented
4C2×#90012C211yesmaximal, characteristic, complemented
5C2×#89778C211yesmaximal, characteristic, complemented
6#11729347C211yesmaximal, characteristic, complemented
7#11729346C211yesmaximal, characteristic, complemented
8#11727788C218yesmaximal, complemented
9C22×C7×#41C2211yescharacteristic
10C22×#1157C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×C7×#117C2211yescharacteristic
13#90524—22no—
14#90523—22no—
15#90521—21no—
16#90519—22no—
17#90516—21no—
18#90507C412yescomplemented
19#90496C412yescomplemented
20#90495C2214yes—
21#90482C414yescomplemented
22C2×#6489C2211yescharacteristic
23C2×#6489C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25#90214—22no—
26#90213—22no—
27#90212—21no—
28D7×#117—22no—
29#90207—21no—
30#90195—22no—
31#90177C2214yes—
32C4×#1157—22no—
33C7×#410—22no—
34C7×#410—22no—
35C2×C7×#99C2214yes—
36#90012—22no—
37#90012—22no—
38C2×#6408C2214yes—
39#89778—22no—
40#89778—22no—
41C2×#6380C2214yes—
42#89322C2214yes—
43#89321C2214yes—
44#21014—71nomaximal, Sylow
45C2×C7×#41—21no—
46C2×C7×#41—21no—
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—
57C22×C7×Q8C2×C411yescharacteristic, complemented
58C22×C7×D4C2×C411yescharacteristic, complemented
59C22×C7×D4C2312yes—
60C23×C4×C7C2×C412yescomplemented
61C23×C4×C7C2311yescharacteristic
62C22×C22⋊D7C2312yes—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157—21no—
70C2×#1157—21no—
71C2×#1157C2×C412yes—
72C2×#1157C2×C412yes—
73C2×#1157D412yes—
74C2×#1157D412yes—
75C22×D28D411yescharacteristic
76C22×C4×D7D412yes—
77C22×Dic14D411yescharacteristic
78C7×#117—21no—
79C7×#117—21no—
80C7×#117—21no—
81C7×#117—21no—
82C7×#117—21no—
83C7×#117—21no—
84C7×#117D412yescomplemented
85C7×#117D412yescomplemented
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C22⋊C4C2312yes—
89C2×C7×C22⋊C4C2312yes—
90C2×C42×C7—21no—
91C2×C42×C7—21no—
92#6516C2×C418yescomplemented
93C2×C22⋊Dic7C2312yes—
94C2×C22⋊Dic7C2312yes—
95C2×C22⋊Dic7C2312yes—
96#6510—22no—
97#6509—24no—
98#6507—22no—
99#6503—22no—
100#6502—28no—
101#6501—24no—
102#6500—24no—
103#6499—22no—
104#6498—24no—
105#6493—24no—
106#6492C2×C418yescomplemented
107C4×C22⋊D7—28no—
108C4×C22⋊D7—28no—
109#6489—21no—
110#6489—21no—
111#6489—21no—
112#6489—21no—
113#6489—21no—
114#6489—21no—
115#6489—21no—
116#6489—21no—
117#6489C2×C412yescomplemented
118#6489C2×C412yescomplemented
119#6489D412yescomplemented
120#6489D412yescomplemented
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124#6487—24no—
125C2×C4×Dic7—21no—
126C2×C4×Dic7—21no—
127C2×C4×Dic7—21no—
128#6456—24no—
129#6455—24no—
130D7×C4⋊C4—24no—
131#6450—24no—
132(C22⋊D7)⋊C4—28no—
133D7×C22⋊C4—24no—
134#6440—24no—
135C4×D28—24no—
136#6435—24no—
137C42×D7—24no—
138C4×Dic14—24no—
139C7×#99—28no—
140#6408—28no—
141#6380—28no—
142#3449—71no—
143#3428—71no—
144C2×#410—71no—
145C2×#410—71no—
146C2×#410D711yescharacteristic, complemented
147#1913—78no—
148#1740—71no—
149#1740—71no—
150C24×C7C22×C412yes—
151C24×C7C2411yescharacteristic
152C23×D7C2×D412yes—
153C7×#41—41no—
154C7×#41—41no—
155C7×#41—41no—
156C7×#41—41no—
157C7×#41—41no—
158C7×#41—41no—
159C7×#41—41no—
160C7×#41—41no—
161C7×#41—41no—
162C7×#41—41no—
163C7×#41—41no—
164C7×#41—41no—
165C7×#41—41no—
166C7×#41—41no—
167C7×#41—41no—
