Finite Group Databasebeta

← #13275835

Subgroups — #13275835

Order 1792.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#89712C212yesmaximal, complemented
4C2×#89436C211yesmaximal, characteristic, complemented
5#11729881C211yesmaximal, characteristic, complemented
6#11729304C212yesmaximal
7#11729301C212yesmaximal, complemented
8#11729290C212yesmaximal, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
10Dic7⋊#95C211yesmaximal, characteristic, complemented
11#11727155C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C42×C7C2212yes—
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2212yes—
19C2×C4×C22⋊D7—28no—
20C2×C4×C22⋊D7C418yescomplemented
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2212yes—
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2212yes—
25C22×Dic7⋊C4C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C4×C7×C22⋊C4—24no—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89712—28no—
39#89436—24no—
40#13886—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×C414yes—
48C23×C4×C7C2312yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C22×C22⋊D7—24no—
53C22×C22⋊D7—24no—
54C22×C22⋊D7—22no—
55C22×C22⋊D7—22no—
56C22×C22⋊D7C2×C414yes—
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2311yescharacteristic
62C22×C4×D7—24no—
63C22×C4×D7—22no—
64C22×C4×D7—22no—
65C22×C4×D7—42no—
66C22×C4×D7C2×C414yes—
67C2×C7×C22⋊C4—24no—
68C2×C7×C22⋊C4—24no—
69C2×C7×C22⋊C4—24no—
70C2×C42×C7—24no—
71C2×C42×C7—24no—
72C2×C42×C7—42no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—42no—
76C2×C22⋊Dic7—42no—
77C2×C22⋊Dic7C2×C414yes—
78C4×C22⋊D7—232no—
79C2×(C2×D7)⋊C4—24no—
80C2×(C2×D7)⋊C4—24no—
81C2×(C2×D7)⋊C4—24no—
82C2×(C2×D7)⋊C4—24no—
83C2×(C2×D7)⋊C4—42no—
84C2×(C2×D7)⋊C4—42no—
85C2×(C2×D7)⋊C4C2×C414yes—
86C2×(C2×D7)⋊C4D418yes—
87C2×Dic7⋊C4—24no—
88C2×Dic7⋊C4—24no—
89C2×Dic7⋊C4—24no—
90C2×Dic7⋊C4—42no—
91C2×Dic7⋊C4C2×C414yes—
92C2×C4×Dic7—24no—
93C2×C4×Dic7C2×C414yes—
94C7×#95—22no—
95C7×#95D414yescomplemented
96C7⋊#95—24no—
97C7⋊#95—22no—
98C7⋊#95—24no—
99C7⋊#95—22no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95—42no—
104C22×C4×D4—71no—
105C2×#388—72no—
106C2×#381—71no—
107C2×C4×C22⋊C4D711yescharacteristic, complemented
108#1439—72no—
109#1438—72no—
110#1436—72no—
111C4⋊#95—71no—
112#1434—71no—
113C22⋊#95—71no—
114C22⋊#95—71no—
115C24×C7—22no—
116C24×C7—21no—
117C24×C7—22no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—22no—
123C24×C7—21no—
124C24×C7C22×C412yes—
125C24×C7#4114yes—
126C24×C7C2411yescharacteristic
127C23×D7—21no—
128C23×D7—22no—
129C23×D7—21no—
130C23×D7—22no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7—21no—
134C23×D7—22no—
135C23×D7—21no—
136C23×D7C22×C412yes—
137C23×D7C2×D414yes—
138C22×C4×C7—22no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
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—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—28no—
156C22×C4×C7—28no—
157C22×C4×C7—44no—
158C22×C4×C7—48no—
159C22×C4×C7—48no—
160C22×C4×C7C22×C412yes—
161C22×C4×C7C22×C412yes—
162C22×C4×C7C2×D414yes—
163C22×C4×C7C2×D414yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7#4114yes—
166C22×C4×C7#4112yes—
167C2×C22⋊D7—216no—
