Finite Group Databasebeta

← #13276514

Subgroups — #13276514

Order 1792.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic7C211yesmaximal, characteristic
2C2×C7×#386C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C22×C7⋊#95C211yesmaximal, characteristic, complemented
5C2×#89714C211yesmaximal, characteristic, complemented
6#11729881C211yesmaximal, characteristic, complemented
7#11729301C212yesmaximal, complemented
8#11729298C212yesmaximal, complemented
9#11729298C211yesmaximal, characteristic, complemented
10#11727165C212yesmaximal, complemented
11#11727157C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2212yes—
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C2×D4×Dic7—24no—
24C2×D4×Dic7—24no—
25C2×D4×Dic7C418yescomplemented
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C7×#386—24no—
30C2×C7×#95C2212yes—
31#89992—24no—
32C2×C7⋊#95—24no—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41#89714—24no—
42#13960—71nomaximal, Sylow
43C25×C7C2311yescharacteristic
44C25×C7C2311yescharacteristic
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C22×C7×D4D414yes—
51C22×C7×D4Q814yes—
52C23×C4×C7—22no—
53C23×C4×C7—24no—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—42no—
57C23×C4×C7C2312yes—
58C23×C4×C7C2312yes—
59C23×C4×C7C2311yescharacteristic
60C23×Dic7—22no—
61C23×Dic7—22no—
62C23×Dic7—22no—
63C23×Dic7—24no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—42no—
67C23×Dic7—42no—
68C23×Dic7—42no—
69C23×Dic7—42no—
70C23×Dic7—42no—
71C23×Dic7C2×C414yes—
72C23×Dic7C2×C414yescomplemented
73C23×Dic7D414yes—
74C23×Dic7D414yes—
75C23×Dic7C2312yes—
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2312yes—
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—24no—
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—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—24no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—24no—
96C2×C22⋊Dic7—42no—
97C2×C22⋊Dic7C2×C414yes—
98C2×C22⋊Dic7C2×C414yescomplemented
99D4×Dic7—232no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7C2×C414yescomplemented
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—42no—
105C2×Dic7⋊C4—42no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7C2×C414yescomplemented
109C7×#95—24no—
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—42no—
117C7⋊#95—42no—
118C22×C4×D4—71no—
119C2×#386—71no—
120C2×#386D711yescharacteristic
121C2×#380—71no—
122C22×#95—71no—
123#1441—72no—
124#1439—72no—
125#1434—72no—
126C22⋊#95—71no—
127C22⋊#95—71no—
128C22⋊#95—72no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7C22×C412yes—
142C24×C7C22×C412yes—
143C24×C7C2×D412yes—
144C24×C7C2×D412yes—
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×Q812yes—
148C24×C7C2×Q812yes—
149C24×C7#4112yes—
150C24×C7#4112yes—
151C24×C7C2411yescharacteristic
152C2×C7×D4—28no—
153C2×C7×D4—28no—
154C2×C7×D4—28no—
155C2×C7×D4—28no—
156C2×C7×D4—28no—
157C2×C7×D4—28no—
158C2×C7×D4C4⋊C4116yescomplemented
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—28no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—48no—
178C22×C4×C7—48no—
179C22×C4×C7—44no—
180C22×C4×C7—44no—
181C22×C4×C7C22×C412yes—
182C22×C4×C7C2×D412yes—
183C22×C4×C7C2×Q812yes—
184C22×C4×C7#4114yes—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—28no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—28no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—48no—
213C22×Dic7—48no—
214C22×Dic7—48no—
215C22×Dic7—44no—
216C22×Dic7—44no—
217C22×Dic7—48no—
218C22×Dic7—48no—
219C22×Dic7—44no—
220C22×Dic7—48no—
221C22×Dic7—44no—
222C22×Dic7—44no—
223C22×Dic7—44no—
224C22×Dic7C22⋊C4116yescomplemented
225C22×Dic7C22×C412yes—
226C22×Dic7C22×C412yes—
227C22×Dic7C22×C412yes—
228C22×Dic7C22×C412yes—
229C22×Dic7C2×D412yes—
230C22×Dic7C2×D412yes—
231C22×Dic7C2×D412yes—
232C22×Dic7C2×D412yes—
233C22×Dic7#4114yes—
234C7×C22⋊C4—48no—
235C7×C22⋊C4—44no—
236C22⋊Dic7—28no—
237C22⋊Dic7—28no—
238C22⋊Dic7—48no—
239C22⋊Dic7—44no—
240C4⋊Dic7—28no—
241Dic7⋊C4—48no—
242C4×Dic7—28no—
243C23×D4C2×D711yescharacteristic
244C24×C4—71no—
245C24×C4—71no—
246C24×C4—71no—
247C24×C4C2×D711yescharacteristic
248C2×C4×D4—78no—
249C2×C4×D4—144no—
250C2×C4×D4—144no—
251C22×C4⋊C4—71no—
252C22×C4⋊C4—72no—
253C22×C22⋊C4—71no—