168C7×#41—41no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—21no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7C22×C412yes—
196C22×C4×C7C22×C411yescharacteristic
197C22×C4×C7C22×C411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7#4111yescharacteristic
207C22×C4×C7#4111yescharacteristic
208C22×C4×C7#4111yescharacteristic
209C22×C4×C7#4111yescharacteristic
210C2×C22⋊D7—22no—
211C2×C22⋊D7—22no—
212C2×C22⋊D7—22no—
213C2×C22⋊D7—22no—
214C2×C22⋊D7—28no—
215C2×C22⋊D7C22×C414yes—
216C2×C22⋊D7C2×D414yes—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7C2×D412yes—
221#1157—22no—
222#1157—22no—
223#1157—22no—
224#1157—22no—
225#1157—22no—
226#1157—22no—
227#1157—22no—
228#1157—22no—
229#1157—22no—
230#1157—22no—
231#1157—22no—
232#1157—22no—
233#1157—22no—
234#1157—22no—
235#1157—22no—
236#1157—22no—
237C2×D28—21no—
238C2×D28—21no—
239C2×D28—21no—
240C2×D28—21no—
241C2×D28C22⋊C412yes—
242C2×D28C22⋊C412yes—
243C2×C4×D7—22no—
244C2×C4×D7—22no—
245C2×C4×D7—22no—
246C2×C4×D7—22no—
247C2×C4×D7—28no—
248C2×C4×D7C22⋊C414yes—
249C2×C4×D7C22⋊C414yes—
250C2×Dic14—21no—
251C2×Dic14—21no—
252C2×Dic14—21no—
253C2×Dic14—21no—
254C2×Dic14C22⋊C412yes—
255C2×Dic14C22⋊C412yes—
256C7×C4⋊C4—22no—
257C7×C4⋊C4—22no—
258C7×C4⋊C4—41no—
259C7×C4⋊C4—41no—
260C7×C22⋊C4—22no—
261C7×C22⋊C4—22no—
262C7×C22⋊C4—22no—
263C7×C22⋊C4C2×D414yes—
264C42×C7—22no—
265C42×C7—22no—
266C42×C7—41no—
267C42×C7—41no—
268C22⋊Dic7—22no—
269C22⋊Dic7—22no—
270C22⋊Dic7—28no—
271C22⋊Dic7—22no—
272C22⋊Dic7—22no—
273C22⋊Dic7C22×C414yes—
274C22⋊Dic7C2×D414yes—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—28no—
277C4⋊Dic7—22no—
278C4⋊Dic7—22no—
279C4⋊Dic7—22no—
280C4⋊Dic7—22no—
281C4⋊Dic7—41no—
282C4⋊Dic7—41no—
283Dic7⋊C4—28no—
284Dic7⋊C4—28no—
285C4×Dic7—28no—
286C4×Dic7—22no—
287C4×Dic7—22no—
288C4×Dic7—22no—
289C4×Dic7—22no—
290C4×Dic7—41no—
291C4×Dic7—41no—
292C22×#41—71no—
293C22×#41C2×D711yescharacteristic
294#537—142no—
295#536—72no—
296#536—141no—
297#535—72no—
298#535—141no—
299#534—74no—
300#532—142no—
301#525—74no—
302#525—142no—
303#520—142no—
304#520—142no—
305#519—141no—
306#518—74no—
307#518—141no—
308C4×#41—142no—
309C4×#41—142no—
310C2×#117—71no—
311C2×#117—71no—
312C2×#117—71no—
313C2×#117—142no—
314C2×#117C2×D711yescharacteristic
315C2×#117C2×D711yescharacteristic
316#410—22no—
317#410—22no—
318#410—142no—
319#410—142no—
320#410—142no—
321#410—142no—
322C2×#99—74no—
323C2×#99—74no—
324C2×#99C2×D714yes—
325#342—74no—
326#342—74no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—81no—
331C23×C7—82no—
332C23×C7C23×C411yescharacteristic
333C23×C7C22×D411yescharacteristic
334C23×C7C22×D411yescharacteristic
335C23×C7C22×D411yescharacteristic
336C23×C7C22×D411yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7C2×#4111yescharacteristic
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—82no—
342C22×D7C2×C22⋊C414yes—
343C7×Q8—41no—
344C7×Q8—41no—
345C7×Q8—41no—
346C7×Q8—41no—
347C7×D4—42no—
348C7×D4—42no—
349C7×D4—42no—
350C7×D4—42no—
351C7×D4—41no—
352C7×D4—41no—
353C7×D4—41no—
354C7×D4—41no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—24no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—82no—
365C2×C4×C7—82no—
366C2×C4×C7C2×C22⋊C411yescharacteristic
367C2×C4×C7C2×C22⋊C411yescharacteristic
368C2×C4×C7C2×C22⋊C411yescharacteristic
369C2×C4×C7C2×C22⋊C411yescharacteristic
