Finite Group Databasebeta

← #13275124

Subgroups — #13275124

Order 1792.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
2C2×#89442C212yesmaximal
3C7×#1434C211yesmaximal, characteristic, complemented
4#11729289C211yesmaximal, characteristic, complemented
5(C2×D7)⋊#95C211yesmaximal, characteristic
6(C2×D7)⋊#95C211yesmaximal, characteristic
7#11727162C212yesmaximal
8#11727161C212yesmaximal, complemented
9#11727157C212yesmaximal, complemented
10Dic7×#95C211yesmaximal, characteristic, complemented
11Dic7×#95C211yesmaximal, characteristic, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×(C2×D7)⋊C4C2211yescharacteristic
15C22×(C2×D7)⋊C4C2212yes—
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×C4⋊Dic7C2212yes—
19C22×C4×Dic7C2212yes—
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C2×C7×#95C2211yescharacteristic
23C2×C7×#95C2211yescharacteristic
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C4×(C2×D7)⋊C4C418yescomplemented
36#89442C4116yescomplemented
37#13788—71nomaximal, Sylow
38C24×D7C2311yescharacteristic
39C23×C4×C7C2312yes—
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2312yes—
45C23×Dic7C2312yes—
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C22×C4×D7—22no—
50C22×C4×D7—22no—
51C22×C4×D7—42no—
52C22×C4×D7—42no—
53C22×C4×D7C2×C414yes—
54C2×C42×C7—42no—
55C2×C42×C7C2×C414yes—
56C2×(C2×D7)⋊C4—24no—
57C2×(C2×D7)⋊C4—42no—
58C2×(C2×D7)⋊C4—42no—
59C2×(C2×D7)⋊C4—42no—
60C2×(C2×D7)⋊C4—42no—
61C2×(C2×D7)⋊C4C2×C414yes—
62C2×(C2×D7)⋊C4C2×C418yes—
63C2×(C2×D7)⋊C4C2×C418yes—
64C2×(C2×D7)⋊C4C2×C418yes—
65C2×(C2×D7)⋊C4C2×C414yes—
66C2×C4⋊Dic7—42no—
67C2×C4⋊Dic7—42no—
68C2×C4⋊Dic7C2×C418yescomplemented
69C2×C4×Dic7—24no—
70C2×C4×Dic7—42no—
71C2×C4×Dic7—42no—
72C2×C4×Dic7—42no—
73C2×C4×Dic7—42no—
74C2×C4×Dic7—42no—
75C2×C4×Dic7C2×C414yes—
76C2×C4×Dic7C2×C418yescomplemented
77C7×#95—22no—
78C7×#95—22no—
79C7×#95—42no—
80C7×#95C2×C418yescomplemented
81C7⋊#95—22no—
82C7⋊#95—22no—
83C7⋊#95—24no—
84C7⋊#95—42no—
85C7⋊#95—42no—
86C7⋊#95—42no—
87C7⋊#95C2×C414yes—
88C7⋊#95C2×C414yes—
89C7⋊#95C2×C418yescomplemented
90C2×#388—72no—
91C2×C4×C22⋊C4—71no—
92#1437—72no—
93#1436—72no—
94C4⋊#95—71no—
95#1434—72no—
96#1434D711yescharacteristic, complemented
97C22⋊#95—71no—
98C22⋊#95—71no—
99C4×#95—71no—
100C4×#95—71no—
101C24×C7C2411yescharacteristic
102C23×D7—22no—
103C23×D7—21no—
104C23×D7—21no—
105C23×D7—21no—
106C23×D7—21no—
107C23×D7—22no—
108C23×D7—22no—
109C23×D7—21no—
110C23×D7—21no—
111C23×D7C22×C414yes—
112C23×D7C22×C412yes—
113C22×C4×C7—22no—
114C22×C4×C7—21no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—21no—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C22×C414yes—
136C22×C4×C7C22×C414yes—
137C22×C4×C7C22×C412yes—
138C22×C4×C7C22×C414yes—
139C22×C4×C7C22×C412yes—
140C22×C4×C7#4112yes—
141C22×C4×C7#4112yes—
142C22×Dic7—22no—
143C22×Dic7—21no—
144C22×Dic7—22no—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7C22×C412yes—
