Finite Group Databasebeta

← #13276895

Subgroups — #13276895

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×#389C211yesmaximal, characteristic, complemented
2C2×#89759C211yesmaximal, characteristic
3C2×#89759C211yesmaximal, characteristic
4C2×#89762C212yesmaximal
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
7#11729321C212yesmaximal, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727183C212yesmaximal
11#11727157C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C22×C4×Dic7C2211yescharacteristic
25C7×#389—24no—
26C2×C7×#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89762—28no—
37#89759—24no—
38#89759C418yescomplemented
39C4⋊C4×Dic7—24no—
40C4×(C2×D7)⋊C4—24no—
41#13994—71nomaximal, Sylow
42C24×D7C2311yescharacteristic
43C23×C4×C7C2312yes—
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×C4×D7—22no—
54C22×C4×D7—22no—
55C22×C4×D7—22no—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7—22no—
59C22×C4×D7C2×C414yes—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—42no—
67C2×C7×C4⋊C4C2×C414yes—
68C2×C7×C4⋊C4D414yes—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—22no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—22no—
76C2×(C2×D7)⋊C4—22no—
77C2×(C2×D7)⋊C4—22no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—24no—
80C2×(C2×D7)⋊C4—24no—
81C2×(C2×D7)⋊C4—42no—
82C2×(C2×D7)⋊C4C2×C418yes—
83C2×(C2×D7)⋊C4D414yes—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7C2×C414yes—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—22no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—24no—
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×#389D711yescharacteristic, complemented
107C2×#388—72no—
108C2×#380—71no—
109C2×#380—71no—
110C2×C4×C4⋊C4—71no—
111C2×C4×C22⋊C4—71no—
112#1442—72no—
113#1440—72no—
114C4⋊#95—71no—
115C4⋊#95—71no—
116#1434—72no—
117C24×C7C2411yescharacteristic
118C23×D7—21no—
119C23×D7—21no—
120C23×D7—21no—
121C23×D7—21no—
122C23×D7—21no—
123C23×D7—21no—
124C23×D7—21no—
125C23×D7—21no—
126C23×D7—21no—
127C23×D7—21no—
128C23×D7—21no—
129C23×D7—21no—
130C23×D7C22×C412yes—
131C23×D7C2×D412yes—
132C23×D7#4112yes—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7C22×C414yes—
158C22×C4×C7C22×C412yes—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D414yes—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×D412yes—
163C22×C4×C7#4112yes—
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—21no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7C22×C412yes—
198C22×Dic7C22×C414yes—
199C22×Dic7C2×D412yes—
200C22×Dic7C2×D412yes—
201C22×Dic7C2×D412yes—
202C22×Dic7#4112yes—
203C2×C4×D7—28no—
204C2×C4×D7—28no—
205C2×C4×D7—28no—
206C2×C4×D7—44no—
207C2×C4×D7—44no—
208C2×C4×D7—44no—
209C2×C4×D7—44no—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—28no—
212C7×C4⋊C4—48no—
213C42×C7—44no—
214(C2×D7)⋊C4—28no—
215(C2×D7)⋊C4—216no—
216(C2×D7)⋊C4—28no—
217(C2×D7)⋊C4—48no—
218C4⋊Dic7—28no—
219C4⋊Dic7—44no—
220C4×Dic7—28no—
221C4×Dic7—48no—
222C24×C4—71no—
223C22×C4⋊C4—71no—
224C22×C4⋊C4—71no—
225C22×C4⋊C4C2×D712yes—
226C22×C4⋊C4C2×D711yescharacteristic
227C22×C4⋊C4C2×D711yescharacteristic
228C22×C22⋊C4—72no—
229C22×C22⋊C4—71no—
230C22×C22⋊C4—71no—
231C22×C22⋊C4—72no—
232C22×C42—71no—
233C22×C42—72no—
234C22×C42C2×D711yescharacteristic
235#389—24no—
236#388—148no—
237#380—78no—
238#380—144no—
239C4×C4⋊C4—144no—
240C4×C22⋊C4—144no—
241C2×#95—72no—
242C2×#95—71no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95—71no—
