Finite Group Databasebeta

← #13276921

Subgroups — #13276921

Order 1792.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic
2C2×#89992C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C2×#89983C211yesmaximal, characteristic, complemented
5C22×C7⋊#95C211yesmaximal, characteristic, complemented
6C2×#89722C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
8#11729323C212yesmaximal, complemented
9#11729317C212yesmaximal, complemented
10#11729300C212yesmaximal, complemented
11#11729299C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C2×C7×#123—24no—
17C2×C7×#123—24no—
18C2×C7×#123C418yescomplemented
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2212yes—
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2212yes—
28C22×C4×Dic7C2212yes—
29#89992—24no—
30#89992—24no—
31#89983—24no—
32C2×C7⋊#95—24no—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#89722—24no—
43C22⋊C4×Dic7—24no—
44#13996—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C25×C7C2311yescharacteristic
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4C2×C414yes—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7C2×C414yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2312yes—
63C23×C4×C7C2312yes—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—24no—
68C23×Dic7—24no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—42no—
72C23×Dic7—42no—
73C23×Dic7D414yes—
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2312yes—
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2312yes—
79C23×Dic7C2311yescharacteristic
80C7×#123—232no—
81C2×C7×C4⋊C4—24no—
82C2×C7×C4⋊C4—24no—
83C2×C7×C4⋊C4C2×C418yescomplemented
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C7×C22⋊C4C2×C418yescomplemented
88C2×C7×C22⋊C4D414yes—
89C2×C7×C22⋊C4D414yes—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—24no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—24no—
99C2×C22⋊Dic7—24no—
100C2×C22⋊Dic7—42no—
101C2×C22⋊Dic7—42no—
102C2×C22⋊Dic7D414yes—
103C2×C4⋊Dic7—24no—
104C2×C4⋊Dic7—24no—
105C2×C4⋊Dic7—42no—
106C2×C4×Dic7—24no—
107C2×C4×Dic7—24no—
108C2×C4×Dic7—42no—
109C7⋊#95—24no—
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C22×#123D711yescharacteristic
119C2×#386—71no—
120C2×#386—71no—
121C2×#385—71no—
122C2×#381—71no—
123C2×C4×C22⋊C4—71no—
124C22×#95—71no—
125#1445—72no—
126#1439—72no—
127#1437—72no—
128C4⋊#95—72no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7C22×C412yes—
144C24×C7C22×C412yes—
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×D412yes—
148C24×C7C2×D412yes—
149C24×C7#4112yes—
150C24×C7#4112yes—
151C24×C7C2411yescharacteristic
152C2×C7×D4—28no—
153C2×C7×D4—28no—
154C2×C7×D4—28no—
155C2×C7×D4—44no—
156C2×C7×D4—44no—
157C2×C7×D4—44no—
158C2×C7×D4—44no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—28no—
164C22×C4×C7—28no—
165C22×C4×C7—28no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—44no—
179C22×C4×C7—44no—
180C22×C4×C7—44no—
181C22×C4×C7—44no—
182C22×C4×C7C22×C414yes—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C22×C414yes—
185C22×C4×C7C2×D414yes—
186C22×C4×C7C2×D414yes—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—28no—
191C22×Dic7—28no—
192C22×Dic7—21no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—21no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—28no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—44no—
220C22×Dic7—48no—
221C22×Dic7—48no—
222C22×Dic7—48no—
223C22×Dic7—48no—
224C22×Dic7—44no—
225C22×Dic7—44no—
226C22×Dic7C2×D414yes—
227C22×Dic7C2×D412yes—
228C22×Dic7C2×D412yes—
229C22×Dic7#4114yes—
230C22×Dic7#4114yes—
231C7×C4⋊C4—216no—
232C7×C22⋊C4—216no—
233C7×C22⋊C4C22⋊C4116yescomplemented
234C22⋊Dic7—28no—
235C22⋊Dic7—48no—
236C22⋊Dic7—44no—
237C22⋊Dic7—44no—
238C22⋊Dic7—44no—
239C4⋊Dic7—48no—
240C4×Dic7—48no—
241C23×D4C2×D711yescharacteristic
242C24×C4—71no—
243C24×C4—71no—
244C24×C4C2×D711yescharacteristic
245C2×#123—24no—
246C2×#123—24no—
247C2×#123Dic718yescomplemented
248C22×C4⋊C4—72no—
249C22×C4⋊C4C2×D712yes—
250C22×C22⋊C4—71no—
251C22×C22⋊C4—71no—
252C22×C22⋊C4—71no—
253C22×C22⋊C4—72no—
254C22×C22⋊C4—71no—
