Finite Group Databasebeta

← #13277205

Subgroups — #13277205

Order 1792.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic7⋊C4C211yesmaximal, characteristic, complemented
2C2×C7×#386C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C2×#89992C211yesmaximal, characteristic
5C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
6C2×#89717C212yesmaximal, complemented
7#11729301C212yesmaximal, complemented
8#11729298C211yesmaximal, characteristic, complemented
9#11729298C211yesmaximal, characteristic, complemented
10#11727168C212yesmaximal, complemented
11#11727159C212yesmaximal, 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⋊Dic7C2212yes—
22C22×C22⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4—24no—
24C22×Dic7⋊C4—28no—
25C22×Dic7⋊C4C2212yes—
26C22×Dic7⋊C4C2212yes—
27C22×C4×Dic7C2212yes—
28C7×#386—24no—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31#89992—24no—
32#89992C418yescomplemented
33C4×C22⋊Dic7—24no—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41#89717—28no—
42#14019—71nomaximal, Sylow
43C25×C7C2311yescharacteristic
44C25×C7C2311yescharacteristic
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4C2×C414yes—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7—24no—
55C23×C4×C7—42no—
56C23×C4×C7D414yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—24no—
65C23×Dic7—24no—
66C23×Dic7—22no—
67C23×Dic7—24no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—42no—
71C23×Dic7C2×C414yes—
72C23×Dic7C2312yes—
73C23×Dic7C2312yes—
74C23×Dic7C2312yes—
75C23×Dic7C2312yes—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—42no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—24no—
88C2×C22⋊Dic7—24no—
89C2×C22⋊Dic7—24no—
90C2×C22⋊Dic7—24no—
91C2×C22⋊Dic7—42no—
92C2×C22⋊Dic7C2×C414yes—
93C2×C22⋊Dic7C2×C418yescomplemented
94C2×C22⋊Dic7D414yes—
95C2×Dic7⋊C4—232no—
96C2×Dic7⋊C4—24no—
97C2×Dic7⋊C4—24no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—24no—
100C2×Dic7⋊C4—24no—
101C2×Dic7⋊C4D418yescomplemented
102C2×C4×Dic7—24no—
103C2×C4×Dic7—24no—
104C2×C4×Dic7—42no—
105C7×#95—22no—
106C7×#95—22no—
107C7⋊#95—24no—
108C7⋊#95—24no—
109C7⋊#95—24no—
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—42no—
113C7⋊#95C2×C418yescomplemented
114C23×C4⋊C4—71no—
115C2×#388—72no—
116C2×#386—71no—
117C2×#386—71no—
118C2×#386D711yescharacteristic
119C2×C4×C22⋊C4—71no—
120#1442—72no—
121#1439—72no—
122#1436—72no—
123C22⋊#95—71no—
124C22⋊#95—71no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7C22×C412yes—
140C24×C7C22×C412yes—
141C24×C7C2×D412yes—
142C24×C7C2×D412yes—
143C24×C7#4112yes—
144C24×C7#4112yes—
145C24×C7#4112yes—
146C24×C7#4112yes—
147C24×C7C2411yescharacteristic
148C2×C7×D4—28no—
149C2×C7×D4—28no—
150C2×C7×D4—28no—
151C2×C7×D4—44no—
152C2×C7×D4—44no—
153C2×C7×D4—44no—
154C2×C7×D4—44no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—28no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—28no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—22no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—44no—
181C22×C4×C7—48no—
182C22×C4×C7—48no—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C2×D412yes—
185C22×C4×C7C2×D414yes—
186C22×C4×C7C2×D412yes—
