Finite Group Databasebeta

← #13277216

Subgroups — #13277216

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#386C211yesmaximal, characteristic
2C2×#89992C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
5C22×C7⋊#95C211yesmaximal, characteristic, complemented
6#11729303C212yesmaximal, complemented
7#11729299C212yesmaximal, complemented
8#11729298C211yesmaximal, characteristic, complemented
9#11729298C211yesmaximal, characteristic, complemented
10#11727172C212yesmaximal, complemented
11#11727157C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic7C2212yes—
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2212yes—
23C22×C4×Dic7C2212yes—
24C7×#386—24no—
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27#89992—24no—
28#89992C418yescomplemented
29C4×C22⋊Dic7—24no—
30C2×C7⋊#95—24no—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40#14020—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C25×C7C2311yescharacteristic
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—24no—
53C23×C4×C7—42no—
54C23×C4×C7D414yes—
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×Dic7—22no—
61C23×Dic7—22no—
62C23×Dic7—22no—
63C23×Dic7—24no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—42no—
67C23×Dic7—42no—
68C23×Dic7—42no—
69C23×Dic7C2×C414yes—
70C23×Dic7C2312yes—
71C23×Dic7C2312yes—
72C23×Dic7C2312yes—
73C23×Dic7C2312yes—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—42no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—24no—
86C2×C22⋊Dic7—24no—
87C2×C22⋊Dic7—42no—
88C2×C22⋊Dic7—42no—
89C2×C22⋊Dic7—42no—
90C2×C22⋊Dic7C2×C414yes—
91C2×C22⋊Dic7C2×C418yescomplemented
92C2×C22⋊Dic7D414yes—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—24no—
95C2×C4×Dic7—42no—
96C7×#95—22no—
97C7×#95—22no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95—42no—
104C7⋊#95—42no—
105C7⋊#95—42no—
106C7⋊#95C2×C418yescomplemented
107C2×#386—71no—
108C2×#386—71no—
109C2×#386D711yescharacteristic
110C2×C4×C22⋊C4—71no—
111C22×#95—71no—
112#1443—72no—
113#1440—72no—
114#1437—72no—
115#1434—72no—
116C22⋊#95—71no—
117C22⋊#95—71no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7C22×C412yes—
133C24×C7C22×C412yes—
134C24×C7C2×D412yes—
135C24×C7C2×D412yes—
136C24×C7#4112yes—
137C24×C7#4112yes—
138C24×C7#4112yes—
139C24×C7#4112yes—
140C24×C7C2411yescharacteristic
141C2×C7×D4—28no—
142C2×C7×D4—28no—
143C2×C7×D4—28no—
144C2×C7×D4—44no—
145C2×C7×D4—44no—
146C2×C7×D4—44no—
147C2×C7×D4—44no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—28no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—28no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—44no—
174C22×C4×C7—48no—
175C22×C4×C7—48no—
176C22×C4×C7C22×C412yes—
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2×D412yes—
179C22×C4×C7#4114yes—
180C22×Dic7—28no—
181C22×Dic7—28no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—48no—
207C22×Dic7—48no—
208C22×Dic7—48no—
209C22×Dic7—44no—
210C22×Dic7—44no—
211C22×Dic7—44no—
212C22×Dic7—48no—
213C22×Dic7—44no—
214C22×Dic7C22×C414yes—
215C22×Dic7C22×C414yes—
216C22×Dic7C2×D414yes—
217C22×Dic7#4114yes—
218C7×C22⋊C4—44no—
219C7×C22⋊C4—44no—
220C7×C22⋊C4—44no—
221C22⋊Dic7—28no—
222C22⋊Dic7—28no—
223C22⋊Dic7—48no—
224C22⋊Dic7—48no—
225C4×Dic7—48no—
226C23×D4C2×D711yescharacteristic
227C24×C4—71no—
228C24×C4—71no—
229C24×C4C2×D711yescharacteristic
230C22×C22⋊C4—71no—
231C22×C22⋊C4—71no—
232C22×C22⋊C4—72no—
233C22×C22⋊C4—72no—
234C22×C22⋊C4C2×D711yescharacteristic
235C22×C22⋊C4C2×D711yescharacteristic
236C22×C22⋊C4C2×D711yescharacteristic
237C22×C42—72no—
238#386—24no—
239#386—78no—
240#386—144no—