255C22×C22⋊C4C2×D712yes—
256C22×C22⋊C4C2×D711yescharacteristic
257C22×C42—72no—
258#386—144no—
259#386—144no—
260#385—144no—
261#381—144no—
262C4×C22⋊C4—144no—
263C2×#95—71no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—72no—
271C2×#95—71no—
272C2×#95—144no—
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—22no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—42no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7C2×C22⋊C414yes—
313C23×C7C4×D414yes—
314C23×C7C4×D414yes—
315C23×C7#12114yes—
316C23×C7#12114yes—
317C23×C7#12414yes—
318C23×C7#12714yes—
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C22×D411yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C72−1+412yes—
330C7×D4—416no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—24no—
335C2×C4×C7—24no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—42no—
348C2×C4×C7—41no—
349C2×C4×C7—42no—
350C2×C4×C7—41no—
351C2×C4×C7—416no—
352C2×C4×C7C2×C22⋊C418yes—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—24no—
356C2×Dic7—24no—
357C2×Dic7—24no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—24no—
361C2×Dic7—22no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—416no—
367C2×Dic7—416no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7#12314yescomplemented
389C25C22×D711yescharacteristic
390C25C22×D711yescharacteristic
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4C2×Dic714yes—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—71no—
405C23×C4—72no—
406C23×C4—72no—
407C23×C4—71no—
408C23×C4—74no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—144no—
412C23×C4—144no—
413C23×C4—142no—
414C23×C4—142no—
415C23×C4—142no—
416C23×C4—142no—
417C23×C4—142no—
418C23×C4—282no—
419C23×C4—282no—
420C23×C4C2×Dic714yes—
421C23×C4C22×D712yes—
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D712yes—
424#123—232no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4C2×Dic718yescomplemented
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—74no—
434C2×C22⋊C4—142no—
435C2×C22⋊C4—142no—
436C2×C22⋊C4—144no—
437C2×C22⋊C4—144no—
438C2×C22⋊C4—142no—
439C2×C22⋊C4—144no—
440C2×C22⋊C4—142no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—282no—
445C2×C22⋊C4—282no—
446C2×C22⋊C4C2×Dic714yes—
447C2×C22⋊C4C2×Dic718yescomplemented
448C2×C22⋊C4C22⋊D714yes—
449C2×C22⋊C4C22⋊D714yes—
450C2×C42—144no—
451C2×C42—144no—
452C2×C42—282no—
453#95—144no—
454#95—144no—
455#95—144no—
456#95—144no—
457#95—142no—
458#95—144no—
459#95—142no—
460#95—144no—
461#95—144no—
462C22×C7—24no—
463C22×C7—28no—
464C22×C7—28no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—24no—
470C22×C7—24no—
471C22×C7—24no—
472C22×C7—42no—
473C22×C7—44no—
474C22×C7—44no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—82no—
480C22×C7—82no—
481C22×C7—81no—
482C22×C7—81no—
483C22×C7#39018yes—
484C22×C7C22×C22⋊C411yescharacteristic
485C22×C7C2×C4×D411yescharacteristic
486C22×C7C2×C4×D411yescharacteristic
487C22×C7C4×#4112yes—
488C22×C7#52012yes—
489C22×C7C2×#12111yescharacteristic
490C22×C7C2×#12111yescharacteristic
491C22×C7C2×#12311yescharacteristic
492C22×C7#52511yescharacteristic
493C22×C7C2×#12411yescharacteristic
494C22×C7#52912yes—
495C22×C7C2×#12711yescharacteristic
496C22×C7#53411yescharacteristic
497C22×C7#53611yescharacteristic
498C22×C7#53912yes—
499C22×C7#54612yes—
500C22×C7#54612yes—
501C22×C7#54612yes—
502C22×C7#54712yes—
503C22×C7#54712yes—
504C22×C7#54712yes—
505C22×C7#55112yes—
506C22×C7#55212yes—
507C4×C7—28no—
508C4×C7—44no—
509C4×C7—42no—
510Dic7—24no—
511Dic7—42no—
512Dic7—44no—
513Dic7—44no—
514Dic7—81no—
515Dic7—81no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24D4×D712yes—
531C24D4×D712yes—
532C24#115912yes—
533C24#115912yes—
534C24C22×Dic712yes—
535C24C22×Dic712yes—
536C24C2×C22⋊D712yes—
537C24C2×C22⋊D712yes—
538C24C23×D711yescharacteristic
539C2×D4—28no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—72no—
570C22×C4—74no—
571C22×C4—74no—
572C22×C4—72no—
573C22×C4—74no—
574C22×C4—148no—
575C22×C4—141no—
576C22×C4—142no—
577C22×C4—141no—
578C22×C4—148no—
