Finite Group Databasebeta

← #13276641

Subgroups — #13276641

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#380C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4C2×#89745C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
6C2×#89716C212yesmaximal
7#11729317C211yesmaximal, characteristic, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729303C212yesmaximal
10#11727171C212yesmaximal, complemented
11#11727160C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C22×C4×Dic7C2211yescharacteristic
25C7×#380—24no—
26C2×C7×#95C2212yes—
27#89984C418yescomplemented
28C4×C22⋊Dic7—24no—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C4⋊C4×Dic7—24no—
39#89745—24no—
40#89716—28no—
41#13974—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7C2×C414yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×Dic7C2312yes—
55C23×Dic7C2312yes—
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2311yescharacteristic
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2311yescharacteristic
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4D414yes—
66C2×C7×C22⋊C4—24no—
67C2×C7×C22⋊C4—24no—
68C2×C7×C22⋊C4—42no—
69C2×C22⋊Dic7—24no—
70C2×C22⋊Dic7—22no—
71C2×C22⋊Dic7—24no—
72C2×C22⋊Dic7—22no—
73C2×C22⋊Dic7—22no—
74C2×C22⋊Dic7—22no—
75C2×C22⋊Dic7—22no—
76C2×C22⋊Dic7C2×C418yes—
77C2×C22⋊Dic7D414yes—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7C2×C414yes—
83C2×C4⋊Dic7C2×C414yes—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—24no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—24no—
91C2×C4×Dic7—22no—
92C2×C4×Dic7—22no—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—42no—
95C2×C4×Dic7D414yes—
96C7×#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—22no—
101C7⋊#95—22no—
102C7⋊#95—24no—
103C7⋊#95—24no—
104C7⋊#95—42no—
105C7⋊#95C2×C418yes—
106C2×#389—71no—
107C2×#388—72no—
108C2×#380—71no—
109C2×#380D711yescharacteristic
110C2×C4×C4⋊C4—71no—
111C2×C4×C22⋊C4—71no—
112#1443—72no—
113#1440—72no—
114#1436—72no—
115C4⋊#95—71no—
116C4⋊#95—71no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7C22×C412yes—
130C24×C7C2×D412yes—
131C24×C7#4112yes—
132C24×C7C2411yescharacteristic
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—28no—
146C22×C4×C7—28no—
147C22×C4×C7—28no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—44no—
156C22×C4×C7—44no—
157C22×C4×C7—44no—
158C22×C4×C7—44no—
159C22×C4×C7C22×C412yes—
160C22×C4×C7C22×C412yes—
161C22×C4×C7C2×D414yes—
162C22×C4×C7C2×D412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7#4112yes—
165C22×C4×C7#4112yes—
166C22×C4×C7#4112yes—
167C22×C4×C7#4112yes—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7C22×C414yes—
203C22×Dic7C22×C414yes—
204C22×Dic7C2×D412yes—
205C22×Dic7C2×D412yes—
206C22×Dic7C2×D412yes—
207C22×Dic7C2×D412yes—
208C22×Dic7#4112yes—
209C22×Dic7#4112yes—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—44no—
212C7×C22⋊C4—48no—
213C22⋊Dic7—28no—
214C22⋊Dic7—216no—
215C22⋊Dic7—28no—
216C4⋊Dic7—28no—
217C4⋊Dic7—28no—
218Dic7⋊C4—48no—
219C4×Dic7—28no—
220C4×Dic7—48no—
221C4×Dic7—44no—
222C24×C4C2×D711yescharacteristic
223C22×C4⋊C4—71no—
224C22×C4⋊C4—71no—
225C22×C4⋊C4—72no—
226C22×C4⋊C4C2×D711yescharacteristic
227C22×C4⋊C4C2×D711yescharacteristic
228C22×C22⋊C4—72no—
229C22×C22⋊C4—71no—
230C22×C22⋊C4—71no—
231C22×C22⋊C4C2×D712yes—
232C22×C42—71no—
233C22×C42—71no—
234C22×C42—72no—
235#389—144no—
236#388—148no—
237#380—24no—
238#380—78no—
239C4×C4⋊C4—144no—
240C4×C22⋊C4—144no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95—71no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95—71no—
249C2×#95—72no—
250C2×#95C2×D712yes—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7C4×D414yes—
286C23×C7C23×C411yescharacteristic
287C23×C7C22×D411yescharacteristic
288C23×C7C22×D411yescharacteristic
289C23×C7C22×D411yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C23×C7C2×#4111yescharacteristic
297C23×C7H(5,𝔽2)11yescharacteristic
298C23×C72−1+411yescharacteristic
299C23×C72−1+411yescharacteristic
300C23×C72−1+411yescharacteristic
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—24no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—416no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7#11714yes—
324C2×C4×C7C4×D414yes—