254C22×C22⋊C4—71no—
255C22×C22⋊C4—71no—
256C22×C22⋊C4—72no—
257C22×C22⋊C4C2×D711yescharacteristic
258C22×C22⋊C4C2×D712yes—
259C22×C42—71no—
260#386—24no—
261#386—144no—
262#380—144no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—72no—
271C2×#95—144no—
272C2×#95C2×D712yes—
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—24no—
292C23×C7—24no—
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—41no—
305C23×C7—42no—
306C23×C7—41no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7C2×C22⋊C414yes—
312C23×C7C2×C4⋊C414yes—
313C23×C7C2×C4⋊C414yes—
314C23×C7#11714yes—
315C23×C7#12114yes—
316C23×C7#12114yes—
317C23×C7C22⋊Q814yes—
318C23×C7C22⋊Q814yes—
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C22×Q811yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C7H(5,𝔽2)12yes—
330C7×D4—232no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—24no—
340C2×C4×C7—416no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7C2×C4⋊C414yes—
353C2×Dic7—24no—
354C2×Dic7—24no—
355C2×Dic7—24no—
356C2×Dic7—22no—
357C2×Dic7—24no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—24no—
367C2×Dic7—24no—
368C2×Dic7—416no—
369C2×Dic7—416no—
370C2×Dic7—416no—
371C2×Dic7—42no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—42no—
375C2×Dic7—41no—
376C2×Dic7—42no—
377C2×Dic7—41no—
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—42no—
388C2×Dic7C2×C22⋊C414yes—
389C2×Dic7C2×C22⋊C414yes—
390C25C22×D711yescharacteristic
391C25C22×D711yescharacteristic
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4Dic1414yes—
397C22×D4C4×D714yes—
398C22×D4C22⋊D714yes—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—74no—
407C23×C4—74no—
408C23×C4—74no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—72no—
412C23×C4—74no—
413C23×C4—72no—
414C23×C4—142no—
415C23×C4—142no—
416C23×C4—144no—
417C23×C4—142no—
418C23×C4—142no—
419C23×C4—142no—
420C23×C4—282no—
421C23×C4—282no—
422C23×C4—282no—
423C23×C4—282no—
424C23×C4—282no—
425C23×C4C22×D712yes—
426C23×C4C22×D712yes—
427C23×C4C22×D711yescharacteristic
428C4×D4—1432no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—282no—
434C2×C4⋊C4—282no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—142no—
445C2×C22⋊C4—142no—
446C2×C22⋊C4—142no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—142no—
449C2×C22⋊C4—142no—
450C2×C22⋊C4—144no—
451C2×C22⋊C4—142no—
452C2×C22⋊C4—282no—
453C2×C42—74no—
454C2×C42—142no—
455C2×C42—142no—
456#95—24no—
457#95—144no—
458#95—144no—
459#95—144no—
460#95—144no—
461#95—144no—
462#95—144no—
463#95—282no—
464#95—282no—
465C22×C7—24no—
466C22×C7—28no—
467C22×C7—24no—
468C22×C7—24no—
469C22×C7—28no—
470C22×C7—28no—
471C22×C7—24no—
472C22×C7—24no—
473C22×C7—28no—
474C22×C7—24no—
475C22×C7—28no—
476C22×C7—24no—
477C22×C7—42no—
478C22×C7—44no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—44no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—44no—
485C22×C7—42no—
486C22×C7#38018yes—
487C22×C7C22×C22⋊C411yescharacteristic
488C22×C7C22×C4⋊C411yescharacteristic
489C22×C7C2×#11711yescharacteristic
490C22×C7C4×#4112yes—
491C22×C7#51812yes—
492C22×C7C2×#12111yescharacteristic
493C22×C7C2×#12111yescharacteristic
494C22×C7C2×C22⋊Q811yescharacteristic
495C22×C7C2×C22⋊Q811yescharacteristic
496C22×C7#52511yescharacteristic
497C22×C7#52511yescharacteristic
498C22×C7#53212yes—
499C22×C7#53411yescharacteristic
500C22×C7#53412yes—
501C22×C7#53411yescharacteristic
502C22×C7#54612yes—
503C22×C7#54612yes—
504C22×C7#55112yes—
505C22×C7#55112yes—
506C22×C7#55312yes—
507C22×C7#55312yes—
508C22×C7#55412yes—
509C22×C7#55412yes—
510C4×C7—24no—
511C4×C7—44no—
512C4×C7—82no—
513Dic7—24no—
514Dic7—24no—
515Dic7—42no—
516Dic7—44no—
517Dic7—42no—
518Dic7—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24C2×Dic1412yes—
532C24C2×Dic1412yes—
533C24C2×C4×D712yes—
534C24C2×C4×D712yes—
535C24D4×D712yes—
536C24D4×D712yes—
537C24#115912yes—
538C24#115912yes—
539C24C2×C22⋊D712yes—
540C24C2×C22⋊D712yes—
541C24C23×D711yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4Dic7⋊C4116yescomplemented
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—28no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—716no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—74no—