249C2×#95—72no—
250C2×#95C2×D712yes—
251C23×C7C23×C411yescharacteristic
252C23×C7C22×D411yescharacteristic
253C23×C7C22×D411yescharacteristic
254C23×C7C22×D411yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7C2×#4111yescharacteristic
258C23×C7C2×#4111yescharacteristic
259C23×C7C2×#4111yescharacteristic
260C23×C7C2×#4111yescharacteristic
261C23×C7C2×#4111yescharacteristic
262C23×C7H(5,𝔽2)11yescharacteristic
263C23×C72−1+411yescharacteristic
264C23×C72−1+411yescharacteristic
265C23×C72−1+411yescharacteristic
266C22×D7—22no—
267C22×D7—22no—
268C22×D7—22no—
269C22×D7—22no—
270C22×D7—22no—
271C22×D7—22no—
272C22×D7—22no—
273C22×D7—22no—
274C22×D7—22no—
275C22×D7—22no—
276C22×D7—22no—
277C22×D7—22no—
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7—22no—
283C22×D7—22no—
284C22×D7—41no—
285C22×D7—41no—
286C22×D7—41no—
287C22×D7—41no—
288C22×D7—41no—
289C22×D7—41no—
290C22×D7—41no—
291C22×D7—41no—
292C22×D7—41no—
293C22×D7—41no—
294C22×D7—41no—
295C22×D7—41no—
296C22×D7—41no—
297C22×D7—41no—
298C22×D7—41no—
299C22×D7—41no—
300C22×D7C4×D414yes—
301C2×C4×C7—24no—
302C2×C4×C7—24no—
303C2×C4×C7—24no—
304C2×C4×C7—22no—
305C2×C4×C7—24no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—22no—
309C2×C4×C7—24no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—42no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—42no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—41no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—41no—
329C2×C4×C7#11714yes—
330C2×C4×C7C4×D414yes—
331C2×C4×C7C4×D414yes—
332C2×C4×C7#12114yes—
333C2×C4×C7#12314yes—
334C2×C4×C7#12414yes—
335C2×C4×C7#12614yes—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—24no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—42no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—42no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—42no—
358C2×Dic7—42no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7#12114yes—
371C4×D7—416no—
372C25—71no—
373C23×C4—71no—
374C23×C4—72no—
375C23×C4—71no—
376C23×C4—71no—
377C23×C4—74no—
378C23×C4—72no—
379C23×C4—142no—
380C23×C4—142no—
381C23×C4—142no—
382C23×C4—142no—
383C23×C4—142no—
384C23×C4—142no—
385C23×C4C22×D712yes—
386C23×C4C22×D711yescharacteristic
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—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—74no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—142no—
401C2×C4⋊C4—142no—
402C2×C4⋊C4—142no—
403C2×C4⋊C4C4×D714yes—
404C2×C4⋊C4C22⋊D714yes—
405C2×C22⋊C4—78no—
406C2×C22⋊C4—74no—
407C2×C22⋊C4—142no—
408C2×C22⋊C4—142no—
409C2×C22⋊C4—142no—
410C2×C22⋊C4—144no—
411C2×C22⋊C4—142no—
412C2×C22⋊C4—144no—
413C2×C22⋊C4—142no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—144no—
416C2×C22⋊C4—282no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—74no—
421C2×C42—142no—
422C2×C42—142no—
423C2×C42—144no—
424C2×C42—144no—
425C2×C42—144no—
426#95—24no—
427#95—78no—
428#95—142no—
429#95—142no—
430#95—144no—
431#95—144no—
432#95—144no—
433#95—144no—
434#95—144no—
435#95—282no—
436C22×C7C2×#11711yescharacteristic
437C22×C7C2×C4×D411yescharacteristic
438C22×C7C2×C4×D411yescharacteristic
439C22×C7C2×C4×D411yescharacteristic
440C22×C7C4×#4111yescharacteristic
441C22×C7#51911yescharacteristic
442C22×C7#52011yescharacteristic
443C22×C7C2×#12111yescharacteristic
444C22×C7C2×#12111yescharacteristic
445C22×C7C2×#12311yescharacteristic
446C22×C7#52511yescharacteristic
447C22×C7C2×#12411yescharacteristic
448C22×C7C2×#12611yescharacteristic