187C22×Dic7—28no—
188C22×Dic7—216no—
189C22×Dic7—28no—
190C22×Dic7—28no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—216no—
196C22×Dic7—28no—
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—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—48no—
216C22×Dic7—48no—
217C22×Dic7—44no—
218C22×Dic7—44no—
219C22×Dic7C22×C414yes—
220C22×Dic7C22×C414yes—
221C22×Dic7C2×D414yes—
222C22×Dic7C2×D414yes—
223C22×Dic7C2×D414yes—
224C22×Dic7#4114yes—
225C7×C22⋊C4—44no—
226C7×C22⋊C4—44no—
227C7×C22⋊C4—44no—
228C22⋊Dic7—28no—
229C22⋊Dic7—28no—
230C22⋊Dic7—216no—
231C22⋊Dic7—48no—
232Dic7⋊C4—216no—
233Dic7⋊C4—216no—
234C4×Dic7—48no—
235C23×D4C2×D711yescharacteristic
236C24×C4—71no—
237C24×C4—71no—
238C24×C4C2×D711yescharacteristic
239C22×C4⋊C4—72no—
240C22×C4⋊C4—72no—
241C22×C4⋊C4—148no—
242C22×C4⋊C4—144no—
243C22×C22⋊C4—71no—
244C22×C22⋊C4—71no—
245C22×C22⋊C4—72no—
246C22×C22⋊C4—72no—
247C22×C22⋊C4C2×D711yescharacteristic
248C22×C22⋊C4C2×D711yescharacteristic
249C22×C22⋊C4C2×D711yescharacteristic
250C22×C42—72no—
251#388—148no—
252#386—24no—
253#386—78no—
254#386—144no—
255C4×C22⋊C4—144no—
256C2×#95—72no—
257C2×#95—72no—
258C2×#95—72no—
259C2×#95—72no—
260C2×#95—72no—
261C2×#95—72no—
262C2×#95—72no—
263C2×#95C2×D711yescharacteristic
264C2×#95C2×D711yescharacteristic
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—24no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—24no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—24no—
276C23×C7—24no—
277C23×C7—24no—
278C23×C7—24no—
279C23×C7—24no—
280C23×C7—24no—
281C23×C7—22no—
282C23×C7—24no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—24no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—42no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—42no—
296C23×C7—42no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—42no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7#11714yes—
305C23×C7C4×D414yes—
306C23×C7C4×D414yes—
307C23×C7#12114yes—
308C23×C7#12314yes—
309C23×C7#12414yes—
310C23×C7#12614yes—
311C23×C7C23×C411yescharacteristic
312C23×C7C22×D412yes—
313C23×C7C22×D411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4112yes—
320C23×C7H(5,𝔽2)12yes—
321C23×C72−1+412yes—
322C7×D4—416no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—24no—
326C2×C4×C7—24no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—416no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
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—42no—
349C2×C4×C7—42no—
350C2×C4×C7#12014yes—
351C2×Dic7—232no—
352C2×Dic7—24no—
353C2×Dic7—24no—
354C2×Dic7—24no—
355C2×Dic7—24no—
356C2×Dic7—24no—
357C2×Dic7—24no—
358C2×Dic7—24no—
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—416no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7C4×D418yes—
381C25C22×D711yescharacteristic
382C25C22×D711yescharacteristic
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4C4×D714yes—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—42no—
394C23×C4—72no—
395C23×C4—74no—
396C23×C4—72no—
397C23×C4—72no—
398C23×C4—72no—
399C23×C4—144no—
400C23×C4—144no—
401C23×C4—144no—
402C23×C4—142no—
403C23×C4—142no—
404C23×C4—142no—
405C23×C4—142no—
406C23×C4—142no—
407C23×C4—282no—
