Finite Group Databasebeta

← #13279145

Subgroups — #13279145

Order 1792.

2422 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D28C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#89763C211yesmaximal, characteristic
4C2×#89761C212yesmaximal, complemented
5C2×#89712C212yesmaximal, complemented
6#11729319C211yesmaximal, characteristic, complemented
7#11729291C212yesmaximal, complemented
8#11729288C211yesmaximal, characteristic, complemented
9#11727180C211yesmaximal, characteristic
10(C2×D7)⋊#95C212yesmaximal, complemented
11#11727174C211yesmaximal, characteristic, complemented
12C23×D28C2211yescharacteristic
13C23×C4×D7C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2212yes—
23C22×(C2×D7)⋊C4C2212yes—
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2212yes—
26C2×C4×D28—24no—
27C2×C4×D28—28no—
28C4×C7×C4⋊C4—24no—
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⋊#95C2211yescharacteristic
38#89763C418yescomplemented
39#89761—28no—
40#89712—28no—
41#14176—71nomaximal, Sylow
42C24×D7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2312yes—
52C23×Dic7C2312yes—
53C22×D28—24no—
54C22×D28—24no—
55C22×D28—22no—
56C22×D28—22no—
57C22×D28C2×C414yes—
58C22×C4×D7—24no—
59C22×C4×D7—24no—
60C22×C4×D7—24no—
61C22×C4×D7—24no—
62C22×C4×D7—24no—
63C22×C4×D7—42no—
64C22×C4×D7—42no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4C2×C414yescomplemented
70C2×C7×C4⋊C4D414yescomplemented
71C2×C42×C7—24no—
72C2×C42×C7—22no—
73C2×C42×C7—22no—
74C2×C42×C7—22no—
75C2×C42×C7—24no—
76C2×C42×C7—22no—
77C2×C42×C7D414yes—
78C2×(C2×D7)⋊C4—24no—
79C2×(C2×D7)⋊C4—24no—
80C2×(C2×D7)⋊C4—24no—
81C2×(C2×D7)⋊C4—24no—
82C2×(C2×D7)⋊C4—24no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—24no—
87C2×(C2×D7)⋊C4—24no—
88C2×(C2×D7)⋊C4—42no—
89C2×(C2×D7)⋊C4—42no—
90C2×(C2×D7)⋊C4C2×C418yescomplemented
91C2×(C2×D7)⋊C4C2×C418yescomplemented
92C2×(C2×D7)⋊C4D418yes—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7—24no—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4—24no—
97C2×Dic7⋊C4—42no—
98C4×D28—232no—
99C7×#95—22no—
100C7×#95—22no—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95—24no—
104C7⋊#95—22no—
105C7⋊#95—24no—
106C7⋊#95—42no—
107C7⋊#95C2×C414yescomplemented
108C22×C4×D4—71no—
109C2×#394—71no—
110C2×#388—72no—
111C2×#385—72no—
112C2×C4×C4⋊C4D711yescharacteristic, complemented
113#1444—71no—
114#1441—71no—
115#1438—71no—
116#1437—72no—
117#1434—71no—
118C22⋊#95—72no—
119C24×C7C2411yescharacteristic
120C23×D7—22no—
121C23×D7—22no—
122C23×D7—22no—
123C23×D7—22no—
124C23×D7—22no—
125C23×D7—22no—
126C23×D7—22no—
127C23×D7—22no—
128C23×D7—22no—
129C23×D7—22no—
130C23×D7—22no—
131C23×D7—22no—
132C23×D7C22×C414yes—
133C23×D7C2×D414yes—
134C23×D7#4114yes—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7C22×C412yes—
159C22×C4×C7C22×C412yes—
160C22×C4×C7C22×C412yes—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×D412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D414yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7#4112yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
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×Dic7C22×C414yes—
192C22×Dic7C2×D414yes—
193C2×D28—28no—
194C2×D28—28no—
195C2×D28—216no—
196C2×D28—216no—
197C2×D28—28no—
198C2×C4×D7—216no—
