Finite Group Databasebeta

← #13282745

Subgroups — #13282745

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89711C211yesmaximal, characteristic
2C2×#89437C212yesmaximal
3C7×#1434C211yesmaximal, characteristic, complemented
4#11729288C211yesmaximal, characteristic, complemented
5#11727182C212yesmaximal, complemented
6#11727182C212yesmaximal, complemented
7(C2×D7)⋊#95C212yesmaximal, complemented
8(C2×D7)⋊#95C212yesmaximal, complemented
9#11727165C212yesmaximal, complemented
10C23×D28C2211yescharacteristic
11C23×C4×D7C2212yes—
12C22×C42×C7C2211yescharacteristic
13C22×(C2×D7)⋊C4C2212yes—
14C22×(C2×D7)⋊C4C2212yes—
15C22×(C2×D7)⋊C4C2212yes—
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C2×C7×#95C2212yes—
21C2×C7×#95C2212yes—
22C2×C7×#95C2211yescharacteristic
23C2×C7×#95C2211yescharacteristic
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2211yescharacteristic
31#89711C418yescomplemented
32#89437—28no—
33#14486—71nomaximal, Sylow
34C24×D7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2312yes—
39C23×C4×C7C2311yescharacteristic
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C22×D28—41no—
44C22×D28—41no—
45C22×D28—41no—
46C22×D28—41no—
47C22×D28C2×C414yes—
48C22×D28D414yes—
49C22×D28Q814yes—
50C22×C4×D7—24no—
51C22×C4×D7—24no—
52C22×C4×D7—24no—
53C22×C4×D7—42no—
54C22×C4×D7—42no—
55C22×C4×D7—42no—
56C22×C4×D7—42no—
57C2×C42×C7—41no—
58C2×C42×C7—41no—
59C2×C42×C7C2×C414yescomplemented
60C2×(C2×D7)⋊C4—24no—
61C2×(C2×D7)⋊C4—24no—
62C2×(C2×D7)⋊C4—24no—
63C2×(C2×D7)⋊C4—24no—
64C2×(C2×D7)⋊C4—24no—
65C2×(C2×D7)⋊C4—42no—
66C2×(C2×D7)⋊C4—42no—
67C2×(C2×D7)⋊C4—42no—
68C2×(C2×D7)⋊C4—42no—
69C2×(C2×D7)⋊C4—42no—
70C2×(C2×D7)⋊C4—42no—
71C2×(C2×D7)⋊C4—42no—
72C2×(C2×D7)⋊C4—42no—
73C2×(C2×D7)⋊C4C2×C418yescomplemented
74C2×(C2×D7)⋊C4C2×C418yescomplemented
75C2×C4⋊Dic7—41no—
76C2×C4⋊Dic7—41no—
77C2×C4⋊Dic7C2×C414yescomplemented
78C2×Dic7⋊C4—42no—
79C2×Dic7⋊C4—42no—
80C2×Dic7⋊C4—42no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—41no—
84C7×#95—41no—
85C7⋊#95—24no—
86C7⋊#95—24no—
87C7⋊#95—42no—
88C7⋊#95—42no—
89C7⋊#95—42no—
90C7⋊#95—41no—
91C7⋊#95—41no—
92C2×#390—71no—
93C2×#386—72no—
94#1441—72no—
95#1439—72no—
96#1439—72no—
97#1434—71no—
98#1434D711yescharacteristic, complemented
99C22⋊#95—72no—
100C22⋊#95—72no—
101C24×C7C2411yescharacteristic
102C23×D7—22no—
103C23×D7—22no—
104C23×D7—22no—
105C23×D7—22no—
106C23×D7—22no—
107C23×D7—22no—
108C23×D7—22no—
109C23×D7—22no—
110C23×D7—22no—
111C23×D7—22no—
112C23×D7—22no—
113C23×D7—22no—
114C23×D7C22×C414yes—
115C23×D7C2×D414yes—
116C23×D7C2×Q814yes—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7C22×C412yes—
143C22×C4×C7C22×C412yes—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×Q812yes—
147C22×C4×C7#4114yes—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
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×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7C22×C414yes—