241C4×C22⋊C4—144no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95—72no—
250C2×#95—72no—
251C2×#95—144no—
252C2×#95C2×D711yescharacteristic
253C2×#95C2×D711yescharacteristic
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—24no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—42no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7#11714yes—
294C23×C7C4×D414yes—
295C23×C7C4×D414yes—
296C23×C7#12114yes—
297C23×C7#12314yes—
298C23×C7#12414yes—
299C23×C7#12614yes—
300C23×C7C23×C411yescharacteristic
301C23×C7C22×D411yescharacteristic
302C23×C7C22×D411yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7C2×#4111yescharacteristic
307C23×C7C2×#4112yes—
308C23×C7C2×#4112yes—
309C23×C7H(5,𝔽2)12yes—
310C23×C7H(5,𝔽2)12yes—
311C7×D4—416no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—416no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7#12314yes—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—24no—
347C2×Dic7—24no—
348C2×Dic7—24no—
349C2×Dic7—24no—
350C2×Dic7—24no—
351C2×Dic7—24no—
352C2×Dic7—416no—
353C2×Dic7—416no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—42no—
358C2×Dic7—42no—
359C2×Dic7—42no—
360C2×Dic7—42no—
361C2×Dic7—42no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C25C22×D711yescharacteristic
371C25C22×D711yescharacteristic
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4C4×D714yes—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—42no—
383C23×C4—72no—
384C23×C4—72no—
385C23×C4—72no—
386C23×C4—72no—
387C23×C4—74no—
388C23×C4—144no—
389C23×C4—142no—
390C23×C4—142no—
391C23×C4—142no—
392C23×C4—142no—
393C23×C4—142no—
394C23×C4—282no—
395C23×C4—282no—
396C23×C4—282no—
397C23×C4C22⋊D714yes—
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—74no—
411C2×C22⋊C4—74no—
412C2×C22⋊C4—78no—
413C2×C22⋊C4—142no—
414C2×C22⋊C4—142no—
415C2×C22⋊C4—142no—
416C2×C22⋊C4—142no—
417C2×C22⋊C4—144no—
418C2×C22⋊C4—144no—
419C2×C22⋊C4—282no—
420C2×C22⋊C4—282no—
421C2×C22⋊C4—282no—
422C2×C42—144no—
423C2×C42—144no—
424C2×C42—282no—
425#95—22no—
426#95—22no—
427#95—78no—
428#95—144no—
429#95—144no—
430#95—144no—
431#95—144no—
432#95—144no—
433#95—282no—
434#95—282no—
435#95—282no—
436C22×C7—24no—
437C22×C7—24no—
438C22×C7—28no—
439C22×C7—28no—
440C22×C7—24no—
441C22×C7—24no—
442C22×C7—28no—
443C22×C7—24no—
444C22×C7—28no—
445C22×C7—24no—
446C22×C7—42no—
447C22×C7—44no—
448C22×C7—44no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7—81no—
452C22×C7—81no—
453C22×C7—81no—
454C22×C7—82no—
455C22×C7—81no—
456C22×C7—82no—
457C22×C7#38818yes—
458C22×C7C2×#11711yescharacteristic
459C22×C7C2×C4×D411yescharacteristic
460C22×C7C2×C4×D411yescharacteristic
461C22×C7C4×#4112yes—
462C22×C7#51812yes—
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×#12311yescharacteristic
465C22×C7C2×#12311yescharacteristic
466C22×C7#52511yescharacteristic
467C22×C7C2×#12411yescharacteristic
468C22×C7C2×#12611yescharacteristic
469C22×C7#52912yes—
470C22×C7#53411yescharacteristic
471C22×C7#53511yescharacteristic
472C22×C7#53812yes—
473C22×C7#54612yes—
474C22×C7#54612yes—
475C22×C7#55112yes—
476C22×C7#55112yes—
477C22×C7#55312yes—
478C22×C7#55312yes—
479C22×C7#55312yes—
480C22×C7#55312yes—
481C4×C7—24no—
482C4×C7—42no—
483C4×C7—42no—
484C4×C7—81no—
485C4×C7—81no—
486Dic7—44no—
487Dic7—44no—
488Dic7—44no—
489Dic7—44no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24C2×C4×D712yes—
505C24C2×C4×D712yes—
506C24#115712yes—
507C24D4×D712yes—
508C24#115912yes—
509C24#115912yes—
510C24#115912yes—
511C24C2×C22⋊D712yes—
512C24C23×D711yescharacteristic
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—74no—
549C22×C4—74no—
550C22×C4—74no—