165C22×Dic7C22×C414yes—
166C22×Dic7C22×C414yes—
167C22×Dic7C22×C412yes—
168C22×Dic7C22×C414yes—
169C22×Dic7C22×C412yes—
170C22×Dic7#4114yes—
171C2×C4×D7—28no—
172C2×C4×D7—44no—
173C2×C4×D7—44no—
174C2×C4×D7—48no—
175C2×C4×D7—48no—
176C42×C7—44no—
177(C2×D7)⋊C4—28no—
178(C2×D7)⋊C4—48no—
179(C2×D7)⋊C4—48no—
180(C2×D7)⋊C4C42116yescomplemented
181C4⋊Dic7—48no—
182C4×Dic7—44no—
183C4×Dic7—48no—
184C4×Dic7—48no—
185C24×C4—71no—
186C22×C4⋊C4—72no—
187C22×C22⋊C4—71no—
188C22×C22⋊C4—71no—
189C22×C22⋊C4—72no—
190C22×C22⋊C4—72no—
191C22×C42—71no—
192C22×C42—72no—
193C22×C42—72no—
194C22×C42C2×D711yescharacteristic
195#388—716no—
196C4×C22⋊C4—78no—
197C2×#95—72no—
198C2×#95—71no—
199C2×#95—71no—
200C2×#95—71no—
201C2×#95—71no—
202C2×#95—72no—
203C2×#95—72no—
204C2×#95—72no—
205C2×#95—72no—
206C2×#95C2×D711yescharacteristic
207C2×#95C2×D711yescharacteristic
208C2×#95C2×D712yes—
209C2×#95C2×D712yes—
210C23×C7C23×C411yescharacteristic
211C23×C7C23×C412yes—
212C23×C7C2×#4111yescharacteristic
213C23×C7C2×#4111yescharacteristic
214C23×C7C2×#4112yes—
215C23×C7H(5,𝔽2)12yes—
216C23×C7H(5,𝔽2)12yes—
217C23×C7H(5,𝔽2)11yescharacteristic
218C23×C7H(5,𝔽2)11yescharacteristic
219C23×C72−1+411yescharacteristic
220C23×C72−1+411yescharacteristic
221C22×D7—22no—
222C22×D7—22no—
223C22×D7—24no—
224C22×D7—24no—
225C22×D7—24no—
226C22×D7—24no—
227C22×D7—22no—
228C22×D7—22no—
229C22×D7—22no—
230C22×D7—22no—
231C22×D7—24no—
232C22×D7—24no—
233C22×D7—42no—
234C22×D7—42no—
235C22×D7—42no—
236C22×D7—42no—
237C22×D7—41no—
238C22×D7—42no—
239C22×D7—41no—
240C22×D7—41no—
241C22×D7—41no—
242C22×D7—42no—
243C22×D7C2×C4214yes—
244C2×C4×C7—22no—
245C2×C4×C7—24no—
246C2×C4×C7—22no—
247C2×C4×C7—22no—
248C2×C4×C7—22no—
249C2×C4×C7—24no—
250C2×C4×C7—24no—
251C2×C4×C7—24no—
252C2×C4×C7—22no—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—42no—
271C2×C4×C7C2×C4214yes—
272C2×C4×C7#11714yes—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—24no—
276C2×Dic7—22no—
277C2×Dic7—22no—
278C2×Dic7—24no—
279C2×Dic7—24no—
280C2×Dic7—24no—
281C2×Dic7—22no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—24no—
287C2×Dic7—24no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7C2×C4214yes—
301C2×Dic7#11714yes—
302C4×D7—416no—
303C25—71no—
304C23×C4—71no—
305C23×C4—71no—
306C23×C4—72no—
307C23×C4—72no—
308C23×C4—71no—
309C23×C4—74no—
310C23×C4—142no—
311C23×C4—142no—
312C23×C4—282no—
313C23×C4—282no—
314C23×C4C22×D711yescharacteristic
315C23×C4C22×D712yes—
316C23×C4C22×D712yes—
317C23×C4C22×D711yescharacteristic
318C23×C4C22×D711yescharacteristic
319C2×C4⋊C4—78no—
320C2×C4⋊C4—282no—
321C2×C4⋊C4—282no—
322C2×C22⋊C4—74no—
323C2×C22⋊C4—78no—
324C2×C22⋊C4—74no—
325C2×C22⋊C4—78no—
326C2×C22⋊C4—78no—
327C2×C22⋊C4—144no—
328C2×C22⋊C4—282no—
329C2×C22⋊C4—282no—
330C2×C22⋊C4—282no—
331C2×C22⋊C4—282no—
332C2×C42—42no—
333C2×C42—74no—
334C2×C42—78no—