168C2×C22⋊D7—216no—
169C2×C22⋊D7—28no—
170C2×C22⋊D7—28no—
171C2×C22⋊D7—28no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—22no—
179C22×Dic7—21no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7C22×C412yes—
196C22×Dic7C22×C412yes—
197C22×Dic7C22×C412yes—
198C22×Dic7C2×D414yes—
199C22×Dic7#4112yes—
200C22×Dic7#4112yes—
201C2×C4×D7—28no—
202C2×C4×D7—28no—
203C2×C4×D7—44no—
204C2×C4×D7—48no—
205C2×C4×D7—48no—
206C7×C22⋊C4—216no—
207C42×C7—48no—
208C22⋊Dic7—28no—
209C22⋊Dic7—48no—
210(C2×D7)⋊C4—48no—
211(C2×D7)⋊C4—48no—
212(C2×D7)⋊C4C22⋊C4116yescomplemented
213Dic7⋊C4—28no—
214Dic7⋊C4—48no—
215C4×Dic7—28no—
216C23×D4—71no—
217C24×C4—71no—
218C24×C4C2×D711yescharacteristic
219C2×C4×D4—78no—
220C2×C4×D4—148no—
221C22×C4⋊C4—71no—
222C22×C4⋊C4—72no—
223C22×C22⋊C4—71no—
224C22×C22⋊C4—71no—
225C22×C22⋊C4—72no—
226C22×C22⋊C4—72no—
227C22×C22⋊C4—72no—
228C22×C22⋊C4C2×D712yes—
229C22×C42—71no—
230C22×C42C2×D712yes—
231#388—148no—
232#381—144no—
233C4×C22⋊C4—24no—
234C2×#95—71no—
235C2×#95—71no—
236C2×#95—72no—
237C2×#95—72no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95C2×D711yescharacteristic
243C2×#95C2×D711yescharacteristic
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—41no—
261C23×C7—41no—
262C23×C7—42no—
263C23×C7—41no—
264C23×C7—41no—
265C23×C7—42no—
266C23×C7#11714yes—
267C23×C7C23×C411yescharacteristic
268C23×C7C22×D412yes—
269C23×C7C22×D411yescharacteristic
270C23×C7C2×#4112yes—
271C23×C7C2×#4111yescharacteristic
272C23×C7C2×#4112yes—
273C23×C7C2×#4111yescharacteristic
274C23×C7C2×#4111yescharacteristic
275C23×C7H(5,𝔽2)12yes—
276C23×C7H(5,𝔽2)11yescharacteristic
277C23×C72−1+411yescharacteristic
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7—22no—
283C22×D7—22no—
284C22×D7—24no—
285C22×D7—24no—
286C22×D7—24no—
287C22×D7—24no—
288C22×D7—24no—
289C22×D7—24no—
290C22×D7—42no—
291C22×D7—42no—
292C22×D7—42no—
293C22×D7—42no—
294C22×D7—41no—
295C22×D7—41no—
296C22×D7—42no—
297C22×D7—41no—
298C22×D7—41no—
299C22×D7—42no—
300C22×D7C2×C22⋊C414yes—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—24no—
306C2×C4×C7—24no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
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×C7C2×C22⋊C414yes—
325C2×C4×C7C4×D414yes—
326C22⋊D7—232no—
327C2×Dic7—22no—
328C2×Dic7—22no—
329C2×Dic7—22no—
330C2×Dic7—22no—
331C2×Dic7—24no—
332C2×Dic7—24no—
333C2×Dic7—24no—
334C2×Dic7—24no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—42no—
339C2×Dic7—42no—
340C2×Dic7—42no—
341C2×Dic7—42no—
342C2×Dic7—42no—
343C2×Dic7—42no—
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×Dic7C2×C22⋊C414yes—
355C2×Dic7#11714yes—
356C4×D7—416no—
357C25—71no—
358C25C22×D711yescharacteristic
359C22×D4—74no—
360C22×D4—142no—
361C22×D4—142no—
362C22×D4—144no—
363C22×D4—144no—
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—42no—
368C23×C4—71no—
369C23×C4—71no—
370C23×C4—71no—
371C23×C4—74no—
372C23×C4—72no—
373C23×C4—72no—
374C23×C4—144no—
375C23×C4—142no—
376C23×C4—142no—
377C23×C4—282no—
378C23×C4C4×D714yes—
379C23×C4C22×D712yes—
380C23×C4C22×D712yes—
381C23×C4C22×D711yescharacteristic
382C23×C4C22×D711yescharacteristic
383C4×D4—1432no—
384C2×C4⋊C4—74no—
385C2×C4⋊C4—144no—
