Finite Group Databasebeta

← #13275931

Subgroups — #13275931

Order 1792.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×#89983C211yesmaximal, characteristic, complemented
3C2×#89728C212yesmaximal
4C2×D7×#95C211yesmaximal, characteristic, complemented
5C7×C22⋊#95C211yesmaximal, characteristic, complemented
6#11729303C212yesmaximal, complemented
7(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C212yesmaximal, complemented
9#11727175C212yesmaximal, complemented
10#11727157C211yesmaximal, characteristic, complemented
11#11727155C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2212yes—
15C23×C4×D7C2211yescharacteristic
16C22×C7×C22⋊C4C2212yes—
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2211yescharacteristic
19C2×C4×C22⋊D7—28no—
20C2×C4×C22⋊D7C418yescomplemented
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2212yes—
28#89983—24no—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38#89728—28no—
39D7×#95—24no—
40#13894—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C24×D7C2311yescharacteristic
43C23×C4×C7—24no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—42no—
47C23×C4×C7C2×C414yescomplemented
48C23×C4×C7C2312yes—
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C22×C22⋊D7—22no—
53C22×C22⋊D7—24no—
54C22×C22⋊D7—22no—
55C22×C22⋊D7C2×C414yes—
56C22×C22⋊D7D418yes—
57C23×Dic7C2312yes—
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2312yes—
61C23×Dic7C2311yescharacteristic
62C22×C4×D7—24no—
63C22×C4×D7—24no—
64C22×C4×D7—22no—
65C22×C4×D7—24no—
66C22×C4×D7—22no—
67C22×C4×D7—24no—
68C22×C4×D7—24no—
69C22×C4×D7—24no—
70C22×C4×D7—42no—
71C22×C4×D7—42no—
72C22×C4×D7—42no—
73C22×C4×D7C2×C414yes—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—42no—
77C2×C22⋊Dic7—24no—
78C2×C22⋊Dic7—24no—
79C2×C22⋊Dic7—24no—
80C2×C22⋊Dic7—42no—
81C2×C22⋊Dic7C2×C414yescomplemented
82C4×C22⋊D7—232no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—24no—
87C2×(C2×D7)⋊C4C2×C414yes—
88C2×Dic7⋊C4—24no—
89C2×Dic7⋊C4C2×C414yescomplemented
90C2×C4×Dic7—24no—
91C2×C4×Dic7C2×C414yescomplemented
92C7×#95—22no—
93C7×#95—22no—
94C7×#95—42no—
95C7⋊#95—22no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—42no—
102C7⋊#95—42no—
103C7⋊#95D414yescomplemented
104C22×C4×D4—71no—
105C2×#386—72no—
106C2×#381—71no—
107C22×#95—71no—
108#1445—72no—
109#1440—72no—
110#1434—71no—
111#1434—71no—
112C22⋊#95—72no—
113C22⋊#95—71no—
114C22⋊#95D711yescharacteristic, complemented
115C24×C7—21no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7C22×C412yes—
125C24×C7C2×D414yes—
126C24×C7C2411yescharacteristic
127C23×D7—21no—
128C23×D7—21no—
129C23×D7—22no—
130C23×D7—22no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7C22×C412yes—
134C23×D7C2×D414yes—
135C23×D7#4112yes—
136C23×D7#4114yes—
137C23×D7#4112yes—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—28no—
141C22×C4×C7—21no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—28no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—44no—
160C22×C4×C7—48no—
161C22×C4×C7—48no—
162C22×C4×C7C22×C412yes—
163C22×C4×C7C22×C412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7#4114yes—
166C22×C4×C7#4112yes—
167C2×C22⋊D7—28no—
168C2×C22⋊D7—28no—