581C22×C4—148no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—148no—
587C22×C4—142no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
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—142no—
607C22×C4—142no—
608C22×C4—288no—
609C22×C4—288no—
610C22×C4—284no—
611C22×C4—288no—
612C22×C4—284no—
613C22×C4—288no—
614C22×C4—288no—
615C22×C4—284no—
616C22×C4—288no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4—284no—
620C22×C4C2×Dic1412yes—
621C22×C4C2×C4×D712yes—
622C22×C4#115914yes—
623C22×C4C2×C22⋊D712yes—
624C4⋊C4—148no—
625C4⋊C4—288no—
626C22⋊C4—48no—
627C22⋊C4—44no—
628C22⋊C4—148no—
629C22⋊C4—148no—
630C22⋊C4—288no—
631C22⋊C4—284no—
632C42—148no—
633C2×C7—28no—
634C2×C7—44no—
635C2×C7C2×#38011yescharacteristic
636C2×C7#229711yescharacteristic
637C2×C7#230811yescharacteristic
638C2×C7#234912yes—
639C2×C7#235312yes—
640C2×C7#253411yescharacteristic
641C2×C7#253411yescharacteristic
642C2×C7#254312yes—
643C2×C7#256412yes—
644C2×C7#257911yescharacteristic
645C2×C7#257911yescharacteristic
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23#644014yes—
685C23#644114yes—
686C23#644114yes—
687C23D7×C22⋊C414yes—
688C23C2×Dic7⋊C414yes—
689C23C2×Dic7⋊C414yes—
690C23#650214yes—
691C23#650214yes—
692C23C22×Dic1411yescharacteristic
693C23C22×C4×D711yescharacteristic
694C23C2×D4×D711yescharacteristic
695C23C2×D4×D711yescharacteristic
696C23C2×#115911yescharacteristic
697C23C2×#115911yescharacteristic
698C23C2×#115912yes—
699C23#654812yes—
700C23D7×#4112yes—
701C23#655312yes—
702C23C22×C22⋊D711yescharacteristic
703D4—232no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—416no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—74no—
726C2×C4—74no—
727C2×C4—144no—
728C2×C4—144no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—144no—
732C2×C4—144no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—144no—
738C2×C4—144no—
739C2×C4—144no—
740C2×C4—144no—
741C2×C4—144no—
742C2×C4—2816no—
743C2×C4—2816no—
744C2×C4—2816no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—281no—
748C2×C4—281no—
749C2×C4—282no—
750C2×C4—282no—
751C2×C4—281no—
752C2×C4—282no—
753C2×C4—281no—
754C2×C4—282no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4C2×Dic7⋊C414yes—
763C7#1396011yescharacteristic, complemented, Sylow
764C22—24no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—28no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22#8971418yes—
786C22C2×#644011yescharacteristic
787C22C2×#644111yescharacteristic
788C22C2×#644111yescharacteristic
789C22C2×D7×C22⋊C411yescharacteristic
790C22C4×#115912yes—
791C22#9023012yes—
792C22#9023412yes—
793C22#9023612yes—
794C22#9027711yescharacteristic
795C22#9027812yes—
796C22#9028011yescharacteristic
797C22#9028712yes—
798C22#9029212yes—
799C22#9029612yes—
800C22#9030912yes—
801C22#9034411yescharacteristic
802C22#9034711yescharacteristic
803C22#9034912yes—
804C22C22×Dic7⋊C411yescharacteristic
805C22C2×#650211yescharacteristic
806C22C2×#650211yescharacteristic
807C22#9049712yes—
808C22#9052012yes—
809C4—24no—
810C4—44no—
811C4—82no—
812C4—144no—
813C4—144no—
814C4—282no—
815C4—282no—
816C4—284no—
817C4—562no—
818C2—28no—
819C2—44no—
820C2#1173210311yescharacteristic
821C2#1173211912yes—
822C2#1173220812yes—
823C2#1173221411yescharacteristic
824C2#1173221511yescharacteristic
825C2#1173231911yescharacteristic
826C2C2×#8971411yescharacteristic
827C2#1173977912yes—
828C2#1174003511yescharacteristic
829C2#1174011512yes—
830C2#1174034511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#386C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7#13960
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C22×C7⋊#95C2semidirect
5. C2×#89714C2semidirect
6. #11729881C2semidirect
7. #11729301C2semidirect
8. #11729298C2semidirect
9. #11729298C2semidirect
10. #11727165C2semidirect
11. #11727157C2semidirect
25. C2×D4×Dic7C4semidirect
72. C23×Dic7C2×C4semidirect
98. C2×C22⋊Dic7C2×C4semidirect
102. C2×C4⋊Dic7C2×C4semidirect
108. C2×C4×Dic7C2×C4semidirect
158. C2×C7×D4C4⋊C4semidirect
224. C22×Dic7C22⋊C4semidirect
548. C2×D4Dic7⋊C4semidirect
763. C7#13960semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic72
C2×C7×#3862
C2×#899922
C22×C7⋊#952
C2×#897142
#117298812
#117293012
#117292982
#117271652
#117271572
#139607