168C22×Dic7#4114yes—
169C2×D28—44no—
170C2×D28—44no—
171C2×D28—44no—
172C2×D28—44no—
173C2×D28—44no—
174C2×D28—44no—
175C2×D28C4⋊C4116yescomplemented
176C2×C4×D7—48no—
177C2×C4×D7—48no—
178C2×C4×D7—48no—
179C2×C4×D7—48no—
180C2×C4×D7—48no—
181C2×C4×D7—48no—
182C2×C4×D7—48no—
183C42×C7—44no—
184(C2×D7)⋊C4—48no—
185(C2×D7)⋊C4—48no—
186(C2×D7)⋊C4—48no—
187(C2×D7)⋊C4—48no—
188(C2×D7)⋊C4—48no—
189C4⋊Dic7—44no—
190Dic7⋊C4—48no—
191C23×D4—71no—
192C24×C4—72no—
193C22×C4⋊C4—71no—
194C22×C4⋊C4—72no—
195C22×C22⋊C4—72no—
196C22×C22⋊C4—72no—
197C22×C22⋊C4—72no—
198C22×C22⋊C4—72no—
199C22×C22⋊C4—72no—
200C22×C42C2×D711yescharacteristic
201#390—78no—
202#386—148no—
203C2×#95—72no—
204C2×#95—72no—
205C2×#95—71no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—71no—
210C2×#95C2×D712yes—
211C2×#95C2×D712yes—
212C2×#95C2×D711yescharacteristic
213C2×#95C2×D711yescharacteristic
214C23×C7C23×C411yescharacteristic
215C23×C7C22×D411yescharacteristic
216C23×C7C22×Q811yescharacteristic
217C23×C7C2×#4112yes—
218C23×C7C2×#4112yes—
219C23×C7H(5,𝔽2)11yescharacteristic
220C23×C7H(5,𝔽2)11yescharacteristic
221C23×C7H(5,𝔽2)11yescharacteristic
222C23×C7H(5,𝔽2)11yescharacteristic
223C23×C7H(5,𝔽2)12yes—
224C23×C7H(5,𝔽2)12yes—
225C22×D7—24no—
226C22×D7—24no—
227C22×D7—24no—
228C22×D7—24no—
229C22×D7—24no—
230C22×D7—24no—
231C22×D7—24no—
232C22×D7—24no—
233C22×D7—24no—
234C22×D7—24no—
235C22×D7—24no—
236C22×D7—24no—
237C22×D7—24no—
238C22×D7—24no—
239C22×D7—24no—
240C22×D7—24no—
241C22×D7—24no—
242C22×D7—24no—
243C22×D7—42no—
244C22×D7—42no—
245C22×D7—42no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C22×D7—42no—
252C22×D7—42no—
253C22×D7—42no—
254C22×D7—42no—
255C22×D7—42no—
256C22×D7—42no—
257C22×D7—42no—
258C22×D7—42no—
259C22×D7C2×C4⋊C418yes—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7C2×C4⋊C414yes—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—24no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303C2×Dic7—42no—
304C2×Dic7—42no—
305C2×Dic7—42no—
306C2×Dic7—42no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312D28—416no—
313C4×D7—432no—
314C25—72no—
315C22×D4—74no—
316C22×D4—74no—
317C22×D4—74no—
318C22×D4—281no—
319C22×D4—281no—
320C22×D4—281no—
321C22×D4—281no—
322C23×C4—72no—
323C23×C4—72no—
324C23×C4—72no—
325C23×C4—144no—
326C23×C4—144no—
327C23×C4—144no—
328C23×C4—282no—
329C23×C4—282no—
330C23×C4—282no—
331C23×C4—282no—
332C23×C4C22×D712yes—
333C23×C4C22×D711yescharacteristic
334C23×C4C22×D711yescharacteristic
335C23×C4C22×D712yes—
336C23×C4C22×D711yescharacteristic
337C2×C4⋊C4—74no—
338C2×C4⋊C4—282no—
339C2×C4⋊C4—282no—
340C2×C4⋊C4—282no—
341C2×C4⋊C4—281no—
342C2×C4⋊C4—281no—
343C2×C22⋊C4—78no—
344C2×C22⋊C4—78no—
345C2×C22⋊C4—144no—
346C2×C22⋊C4—144no—
347C2×C22⋊C4—144no—
348C2×C22⋊C4—144no—
349C2×C22⋊C4—144no—
350C2×C22⋊C4—282no—
351C2×C22⋊C4—282no—
352C2×C22⋊C4—282no—
353C2×C22⋊C4—282no—