199C2×C4×D7—48no—
200C2×C4×D7—48no—
201C2×C4×D7—48no—
202C2×C4×D7—48no—
203C2×C4×D7—48no—
204C2×C4×D7—48no—
205C7×C4⋊C4—28no—
206C7×C4⋊C4—28no—
207C42×C7—28no—
208C42×C7—28no—
209C42×C7—44no—
210(C2×D7)⋊C4—216no—
211(C2×D7)⋊C4—216no—
212(C2×D7)⋊C4—216no—
213(C2×D7)⋊C4—48no—
214(C2×D7)⋊C4—48no—
215C4⋊Dic7—28no—
216Dic7⋊C4—48no—
217C23×D4—71no—
218C24×C4—72no—
219C2×C4×D4—148no—
220C2×C4×D4—144no—
221C22×C4⋊C4—71no—
222C22×C4⋊C4—72no—
223C22×C4⋊C4C2×D711yescharacteristic
224C22×C4⋊C4C2×D711yescharacteristic
225C22×C22⋊C4—72no—
226C22×C22⋊C4—72no—
227C22×C22⋊C4—72no—
228C22×C22⋊C4—72no—
229C22×C22⋊C4—72no—
230C22×C42C2×D711yescharacteristic
231C22×C42C2×D711yescharacteristic
232C22×C42C2×D711yescharacteristic
233#394—78no—
234#388—148no—
235#385—148no—
236C4×C4⋊C4—24no—
237C2×#95—71no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—71no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95C2×D711yescharacteristic
245C2×#95C2×D711yescharacteristic
246C23×C7C23×C411yescharacteristic
247C23×C7C22×D411yescharacteristic
248C23×C7C22×D412yes—
249C23×C7C22×D411yescharacteristic
250C23×C7C2×#4111yescharacteristic
251C23×C7C2×#4111yescharacteristic
252C23×C7C2×#4111yescharacteristic
253C23×C7C2×#4111yescharacteristic
254C23×C7C2×#4112yes—
255C23×C7H(5,𝔽2)12yes—
256C23×C72−1+412yes—
257C22×D7—24no—
258C22×D7—24no—
259C22×D7—24no—
260C22×D7—24no—
261C22×D7—24no—
262C22×D7—24no—
263C22×D7—24no—
264C22×D7—24no—
265C22×D7—24no—
266C22×D7—24no—
267C22×D7—24no—
268C22×D7—24no—
269C22×D7—24no—
270C22×D7—24no—
271C22×D7—24no—
272C22×D7—24no—
273C22×D7—24no—
274C22×D7—24no—
275C22×D7—42no—
276C22×D7—42no—
277C22×D7—42no—
278C22×D7—42no—
279C22×D7—42no—
280C22×D7—42no—
281C22×D7—42no—
282C22×D7—42no—
283C22×D7—42no—
284C22×D7—42no—
285C22×D7—42no—
286C22×D7—42no—
287C22×D7—42no—
288C22×D7—42no—
289C22×D7—42no—
290C22×D7—42no—
291C22×D7C4×D418yes—
292C2×C4×C7—22no—
293C2×C4×C7—24no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—24no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—24no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—42no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7C4×D414yes—
326C2×C4×C7C4×D414yescomplemented
327C2×C4×C7#12014yes—
328C2×C4×C7#12114yes—
329C2×Dic7—24no—
330C2×Dic7—24no—
331C2×Dic7—24no—
332C2×Dic7—24no—
333C2×Dic7—24no—
334C2×Dic7—24no—
335C2×Dic7—42no—
336C2×Dic7—42no—
337C2×Dic7—42no—
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—
350D28—232no—
351C4×D7—432no—
352C25—72no—
353C22×D4—74no—
354C22×D4—144no—
355C22×D4—144no—
356C22×D4—142no—
357C22×D4—142no—
358C23×C4—72no—
359C23×C4—72no—
360C23×C4—72no—
361C23×C4—144no—
362C23×C4—144no—
363C23×C4—144no—
364C23×C4—144no—
365C23×C4—144no—
366C23×C4—282no—
367C23×C4—282no—
368C23×C4C22×D711yescharacteristic
369C23×C4C22×D711yescharacteristic
370C23×C4C22×D711yescharacteristic
371C23×C4C22×D711yescharacteristic
372C23×C4C22×D711yescharacteristic
373C23×C4C22×D711yescharacteristic
374C23×C4C22×D711yescharacteristic
375C4×D4—1432no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—144no—
381C2×C4⋊C4—142no—
382C2×C4⋊C4—144no—
383C2×C4⋊C4—144no—
384C2×C4⋊C4—282no—
385C2×C4⋊C4C4×D714yescomplemented
386C2×C4⋊C4D2814yescomplemented
387C2×C22⋊C4—78no—
388C2×C22⋊C4—78no—
389C2×C22⋊C4—78no—
