Finite Group Databasebeta

← #13276920

Subgroups — #13276920

Order 1792.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6498C211yesmaximal, characteristic
2C2×C7×#386C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
5C22×C7⋊#95C211yesmaximal, characteristic, complemented
6C2×#89718C211yesmaximal, characteristic, complemented
7C2×#89715C211yesmaximal, characteristic, complemented
8#11729301C212yesmaximal, complemented
9#11729299C212yesmaximal, complemented
10#11727175C212yesmaximal, complemented
11Dic7⋊#95C212yesmaximal, 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⋊Dic7C2212yes—
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C2×#6498—24no—
24C2×#6498—24no—
25C2×#6498C418yescomplemented
26C22×Dic7⋊C4C2212yes—
27C22×Dic7⋊C4C2212yes—
28C22×C4×Dic7C2212yes—
29C7×#386—24no—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32#89992—24no—
33C4×C22⋊Dic7—24no—
34C2×C7⋊#95—24no—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#89718—24no—
43#89715—24no—
44#13996—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C25×C7C2311yescharacteristic
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4C2×C414yes—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—24no—
57C23×C4×C7—42no—
58C23×C4×C7D414yes—
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—24no—
72C23×Dic7—22no—
73C23×Dic7—22no—
74C23×Dic7—42no—
75C23×Dic7C2×C414yes—
76C23×Dic7C2312yes—
77C23×Dic7C2312yes—
78C23×Dic7C2312yes—
79C23×Dic7C2312yes—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—42no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—24no—
90C2×C22⋊Dic7—24no—
91C2×C22⋊Dic7—24no—
92C2×C22⋊Dic7—24no—
93C2×C22⋊Dic7—42no—
94C2×C22⋊Dic7C2×C414yes—
95C2×C22⋊Dic7C2×C418yescomplemented
96C2×C22⋊Dic7D414yes—
97C2×C22⋊Dic7D414yes—
98C2×C22⋊Dic7D414yes—
99#6498—232no—
100C2×Dic7⋊C4—24no—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—42no—
105C2×Dic7⋊C4C2×C418yescomplemented
106C2×C4×Dic7—24no—
107C2×C4×Dic7—24no—
108C2×C4×Dic7—42no—
109C7×#95—22no—
110C7×#95—22no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—24no—
117C7⋊#95—24no—
118C22×#123—71no—
119C2×#386—71no—
120C2×#386D711yescharacteristic
121C2×#385—71no—
122C2×#381—71no—
123C2×C4×C22⋊C4—71no—
124C22×#95—71no—
125#1445—72no—
126#1439—72no—
127#1437—72no—
128C4⋊#95—72no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7C22×C412yes—
144C24×C7C22×C412yes—
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×D412yes—
148C24×C7C2×D412yes—
149C24×C7#4112yes—
150C24×C7#4112yes—
151C24×C7C2411yescharacteristic
152C2×C7×D4—28no—
153C2×C7×D4—28no—
154C2×C7×D4—28no—
155C2×C7×D4—44no—
156C2×C7×D4—44no—
157C2×C7×D4—44no—
158C2×C7×D4—44no—
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—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—28no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—44no—
185C22×C4×C7—48no—
186C22×C4×C7—48no—
187C22×C4×C7C22×C412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7#4114yes—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—28no—
196C22×Dic7—28no—
197C22×Dic7—28no—
198C22×Dic7—28no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—48no—
218C22×Dic7—48no—
219C22×Dic7—44no—
220C22×Dic7—44no—
221C22×Dic7—44no—
222C22×Dic7—44no—
223C22×Dic7—44no—
224C22×Dic7—44no—
225C22×Dic7C22×C414yes—
226C22×Dic7C22×C414yes—
227C22×Dic7C2×D414yes—
228C22×Dic7C2×D414yes—
229C22×Dic7C2×D414yes—
230C22×Dic7#4114yes—
231C7×C22⋊C4—44no—
232C7×C22⋊C4—44no—
233C7×C22⋊C4—44no—
234C22⋊Dic7—28no—
235C22⋊Dic7—216no—
236C22⋊Dic7—48no—
237C22⋊Dic7C22⋊C4116yescomplemented
238Dic7⋊C4—216no—
239Dic7⋊C4—48no—
240C4×Dic7—48no—
241C23×D4C2×D711yescharacteristic
242C24×C4—71no—
243C24×C4—71no—
244C24×C4C2×D711yescharacteristic
245C2×#123—78no—
246C2×#123—144no—
247C2×#123—144no—
248C22×C4⋊C4—72no—
249C22×C4⋊C4—72no—
250C22×C22⋊C4—71no—
251C22×C22⋊C4—72no—
252C22×C22⋊C4—71no—
253C22×C22⋊C4—72no—
254C22×C22⋊C4C2×D711yescharacteristic
255C22×C22⋊C4C2×D711yescharacteristic
256C22×C22⋊C4C2×D711yescharacteristic
257C22×C42—72no—