354C2×C22⋊C4—282no—
355C2×C22⋊C4—282no—
356C2×C22⋊C4—282no—
357C2×C22⋊C4—282no—
358C2×C42—41no—
359C2×C42—41no—
360C2×C42C4×D714yescomplemented
361#95—24no—
362#95—24no—
363#95—41no—
364#95—41no—
365#95—144no—
366#95—144no—
367#95—281no—
368#95—281no—
369#95—282no—
370#95—282no—
371#95—282no—
372C22×C7C22×C4⋊C411yescharacteristic
373C22×C7C4×#4111yescharacteristic
374C22×C7C4×#4111yescharacteristic
375C22×C7#51811yescharacteristic
376C22×C7#51811yescharacteristic
377C22×C7#51811yescharacteristic
378C22×C7#51811yescharacteristic
379C22×C7#53411yescharacteristic
380C22×C7#53411yescharacteristic
381C22×C7#53812yes—
382C22×C7#53812yes—
383C22×C7#54012yes—
384C22×C7#54012yes—
385C22×C7#54311yescharacteristic
386C22×C7#54311yescharacteristic
387C22×C7#54612yes—
388C22×C7#54612yes—
389C22×C7#55112yes—
390C22×C7#55412yes—
391C22×C7#55412yes—
392C22×C7#55512yes—
393C22×C7#56012yes—
394C22×C7#56012yes—
395C2×D7—28no—
396C2×D7—28no—
397C2×D7—28no—
398C2×D7—44no—
399C2×D7—44no—
400C2×D7—44no—
401C2×D7—44no—
402C2×D7—44no—
403C2×D7—44no—
404C2×D7—44no—
405C2×D7—44no—
406C2×D7—44no—
407C2×D7—44no—
408C2×D7—44no—
409C2×D7—44no—
410C4×C7—24no—
411C4×C7—42no—
412C4×C7—42no—
413C4×C7—44no—
414C4×C7—82no—
415Dic7—44no—
416Dic7—44no—
417Dic7—82no—
418C24—74no—
419C24—74no—
420C24—74no—
421C24—142no—
422C24—142no—
423C24—142no—
424C24—142no—
425C24—142no—
426C24—142no—
427C24—142no—
428C24—142no—
429C24—142no—
430C24—142no—
431C24—142no—
432C24—142no—
433C24C23×D711yescharacteristic
434C2×D4—716no—
435C2×D4—284no—
436C2×D4—284no—
437C2×D4—284no—
438C2×D4—284no—
439C2×D4—284no—
440C2×D4—284no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—74no—
467C22×C4—74no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—142no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—288no—
488C22×C4—288no—
489C22×C4—288no—
490C22×C4—288no—
491C22×C4—288no—
492C22×C4—288no—
493C22×C4—288no—
494C22×C4C2×C4×D712yes—
495C22×C4C2×C4×D712yes—
496C22×C4C2×C4×D712yes—
497C22×C4#115714yes—
498C22×C4D4×D712yes—
499C22×C4Q8×D712yes—
500C4⋊C4—284no—
501C4⋊C4—288no—
502C22⋊C4—288no—
503C22⋊C4—288no—
504C22⋊C4—288no—
505C22⋊C4—288no—
506C22⋊C4—288no—
507C42—44no—
508C2×C7#231511yescharacteristic
509C2×C7#233311yescharacteristic
510C2×C7#233311yescharacteristic
511C2×C7#234911yescharacteristic
512C2×C7#234911yescharacteristic
513C2×C7#237211yescharacteristic
514C2×C7#238011yescharacteristic
515C2×C7#269712yes—
516C2×C7#269912yes—
517C2×C7#274812yes—
518C2×C7#278412yes—
519D7—48no—
520C23—78no—
521C23—144no—
522C23—144no—
523C23—144no—
524C23—144no—
525C23—144no—
526C23—144no—
527C23—144no—
528C23—144no—
529C23—144no—
530C23—144no—
531C23—144no—
532C23—144no—
533C23—144no—
534C23—144no—
535C23—144no—
536C23—144no—
537C23—144no—
538C23—144no—
539C23—282no—
540C23—282no—
541C23—282no—
542C23—282no—
543C23—282no—
544C23—282no—
545C23—282no—
546C23—282no—
547C23—282no—
548C23—282no—
