Finite Group Databasebeta

← #13277172

Subgroups — #13277172

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×#89722C211yesmaximal, characteristic, complemented
6#11729881C211yesmaximal, characteristic, complemented
7#11729300C212yesmaximal, complemented
8#11729298C212yesmaximal, complemented
9#11729298C211yesmaximal, characteristic, complemented
10#11727166C212yesmaximal, complemented
11#11727161C212yesmaximal, 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⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2212yes—
22C22×C22⋊Dic7C2211yescharacteristic
23C2×D4×Dic7—24no—
24C2×D4×Dic7—24no—
25C2×D4×Dic7—24no—
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C7×#386C418yescomplemented
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#89722—24no—
42#14016—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—22no—
54C23×C4×C7—42no—
55C23×C4×C7—42no—
56C23×C4×C7C2×C414yescomplemented
57C23×C4×C7C2312yes—
58C23×C4×C7C2312yes—
59C23×C4×C7C2311yescharacteristic
60C23×Dic7—22no—
61C23×Dic7—22no—
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—24no—
67C23×Dic7—24no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—24no—
71C23×Dic7—42no—
72C23×Dic7—42no—
73C23×Dic7—42no—
74C23×Dic7D414yes—
75C23×Dic7C2312yes—
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2312yes—
80C23×Dic7C2311yescharacteristic
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4C2×C414yescomplemented
86C2×C7×C22⋊C4C2×C418yescomplemented
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—22no—
96C2×C22⋊Dic7—24no—
97C2×C22⋊Dic7—42no—
98C2×C22⋊Dic7D414yes—
99D4×Dic7—232no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—24no—
104C2×C4⋊Dic7—24no—
105C2×C4⋊Dic7—42no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C7×#95C2×C418yescomplemented
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—42no—
116C7⋊#95—42no—
117C7⋊#95—42no—
118C22×C4×D4—71no—
119C2×#386—71no—
120C2×#386D711yescharacteristic
121C2×#385—71no—
122C22×#95—71no—
123#1442—72no—
124#1439—72no—
125#1436—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—48no—
177C22×C4×C7—44no—
178C22×C4×C7—44no—
179C22×C4×C7—48no—
180C22×C4×C7C22×C414yes—
181C22×C4×C7C22×C414yes—
182C22×C4×C7C22×C412yes—
183C22×C4×C7C2×D412yes—
184C22×C4×C7C2×Q812yes—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—22no—
188C22×Dic7—28no—
189C22×Dic7—28no—
190C22×Dic7—28no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
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—28no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—44no—
218C22×Dic7—48no—
219C22×Dic7—48no—
220C22×Dic7—48no—
221C22×Dic7—48no—
222C22×Dic7—48no—
223C22×Dic7—48no—
224C22×Dic7—44no—
225C22×Dic7—44no—
226C22×Dic7—44no—
227C22×Dic7—44no—
228C22×Dic7C2×D412yes—
229C22×Dic7C2×D412yes—
230C22×Dic7C2×D412yes—
231C22×Dic7C2×D412yes—
232C22×Dic7#4114yes—
233C22×Dic7#4114yes—
234C7×C22⋊C4—28no—
235C7×C22⋊C4—48no—
236C22⋊Dic7—28no—
237C22⋊Dic7—28no—
238C22⋊Dic7—48no—
239C22⋊Dic7—44no—
240C4⋊Dic7—28no—
241C4⋊Dic7—48no—
242C4×Dic7—28no—
243C23×D4C2×D711yescharacteristic
244C24×C4—71no—
245C24×C4—71no—
246C24×C4—71no—
247C24×C4C2×D711yescharacteristic
248C2×C4×D4—144no—
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—144no—
261#386Dic718yescomplemented
262#385—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—41no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7C2×C4⋊C414yes—
312C23×C7C2×C4⋊C414yes—
313C23×C7C4×D414yes—
314C23×C7C4×D414yes—
315C23×C7#12014yes—
316C23×C7C22⋊Q814yes—
317C23×C7C22⋊Q814yes—
318C23×C7#12314yes—
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—24no—
341C2×C4×C7—24no—
342C2×C4×C7—24no—
343C2×C4×C7—416no—
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—22no—
354C2×Dic7—22no—
355C2×Dic7—24no—