579C22×C4—148no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—141no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—141no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—284no—
607C22×C4—288no—
608C22×C4—288no—
609C22×C4—288no—
610C22×C4—288no—
611C22×C4—284no—
612C22×C4—284no—
613C22×C4C22×Dic714yes—
614C22×C4C22×Dic712yes—
615C22×C4C22×Dic714yes—
616C22×C4C2×C22⋊D714yes—
617C22×C4C2×C22⋊D714yes—
618C4⋊C4—216no—
619C4⋊C4—288no—
620C22⋊C4—216no—
621C22⋊C4—148no—
622C22⋊C4—284no—
623C22⋊C4—288no—
624C22⋊C4—284no—
625C22⋊C4—284no—
626C22⋊C4C22⋊Dic7116yescomplemented
627C42—288no—
628C2×C7—28no—
629C2×C7—82no—
630C2×C7C2×#39011yescharacteristic
631C2×C7C4×#12311yescharacteristic
632C2×C7#232211yescharacteristic
633C2×C7#233912yes—
634C2×C7#235912yes—
635C2×C7#241211yescharacteristic
636C2×C7#241311yescharacteristic
637C2×C7#242512yes—
638C2×C7#248812yes—
639C2×C7#250111yescharacteristic
640C2×C7#253911yescharacteristic
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23D4×Dic714yes—
681C23D4×Dic714yes—
682C23#649914yes—
683C23#650114yes—
684C23#650114yes—
685C23#650314yes—
686C23C2×C22⋊Dic714yes—
687C23C2×D4×D711yescharacteristic
688C23C2×D4×D711yescharacteristic
689C23C2×#115911yescharacteristic
690C23C2×#115911yescharacteristic
691C23D7×#4112yes—
692C23D7×#4112yes—
693C23#655312yes—
694C23#655412yes—
695C23C23×Dic711yescharacteristic
696C23C22×C22⋊D711yescharacteristic
697C23C22×C22⋊D711yescharacteristic
698D4—416no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—416no—
720C2×C4—74no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—142no—
724C2×C4—144no—
725C2×C4—144no—
726C2×C4—142no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—144no—
731C2×C4—144no—
732C2×C4—144no—
733C2×C4—144no—
734C2×C4—2816no—
735C2×C4—2816no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—282no—
749C2×C4—282no—
750C2×C4—281no—
751C2×C4—281no—
752C2×C4—281no—
753C2×C4—282no—
754C2×C4—282no—
755C2×C4—281no—
756C2×C4C2×C22⋊Dic718yes—
757C7#1399611yescharacteristic, complemented, Sylow
758C22—28no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—81no—
774C22—82no—
775C22—82no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#8999318yes—
780C22#9033911yescharacteristic
781C22#9034012yes—
782C22#9034112yes—
783C22D7×#12311yescharacteristic
784C22#9034411yescharacteristic
785C22#9034512yes—
786C22#9034612yes—
787C22#9034711yescharacteristic
788C22#9034912yes—
789C22#9035612yes—
790C22C2×D4×Dic711yescharacteristic
791C22C2×D4×Dic711yescharacteristic
792C22C2×#649911yescharacteristic
793C22C2×#650111yescharacteristic
794C22C2×#650111yescharacteristic
795C22C2×#650311yescharacteristic
796C22#9051512yes—
797C22#9051512yes—
798C22#41×Dic712yes—
799C22#9051812yes—
800C22#9052012yes—
801C22#9052012yes—
802C22C22×C22⋊Dic711yescharacteristic
803C4—28no—
804C4—44no—
805C4—42no—
806C4—144no—
807C4—284no—
808C4—282no—
809C4—284no—
810C4—561no—
811C4—561no—
812C2—28no—
813C2—82no—
814C2Dic7×#12311yescharacteristic
815C2#1174028111yescharacteristic
816C2#1174028312yes—
817C2#1174028711yescharacteristic
818C2#1174029112yes—
819C2#1174030212yes—
820C2#1174030411yescharacteristic
821C2#1174034011yescharacteristic
822C2#1174034611yescharacteristic
823C2C2×#8999311yescharacteristic
824C2#1174153312yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×#123C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×#123D7
hypocenterC7#13996
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
4. C2×#89983C2semidirect
5. C22×C7⋊#95C2semidirect
6. C2×#89722C2semidirect
7. C2×C22⋊C4×Dic7C2semidirect
8. #11729323C2semidirect
9. #11729317C2semidirect
10. #11729300C2semidirect
11. #11729299C2semidirect
18. C2×C7×#123C4semidirect
83. C2×C7×C4⋊C4C2×C4semidirect
87. C2×C7×C22⋊C4C2×C4semidirect
233. C7×C22⋊C4C22⋊C4semidirect
247. C2×#123Dic7semidirect
388. C2×Dic7#123semidirect
430. C2×C4⋊C4C2×Dic7semidirect
447. C2×C22⋊C4C2×Dic7semidirect
626. C22⋊C4C22⋊Dic7semidirect
757. C7#13996semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C2×#899922
C2×#899832
C22×C7⋊#952
C2×#897222
C2×C22⋊C4×Dic72
#117293232
#117293172
#117293002
#117292992
#139967