549C23—282no—
550C23—282no—
551C23—282no—
552C23—282no—
553C23—282no—
554C23—282no—
555C23C22×C4×D711yescharacteristic
556C23C2×#115712yes—
557C23C2×D4×D711yescharacteristic
558C23#654811yescharacteristic
559C23#654811yescharacteristic
560C23C2×Q8×D711yescharacteristic
561C23D7×#4112yes—
562C23#655312yes—
563C23#655311yescharacteristic
564C23#655311yescharacteristic
565C23#655312yes—
566D4—2816no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—144no—
598C2×C4—144no—
599C2×C4—144no—
600C2×C4—144no—
601C2×C4—144no—
602C2×C4—144no—
603C2×C4—2832no—
604C2×C4—282no—
605C2×C4—282no—
606C2×C4—282no—
607C2×C4—282no—
608C2×C4—282no—
609C2×C4—282no—
610C2×C4—282no—
611C2×C4—282no—
612C2×C4—282no—
613C2×C4—282no—
614C2×C4—282no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4D7×C4⋊C414yes—
620C7#1448611yescharacteristic, complemented, Sylow
621C22—148no—
622C22—148no—
623C22—148no—
624C22—284no—
625C22—284no—
626C22—284no—
627C22—284no—
628C22—284no—
629C22—284no—
630C22—284no—
631C22—284no—
632C22—284no—
633C22—284no—
634C22—284no—
635C22—284no—
636C22C4×#115711yescharacteristic
637C22#9017711yescharacteristic
638C22C2×D7×C4⋊C411yescharacteristic
639C22#9021211yescharacteristic
640C22#9021211yescharacteristic
641C22#9021211yescharacteristic
642C22#9021311yescharacteristic
643C22#9021812yes—
644C22#9022312yes—
645C22#9024112yes—
646C22#9025112yes—
647C22#9025312yes—
648C22#9027012yes—
649C22#9029611yescharacteristic
650C22#9029611yescharacteristic
651C22#9032511yescharacteristic
652C22#9032511yescharacteristic
653C22#9034812yes—
654C22#9035412yes—
655C22#9036712yes—
656C22#9038112yes—
657C22#9040212yes—
658C22#9040212yes—
659C4—24no—
660C4—42no—
661C4—44no—
662C4—42no—
663C4—82no—
664C4—284no—
665C4—284no—
666C4—562no—
667C2—288no—
668C2#1173084011yescharacteristic
669C2#1173089411yescharacteristic
670C2#1173121511yescharacteristic
671C2#1173145011yescharacteristic
672C2#1173150311yescharacteristic
673C2#1173167311yescharacteristic
674C2#1173174311yescharacteristic
675C2#1173286712yes—
676C2#1173287812yes—
677C2#1173336812yes—
678C2#1173336912yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1434C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenter#1434D7
hypocenterC7#14486
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C7×#1434C2semidirect
4. #11729288C2semidirect
5. #11727182C2semidirect
6. #11727182C2semidirect
7. (C2×D7)⋊#95C2semidirect
8. (C2×D7)⋊#95C2semidirect
9. #11727165C2semidirect
31. #89711C4semidirect
59. C2×C42×C7C2×C4semidirect
73. C2×(C2×D7)⋊C4C2×C4semidirect
74. C2×(C2×D7)⋊C4C2×C4semidirect
77. C2×C4⋊Dic7C2×C4semidirect
98. #1434D7semidirect
175. C2×D28C4⋊C4semidirect
360. C2×C42C4×D7semidirect
620. C7#14486semidirect

Maximal subgroups

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

subgroupindex
C2×#897112
C2×#894372
C7×#14342
#117292882
#117271822
(C2×D7)⋊#952
#117271652
#144867