408C23×C4C22⋊D714yes—
409C23×C4C22×D711yescharacteristic
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C2×C4⋊C4—78no—
415C2×C4⋊C4—144no—
416C2×C4⋊C4—144no—
417C2×C4⋊C4—1432no—
418C2×C4⋊C4—144no—
419C2×C4⋊C4—144no—
420C2×C4⋊C4—144no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—74no—
429C2×C22⋊C4—78no—
430C2×C22⋊C4—74no—
431C2×C22⋊C4—144no—
432C2×C22⋊C4—144no—
433C2×C22⋊C4—142no—
434C2×C22⋊C4—142no—
435C2×C22⋊C4—142no—
436C2×C22⋊C4—142no—
437C2×C22⋊C4—144no—
438C2×C22⋊C4—144no—
439C2×C22⋊C4—282no—
440C2×C42—144no—
441C2×C42—144no—
442C2×C42—282no—
443#95—22no—
444#95—22no—
445#95—78no—
446#95—144no—
447#95—144no—
448#95—144no—
449#95—144no—
450#95—144no—
451#95—282no—
452C22×C7—24no—
453C22×C7—24no—
454C22×C7—28no—
455C22×C7—28no—
456C22×C7—24no—
457C22×C7—24no—
458C22×C7—24no—
459C22×C7—28no—
460C22×C7—28no—
461C22×C7—24no—
462C22×C7—42no—
463C22×C7—44no—
464C22×C7—44no—
465C22×C7—42no—
466C22×C7—42no—
467C22×C7—81no—
468C22×C7—81no—
469C22×C7—81no—
470C22×C7—81no—
471C22×C7—82no—
472C22×C7—82no—
473C22×C7#38818yescomplemented
474C22×C7C2×#11711yescharacteristic
475C22×C7C2×C4×D411yescharacteristic
476C22×C7C2×C4×D411yescharacteristic
477C22×C7C2×C4×D412yes—
478C22×C7#52012yes—
479C22×C7C2×#12011yescharacteristic
480C22×C7C2×#12111yescharacteristic
481C22×C7C2×#12311yescharacteristic
482C22×C7#52512yes—
483C22×C7#52511yescharacteristic
484C22×C7C2×#12411yescharacteristic
485C22×C7C2×#12611yescharacteristic
486C22×C7#53411yescharacteristic
487C22×C7#53611yescharacteristic
488C22×C7#53912yes—
489C22×C7D4212yes—
490C22×C7#54612yes—
491C22×C7#54712yes—
492C22×C7#54812yes—
493C22×C7#54812yes—
494C22×C7#55212yes—
495C22×C7#55312yes—
496C22×C7#55312yes—
497C4×C7—24no—
498C4×C7—42no—
499C4×C7—42no—
500C4×C7—81no—
501C4×C7—81no—
502Dic7—28no—
503Dic7—44no—
504Dic7—44no—
505Dic7—44no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24C2×C4×D712yes—
521C24C2×C4×D712yes—
522C24#115712yes—
523C24D4×D712yes—
524C24#115912yes—
525C24#115912yes—
526C24#115912yes—
527C24C2×C22⋊D712yes—
528C24C23×D711yescharacteristic
529C2×D4—28no—
530C2×D4—28no—
531C2×D4—28no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—28no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—74no—
565C22×C4—74no—
566C22×C4—74no—
567C22×C4—74no—
568C22×C4—74no—
569C22×C4—74no—
570C22×C4—1416no—
571C22×C4—148no—
572C22×C4—1416no—
573C22×C4—148no—
574C22×C4—148no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—148no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
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—288no—
599C22×C4—288no—
600C22×C4—284no—
601C22×C4—284no—
602C22×C4C2×C4×D712yes—
603C22×C4D4×D714yes—
604C22×C4C2×C22⋊D712yes—
605C22×C4C2×C22⋊D712yes—
606C4⋊C4—1416no—
607C4⋊C4—1416no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—1416no—
612C22⋊C4—148no—
613C22⋊C4—148no—
614C22⋊C4—288no—
615C42—288no—
616C2×C7—28no—
617C2×C7—82no—
618C2×C7C2×#38811yescharacteristic
619C2×C7C4×#12011yescharacteristic
620C2×C7#232211yescharacteristic
621C2×C7#235212yes—
622C2×C7#236112yes—
623C2×C7#241011yescharacteristic
624C2×C7#241311yescharacteristic
625C2×C7#243611yescharacteristic
626C2×C7#244312yes—
627C2×C7#248112yes—