356C2×Dic7—24no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—24no—
362C2×Dic7—22no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—24no—
367C2×Dic7—416no—
368C2×Dic7—416no—
369C2×Dic7—416no—
370C2×Dic7—42no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
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×Dic7—42no—
389C2×Dic7#12314yes—
390C25C22×D711yescharacteristic
391C25C22×D711yescharacteristic
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4Dic1414yes—
397C22×D4D2814yes—
398C22×D4C2×Dic714yes—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—72no—
408C23×C4—74no—
409C23×C4—72no—
410C23×C4—142no—
411C23×C4—142no—
412C23×C4—144no—
413C23×C4—144no—
414C23×C4—144no—
415C23×C4—142no—
416C23×C4—142no—
417C23×C4—142no—
418C23×C4—142no—
419C23×C4—142no—
420C23×C4—142no—
421C23×C4—282no—
422C23×C4—282no—
423C23×C4—282no—
424C23×C4C2×Dic714yescomplemented
425C23×C4C22×D712yes—
426C23×C4C22×D712yes—
427C23×C4C22×D711yescharacteristic
428C4×D4—1432no—
429C2×C4⋊C4—142no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—282no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—142no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—142no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—142no—
448C2×C22⋊C4—142no—
449C2×C22⋊C4—142no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4C2×Dic714yescomplemented
452C2×C22⋊C4C2×Dic718yescomplemented
453C2×C42—142no—
454C2×C42—142no—
455C2×C42—142no—
456#95—144no—
457#95—144no—
458#95—144no—
459#95—144no—
460#95—144no—
461#95—282no—
462#95—282no—
463#95—282no—
464#95C2×Dic718yescomplemented
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—24no—
470C22×C7—24no—
471C22×C7—28no—
472C22×C7—28no—
473C22×C7—24no—
474C22×C7—24no—
475C22×C7—28no—
476C22×C7—24no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—44no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—44no—
483C22×C7—44no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7#38518yes—
487C22×C7C22×C4⋊C411yescharacteristic
488C22×C7C2×C4×D411yescharacteristic
489C22×C7C2×C4×D411yescharacteristic
490C22×C7C4×#4112yes—
491C22×C7#51812yes—
492C22×C7C2×#12011yescharacteristic
493C22×C7C2×C22⋊Q811yescharacteristic
494C22×C7C2×C22⋊Q811yescharacteristic
495C22×C7C2×#12311yescharacteristic
496C22×C7C2×#12311yescharacteristic
497C22×C7#52511yescharacteristic
498C22×C7#52912yes—
499C22×C7#53411yescharacteristic
500C22×C7#53511yescharacteristic
501C22×C7#53812yes—
502C22×C7#54612yes—
503C22×C7#54612yes—
504C22×C7#54612yes—
505C22×C7#54612yes—
506C22×C7#55312yes—
507C22×C7#55312yes—
508C22×C7#55412yes—
509C22×C7#55412yes—
510C4×C7—24no—
511C4×C7—44no—
512C4×C7—44no—
513Dic7—24no—
514Dic7—42no—
515Dic7—44no—
516Dic7—42no—
517Dic7—42no—
518Dic7—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24C2×Dic1412yes—
532C24C2×Dic1412yes—
533C24C2×D2812yes—
534C24C2×D2812yes—
535C24D4×D712yes—
536C24D4×D712yes—
537C24#115912yes—
538C24#115912yes—
539C24C22×Dic712yes—
540C24C22×Dic712yes—
541C24C23×D711yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4C4⋊Dic7116yescomplemented
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—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—72no—
571C22×C4—74no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—74no—
576C22×C4—148no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—142no—
580C22×C4—148no—
581C22×C4—148no—
582C22×C4—148no—
583C22×C4—142no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—142no—
588C22×C4—142no—
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—284no—
609C22×C4—284no—
610C22×C4—288no—
611C22×C4—288no—
612C22×C4—288no—
613C22×C4—288no—
614C22×C4—288no—
615C22×C4—288no—
616C22×C4—284no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4C2×Dic1412yes—
620C22×C4C2×D2812yes—
621C22×C4C22×Dic714yes—