386C2×C4⋊C4—144no—
387C2×C4⋊C4—144no—
388C2×C4⋊C4—282no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—74no—
393C2×C22⋊C4—78no—
394C2×C22⋊C4—74no—
395C2×C22⋊C4—144no—
396C2×C22⋊C4—144no—
397C2×C22⋊C4—144no—
398C2×C22⋊C4—144no—
399C2×C22⋊C4—144no—
400C2×C22⋊C4—144no—
401C2×C22⋊C4—282no—
402C2×C22⋊C4—282no—
403C2×C22⋊C4—282no—
404C2×C22⋊C4—282no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—42no—
408C2×C42—74no—
409C2×C42—144no—
410#95—22no—
411#95—144no—
412#95—144no—
413#95—144no—
414#95—142no—
415#95—144no—
416#95—144no—
417#95—142no—
418#95—282no—
419#95C22⋊D714yescomplemented
420C22×C7—24no—
421C22×C7—24no—
422C22×C7—24no—
423C22×C7—42no—
424C22×C7—42no—
425C22×C7—42no—
426C22×C7—42no—
427C22×C7—44no—
428C22×C7—44no—
429C22×C7—44no—
430C22×C7—44no—
431C22×C7C22×C22⋊C411yescharacteristic
432C22×C7C2×#11711yescharacteristic
433C22×C7C2×#11711yescharacteristic
434C22×C7C2×C4×D411yescharacteristic
435C22×C7C4×#4111yescharacteristic
436C22×C7#51811yescharacteristic
437C22×C7#52011yescharacteristic
438C22×C7#52512yes—
439C22×C7#52512yes—
440C22×C7#52512yes—
441C22×C7#52912yes—
442C22×C7#53812yes—
443C22×C7#53912yes—
444C22×C7D4212yes—
445C22×C7#54612yes—
446C22×C7#54612yes—
447C22×C7#54712yes—
448C22×C7#54711yescharacteristic
449C22×C7#55011yescharacteristic
450C22×C7#55312yes—
451C22×C7#55511yescharacteristic
452C22×C7#55611yescharacteristic
453C22×C7#55912yes—
454C2×D7—24no—
455C2×D7—24no—
456C2×D7—24no—
457C2×D7—42no—
458C2×D7—42no—
459C2×D7—42no—
460C2×D7—44no—
461C2×D7—44no—
462C2×D7—44no—
463C2×D7—44no—
464C2×D7—42no—
465C4×C7—24no—
466C4×C7—24no—
467C4×C7—44no—
468C4×C7—44no—
469Dic7—24no—
470Dic7—24no—
471Dic7—42no—
472Dic7—82no—
473Dic7—82no—
474C24—22no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—72no—
484C24—74no—
485C24—142no—
486C24—141no—
487C24—142no—
488C24—142no—
489C24—141no—
490C24—141no—
491C24—141no—
492C24—141no—
493C24—141no—
494C24C2×C4×D712yes—
495C24#115714yes—
496C24C23×D711yescharacteristic
497C2×D4—148no—
498C2×D4—148no—
499C2×D4—1416no—
500C2×D4—1416no—
501C2×D4—148no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—72no—
525C22×C4—72no—
526C22×C4—74no—
527C22×C4—72no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—148no—
531C22×C4—142no—
532C22×C4—142no—
533C22×C4—142no—
534C22×C4—141no—
535C22×C4—141no—
536C22×C4—141no—
537C22×C4—142no—
538C22×C4—142no—
539C22×C4—141no—
540C22×C4—148no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—284no—
556C22×C4—288no—
557C22×C4—288no—
558C22×C4C2×C4×D712yes—
559C22×C4C2×C4×D712yes—
560C22×C4#115714yes—
561C22×C4#115712yes—
562C22×C4D4×D714yes—
563C22×C4C2×C22⋊D714yes—
564C22×C4C2×C22⋊D712yes—
565C4⋊C4—148no—
566C4⋊C4—288no—
567C22⋊C4—216no—
568C22⋊C4—716no—
569C22⋊C4—148no—
570C22⋊C4—288no—
571C22⋊C4—288no—
572C22⋊C4—288no—
573C42—48no—
574C42—148no—
575C2×C7—44no—
576C2×C7#228011yescharacteristic
577C2×C7#229011yescharacteristic
578C2×C7#231811yescharacteristic
579C2×C7D4×C22⋊C411yescharacteristic
580C2×C7#233911yescharacteristic
581C2×C7#235411yescharacteristic
582C2×C7#235711yescharacteristic
583C2×C7#245512yes—
584C2×C7#245612yes—
585C2×C7#245912yes—
586C2×C7#246612yes—