449C22×C7#52911yescharacteristic
450C22×C7#53211yescharacteristic
451C22×C7#53611yescharacteristic
452C22×C7#53711yescharacteristic
453C22×C7#54111yescharacteristic
454C22×C7#54211yescharacteristic
455C22×C7D4211yescharacteristic
456C22×C7#54711yescharacteristic
457C22×C7#54711yescharacteristic
458C22×C7#54711yescharacteristic
459C22×C7#54711yescharacteristic
460C22×C7#54811yescharacteristic
461C22×C7#54811yescharacteristic
462C22×C7#55211yescharacteristic
463C22×C7#55211yescharacteristic
464C22×C7#55211yescharacteristic
465C22×C7#55211yescharacteristic
466C22×C7#55211yescharacteristic
467C22×C7#55311yescharacteristic
468C22×C7#55511yescharacteristic
469C22×C7#55511yescharacteristic
470C22×C7#55611yescharacteristic
471C2×D7—24no—
472C2×D7—24no—
473C2×D7—24no—
474C2×D7—42no—
475C2×D7—42no—
476C2×D7—42no—
477C2×D7—42no—
478C2×D7—42no—
479C2×D7—42no—
480C2×D7—42no—
481C2×D7—42no—
482C2×D7—42no—
483C2×D7—42no—
484C2×D7—42no—
485C2×D7—42no—
486C4×C7—44no—
487C4×C7—42no—
488C4×C7—42no—
489C4×C7—44no—
490C4×C7#38818yescomplemented
491Dic7—24no—
492Dic7—42no—
493Dic7—42no—
494Dic7—44no—
495Dic7—82no—
496C24—72no—
497C24—72no—
498C24—72no—
499C24—141no—
500C24—141no—
501C24—141no—
502C24—141no—
503C24—141no—
504C24—141no—
505C24—141no—
506C24—141no—
507C24—141no—
508C24—141no—
509C24—141no—
510C24—141no—
511C24C23×D711yescharacteristic
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—72no—
539C22×C4—72no—
540C22×C4—74no—
541C22×C4—72no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—142no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—142no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—148no—
565C22×C4—148no—
566C22×C4—148no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—284no—
575C22×C4—284no—
576C22×C4—284no—
577C22×C4—284no—
578C22×C4C2×C4×D714yes—
579C22×C4C2×C4×D712yes—
580C22×C4#115712yes—
581C22×C4D4×D712yes—
582C22×C4D4×D712yes—
583C22×C4#115912yes—
584C22×C4#116112yes—
585C22×C4#116112yes—
586C22×C4#116112yes—
587C22×C4C2×C22⋊D714yes—
588C22×C4C2×C22⋊D712yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—48no—
592C4⋊C4—148no—
593C4⋊C4—284no—
594C22⋊C4—148no—
595C22⋊C4—1416no—
596C22⋊C4—148no—
597C22⋊C4—288no—
598C42—44no—
599C42—148no—
600C42—288no—
601C2×C7C2×#38811yescharacteristic
602C2×C7C4×#12111yescharacteristic
603C2×C7#232311yescharacteristic
604C2×C7#234411yescharacteristic
605C2×C7#234611yescharacteristic
606C2×C7#236111yescharacteristic
607C2×C7#236211yescharacteristic
608C2×C7#248511yescharacteristic
609C2×C7#248611yescharacteristic
610C2×C7#248911yescharacteristic
611C2×C7#249111yescharacteristic
612C2×C7#249511yescharacteristic
613C2×C7#249611yescharacteristic
614C2×C7#253611yescharacteristic
615C2×C7#253711yescharacteristic
616D7—44no—
617C23—74no—
618C23—142no—
619C23—142no—
620C23—142no—
621C23—142no—
622C23—142no—
623C23—142no—
624C23—142no—
625C23—142no—
626C23—142no—
627C23—142no—
628C23—142no—
629C23—142no—
630C23—142no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23—142no—
635C23—142no—
636C23—281no—
637C23—281no—
638C23—281no—
639C23—281no—
640C23—281no—
641C23—281no—
642C23—281no—
643C23—281no—
644C23—281no—
645C23—281no—
646C23—281no—
647C23—281no—
648C23—281no—
649C23—281no—
650C23—281no—
651C23—281no—
652C23C22×C4×D711yescharacteristic
653C23C2×#115711yescharacteristic
654C23C2×D4×D711yescharacteristic
655C23C2×D4×D711yescharacteristic
656C23C2×#115911yescharacteristic
657C23#654811yescharacteristic
658C23C2×#116111yescharacteristic