335C2×C42—144no—
336C2×C42—282no—
337C2×C42—282no—
338C2×C42—282no—
339C2×C42—282no—
340C2×C42—282no—
341C2×C42C4×D714yes—
342#95—22no—
343#95—22no—
344#95—42no—
345#95—74no—
346#95—74no—
347#95—78no—
348#95—144no—
349#95—142no—
350#95—142no—
351#95—282no—
352#95—282no—
353#95—282no—
354#95C4×D718yescomplemented
355C22×C7C22×C4211yescharacteristic
356C22×C7C2×#11711yescharacteristic
357C22×C7C2×#11711yescharacteristic
358C22×C7C4×#4112yes—
359C22×C7C4×#4112yes—
360C22×C7#51811yescharacteristic
361C22×C7#51811yescharacteristic
362C22×C7#51812yes—
363C22×C7#51812yes—
364C22×C7#52011yescharacteristic
365C22×C7#52011yescharacteristic
366C22×C7#52012yes—
367C22×C7#52012yes—
368C22×C7#53812yes—
369C22×C7#53812yes—
370C22×C7#53812yes—
371C22×C7#53912yes—
372C22×C7#54011yescharacteristic
373C22×C7#54012yes—
374C22×C7#54111yescharacteristic
375C22×C7#54211yescharacteristic
376C22×C7#54211yescharacteristic
377C22×C7#54212yes—
378C2×D7—24no—
379C2×D7—24no—
380C2×D7—24no—
381C2×D7—42no—
382C2×D7—42no—
383C2×D7—42no—
384C2×D7—42no—
385C2×D7—44no—
386C2×D7—44no—
387C2×D7—44no—
388C2×D7—44no—
389C4×C7—24no—
390C4×C7—24no—
391C4×C7—42no—
392C4×C7—44no—
393C4×C7—44no—
394Dic7—24no—
395Dic7—24no—
396Dic7—42no—
397Dic7—44no—
398Dic7—44no—
399C24—74no—
400C24—72no—
401C24—141no—
402C24—142no—
403C24—141no—
404C24—142no—
405C24—141no—
406C24—141no—
407C24—142no—
408C24—141no—
409C24—141no—
410C24C23×D711yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—72no—
433C22×C4—74no—
434C22×C4—72no—
435C22×C4—74no—
436C22×C4—72no—
437C22×C4—74no—
438C22×C4—74no—
439C22×C4—141no—
440C22×C4—142no—
441C22×C4—141no—
442C22×C4—142no—
443C22×C4—141no—
444C22×C4—141no—
445C22×C4—141no—
446C22×C4—142no—
447C22×C4—142no—
448C22×C4—142no—
449C22×C4—142no—
450C22×C4—142no—
451C22×C4—141no—
452C22×C4—142no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—148no—
462C22×C4—284no—
463C22×C4—284no—
464C22×C4—288no—
465C22×C4—288no—
466C22×C4C2×C4×D714yes—
467C22×C4C2×C4×D712yes—
468C22×C4C2×C4×D714yes—
469C22×C4C2×C4×D712yes—
470C22×C4C2×C4×D714yes—
471C22×C4C2×C4×D712yes—
472C22×C4#115912yes—
473C22×C4#116112yes—
474C4⋊C4—288no—
475C22⋊C4—716no—
476C22⋊C4—148no—
477C22⋊C4—288no—
478C22⋊C4—288no—
479C42—44no—
480C42—284no—
481C42—288no—
482C42—288no—
483C2×C7C4×#11711yescharacteristic
484C2×C7#227511yescharacteristic
485C2×C7#227511yescharacteristic
486C2×C7#231211yescharacteristic
487C2×C7#231411yescharacteristic
488C2×C7#231811yescharacteristic
489C2×C7#231911yescharacteristic
490C2×C7#233312yes—
491C2×C7#233412yes—
492C2×C7#233512yes—
493C2×C7#233712yes—
494D7—44no—
495C23—74no—
496C23—142no—
497C23—142no—
498C23—142no—
499C23—144no—
500C23—142no—
501C23—142no—
502C23—144no—
503C23—142no—
504C23—144no—
505C23—144no—
506C23—144no—
507C23—144no—
508C23—281no—
509C23—281no—
510C23—281no—
511C23—281no—
512C23—282no—
513C23—282no—
514C23—282no—
515C23—282no—
516C23—282no—