628C2×C7#259111yescharacteristic
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23#644014yes—
669C23#644214yes—
670C23(C22⋊D7)⋊C414yes—
671C23#644614yes—
672C23C4×C22⋊D714yes—
673C23#649914yes—
674C23#650214yes—
675C23C22×C4×D711yescharacteristic
676C23C2×#115711yescharacteristic
677C23C2×D4×D711yescharacteristic
678C23C2×D4×D712yes—
679C23C2×#115911yescharacteristic
680C23C2×#115911yescharacteristic
681C23C2×#115911yescharacteristic
682C23#654812yes—
683C23D7×#4112yes—
684C23#655412yes—
685C23C22×C22⋊D711yescharacteristic
686D4—416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—416no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—78no—
715C2×C4—1432no—
716C2×C4—144no—
717C2×C4—144no—
718C2×C4—144no—
719C2×C4—144no—
720C2×C4—144no—
721C2×C4—144no—
722C2×C4—144no—
723C2×C4—144no—
724C2×C4—144no—
725C2×C4—144no—
726C2×C4—144no—
727C2×C4—144no—
728C2×C4—144no—
729C2×C4—144no—
730C2×C4—144no—
731C2×C4—2816no—
732C2×C4—282no—
733C2×C4—282no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4#650014yes—
745C7#1401911yescharacteristic, complemented, Sylow
746C22—24no—
747C22—24no—
748C22—24no—
749C22—28no—
750C22—28no—
751C22—28no—
752C22—24no—
753C22—24no—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—44no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—82no—
764C22—81no—
765C22—82no—
766C22—81no—
767C22#8971718yescomplemented
768C22C2×#644011yescharacteristic
769C22C2×#644211yescharacteristic
770C22C2×(C22⋊D7)⋊C411yescharacteristic
771C22C2×#644611yescharacteristic
772C22C4×D4×D712yes—
773C22#9023712yes—
774C22#9023812yes—
775C22#9025512yes—
776C22#9028112yes—
777C22#9028212yes—
778C22#9028912yes—
779C22#9028912yes—
780C22#9029212yes—
781C22#9029212yes—
782C22#9034112yes—
783C22#9034612yes—
784C22C2×C4×C22⋊D711yescharacteristic
785C22C2×#649911yescharacteristic
786C22C2×#650011yescharacteristic
787C22C2×#650211yescharacteristic
788C22#9049511yescharacteristic
789C22#9051611yescharacteristic
790C22#9051911yescharacteristic
791C4—24no—
792C4—42no—
793C4—42no—
794C4—81no—
795C4—81no—
796C4—148no—
797C4—284no—
798C4—284no—
799C4—284no—
800C2—28no—
801C2—82no—
802C2#1173211812yes—
803C2#1173212112yes—
804C2#1173214712yes—
805C2#1173218012yes—
806C2C2×#8971711yescharacteristic
807C2#1173977111yescharacteristic
808C2C4×#650011yescharacteristic
809C2#1174005111yescharacteristic
810C2#1174009911yescharacteristic
811C2#1174011911yescharacteristic
812C2#1174028811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#386C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7#14019
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×Dic7⋊C4C2semidirect
5. C2×C4×C22⋊Dic7C2semidirect
6. C2×#89717C2semidirect
7. #11729301C2semidirect
8. #11729298C2semidirect
9. #11729298C2semidirect
10. #11727168C2semidirect
11. #11727159C2semidirect
32. #89992C4semidirect
93. C2×C22⋊Dic7C2×C4semidirect
101. C2×Dic7⋊C4D4semidirect
113. C7⋊#95C2×C4semidirect
473. C22×C7#388semidirect
745. C7#14019semidirect
767. C22#89717semidirect

Maximal subgroups

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

subgroupindex
C23×Dic7⋊C42
C2×C7×#3862
C2×#899922
C2×C4×C22⋊Dic72
C2×#897172
#117293012
#117292982
#117271682
#117271592
#140197