370C2×C4×C7C4×D411yescharacteristic
371C2×C4×C7C4×D411yescharacteristic
372C2×C4×C7C4×D411yescharacteristic
373C2×C4×C7C4×D411yescharacteristic
374C2×C4×C7C4×D411yescharacteristic
375C2×C4×C7C4×D411yescharacteristic
376C2×C4×C7C4×D411yescharacteristic
377C2×C4×C7C4×D411yescharacteristic
378C2×C4×C7#12011yescharacteristic
379C2×C4×C7#12011yescharacteristic
380C2×C4×C7#12011yescharacteristic
381C2×C4×C7#12011yescharacteristic
382C2×C4×C7#12111yescharacteristic
383C2×C4×C7#12111yescharacteristic
384C2×C4×C7#12111yescharacteristic
385C2×C4×C7#12111yescharacteristic
386C2×C4×C7#12111yescharacteristic
387C2×C4×C7#12111yescharacteristic
388C2×C4×C7#12111yescharacteristic
389C2×C4×C7#12111yescharacteristic
390C2×C4×C7#12311yescharacteristic
391C2×C4×C7#12311yescharacteristic
392C2×C4×C7#12311yescharacteristic
393C2×C4×C7#12311yescharacteristic
394C22⋊D7—24no—
395C22⋊D7—24no—
396C22⋊D7—24no—
397C22⋊D7—24no—
398C22⋊D7—88no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—24no—
402C2×Dic7—24no—
403C2×Dic7—42no—
404C2×Dic7—82no—
405C2×Dic7—82no—
406C2×Dic7—82no—
407C2×Dic7C2×C22⋊C414yes—
408D28—22no—
409D28—22no—
410D28—22no—
411D28—22no—
412C4×D7—24no—
413C4×D7—24no—
414C4×D7—24no—
415C4×D7—24no—
416C4×D7—88no—
417Dic14—22no—
418Dic14—22no—
419Dic14—22no—
420Dic14—22no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—72no—
434C2×#41—72no—
435C2×#41—72no—
436C2×#41—72no—
437C2×#41—141no—
438C2×#41—141no—
439C2×#41—141no—
440C2×#41—141no—
441C2×#41—141no—
442C2×#41—141no—
443C2×#41—141no—
444C2×#41—141no—
445C22×Q8—71no—
446C22×Q8C4×D711yescharacteristic, complemented
447C22×D4—72no—
448C22×D4—71no—
449C22×D4C4×D711yescharacteristic, complemented
450C22×D4C22×D712yes—
451C23×C4—72no—
452C23×C4C4×D712yescomplemented
453C23×C4C22×D711yescharacteristic
454C4⋊Q8—142no—
455#127—142no—
456#124—142no—
457#124—142no—
458#123—78no—
459#123—144no—
460C22⋊Q8—144no—
461C22⋊Q8—144no—
462#121—144no—
463#121—144no—
464#121—148no—
465#120—78no—
466#120—144no—
467C4×Q8—144no—
468C4×Q8—144no—
469C4×D4—144no—
470C4×D4—148no—
471C4×D4—144no—
472C4×D4—148no—
473C4×D4—148no—
474#117—21no—
475#117—21no—
476#117—21no—
477#117—21no—
478#117—21no—
479#117—21no—
480#117—72no—
481#117—72no—
482#117—72no—
483#117—72no—
484#117—144no—
485#117—144no—
486#117—144no—
487#117—141no—
488#117—141no—
489#117—141no—
490#117—141no—
491#117—141no—
492#117—141no—
493#117—141no—
494#117—141no—
495#117C22⋊D712yescomplemented
496#117C22⋊D712yescomplemented
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—144no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C22⋊C4—72no—
504C2×C22⋊C4—72no—
505C2×C22⋊C4—72no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4C22×D712yes—
508C2×C22⋊C4C22×D712yes—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—144no—
512C2×C42—141no—
513C2×C42—141no—
514C2×C42—141no—
515#99—28no—
516#99—148no—
517#99—148no—
518C22×C7—41no—
519C22×C7—41no—
520C22×C7—41no—
521C22×C7—41no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—44no—
526C22×C7—42no—
527C22×C7—82no—
528C22×C7—82no—
529C22×C7C22×C22⋊C411yescharacteristic
530C22×C7C2×C4×D411yescharacteristic
531C22×C7C2×C4×D411yescharacteristic
532C22×C7C2×#12011yescharacteristic
533C22×C7C2×#12111yescharacteristic
534C22×C7C2×#12111yescharacteristic
535C22×C7C2×#12311yescharacteristic