517C23—282no—
518C23C22×C4×D711yescharacteristic
519C23C22×C4×D712yes—
520C23C2×#115911yescharacteristic
521C23#654812yes—
522C23C2×#116111yescharacteristic
523C23D7×#4112yes—
524C23#655311yescharacteristic
525C23#655311yescharacteristic
526C23#655312yes—
527C23#655411yescharacteristic
528C23#655411yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—74no—
557C2×C4—74no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—142no—
561C2×C4—142no—
562C2×C4—144no—
563C2×C4—142no—
564C2×C4—142no—
565C2×C4—144no—
566C2×C4—142no—
567C2×C4—142no—
568C2×C4—144no—
569C2×C4—144no—
570C2×C4—142no—
571C2×C4—144no—
572C2×C4—144no—
573C2×C4—144no—
574C2×C4—144no—
575C2×C4—2816no—
576C2×C4—282no—
577C2×C4—282no—
578C2×C4—282no—
579C2×C4—282no—
580C2×C4—282no—
581C2×C4—282no—
582C2×C4—282no—
583C2×C4—282no—
584C2×C4—282no—
585C2×C4—282no—
586C2×C4C42×D714yes—
587C2×C4#645514yes—
588C7#1378811yescharacteristic, complemented, Sylow
589C22—144no—
590C22—144no—
591C22—144no—
592C22—282no—
593C22—282no—
594C22—284no—
595C22—284no—
596C22—284no—
597C22—284no—
598C22—282no—
599C22—282no—
600C22C2×C42×D711yescharacteristic
601C22#9017711yescharacteristic
602C22C2×#645511yescharacteristic
603C22D7×#11711yescharacteristic
604C22#9021211yescharacteristic
605C22#9021212yes—
606C22#9021411yescharacteristic
607C22#9021411yescharacteristic
608C22#9021412yes—
609C22C4×#115912yes—
610C22#9023612yes—
611C22#9023712yes—
612C22C4×#116112yes—
613C22#9030812yes—
614C22#9033512yes—
615C22#9035312yes—
616C22#9035412yes—
617C22#9037311yescharacteristic
618C22#9037311yescharacteristic
619C22#9038811yescharacteristic
620C22#9038911yescharacteristic
621C22#9039512yes—
622C22#9039812yes—
623C4—24no—
624C4—24no—
625C4—42no—
626C4—44no—
627C4—44no—
628C4—144no—
629C4—144no—
630C4—284no—
631C4—284no—
632C4—282no—
633C2—284no—
634C2#1173085711yescharacteristic
635C2#1173088111yescharacteristic
636C2C4×#645511yescharacteristic
637C2#1173144911yescharacteristic
638C2#1173150011yescharacteristic
639C2#1173166911yescharacteristic
640C2#1173174011yescharacteristic
641C2#1173239712yes—
642C2#1173240012yes—
643C2#1173291312yes—
644C2#1173291712yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×#1434C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1434D7
hypocenterC7#13788
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C7×#1434C2semidirect
4. #11729289C2semidirect
8. #11727161C2semidirect
9. #11727157C2semidirect
10. Dic7×#95C2semidirect
11. Dic7×#95C2semidirect
35. C4×(C2×D7)⋊C4C4semidirect
36. #89442C4semidirect
68. C2×C4⋊Dic7C2×C4semidirect
76. C2×C4×Dic7C2×C4semidirect
80. C7×#95C2×C4semidirect
89. C7⋊#95C2×C4semidirect
96. #1434D7semidirect
180. (C2×D7)⋊C4C42semidirect
354. #95C4×D7semidirect
588. C7#13788semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D7)⋊C42
C2×#894422
C7×#14342
#117292892
(C2×D7)⋊#952
#117271622
#117271612
#117271572
Dic7×#952
#137887