Finite Group Databasebeta

← #13275732

Subgroups — #13275732

Order 1792.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 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×#89749C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
6#11729317C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729303C212yesmaximal
9#11729299C212yesmaximal
10#11727171C212yesmaximal, complemented
11#11727156C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2212yes—
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C7×#380—24no—
25C2×C7×#95C2212yes—
26#89984—24no—
27C4×C22⋊Dic7C418yescomplemented
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38#89749—24no—
39C4⋊C4×Dic7—24no—
40#13875—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2312yes—
52C23×C4×C7C2311yescharacteristic
53C23×Dic7C2312yes—
54C23×Dic7C2311yescharacteristic
55C23×Dic7C2311yescharacteristic
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2312yes—
58C23×Dic7C2311yescharacteristic
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4D414yes—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—24no—
67C2×C7×C22⋊C4—42no—
68C2×C22⋊Dic7—22no—
69C2×C22⋊Dic7—22no—
70C2×C22⋊Dic7—22no—
71C2×C22⋊Dic7—22no—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—42no—
75C2×C22⋊Dic7C2×C414yes—
76C2×C22⋊Dic7C2×C414yes—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7D414yes—
83C2×C4×Dic7—22no—
84C2×C4×Dic7—22no—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—24no—
88C2×C4×Dic7—24no—
89C2×C4×Dic7—42no—
90C2×C4×Dic7C2×C414yes—
91C2×C4×Dic7C2×C414yes—
92C7×#95—24no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—42no—
99C7⋊#95—42no—
100C7⋊#95—42no—
101C7⋊#95C2×C414yes—
102C7⋊#95C2×C414yes—
103C2×#382—71no—
104C2×#380—71no—
105C2×#380D711yescharacteristic
106C2×C4×C4⋊C4—71no—
107C2×C4×C22⋊C4—71no—
108#1443—72no—
109#1440—72no—
110#1437—72no—
111C4⋊#95—71no—
112C4⋊#95—71no—
113#1434—72no—
114C24×C7—21no—
115C24×C7—21no—
116C24×C7—21no—
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×C7C22×C412yes—
127C24×C7#4112yes—
128C24×C7#4112yes—
129C24×C7C2411yescharacteristic
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—28no—
143C22×C4×C7—28no—
144C22×C4×C7—28no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—44no—
153C22×C4×C7—44no—
154C22×C4×C7—44no—
155C22×C4×C7—44no—
156C22×C4×C7C22×C412yes—
157C22×C4×C7C22×C412yes—
158C22×C4×C7C2×D414yes—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D412yes—
161C22×C4×C7#4112yes—
162C22×C4×C7#4112yes—
163C22×C4×C7#4112yes—
164C22×C4×C7#4112yes—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—22no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—22no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
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×Dic7C22×C412yes—
201C22×Dic7C22×C412yes—
202C22×Dic7C22×C412yes—
203C22×Dic7C22×C412yes—
204C22×Dic7C2×D414yes—
205C22×Dic7#4112yes—
206C22×Dic7#4112yes—
207C7×C4⋊C4—28no—
208C7×C4⋊C4—44no—
209C7×C22⋊C4—48no—
210C22⋊Dic7—28no—
211C22⋊Dic7—28no—
212C22⋊Dic7—48no—
213C4⋊Dic7—28no—
214C4⋊Dic7—44no—
215C4×Dic7—28no—
216C4×Dic7—28no—
217C4×Dic7—48no—
218C24×C4C2×D711yescharacteristic
219C22×C4⋊C4—71no—
220C22×C4⋊C4—71no—
221C22×C4⋊C4C2×D711yescharacteristic
222C22×C4⋊C4C2×D711yescharacteristic
223C22×C22⋊C4—71no—
224C22×C22⋊C4—71no—
225C22×C22⋊C4—72no—
226C22×C22⋊C4C2×D712yes—
227C22×C42—71no—
228C22×C42—71no—
229C22×C42—72no—
230#382—144no—
231#380—24no—
232#380—144no—
233C4×C4⋊C4—144no—
234C4×C22⋊C4—78no—
235C2×#95—71no—
236C2×#95—71no—
237C2×#95—72no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95C2×D712yes—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
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—41no—
265C23×C7—41no—
266C23×C7—41no—
267C23×C7—41no—
268C23×C7—41no—
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#11714yes—
281C23×C7C23×C411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D411yescharacteristic
284C23×C7C2×#4111yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7H(5,𝔽2)11yescharacteristic
293C23×C7H(5,𝔽2)11yescharacteristic
294C23×C72−1+411yescharacteristic
295C23×C72−1+411yescharacteristic