325C2×C4×C7C4×D414yes—
326C2×C4×C7#12114yes—
327C2×C4×C7#12314yes—
328C2×C4×C7#12414yes—
329C2×C4×C7#12614yes—
330C2×Dic7—22no—
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—22no—
335C2×Dic7—22no—
336C2×Dic7—24no—
337C2×Dic7—24no—
338C2×Dic7—24no—
339C2×Dic7—24no—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—42no—
360C2×Dic7—42no—
361C2×Dic7—41no—
362C2×Dic7—42no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—42no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7#12114yes—
372C25C22×D711yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—71no—
380C23×C4—72no—
381C23×C4—72no—
382C23×C4—71no—
383C23×C4—71no—
384C23×C4—71no—
385C23×C4C4×D714yes—
386C23×C4C22×D712yes—
387C23×C4C22×D711yescharacteristic
388C23×C4C22×D712yes—
389C23×C4C22×D711yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—74no—
396C2×C4⋊C4—74no—
397C2×C4⋊C4—142no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—142no—
401C2×C4⋊C4—144no—
402C2×C4⋊C4—144no—
403C2×C4⋊C4—144no—
404C2×C4⋊C4C22⋊D714yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—78no—
409C2×C22⋊C4—74no—
410C2×C22⋊C4—142no—
411C2×C22⋊C4—142no—
412C2×C22⋊C4—142no—
413C2×C22⋊C4—142no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—142no—
416C2×C22⋊C4—144no—
417C2×C42—74no—
418C2×C42—142no—
419C2×C42—142no—
420C2×C42—144no—
421C2×C42—142no—
422C2×C42—142no—
423C2×C42—142no—
424C2×C42—144no—
425C2×C42—282no—
426#95—24no—
427#95—78no—
428#95—144no—
429#95—142no—
430#95—142no—
431#95—144no—
432#95—144no—
433#95—144no—
434#95—144no—
435#95—282no—
436C22×C7—24no—
437C22×C7—24no—
438C22×C7—24no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7—42no—
448C22×C7—42no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7C2×#11711yescharacteristic
452C22×C7C2×C4×D411yescharacteristic
453C22×C7C2×C4×D411yescharacteristic
454C22×C7C2×C4×D411yescharacteristic
455C22×C7C4×#4111yescharacteristic
456C22×C7#51911yescharacteristic
457C22×C7#52011yescharacteristic
458C22×C7C2×#12111yescharacteristic
459C22×C7C2×#12111yescharacteristic
460C22×C7C2×#12311yescharacteristic
461C22×C7#52511yescharacteristic
462C22×C7C2×#12411yescharacteristic
463C22×C7C2×#12611yescharacteristic
464C22×C7#52911yescharacteristic
465C22×C7#53211yescharacteristic
466C22×C7#53611yescharacteristic
467C22×C7#53711yescharacteristic
468C22×C7#54111yescharacteristic
469C22×C7#54211yescharacteristic
470C22×C7D4211yescharacteristic
471C22×C7#54711yescharacteristic
472C22×C7#54711yescharacteristic
473C22×C7#54711yescharacteristic
474C22×C7#54711yescharacteristic
475C22×C7#54811yescharacteristic
476C22×C7#54811yescharacteristic
477C22×C7#55211yescharacteristic
478C22×C7#55211yescharacteristic
479C22×C7#55211yescharacteristic
480C22×C7#55311yescharacteristic
481C22×C7#55311yescharacteristic
482C22×C7#55311yescharacteristic
483C22×C7#55611yescharacteristic
484C22×C7#55611yescharacteristic
485C22×C7#55611yescharacteristic
486C4×C7—44no—
487C4×C7—42no—
488C4×C7—82no—
489C4×C7#38818yescomplemented
490Dic7—24no—
491Dic7—42no—
492Dic7—44no—
493Dic7—42no—
494Dic7—42no—
495Dic7—44no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24C2×C4×D712yes—
509C24D4×D712yes—
510C24#116112yes—
511C24C23×D711yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—72no—
539C22×C4—72no—
540C22×C4—72no—
541C22×C4—74no—
542C22×C4—74no—
543C22×C4—72no—
544C22×C4—72no—
545C22×C4—72no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—141no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—142no—
562C22×C4—141no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—142no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—142no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—142no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—142no—
580C22×C4C2×C4×D712yes—
581C22×C4C2×C4×D712yes—
582C22×C4#115712yes—
583C22×C4D4×D712yes—
584C22×C4#115912yes—
585C22×C4#115912yes—
586C22×C4#115912yes—
587C22×C4C2×C22⋊D714yes—
588C22×C4C2×C22⋊D712yes—
589C4⋊C4—28no—
590C4⋊C4—44no—
591C4⋊C4—148no—
592C4⋊C4—148no—
593C4⋊C4—288no—
594C22⋊C4—48no—
595C22⋊C4—148no—
596C22⋊C4—148no—
597C22⋊C4—1416no—
598C42—148no—
599C42—288no—
600C42—284no—
601C2×C7—44no—
602C2×C7C2×#38811yescharacteristic
603C2×C7C4×#12111yescharacteristic
604C2×C7#232311yescharacteristic