536C2×D7—24no—
537C2×D7—44no—
538C2×D7—44no—
539C2×D7—82no—
540C4×C7—44no—
541C4×C7—42no—
542C4×C7—82no—
543C4×C7#38611yescharacteristic
544C4×C7#38611yescharacteristic
545C4×C7#38611yescharacteristic
546C4×C7#38611yescharacteristic
547C4×C7#38611yescharacteristic
548C4×C7#38611yescharacteristic
549C4×C7#38611yescharacteristic
550C4×C7#38611yescharacteristic
551Dic7—24no—
552Dic7—44no—
553Dic7—44no—
554Dic7—82no—
555C24—72no—
556C24C2×C4×D712yes—
557C24C23×D711yescharacteristic
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—142no—
575#41—142no—
576#41—142no—
577#41—142no—
578#41—142no—
579#41—142no—
580#41—142no—
581#41—142no—
582#41—142no—
583#41—142no—
584#41—142no—
585#41—142no—
586#41—142no—
587#41—142no—
588#41—142no—
589#41—142no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—72no—
597C2×Q8—72no—
598C2×Q8—141no—
599C2×Q8—141no—
600C2×Q8—141no—
601C2×Q8—141no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—74no—
615C2×D4—74no—
616C2×D4—72no—
617C2×D4—72no—
618C2×D4—142no—
619C2×D4—142no—
620C2×D4—142no—
621C2×D4—142no—
622C2×D4—148no—
623C2×D4—141no—
624C2×D4—141no—
625C2×D4—141no—
626C2×D4—141no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—72no—
636C22×C4—74no—
637C22×C4—74no—
638C22×C4—148no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4C2×C4×D712yes—
647C22×C4C2×C4×D711yescharacteristic
648C22×C4C2×C4×D711yescharacteristic
649C22×C4#115711yescharacteristic
650C22×C4#115711yescharacteristic
651C22×C4D4×D711yescharacteristic
652C22×C4D4×D711yescharacteristic
653C22×C4D4×D711yescharacteristic
654C22×C4D4×D711yescharacteristic
655C22×C4D4×D711yescharacteristic
656C22×C4D4×D711yescharacteristic
657C22×C4#115911yescharacteristic
658C22×C4#115911yescharacteristic
659C22×C4C2×C22⋊D711yescharacteristic
660C22×C4C2×C22⋊D711yescharacteristic
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—148no—
666C4⋊C4—148no—
667C4⋊C4—142no—
668C4⋊C4—142no—
669C4⋊C4—142no—
670C4⋊C4—142no—
671C4⋊C4—281no—
672C4⋊C4—281no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—74no—
677C22⋊C4—74no—
678C22⋊C4—148no—
679C22⋊C4—148no—
680C22⋊C4—148no—
681C22⋊C4—142no—
682C22⋊C4—142no—
683C22⋊C4—142no—
684C22⋊C4—142no—
685C22⋊C4C2×C22⋊D714yes—
686C42—22no—
687C42—22no—
688C42—41no—
689C42—41no—
690C42—148no—
691C42—142no—
692C42—142no—
693C42—142no—
694C42—142no—
695C42—281no—
696C42—281no—
697C2×C7—21no—
698C2×C7—21no—
699C2×C7—21no—
700C2×C7—21no—
701C2×C7—21no—
702C2×C7—21no—
703C2×C7—21no—
704C2×C7—82no—
705C2×C7C2×#38611yescharacteristic
706D7—44no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—74no—
711C23—81no—
712C23—82no—
713C23—142no—
714C23—142no—
715C23—562no—
716C23C22×C4×D711yescharacteristic
717C23C2×#115711yescharacteristic
718C23C2×D4×D711yescharacteristic
719C23C2×D4×D711yescharacteristic
720C23C2×D4×D711yescharacteristic
721C23C2×#115911yescharacteristic
722C23C22×C22⋊D711yescharacteristic
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—142no—
728Q8—142no—
729Q8—142no—
730Q8—142no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—42no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—144no—
740D4—144no—
741D4—144no—
742D4—144no—
743D4—142no—
744D4—142no—
745D4—142no—
746D4—142no—
747D4—568no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—74no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—144no—