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—416no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7#11714yes—
319C2×C4×C7C4×D414yes—
320C2×C4×C7C4×D414yes—
321C2×C4×C7#12114yes—
322C2×C4×C7#12314yes—
323C2×C4×C7#12414yes—
324C2×C4×C7#12614yes—
325C2×Dic7—22no—
326C2×Dic7—22no—
327C2×Dic7—22no—
328C2×Dic7—22no—
329C2×Dic7—22no—
330C2×Dic7—22no—
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—22no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—42no—
344C2×Dic7—42no—
345C2×Dic7—42no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—42no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—42no—
360C2×Dic7—42no—
361C2×Dic7—42no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7#11714yes—
367C25C22×D711yescharacteristic
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—71no—
375C23×C4—72no—
376C23×C4—71no—
377C23×C4—71no—
378C23×C4—71no—
379C23×C4—72no—
380C23×C4C4×D714yes—
381C23×C4C22×D712yes—
382C23×C4C22×D711yescharacteristic
383C23×C4C22×D712yes—
384C23×C4C22×D711yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—74no—
391C2×C4⋊C4—142no—
392C2×C4⋊C4—142no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—142no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4C22⋊D714yes—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—74no—
401C2×C22⋊C4—74no—
402C2×C22⋊C4—142no—
403C2×C22⋊C4—142no—
404C2×C22⋊C4—142no—
405C2×C22⋊C4—142no—
406C2×C22⋊C4—144no—
407C2×C22⋊C4—144no—
408C2×C22⋊C4—282no—
409C2×C42—74no—
410C2×C42—74no—
411C2×C42—142no—
412C2×C42—142no—
413C2×C42—142no—
414C2×C42—142no—
415C2×C42—144no—
416C2×C42—144no—
417C2×C42—282no—
418#95—24no—
419#95—74no—
420#95—74no—
421#95—144no—
422#95—144no—
423#95—144no—
424#95—144no—
425#95—144no—
426#95—282no—
427#95—282no—
428#95—282no—
429C22×C7—24no—
430C22×C7—24no—
431C22×C7—24no—
432C22×C7—42no—
433C22×C7—42no—
434C22×C7—42no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7C2×#11711yescharacteristic
445C22×C7C2×#11711yescharacteristic
446C22×C7C2×#11711yescharacteristic
447C22×C7C2×C4×D411yescharacteristic
448C22×C7C2×C4×D411yescharacteristic
449C22×C7#52011yescharacteristic
450C22×C7#52011yescharacteristic
451C22×C7C2×#12111yescharacteristic
452C22×C7C2×#12311yescharacteristic
453C22×C7C2×#12411yescharacteristic
454C22×C7C2×#12611yescharacteristic
455C22×C7#52911yescharacteristic
456C22×C7#52911yescharacteristic
457C22×C7#52911yescharacteristic
458C22×C7#52911yescharacteristic
459C22×C7#54011yescharacteristic
460C22×C7#54111yescharacteristic
461C22×C7#54211yescharacteristic
462C22×C7#54211yescharacteristic
463C22×C7#54611yescharacteristic
464C22×C7#54611yescharacteristic
465C22×C7#54611yescharacteristic
466C22×C7#54711yescharacteristic
467C22×C7#54811yescharacteristic
468C22×C7#54811yescharacteristic
469C22×C7#54811yescharacteristic
470C22×C7#55011yescharacteristic
471C22×C7#55211yescharacteristic
472C22×C7#55211yescharacteristic
473C22×C7#55211yescharacteristic
474C22×C7#55311yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55311yescharacteristic
477C22×C7#55511yescharacteristic
478C22×C7#55611yescharacteristic
479C4×C7—44no—
480C4×C7—42no—
481C4×C7—82no—
482C4×C7#38818yes—
483Dic7—24no—
484Dic7—42no—
485Dic7—42no—
486Dic7—42no—
487Dic7—44no—
488Dic7—82no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24C2×C4×D712yes—
502C24#115912yes—
503C24#116112yes—
504C24C23×D711yescharacteristic
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—74no—
538C22×C4—141no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—141no—
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—141no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—141no—
554C22×C4—142no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—141no—
562C22×C4—142no—
563C22×C4—141no—
564C22×C4—141no—
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×C4C2×C4×D712yes—
574C22×C4C2×C4×D712yes—
575C22×C4#115712yes—
576C22×C4D4×D712yes—
577C22×C4#115912yes—
578C22×C4#115912yes—
579C22×C4#115912yes—
580C22×C4C2×C22⋊D714yes—
581C22×C4C2×C22⋊D712yes—
582C4⋊C4—28no—
583C4⋊C4—44no—
584C4⋊C4—148no—
585C4⋊C4—284no—
586C22⋊C4—48no—
587C22⋊C4—148no—