258#386—24no—
259#386—144no—
260#385—144no—
261#381—144no—
262C4×C22⋊C4—144no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—144no—
271C2×#95C2×D711yescharacteristic
272C2×#95C2×D711yescharacteristic
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—24no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—42no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7C2×C22⋊C414yes—
313C23×C7C4×D414yes—
314C23×C7C4×D414yes—
315C23×C7#12114yes—
316C23×C7#12114yes—
317C23×C7#12414yes—
318C23×C7#12714yes—
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C22×D411yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C72−1+412yes—
330C7×D4—416no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—24no—
334C2×C4×C7—24no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—416no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7#12314yescomplemented
359C2×Dic7—24no—
360C2×Dic7—24no—
361C2×Dic7—24no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—24no—
367C2×Dic7—24no—
368C2×Dic7—24no—
369C2×Dic7—24no—
370C2×Dic7—24no—
371C2×Dic7—24no—
372C2×Dic7—24no—
373C2×Dic7—24no—
374C2×Dic7—416no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—42no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—416no—
388C2×Dic7C2×C22⋊C418yes—
389C25C22×D711yescharacteristic
390C25C22×D711yescharacteristic
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4C4×D714yes—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—42no—
402C23×C4—72no—
403C23×C4—74no—
404C23×C4—72no—
405C23×C4—72no—
406C23×C4—72no—
407C23×C4—144no—
408C23×C4—142no—
409C23×C4—142no—
410C23×C4—142no—
411C23×C4—142no—
412C23×C4—142no—
413C23×C4—142no—
414C23×C4—142no—
415C23×C4—142no—
416C23×C4—142no—
417C23×C4—282no—
418C23×C4C22⋊D714yes—
419C23×C4C22×D711yescharacteristic
420C23×C4C22×D711yescharacteristic
421C23×C4C22×D711yescharacteristic
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D711yescharacteristic
424#123—1432no—
425C2×C4⋊C4—78no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—282no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—78no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—144no—
444C2×C22⋊C4—144no—
445C2×C22⋊C4—142no—
446C2×C22⋊C4—142no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—282no—
450C2×C42—144no—
451C2×C42—144no—
452C2×C42—282no—
453#95—22no—
454#95—22no—
455#95—144no—
456#95—144no—
457#95—144no—
458#95—144no—
459#95—144no—
460#95—144no—
461#95—144no—
462C22×C7—24no—
463C22×C7—28no—
464C22×C7—28no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—24no—
470C22×C7—24no—
471C22×C7—24no—
472C22×C7—42no—
473C22×C7—44no—
474C22×C7—44no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—82no—
480C22×C7—82no—
481C22×C7—81no—
482C22×C7—81no—
483C22×C7#39018yes—
484C22×C7C22×C22⋊C411yescharacteristic
485C22×C7C2×C4×D411yescharacteristic
486C22×C7C2×C4×D411yescharacteristic
487C22×C7C4×#4112yes—
488C22×C7#52012yes—
489C22×C7C2×#12111yescharacteristic
490C22×C7C2×#12111yescharacteristic
491C22×C7C2×#12311yescharacteristic
492C22×C7#52511yescharacteristic
493C22×C7C2×#12411yescharacteristic
494C22×C7#52912yes—
495C22×C7C2×#12711yescharacteristic
496C22×C7#53411yescharacteristic
497C22×C7#53611yescharacteristic
498C22×C7#53912yes—
499C22×C7#54612yes—
500C22×C7#54612yes—
501C22×C7#54612yes—
502C22×C7#54712yes—
503C22×C7#54712yes—
504C22×C7#54712yes—
505C22×C7#55112yes—
506C22×C7#55212yes—
507C4×C7—24no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—81no—
511C4×C7—81no—
512Dic7—28no—
513Dic7—44no—
514Dic7—44no—
515Dic7—44no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—21no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—21no—
530C24C2×C4×D712yes—
531C24C2×C4×D712yes—
532C24#115712yes—
533C24D4×D712yes—
534C24D4×D712yes—
535C24D4×D712yes—
536C24#115912yes—
537C24C2×C22⋊D712yes—
538C24C23×D711yescharacteristic
539C2×D4—28no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—28no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—74no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—74no—