169C2×C22⋊D7—216no—
170C2×C22⋊D7—216no—
171C2×C22⋊D7C22⋊C4116yes—
172C22×Dic7—22no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—21no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7C22×C412yes—
197C22×Dic7C22×C412yes—
198C22×Dic7C22×C412yes—
199C22×Dic7C2×D414yes—
200C22×Dic7C2×D414yes—
201C2×C4×D7—216no—
202C2×C4×D7—28no—
203C2×C4×D7—28no—
204C2×C4×D7—44no—
205C2×C4×D7—48no—
206C2×C4×D7—48no—
207C2×C4×D7—48no—
208C2×C4×D7—48no—
209C2×C4×D7—48no—
210C2×C4×D7—48no—
211C2×C4×D7—48no—
212C2×C4×D7—48no—
213C7×C22⋊C4—48no—
214C22⋊Dic7—28no—
215C22⋊Dic7—48no—
216(C2×D7)⋊C4—28no—
217(C2×D7)⋊C4—48no—
218Dic7⋊C4—28no—
219C4×Dic7—28no—
220C23×D4—71no—
221C24×C4—71no—
222C24×C4—72no—
223C24×C4C2×D711yescharacteristic
224C2×C4×D4—78no—
225C2×C4×D4—148no—
226C22×C4⋊C4—71no—
227C22×C22⋊C4—71no—
228C22×C22⋊C4—71no—
229C22×C22⋊C4—72no—
230C22×C22⋊C4—72no—
231C22×C22⋊C4C2×D712yes—
232C22×C42—71no—
233#386—148no—
234#381—144no—
235C2×#95—71no—
236C2×#95—72no—
237C2×#95—71no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—144no—
245C2×#95C2×D711yescharacteristic
246C2×#95C2×D711yescharacteristic
247C2×#95C2×D712yes—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—41no—
265C23×C7—41no—
266C23×C7—42no—
267C23×C7—41no—
268C23×C7—42no—
269C23×C7—41no—
270C23×C7C2×C22⋊C414yes—
271C23×C7C23×C411yescharacteristic
272C23×C7C22×D412yes—
273C23×C7C22×D411yescharacteristic
274C23×C7C2×#4112yes—
275C23×C7C2×#4111yescharacteristic
276C23×C7C2×#4112yes—
277C23×C7C2×#4111yescharacteristic
278C23×C7C2×#4111yescharacteristic
279C23×C7H(5,𝔽2)12yes—
280C23×C7H(5,𝔽2)11yescharacteristic
281C23×C72−1+411yescharacteristic
282C22×D7—22no—
283C22×D7—22no—
284C22×D7—22no—
285C22×D7—22no—
286C22×D7—24no—
287C22×D7—24no—
288C22×D7—24no—
289C22×D7—24no—
290C22×D7—24no—
291C22×D7—22no—
292C22×D7—24no—
293C22×D7—24no—
294C22×D7—24no—
295C22×D7—22no—
296C22×D7—24no—
297C22×D7—22no—
298C22×D7—24no—
299C22×D7—22no—
300C22×D7C2×C22⋊C414yes—
301C22×D7#11714yes—
302C22×D7#11714yes—
303C22×D7#12318yes—
304C22×D7#12318yes—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—416no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7C4×D414yes—
330C22⋊D7—232no—
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—24no—
334C2×Dic7—24no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—42no—
345C2×Dic7—42no—
346C2×Dic7—42no—
347C2×Dic7—42no—
348C2×Dic7—42no—
349C2×Dic7—42no—
350C2×Dic7—42no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—42no—
358C2×Dic7—42no—
359C2×Dic7C2×C22⋊C414yes—
360C4×D7—416no—
361C4×D7—432no—
362C25—71no—
363C25C22×D711yescharacteristic
364C22×D4—74no—
365C22×D4—78no—
366C22×D4—142no—
367C22×D4—144no—
368C22×D4—142no—
369C23×C4—24no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—42no—
373C23×C4—71no—
374C23×C4—71no—
375C23×C4—71no—
376C23×C4—72no—
377C23×C4—74no—
378C23×C4—72no—
379C23×C4—144no—
380C23×C4—144no—
381C23×C4—144no—
382C23×C4—144no—
383C23×C4—144no—
384C23×C4—144no—
385C23×C4—142no—
386C23×C4—142no—
387C23×C4—282no—
388C23×C4—282no—
389C23×C4—282no—
390C23×C4C4×D714yescomplemented
391C23×C4C22×D712yes—
392C23×C4C22×D711yescharacteristic
393C23×C4C22×D712yes—
394C23×C4C22×D711yescharacteristic
395C4×D4—1432no—