588C22⋊C4—148no—
589C22⋊C4—288no—
590C42—148no—
591C42—148no—
592C42—288no—
593C2×C7—44no—
594C2×C7#228311yescharacteristic
595C2×C7C2×#38811yescharacteristic
596C2×C7#231411yescharacteristic
597C2×C7#235211yescharacteristic
598C2×C7#235211yescharacteristic
599C2×C7#235211yescharacteristic
600C2×C7#235411yescharacteristic
601C2×C7#242011yescharacteristic
602C2×C7#242111yescharacteristic
603C2×C7#242611yescharacteristic
604C2×C7#242711yescharacteristic
605C2×C7#248911yescharacteristic
606C2×C7#249011yescharacteristic
607C2×C7#249411yescharacteristic
608C2×C7#249511yescharacteristic
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23#645514yes—
644C23C22×C4×D711yescharacteristic
645C23C2×#115711yescharacteristic
646C23C2×D4×D711yescharacteristic
647C23C2×#115911yescharacteristic
648C23C2×#115911yescharacteristic
649C23C2×#115911yescharacteristic
650C23C2×#115911yescharacteristic
651C23#654811yescharacteristic
652C23C2×#116111yescharacteristic
653C23#655111yescharacteristic
654C23D7×#4111yescharacteristic
655C23D7×#4111yescharacteristic
656C23#655311yescharacteristic
657C23#655411yescharacteristic
658C23C22×C22⋊D711yescharacteristic
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—74no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—144no—
698C2×C4—144no—
699C2×C4—144no—
700C2×C4—281no—
701C2×C4—281no—
702C2×C4—281no—
703C2×C4—282no—
704C2×C4—281no—
705C2×C4—282no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—281no—
709C2×C4—281no—
710C2×C4—282no—
711C2×C4—281no—
712C2×C4—281no—
713C2×C4—281no—
714C2×C4—281no—
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#644014yes—
724C2×C4#644214yes—
725C2×C4(C22⋊D7)⋊C414yes—
726C2×C4#644814yes—
727C2×C4C4×C22⋊D714yes—
728C2×C4#649814yes—
729C2×C4#650114yes—
730C7#1387511yescharacteristic, complemented, Sylow
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#644011yescharacteristic
747C22C2×#644211yescharacteristic
748C22C2×(C22⋊D7)⋊C411yescharacteristic
749C22C2×#644811yescharacteristic
750C22C2×#645511yescharacteristic
751C22#9019511yescharacteristic
752C22#9020411yescharacteristic
753C22#9020511yescharacteristic
754C22D7×#11711yescharacteristic
755C22#9021411yescharacteristic
756C22#9022011yescharacteristic
757C22#9022111yescharacteristic
758C22#9028911yescharacteristic
759C22#9029011yescharacteristic
760C22#9029111yescharacteristic
761C22#9029111yescharacteristic
762C22#9029411yescharacteristic
763C22#9030711yescharacteristic
764C22#9030911yescharacteristic
765C22#9031011yescharacteristic
766C22#9031511yescharacteristic
767C22#9031511yescharacteristic
768C22#9031611yescharacteristic
769C22#9032111yescharacteristic
770C22#9032211yescharacteristic
771C22#9033211yescharacteristic
772C22#9033311yescharacteristic
773C22#9033411yescharacteristic
774C22C2×C4×C22⋊D711yescharacteristic
775C22C2×#649811yescharacteristic
776C22C2×#650111yescharacteristic
777C22#9049711yescharacteristic
778C22#9050811yescharacteristic
779C22#9052011yescharacteristic
780C22#9052211yescharacteristic
781C4—42no—
782C4—44no—
783C4—82no—
784C4—144no—
785C4—284no—
786C4—282no—
787C4—282no—
788C4—282no—
789C4—562no—
790C4#8971618yes—
791C2—44no—
792C2#1173130811yescharacteristic
793C2#1173131311yescharacteristic
794C2#1173132811yescharacteristic
795C2#1173133011yescharacteristic
796C2#1173135811yescharacteristic
797C2#1173135911yescharacteristic
798C2#1173136311yescharacteristic
799C2#1173136511yescharacteristic
800C2C2×#8971611yescharacteristic
801C2#1173960611yescharacteristic
802C2#1173971711yescharacteristic
803C2#1174008811yescharacteristic
804C2#1174009111yescharacteristic
805C2#1174019811yescharacteristic
806C2#1174020111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#380D7
hypocenterC7#13875
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#89749C2semidirect
5. C2×C4⋊C4×Dic7C2semidirect
6. #11729317C2semidirect
7. #11729317C2semidirect
10. #11727171C2semidirect
11. #11727156C2semidirect
27. C4×C22⋊Dic7C4semidirect
730. C7#13875semidirect

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×#897492
C2×C4⋊C4×Dic72
#117293172
#117293032
#117292992
#117271712
#117271562
#138757