659C23C2×#116111yescharacteristic
660C23C2×#116111yescharacteristic
661C23#655111yescharacteristic
662C23D7×#4111yescharacteristic
663C23D7×#4111yescharacteristic
664C23#655411yescharacteristic
665C23#655411yescharacteristic
666C23C22×C22⋊D711yescharacteristic
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—74no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—144no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—144no—
708C2×C4—144no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—282no—
712C2×C4—281no—
713C2×C4—282no—
714C2×C4—281no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—281no—
719C2×C4—281no—
720C2×C4—281no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—2816no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4—282no—
731C2×C4#645514yes—
732C2×C4#645614yes—
733C2×C4#645714yes—
734C2×C4#646114yes—
735C2×C4C4×C22⋊D714yes—
736C2×C4#650214yes—
737C2×C4#651014yes—
738C7#1399411yescharacteristic, complemented, Sylow
739C22—144no—
740C22—144no—
741C22—144no—
742C22—282no—
743C22—282no—
744C22—282no—
745C22—282no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22C2×#645511yescharacteristic
755C22C2×#645611yescharacteristic
756C22C2×#645711yescharacteristic
757C22C2×#646111yescharacteristic
758C22C4×D4×D711yescharacteristic
759C22#9023711yescharacteristic
760C22#9024211yescharacteristic
761C22#9024911yescharacteristic
762C22#9026311yescharacteristic
763C22C4×#116111yescharacteristic
764C22#9027211yescharacteristic
765C22#9027511yescharacteristic
766C22D7×#12111yescharacteristic
767C22#9029911yescharacteristic
768C22#9030211yescharacteristic
769C22#9030711yescharacteristic
770C22#9031811yescharacteristic
771C22#9031911yescharacteristic
772C22#9033011yescharacteristic
773C22#9033311yescharacteristic
774C22#9038211yescharacteristic
775C22#9038511yescharacteristic
776C22#9038511yescharacteristic
777C22#9038811yescharacteristic
778C22#9041611yescharacteristic
779C22#9041711yescharacteristic
780C22#9042411yescharacteristic
781C22#9042511yescharacteristic
782C22C2×C4×C22⋊D711yescharacteristic
783C22D4×C22⋊D711yescharacteristic
784C22C2×#650211yescharacteristic
785C22C2×#651011yescharacteristic
786C22#9050811yescharacteristic
787C22#9051511yescharacteristic
788C22#9052211yescharacteristic
789C4—42no—
790C4—44no—
791C4—44no—
792C4—42no—
793C4—144no—
794C4—284no—
795C4—282no—
796C4—282no—
797C4—562no—
798C4#8976218yescomplemented
799C2—284no—
800C2#1173340911yescharacteristic
801C2#1173342411yescharacteristic
802C2#1173364211yescharacteristic
803C2#1173364511yescharacteristic
804C2#1173367511yescharacteristic
805C2#1173367611yescharacteristic
806C2#1173368111yescharacteristic
807C2#1173368311yescharacteristic
808C2C2×#8976211yescharacteristic
809C2#1173984411yescharacteristic
810C2#1173990911yescharacteristic
811C2#1174011211yescharacteristic
812C2#1174022211yescharacteristic
813C2#1174050511yescharacteristic
814C2#1174070211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#389D7
hypocenterC7#13994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
5. C2×C4⋊C4×Dic7C2semidirect
7. #11729321C2semidirect
8. #11729317C2semidirect
9. #11729289C2semidirect
11. #11727157C2semidirect
38. #89759C4semidirect
106. C2×#389D7semidirect
490. C4×C7#388semidirect
738. C7#13994semidirect
798. C4#89762semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897592
C2×#897622
C2×C4⋊C4×Dic72
C2×C4×(C2×D7)⋊C42
#117293212
#117293172
#117292892
#117271832
#117271572
#139947