605C2×C7#234411yescharacteristic
606C2×C7#234711yescharacteristic
607C2×C7#236111yescharacteristic
608C2×C7#236211yescharacteristic
609C2×C7#241511yescharacteristic
610C2×C7#241611yescharacteristic
611C2×C7#242111yescharacteristic
612C2×C7#242211yescharacteristic
613C2×C7#249411yescharacteristic
614C2×C7#249611yescharacteristic
615C2×C7#254711yescharacteristic
616C2×C7#256211yescharacteristic
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23#645614yes—
652C23C22×C4×D711yescharacteristic
653C23C2×#115711yescharacteristic
654C23C2×D4×D711yescharacteristic
655C23C2×D4×D711yescharacteristic
656C23C2×#115911yescharacteristic
657C23C2×#115911yescharacteristic
658C23C2×#115911yescharacteristic
659C23#654811yescharacteristic
660C23C2×#116111yescharacteristic
661C23#655111yescharacteristic
662C23D7×#4111yescharacteristic
663C23D7×#4111yescharacteristic
664C23#655411yescharacteristic
665C23#655411yescharacteristic
666C23C22×C22⋊D711yescharacteristic
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—416no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—74no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—144no—
699C2×C4—144no—
700C2×C4—142no—
701C2×C4—144no—
702C2×C4—142no—
703C2×C4—144no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—281no—
712C2×C4—281no—
713C2×C4—282no—
714C2×C4—281no—
715C2×C4—282no—
716C2×C4—281no—
717C2×C4—282no—
718C2×C4—281no—
719C2×C4—282no—
720C2×C4—281no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—281no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—281no—
727C2×C4—281no—
728C2×C4—281no—
729C2×C4—281no—
730C2×C4—281no—
731C2×C4#644014yes—
732C2×C4#644214yes—
733C2×C4(C22⋊D7)⋊C414yes—
734C2×C4#644814yes—
735C2×C4C4×C22⋊D714yes—
736C2×C4#649814yes—
737C2×C4#650114yes—
738C7#1397411yescharacteristic, complemented, Sylow
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×#644011yescharacteristic
755C22C2×#644211yescharacteristic
756C22C2×(C22⋊D7)⋊C411yescharacteristic
757C22C2×#644811yescharacteristic
758C22C2×#645611yescharacteristic
759C22#9019511yescharacteristic
760C22#9019811yescharacteristic
761C22#9020511yescharacteristic
762C22#9020711yescharacteristic
763C22#9021311yescharacteristic
764C22#9022011yescharacteristic
765C22#9022411yescharacteristic
766C22#9028711yescharacteristic
767C22#9029411yescharacteristic
768C22D7×#12111yescharacteristic
769C22#9029911yescharacteristic
770C22#9030211yescharacteristic
771C22#9030211yescharacteristic
772C22#9030511yescharacteristic
773C22#9030511yescharacteristic
774C22#9031511yescharacteristic
775C22#9031611yescharacteristic
776C22#9031811yescharacteristic
777C22#9031911yescharacteristic
778C22#9033211yescharacteristic
779C22#9033211yescharacteristic
780C22#9033311yescharacteristic
781C22#9033311yescharacteristic
782C22C2×C4×C22⋊D711yescharacteristic
783C22C2×#649811yescharacteristic
784C22C2×#650111yescharacteristic
785C22D4×C22⋊D711yescharacteristic
786C22#9050811yescharacteristic
787C22#9051511yescharacteristic
788C22#9052211yescharacteristic
789C4—42no—
790C4—44no—
791C4—82no—
792C4—144no—
793C4—282no—
794C4—284no—
795C4—282no—
796C4—282no—
797C4—284no—
798C4#8971618yescomplemented
799C2—44no—
800C2#1173131011yescharacteristic
801C2#1173131611yescharacteristic
802C2#1173132311yescharacteristic
803C2#1173132711yescharacteristic
804C2#1173136411yescharacteristic
805C2#1173136811yescharacteristic
806C2#1173138211yescharacteristic
807C2#1173138611yescharacteristic
808C2C2×#8971611yescharacteristic
809C2#1173960811yescharacteristic
810C2#1173968811yescharacteristic
811C2#1174008611yescharacteristic
812C2#1174008911yescharacteristic
813C2#1174019811yescharacteristic
814C2#1174025811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#380D7
hypocenterC7#13974
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#89745C2semidirect
5. C2×C4⋊C4×Dic7C2semidirect
7. #11729317C2semidirect
8. #11729317C2semidirect
10. #11727171C2semidirect
11. #11727160C2semidirect
27. #89984C4semidirect
489. C4×C7#388semidirect
738. C7#13974semidirect
798. C4#89716semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3802
C2×#899842
C2×C4×C22⋊Dic72
C2×#897452
C2×C4⋊C4×Dic72
C2×#897162
#117293172
#117293032
#117271712
#117271602
#139747