587D7—44no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—41no—
609C23—41no—
610C23—74no—
611C23—142no—
612C23—142no—
613C23—142no—
614C23—144no—
615C23—142no—
616C23—142no—
617C23—142no—
618C23—144no—
619C23—144no—
620C23—144no—
621C23—144no—
622C23—144no—
623C23—282no—
624C23—281no—
625C23—281no—
626C23—282no—
627C23—282no—
628C23—282no—
629C23—282no—
630C23—282no—
631C23—281no—
632C23—281no—
633C23#643514yes—
634C23C22×C4×D711yescharacteristic
635C23C2×#115712yes—
636C23C2×#115712yes—
637C23C2×#115711yescharacteristic
638C23C2×D4×D712yes—
639C23#654812yes—
640C23D7×#4111yescharacteristic
641C23D7×#4111yescharacteristic
642C23#655311yescharacteristic
643C23#655411yescharacteristic
644C23C22×C22⋊D711yescharacteristic
645D4—1432no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—416no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—74no—
670C2×C4—74no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—144no—
676C2×C4—144no—
677C2×C4—144no—
678C2×C4—144no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—2816no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4D7×C22⋊C414yes—
700C2×C4C4×C22⋊D714yes—
701C7#1388611yescharacteristic, complemented, Sylow
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—44no—
708C22—44no—
709C22—42no—
710C22—44no—
711C22—44no—
712C22—42no—
713C22—144no—
714C22—144no—
715C22—144no—
716C22—282no—
717C22—282no—
718C22—284no—
719C22—284no—
720C22—282no—
721C22—284no—
722C22—284no—
723C22—282no—
724C22C2×#643511yescharacteristic
725C22C4×#115711yescharacteristic
726C22#9017012yes—
727C22C2×D7×C22⋊C411yescharacteristic
728C22#9017711yescharacteristic
729C22#9018112yes—
730C22D7×#11711yescharacteristic
731C22#9021411yescharacteristic
732C22#9022311yescharacteristic
733C22#9022411yescharacteristic
734C22#9023112yes—
735C22#9023812yes—
736C22#9023812yes—
737C22#9024112yes—
738C22#9024212yes—
739C22#9025012yes—
740C22#9025112yes—
741C22#9025512yes—
742C22C2×C4×C22⋊D711yescharacteristic
743C22#9048212yes—
744C22D4×C22⋊D712yes—
745C22#9051511yescharacteristic
746C22#9052511yescharacteristic
747C4—24no—
748C4—24no—
749C4—44no—
750C4—44no—
751C4—144no—
752C4—144no—
753C4—282no—
754C4—562no—
755C4—562no—
756C2—44no—
757C2—284no—
758C2#1173090811yescharacteristic
759C2#1173100611yescharacteristic
760C2#1173101311yescharacteristic
761C2#1173101811yescharacteristic
762C2#1173103512yes—
763C2#1173103712yes—
764C2#1173951011yescharacteristic
765C2C22⋊C4×C22⋊D711yescharacteristic
766C2#1173968611yescharacteristic
767C2#1173985512yes—
768C2#1173985612yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13886
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C22⋊C4C2semidirect
3. C2×#89712C2semidirect
4. C2×#89436C2semidirect
5. #11729881C2semidirect
7. #11729301C2semidirect
8. #11729290C2semidirect
9. (C2×D7)⋊#95C2semidirect
10. Dic7⋊#95C2semidirect
11. #11727155C2semidirect
20. C2×C4×C22⋊D7C4semidirect
95. C7×#95D4semidirect
107. C2×C4×C22⋊C4D7semidirect
212. (C2×D7)⋊C4C22⋊C4semidirect
419. #95C22⋊D7semidirect
701. C7#13886semidirect

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×C4×C7×C22⋊C42
C2×#897122
C2×#894362
#117298812
#117293042
#117293012
#117292902
(C2×D7)⋊#952
Dic7⋊#952
#117271552
#138867