390C2×C22⋊C4—144no—
391C2×C22⋊C4—144no—
392C2×C22⋊C4—144no—
393C2×C22⋊C4—144no—
394C2×C22⋊C4—144no—
395C2×C22⋊C4—144no—
396C2×C22⋊C4—144no—
397C2×C22⋊C4—144no—
398C2×C22⋊C4—144no—
399C2×C22⋊C4—144no—
400C2×C22⋊C4—282no—
401C2×C22⋊C4—282no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—22no—
408C2×C42C22⋊D714yes—
409#95—22no—
410#95—22no—
411#95—74no—
412#95—144no—
413#95—144no—
414#95—144no—
415#95—142no—
416#95—144no—
417#95—282no—
418C22×C7C2×C4×D411yescharacteristic
419C22×C7C2×C4×D411yescharacteristic
420C22×C7C2×C4×D412yes—
421C22×C7C4×#4111yescharacteristic
422C22×C7#52012yes—
423C22×C7C2×#12011yescharacteristic
424C22×C7C2×#12111yescharacteristic
425C22×C7#52511yescharacteristic
426C22×C7#52512yes—
427C22×C7#52511yescharacteristic
428C22×C7#52911yescharacteristic
429C22×C7#53211yescharacteristic
430C22×C7#53511yescharacteristic
431C22×C7#53611yescharacteristic
432C22×C7#54212yes—
433C22×C7D4212yes—
434C22×C7#54612yes—
435C22×C7#54712yes—
436C22×C7#54712yes—
437C22×C7#54812yes—
438C22×C7#55112yes—
439C22×C7#55212yes—
440C22×C7#55312yes—
441C2×D7—28no—
442C2×D7—28no—
443C2×D7—28no—
444C2×D7—44no—
445C2×D7—44no—
446C2×D7—44no—
447C2×D7—44no—
448C2×D7—44no—
449C2×D7—44no—
450C2×D7—44no—
451C2×D7—44no—
452C2×D7—44no—
453C2×D7—44no—
454C2×D7—44no—
455C2×D7—44no—
456C4×C7—24no—
457C4×C7—24no—
458C4×C7—24no—
459C4×C7—24no—
460C4×C7—42no—
461C4×C7—42no—
462C4×C7—42no—
463Dic7—44no—
464Dic7—44no—
465Dic7—82no—
466C24—74no—
467C24—74no—
468C24—74no—
469C24—142no—
470C24—142no—
471C24—142no—
472C24—142no—
473C24—142no—
474C24—142no—
475C24—142no—
476C24—142no—
477C24—142no—
478C24—142no—
479C24—142no—
480C24—142no—
481C24C23×D711yescharacteristic
482C2×D4—1416no—
483C2×D4—148no—
484C2×D4—1416no—
485C2×D4—148no—
486C2×D4—148no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—74no—
511C22×C4—74no—
512C22×C4—1416no—
513C22×C4—142no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—142no—
518C22×C4—142no—
519C22×C4—142no—
520C22×C4—142no—
521C22×C4—142no—
522C22×C4—142no—
523C22×C4—142no—
524C22×C4—142no—
525C22×C4—142no—
526C22×C4—142no—
527C22×C4—142no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—142no—
531C22×C4—142no—
532C22×C4—288no—
533C22×C4—288no—
534C22×C4—288no—
535C22×C4—288no—
536C22×C4—288no—
537C22×C4—288no—
538C22×C4C2×C4×D712yes—
539C22×C4C2×C4×D712yes—
540C22×C4C2×C4×D712yes—
541C22×C4C2×D2812yes—
542C22×C4C2×D2812yes—
543C22×C4C2×D2812yes—
544C22×C4#115712yes—
545C22×C4#115712yes—
546C22×C4#115712yes—
547C22×C4#115712yes—
548C22×C4D4×D714yes—
549C22×C4C2×C22⋊D712yes—
550C22×C4C2×C22⋊D712yes—
551C22×C4C2×C22⋊D712yes—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—148no—
555C4⋊C4—288no—
556C22⋊C4—1416no—
557C22⋊C4—1416no—
558C22⋊C4—1416no—
559C22⋊C4—288no—
560C22⋊C4—288no—
561C42—28no—
562C42—28no—
563C42—44no—
564C2×C7C4×#12011yescharacteristic
565C2×C7C4×#12111yescharacteristic
566C2×C7#232611yescharacteristic
567C2×C7#235912yes—
568C2×C7#236112yes—
569C2×C7#240611yescharacteristic
570C2×C7#240811yescharacteristic
571C2×C7#246112yes—
572C2×C7#246812yes—
573C2×C7#253611yescharacteristic
574C2×C7#259811yescharacteristic
575D7—48no—
576C23—78no—
577C23—144no—
578C23—144no—
579C23—144no—
580C23—144no—
581C23—144no—
582C23—144no—
583C23—144no—