763C2×C4—144no—
764C2×C4—144no—
765C2×C4—144no—
766C2×C4—144no—
767C2×C4—144no—
768C2×C4—282no—
769C2×C4—568no—
770C2×C4—562no—
771C2×C4—562no—
772C2×C4—562no—
773C2×C4D7×C22⋊C411yescharacteristic
774C2×C4D7×C22⋊C411yescharacteristic
775C2×C4D7×C22⋊C411yescharacteristic
776C2×C4D7×C22⋊C411yescharacteristic
777C2×C4(C22⋊D7)⋊C411yescharacteristic
778C2×C4(C22⋊D7)⋊C411yescharacteristic
779C2×C4(C22⋊D7)⋊C411yescharacteristic
780C2×C4(C22⋊D7)⋊C411yescharacteristic
781C2×C4#644611yescharacteristic
782C2×C4#644611yescharacteristic
783C2×C4#644611yescharacteristic
784C2×C4#644611yescharacteristic
785C2×C4#644711yescharacteristic
786C2×C4#644711yescharacteristic
787C2×C4#644711yescharacteristic
788C2×C4#644711yescharacteristic
789C2×C4C4×C22⋊D711yescharacteristic
790C2×C4C4×C22⋊D711yescharacteristic
791C2×C4C4×C22⋊D711yescharacteristic
792C2×C4C4×C22⋊D711yescharacteristic
793C2×C4#650011yescharacteristic
794C2×C4#650011yescharacteristic
795C2×C4#650011yescharacteristic
796C2×C4#650011yescharacteristic
797C2×C4#650111yescharacteristic
798C2×C4#650111yescharacteristic
799C2×C4#650111yescharacteristic
800C2×C4#650111yescharacteristic
801C7#2101411yescharacteristic, complemented, Sylow
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—44no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22—144no—
814C22—284no—
815C22—284no—
816C22—562no—
817C22C2×D7×C22⋊C411yescharacteristic
818C22C2×(C22⋊D7)⋊C411yescharacteristic
819C22C2×#644611yescharacteristic
820C22C2×#644711yescharacteristic
821C22C2×C4×C22⋊D711yescharacteristic
822C22C2×#650011yescharacteristic
823C22C2×#650111yescharacteristic
824C4—44no—
825C4—42no—
826C4—82no—
827C4—144no—
828C4—284no—
829C4—284no—
830C4—562no—
831C4#8972811yescharacteristic
832C4#8972811yescharacteristic
833C4#8972811yescharacteristic
834C4#8972811yescharacteristic
835C4#8972811yescharacteristic
836C4#8972811yescharacteristic
837C4#8972811yescharacteristic
838C4#8972811yescharacteristic
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—21no—
844C2—21no—
845C2—21no—
846C2—82no—
847C2—284no—
848C2C2×#8972811yescharacteristic
subgroupG/H
centerC4#89728
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C7×#410C2
socleC2×C7C2×#386
prime radical#11744336C2
cosocleC24×C7C24
hypercenterC2×#410D7
hypocenterC7#21014
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #11742799C2semidirect
3. C2×C7×#410C2semidirect
4. C2×#90012C2semidirect
5. C2×#89778C2semidirect
6. #11729347C2semidirect
7. #11729346C2semidirect
8. #11727788C2semidirect
18. #90507C4semidirect
19. #90496C4semidirect
21. #90482C4semidirect
57. C22×C7×Q8C2×C4semidirect
58. C22×C7×D4C2×C4semidirect
60. C23×C4×C7C2×C4semidirect
84. C7×#117D4semidirect
85. C7×#117D4semidirect
92. #6516C2×C4semidirect
106. #6492C2×C4semidirect
117. #6489C2×C4semidirect
118. #6489C2×C4semidirect
119. #6489D4semidirect
120. #6489D4semidirect
146. C2×#410D7semidirect
446. C22×Q8C4×D7semidirect
449. C22×D4C4×D7semidirect
452. C23×C4C4×D7semidirect
495. #117C22⋊D7semidirect
496. #117C22⋊D7semidirect
801. C7#21014semidirect

Maximal subgroups

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

subgroupindex
#117443362
#117427992
C2×C7×#4102
C2×#900122
C2×#897782
#117293472
#117293462
#117277882
#210147