622C22×C4C22×Dic714yes—
623C22×C4C22×Dic712yes—
624C4⋊C4—148no—
625C4⋊C4—288no—
626C22⋊C4—28no—
627C22⋊C4—48no—
628C22⋊C4—148no—
629C22⋊C4—148no—
630C22⋊C4—288no—
631C22⋊C4—284no—
632C42—148no—
633C2×C7—28no—
634C2×C7—44no—
635C2×C7C2×#38511yescharacteristic
636C2×C7C4×#12311yescharacteristic
637C2×C7#232111yescharacteristic
638C2×C7#234912yes—
639C2×C7#236412yes—
640C2×C7#240411yescharacteristic
641C2×C7#240511yescharacteristic
642C2×C7#244412yes—
643C2×C7#245012yes—
644C2×C7#248711yescharacteristic
645C2×C7#257911yescharacteristic
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23#644114yes—
685C23#644114yes—
686C23#644514yes—
687C23#644914yes—
688C23C2×C4⋊Dic714yes—
689C23C2×C4⋊Dic714yes—
690C23D4×Dic714yes—
691C23D4×Dic714yes—
692C23C22×Dic1411yescharacteristic
693C23C22×D2811yescharacteristic
694C23C2×D4×D711yescharacteristic
695C23C2×D4×D711yescharacteristic
696C23C2×#115911yescharacteristic
697C23C2×#115911yescharacteristic
698C23#654812yes—
699C23#654812yes—
700C23D7×#4112yes—
701C23D7×#4112yes—
702C23C23×Dic711yescharacteristic
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—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—416no—
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—142no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—144no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—144no—
734C2×C4—142no—
735C2×C4—144no—
736C2×C4—144no—
737C2×C4—144no—
738C2×C4—142no—
739C2×C4—144no—
740C2×C4—2816no—
741C2×C4—2816no—
742C2×C4—2816no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4—281no—
749C2×C4—281no—
750C2×C4—282no—
751C2×C4—282no—
752C2×C4—282no—
753C2×C4—281no—
754C2×C4—281no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4C2×C4⋊Dic714yes—
763C7#1401611yescharacteristic, complemented, Sylow
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22#8972218yes—
786C22C2×#644111yescharacteristic
787C22C2×#644111yescharacteristic
788C22C2×#644511yescharacteristic
789C22C2×#644911yescharacteristic
790C22#9023012yes—
791C22#9023012yes—
792C22#9024512yes—
793C22#9024512yes—
794C22#9028011yescharacteristic
795C22#9028311yescharacteristic
796C22#9028412yes—
797C22#9029212yes—
798C22#9029212yes—
799C22#9030112yes—
800C22#9030112yes—
801C22#9034012yes—
802C22D7×#12311yescharacteristic
803C22#9034711yescharacteristic
804C22C22×C4⋊Dic711yescharacteristic
805C22C2×D4×Dic711yescharacteristic
806C22C2×D4×Dic711yescharacteristic
807C22#9048912yes—
808C22#41×Dic712yes—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—144no—
813C4—284no—
814C4—282no—
815C4—282no—
816C4—282no—
817C4—562no—
818C2—28no—
819C2—44no—
820C2#1173213111yescharacteristic
821C2#1173215112yes—
822C2#1173215712yes—
823C2#1173218311yescharacteristic
824C2#1173221511yescharacteristic
825C2#1173233011yescharacteristic
826C2C2×#8972211yescharacteristic
827C2#1173977812yes—
828C2#1174002311yescharacteristic
829C2#1174008312yes—
830C2Dic7×#12311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#386C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7#14016
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×#89722C2semidirect
6. #11729881C2semidirect
7. #11729300C2semidirect
8. #11729298C2semidirect
9. #11729298C2semidirect
10. #11727166C2semidirect
11. #11727161C2semidirect
29. C7×#386C4semidirect
56. C23×C4×C7C2×C4semidirect
85. C2×C7×C22⋊C4C2×C4semidirect
86. C2×C7×C22⋊C4C2×C4semidirect
109. C7×#95C2×C4semidirect
158. C2×C7×D4C4⋊C4semidirect
261. #386Dic7semidirect
424. C23×C4C2×Dic7semidirect
451. C2×C22⋊C4C2×Dic7semidirect
452. C2×C22⋊C4C2×Dic7semidirect
464. #95C2×Dic7semidirect
548. C2×D4C4⋊Dic7semidirect
763. C7#14016semidirect

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×#897222
#117298812
#117293002
#117292982
#117271662
#117271612
#140167