551C22×C4—74no—
552C22×C4—148no—
553C22×C4—148no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—288no—
579C22×C4—288no—
580C22×C4—288no—
581C22×C4—284no—
582C22×C4—288no—
583C22×C4—284no—
584C22×C4—284no—
585C22×C4—284no—
586C22×C4C2×C4×D712yes—
587C22×C4#115914yes—
588C22×C4C2×C22⋊D712yes—
589C22×C4C2×C22⋊D712yes—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—148no—
594C22⋊C4—148no—
595C22⋊C4—288no—
596C22⋊C4—288no—
597C42—288no—
598C2×C7—28no—
599C2×C7—82no—
600C2×C7C2×#38811yescharacteristic
601C2×C7C4×#12311yescharacteristic
602C2×C7#232111yescharacteristic
603C2×C7#235312yes—
604C2×C7#236412yes—
605C2×C7#241111yescharacteristic
606C2×C7#241211yescharacteristic
607C2×C7#244412yes—
608C2×C7#250411yescharacteristic
609C2×C7#251012yes—
610C2×C7#259111yescharacteristic
611C23—24no—
612C23—24no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23#644014yes—
651C23#644214yes—
652C23(C22⋊D7)⋊C414yes—
653C23#644614yes—
654C23C4×C22⋊D714yes—
655C23#649914yes—
656C23#650214yes—
657C23C22×C4×D711yescharacteristic
658C23C2×#115711yescharacteristic
659C23C2×D4×D711yescharacteristic
660C23C2×#115911yescharacteristic
661C23C2×#115911yescharacteristic
662C23C2×#115911yescharacteristic
663C23C2×#115912yes—
664C23#654812yes—
665C23D7×#4112yes—
666C23#655312yes—
667C23C22×C22⋊D711yescharacteristic
668D4—416no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—416no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—144no—
699C2×C4—144no—
700C2×C4—144no—
701C2×C4—144no—
702C2×C4—144no—
703C2×C4—144no—
704C2×C4—144no—
705C2×C4—144no—
706C2×C4—144no—
707C2×C4—144no—
708C2×C4—2816no—
709C2×C4—2816no—
710C2×C4—282no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4#649814yes—
727C7#1402011yescharacteristic, complemented, Sylow
728C22—24no—
729C22—24no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—28no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—82no—
749C22#8971718yes—
750C22C2×#644011yescharacteristic
751C22C2×#644211yescharacteristic
752C22C2×(C22⋊D7)⋊C411yescharacteristic
753C22C2×#644611yescharacteristic
754C22C4×#115912yes—
755C22#9022912yes—
756C22#9023612yes—
757C22#9025112yes—
758C22#9027812yes—
759C22#9028212yes—
760C22#9029212yes—
761C22#9029212yes—
762C22#9030912yes—
763C22#9030912yes—
764C22#9034512yes—
765C22#9034912yes—
766C22C2×C4×C22⋊D711yescharacteristic
767C22C2×#649811yescharacteristic
768C22C2×#649911yescharacteristic
769C22C2×#650211yescharacteristic
770C22#9049511yescharacteristic
771C22#9051911yescharacteristic
772C22#9052111yescharacteristic
773C4—24no—
774C4—42no—
775C4—42no—
776C4—81no—
777C4—81no—
778C4—284no—
779C4—284no—
780C4—284no—
781C4—284no—
782C2—28no—
783C2—82no—
784C2#1173211912yes—
785C2#1173212312yes—
786C2#1173215012yes—
787C2#1173218912yes—
788C2C2×#8971711yescharacteristic
789C2C4×#649811yescharacteristic
790C2#1173984011yescharacteristic
791C2#1174002911yescharacteristic
792C2#1174011011yescharacteristic
793C2#1174011911yescharacteristic
794C2#1174033911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#386C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7#14020
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×C4×C22⋊Dic7C2semidirect
5. C22×C7⋊#95C2semidirect
6. #11729303C2semidirect
7. #11729299C2semidirect
8. #11729298C2semidirect
9. #11729298C2semidirect
10. #11727172C2semidirect
11. #11727157C2semidirect
28. #89992C4semidirect
91. C2×C22⋊Dic7C2×C4semidirect
106. C7⋊#95C2×C4semidirect
727. C7#14020semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3862
C2×#899922
C2×C4×C22⋊Dic72
C22×C7⋊#952
#117293032
#117292992
#117292982
#117271722
#117271572
#140207