584C23—144no—
585C23—144no—
586C23—144no—
587C23—144no—
588C23—144no—
589C23—144no—
590C23—144no—
591C23—144no—
592C23—144no—
593C23—144no—
594C23—144no—
595C23—282no—
596C23—282no—
597C23—282no—
598C23—282no—
599C23—282no—
600C23—282no—
601C23—282no—
602C23—282no—
603C23—282no—
604C23—282no—
605C23—282no—
606C23—282no—
607C23—282no—
608C23—282no—
609C23—282no—
610C23—282no—
611C23C22×C4×D711yescharacteristic
612C23C22×D2811yescharacteristic
613C23C2×#115711yescharacteristic
614C23C2×#115711yescharacteristic
615C23C2×#115711yescharacteristic
616C23C2×#115711yescharacteristic
617C23C2×D4×D712yes—
618C23#655112yes—
619C23D7×#4112yes—
620C23#655312yes—
621C23C22×C22⋊D711yescharacteristic
622D4—1432no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—144no—
657C2×C4—144no—
658C2×C4—144no—
659C2×C4—144no—
660C2×C4—144no—
661C2×C4—144no—
662C2×C4—2832no—
663C2×C4—282no—
664C2×C4—282no—
665C2×C4—282no—
666C2×C4—282no—
667C2×C4—282no—
668C2×C4—282no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—282no—
675C2×C4—282no—
676C2×C4—282no—
677C2×C4—282no—
678C2×C4C4×D2814yescomplemented
679C2×C4C4×C22⋊D714yes—
680C2×C4#649314yes—
681C2×C4#650014yes—
682C7#1417611yescharacteristic, complemented, Sylow
683C22—148no—
684C22—148no—
685C22—148no—
686C22—284no—
687C22—284no—
688C22—284no—
689C22—284no—
690C22—284no—
691C22—284no—
692C22—284no—
693C22—284no—
694C22—284no—
695C22—284no—
696C22—284no—
697C22—284no—
698C22C2×C4×D2811yescharacteristic
699C22C4×#115711yescharacteristic
700C22#9016811yescharacteristic
701C22#9017011yescharacteristic
702C22#9019812yes—
703C22#9019812yes—
704C22#9021812yes—
705C22#9022112yes—
706C22C4×D4×D712yes—
707C22#9023812yes—
708C22D4×D2812yes—
709C22#9024112yes—
710C22#9026512yes—
711C22#9026712yes—
712C22#9027212yes—
713C22#9027312yes—
714C22C2×C4×C22⋊D711yescharacteristic
715C22C2×#649311yescharacteristic
716C22#9048211yescharacteristic
717C22C2×#650011yescharacteristic
718C22#9050711yescharacteristic
719C22#9051911yescharacteristic
720C22#9052111yescharacteristic
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—284no—
729C4—284no—
730C4—562no—
731C2—288no—
732C2#1173121712yes—
733C2#1173121912yes—
734C2#1173122712yes—
735C2#1173122812yes—
736C2C4×#649311yescharacteristic
737C2#1173963711yescharacteristic
738C2#1173972911yescharacteristic
739C2C4×#650011yescharacteristic
740C2#1173984811yescharacteristic
741C2#1173990011yescharacteristic
742C2#1173994411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14176
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C4⋊C4C2semidirect
4. C2×#89761C2semidirect
5. C2×#89712C2semidirect
6. #11729319C2semidirect
7. #11729291C2semidirect
8. #11729288C2semidirect
10. (C2×D7)⋊#95C2semidirect
11. #11727174C2semidirect
38. #89763C4semidirect
69. C2×C7×C4⋊C4C2×C4semidirect
70. C2×C7×C4⋊C4D4semidirect
90. C2×(C2×D7)⋊C4C2×C4semidirect
91. C2×(C2×D7)⋊C4C2×C4semidirect
107. C7⋊#95C2×C4semidirect
112. C2×C4×C4⋊C4D7semidirect
326. C2×C4×C7C4×D4semidirect
385. C2×C4⋊C4C4×D7semidirect
386. C2×C4⋊C4D28semidirect
678. C2×C4C4×D28semidirect
682. C7#14176semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D282
C2×C4×C7×C4⋊C42
C2×#897632
C2×#897612
C2×#897122
#117293192
#117292912
#117292882
#117271802
(C2×D7)⋊#952
#117271742
#141767