396C2×C4⋊C4—74no—
397C2×C4⋊C4—144no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—74no—
402C2×C22⋊C4—74no—
403C2×C22⋊C4—144no—
404C2×C22⋊C4—144no—
405C2×C22⋊C4—144no—
406C2×C22⋊C4—144no—
407C2×C22⋊C4—144no—
408C2×C22⋊C4—144no—
409C2×C22⋊C4—144no—
410C2×C22⋊C4—282no—
411C2×C42—74no—
412C2×C42—144no—
413#95—22no—
414#95—22no—
415#95—42no—
416#95—74no—
417#95—144no—
418#95—144no—
419#95—144no—
420#95—144no—
421#95—144no—
422#95—142no—
423#95—282no—
424#95—282no—
425C22×C7—24no—
426C22×C7—24no—
427C22×C7—24no—
428C22×C7—42no—
429C22×C7—42no—
430C22×C7—42no—
431C22×C7—44no—
432C22×C7—44no—
433C22×C7—44no—
434C22×C7—44no—
435C22×C7—42no—
436C22×C7C22×C22⋊C411yescharacteristic
437C22×C7C2×#11711yescharacteristic
438C22×C7C2×#11711yescharacteristic
439C22×C7C2×C4×D411yescharacteristic
440C22×C7C4×#4111yescharacteristic
441C22×C7#51811yescharacteristic
442C22×C7#52011yescharacteristic
443C22×C7C2×#12312yes—
444C22×C7C2×#12312yes—
445C22×C7#52512yes—
446C22×C7#52912yes—
447C22×C7#53812yes—
448C22×C7#53912yes—
449C22×C7D4212yes—
450C22×C7#54612yes—
451C22×C7#54612yes—
452C22×C7#54611yescharacteristic
453C22×C7#54712yes—
454C22×C7#54811yescharacteristic
455C22×C7#55112yes—
456C22×C7#55211yescharacteristic
457C22×C7#55312yes—
458C22×C7#55311yescharacteristic
459C2×D7—24no—
460C2×D7—24no—
461C2×D7—24no—
462C2×D7—24no—
463C2×D7—24no—
464C2×D7—28no—
465C2×D7—28no—
466C2×D7—28no—
467C2×D7—28no—
468C2×D7—24no—
469C2×D7#38118yescomplemented
470C4×C7—24no—
471C4×C7—42no—
472C4×C7—44no—
473C4×C7—82no—
474Dic7—24no—
475Dic7—42no—
476Dic7—42no—
477Dic7—44no—
478Dic7—82no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—72no—
489C24—74no—
490C24—72no—
491C24—74no—
492C24—72no—
493C24—142no—
494C24—141no—
495C24—141no—
496C24—142no—
497C24—141no—
498C24—141no—
499C24C2×C4×D712yes—
500C24D4×D714yes—
501C24C23×D711yescharacteristic
502C2×D4—716no—
503C2×D4—148no—
504C2×D4—148no—
505C2×D4—1416no—
506C2×D4—1416no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—72no—
532C22×C4—74no—
533C22×C4—72no—
534C22×C4—72no—
535C22×C4—74no—
536C22×C4—148no—
537C22×C4—1416no—
538C22×C4—142no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—141no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—141no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—148no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—284no—
564C22×C4—288no—
565C22×C4—288no—
566C22×C4—288no—
567C22×C4—288no—
568C22×C4—288no—
569C22×C4—288no—
570C22×C4—288no—
571C22×C4—288no—
572C22×C4C2×C4×D712yes—
573C22×C4C2×C4×D712yes—
574C22×C4#115714yes—
575C22×C4D4×D712yes—
576C22×C4#115912yes—
577C4⋊C4—148no—
578C22⋊C4—48no—
579C22⋊C4—148no—
580C22⋊C4—148no—
581C22⋊C4—288no—
582C22⋊C4—288no—
583C42—148no—
584C2×C7—44no—
585C2×C7C2×#38111yescharacteristic
586C2×C7#229011yescharacteristic
587C2×C7#231811yescharacteristic
588C2×C7D4×C22⋊C411yescharacteristic
589C2×C7#233911yescharacteristic
590C2×C7#235211yescharacteristic
591C2×C7#235311yescharacteristic
592C2×C7#241812yes—
593C2×C7#241912yes—
594C2×C7#244312yes—
595C2×C7#244412yes—
596D7—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—41no—
619C23—74no—
620C23—74no—
621C23—74no—
622C23—78no—
623C23—78no—
624C23—142no—