578C22×C4—74no—
579C22×C4—74no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—148no—
585C22×C4—148no—
586C22×C4—148no—
587C22×C4—148no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—288no—
607C22×C4—288no—
608C22×C4—284no—
609C22×C4—284no—
610C22×C4—284no—
611C22×C4—284no—
612C22×C4—284no—
613C22×C4—284no—
614C22×C4C2×C4×D712yes—
615C22×C4#115914yes—
616C22×C4C2×C22⋊D712yes—
617C22×C4C2×C22⋊D712yes—
618C4⋊C4—1416no—
619C4⋊C4—288no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—716no—
624C22⋊C4—1416no—
625C22⋊C4—148no—
626C22⋊C4—288no—
627C42—288no—
628C2×C7—28no—
629C2×C7—82no—
630C2×C7C2×#39011yescharacteristic
631C2×C7C4×#12311yescharacteristic
632C2×C7#232211yescharacteristic
633C2×C7#233912yes—
634C2×C7#235912yes—
635C2×C7#241211yescharacteristic
636C2×C7#241311yescharacteristic
637C2×C7#242512yes—
638C2×C7#248812yes—
639C2×C7#250111yescharacteristic
640C2×C7#253911yescharacteristic
641C23—24no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23D7×C22⋊C414yes—
681C23(C22⋊D7)⋊C414yes—
682C23#644714yes—
683C23#644814yes—
684C23C4×C22⋊D714yes—
685C23#650214yes—
686C23#650314yes—
687C23C22×C4×D711yescharacteristic
688C23C2×#115711yescharacteristic
689C23C2×D4×D711yescharacteristic
690C23C2×D4×D711yescharacteristic
691C23C2×D4×D711yescharacteristic
692C23C2×#115911yescharacteristic
693C23C2×#115912yes—
694C23#654812yes—
695C23D7×#4112yes—
696C23#655412yes—
697C23C22×C22⋊D711yescharacteristic
698D4—416no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—78no—
727C2×C4—144no—
728C2×C4—144no—
729C2×C4—144no—
730C2×C4—144no—
731C2×C4—144no—
732C2×C4—144no—
733C2×C4—144no—
734C2×C4—144no—
735C2×C4—144no—
736C2×C4—144no—
737C2×C4—144no—
738C2×C4—144no—
739C2×C4—144no—
740C2×C4—144no—
741C2×C4—144no—
742C2×C4—2816no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4—282no—
749C2×C4—282no—
750C2×C4—2816no—
751C2×C4—282no—
752C2×C4—282no—
753C2×C4—282no—
754C2×C4—282no—
755C2×C4—282no—
756C2×C4#649814yescomplemented
757C7#1399611yescharacteristic, complemented, Sylow
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—28no—
763C22—28no—
764C22—28no—
765C22—24no—
766C22—28no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—81no—
777C22—82no—
778C22—81no—
779C22#8972918yes—
780C22C2×D7×C22⋊C411yescharacteristic
781C22C2×(C22⋊D7)⋊C411yescharacteristic
782C22C2×#644711yescharacteristic
783C22C2×#644811yescharacteristic
784C22C4×#115912yes—
785C22#9022912yes—
786C22#9023712yes—
787C22#9025512yes—
788C22#9027812yes—
789C22#9028212yes—
790C22#9030112yes—
791C22#9030112yes—
792C22#9030212yes—
793C22#9030212yes—
794C22#9034112yes—
795C22#9034612yes—
796C22C2×C4×C22⋊D711yescharacteristic
797C22C2×#649811yescharacteristic
798C22C2×#650211yescharacteristic
799C22C2×#650311yescharacteristic
800C22#9049511yescharacteristic
801C22#9051611yescharacteristic
802C22#9051911yescharacteristic
803C4—24no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4—148no—
809C4—284no—
810C4—284no—
811C4—284no—
812C2—28no—
813C2—82no—
814C2#1173211712yes—
815C2#1173212012yes—
816C2#1173214112yes—
817C2#1173218412yes—
818C2C2×#8972911yescharacteristic
819C2C4×#649811yescharacteristic
820C2#1173977111yescharacteristic
821C2#1174002911yescharacteristic
822C2#1174010911yescharacteristic
823C2#1174015311yescharacteristic
824C2#1174028811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#386C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7#13996
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. C2×#89718C2semidirect
7. C2×#89715C2semidirect
8. #11729301C2semidirect
9. #11729299C2semidirect
10. #11727175C2semidirect
11. Dic7⋊#95C2semidirect
25. C2×#6498C4semidirect
95. C2×C22⋊Dic7C2×C4semidirect
105. C2×Dic7⋊C4C2×C4semidirect
237. C22⋊Dic7C22⋊C4semidirect
358. C2×C4×C7#123semidirect
756. C2×C4#6498semidirect
757. C7#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#64982
C2×C7×#3862
C2×#899922
C2×C4×C22⋊Dic72
C22×C7⋊#952
C2×#897182
C2×#897152
#117293012
#117292992
#117271752
Dic7⋊#952
#139967