625C23—142no—
626C23—142no—
627C23—144no—
628C23—142no—
629C23—144no—
630C23—144no—
631C23—144no—
632C23—144no—
633C23—144no—
634C23—144no—
635C23—144no—
636C23—142no—
637C23—144no—
638C23—142no—
639C23—142no—
640C23—144no—
641C23—142no—
642C23D7×C22⋊C414yes—
643C23C22×C4×D711yescharacteristic
644C23C2×#115712yes—
645C23C2×D4×D712yes—
646C23C2×D4×D711yescharacteristic
647C23C2×#115911yescharacteristic
648C23#654812yes—
649C23#654811yescharacteristic
650C23#655111yescharacteristic
651C23D7×#4112yes—
652C23D7×#4111yescharacteristic
653C23D7×#4111yescharacteristic
654D4—1432no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—416no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—74no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—144no—
683C2×C4—144no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—144no—
691C2×C4—144no—
692C2×C4—144no—
693C2×C4—2816no—
694C2×C4—2832no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—282no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4(C22⋊D7)⋊C414yes—
711C7#1389411yescharacteristic, complemented, Sylow
712C22—24no—
713C22—24no—
714C22—24no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—42no—
723C22—78no—
724C22—144no—
725C22—144no—
726C22—144no—
727C22—148no—
728C22—148no—
729C22—144no—
730C22—148no—
731C22—148no—
732C22—144no—
733C22—144no—
734C22C4×#115711yescharacteristic
735C22C2×D7×C22⋊C411yescharacteristic
736C22C2×(C22⋊D7)⋊C411yescharacteristic
737C22#9017711yescharacteristic
738C22#9018112yes—
739C22#9019511yescharacteristic
740C22#9019812yes—
741C22D7×#11711yescharacteristic
742C22D7×#11711yescharacteristic
743C22#9023812yes—
744C22#9024712yes—
745C22#9024812yes—
746C22#9024912yes—
747C22#9028112yes—
748C22#9028212yes—
749C22#9030311yescharacteristic
750C22#9030412yes—
751C22#9030511yescharacteristic
752C22#9032411yescharacteristic
753C22#9032912yes—
754C22#9033011yescharacteristic
755C22D7×#12312yes—
756C22D7×#12312yes—
757C4—24no—
758C4—42no—
759C4—44no—
760C4—82no—
761C4—144no—
762C4—282no—
763C4—284no—
764C4—282no—
765C4—562no—
766C2—44no—
767C2—148no—
768C2#1173081311yescharacteristic
769C2#1173100711yescharacteristic
770C2#1173102111yescharacteristic
771C2#1173129511yescharacteristic
772C2#1173145111yescharacteristic
773C2#1173145711yescharacteristic
774C2D7×#38111yescharacteristic
775C2#1173204912yes—
776C2#1173205312yes—
777C2#1173233712yes—
778C2#1173234212yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22⋊#95D7
hypocenterC7#13894
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#89983C2semidirect
4. C2×D7×#95C2semidirect
5. C7×C22⋊#95C2semidirect
6. #11729303C2semidirect
7. (C2×D7)⋊#95C2semidirect
8. (C2×D7)⋊#95C2semidirect
9. #11727175C2semidirect
10. #11727157C2semidirect
11. #11727155C2semidirect
20. C2×C4×C22⋊D7C4semidirect
47. C23×C4×C7C2×C4semidirect
81. C2×C22⋊Dic7C2×C4semidirect
89. C2×Dic7⋊C4C2×C4semidirect
91. C2×C4×Dic7C2×C4semidirect
103. C7⋊#95D4semidirect
114. C22⋊#95D7semidirect
390. C23×C4C4×D7semidirect
469. C2×D7#381semidirect
711. C7#13894semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×#899832
C2×#897282
C2×D7×#952
C7×C22⋊#952
#117293032
(C2×D7)⋊#952
#117271752
#117271572
#117271552
#138947