Finite Group Databasebeta

← #13282746

Subgroups — #13282746

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89760C211yesmaximal, characteristic
2C2×#89437C212yesmaximal
3C7×#1441C211yesmaximal, characteristic, complemented
4#11729324C212yesmaximal, complemented
5#11729319C211yesmaximal, characteristic, complemented
6#11727181C212yesmaximal, complemented
7(C2×D7)⋊#95C212yesmaximal, complemented
8(C2×D7)⋊#95C212yesmaximal, complemented
9#11727157C212yesmaximal, complemented
10C23×D28C2211yescharacteristic
11C23×C4×D7C2212yes—
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×(C2×D7)⋊C4C2212yes—
15C22×(C2×D7)⋊C4C2212yes—
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C2×C7×#95C2212yes—
22C2×C7×#95C2211yescharacteristic
23C2×C7×#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31#89760C418yescomplemented
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×C7×C4⋊C4—41no—
58C2×C7×C4⋊C4—41no—
59C2×C7×C4⋊C4—42no—
60C2×C7×C4⋊C4—41no—
61C2×C7×C4⋊C4C2×C414yescomplemented
62C2×(C2×D7)⋊C4—24no—
63C2×(C2×D7)⋊C4—24no—
64C2×(C2×D7)⋊C4—24no—
65C2×(C2×D7)⋊C4—24no—
66C2×(C2×D7)⋊C4—24no—
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)⋊C4—42no—
74C2×(C2×D7)⋊C4—42no—
75C2×(C2×D7)⋊C4C2×C418yescomplemented
76C2×(C2×D7)⋊C4C2×C418yescomplemented
77C2×C4⋊Dic7—42no—
78C2×C4⋊Dic7—41no—
79C2×C4×Dic7—41no—
80C2×C4×Dic7—41no—
81C2×C4×Dic7C2×C414yescomplemented
82C7×#95—24no—
83C7×#95—42no—
84C7×#95—41no—
85C7⋊#95—24no—
86C7⋊#95—24no—
87C7⋊#95—24no—
88C7⋊#95—42no—
89C7⋊#95—42no—
90C7⋊#95—41no—
91C7⋊#95—42no—
92C2×#390—71no—
93C2×#386—72no—
94#1441—71no—
95#1441D711yescharacteristic, complemented
96#1439—72no—
97#1439—72no—
98#1434—72no—
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—21no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—21no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
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—
183C7×C4⋊C4—44no—
184C7×C4⋊C4—44no—
185(C2×D7)⋊C4—48no—
186(C2×D7)⋊C4—48no—
187(C2×D7)⋊C4—48no—
188(C2×D7)⋊C4—48no—
189(C2×D7)⋊C4—48no—
190C4⋊Dic7—44no—
191C4×Dic7—44no—
192C23×D4—71no—
193C24×C4—72no—
194C22×C4⋊C4—71no—
195C22×C4⋊C4C2×D711yescharacteristic
196C22×C4⋊C4C2×D711yescharacteristic
197C22×C22⋊C4—72no—
198C22×C22⋊C4—72no—
199C22×C22⋊C4—72no—
200C22×C22⋊C4—72no—
201C22×C22⋊C4—72no—
202C22×C42—71no—
203#390—78no—
204#386—148no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—71no—
210C2×#95—72no—
211C2×#95—72no—
212C2×#95C2×D712yes—
213C2×#95C2×D711yescharacteristic
214C2×#95C2×D712yes—
215C23×C7C23×C411yescharacteristic
216C23×C7C22×D411yescharacteristic
217C23×C7C22×Q811yescharacteristic
218C23×C7C2×#4112yes—
219C23×C7C2×#4112yes—
220C23×C7H(5,𝔽2)11yescharacteristic
221C23×C7H(5,𝔽2)11yescharacteristic
222C23×C7H(5,𝔽2)12yes—
223C23×C7H(5,𝔽2)11yescharacteristic
224C23×C7H(5,𝔽2)11yescharacteristic
225C23×C7H(5,𝔽2)12yes—
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—24no—
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×D7—42no—
260C22×D7C2×C4⋊C418yes—
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—24no—
268C2×C4×C7—24no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—42no—
280C2×C4×C7—41no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—41no—
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×C7—42no—
291C2×C4×C7C2×C4⋊C414yes—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—24no—
297C2×Dic7—24no—
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—
312C2×Dic7—42no—
313D28—416no—
314C4×D7—432no—
315C25—72no—
316C22×D4—74no—
317C22×D4—74no—
318C22×D4—74no—
319C22×D4—281no—
320C22×D4—281no—
321C22×D4—281no—
322C22×D4—281no—
323C23×C4—72no—
324C23×C4—72no—
325C23×C4—72no—
326C23×C4—144no—
327C23×C4—144no—
328C23×C4—144no—
329C23×C4—282no—
330C23×C4—282no—
331C23×C4—282no—
332C23×C4—282no—
333C23×C4C22×D712yes—
334C23×C4C22×D711yescharacteristic
335C23×C4C22×D711yescharacteristic
336C23×C4C22×D712yes—
337C23×C4C22×D711yescharacteristic
338C2×C4⋊C4—41no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—281no—
343C2×C4⋊C4—282no—
344C2×C4⋊C4C4×D714yescomplemented
345C2×C22⋊C4—78no—
346C2×C22⋊C4—78no—
347C2×C22⋊C4—144no—
348C2×C22⋊C4—144no—
349C2×C22⋊C4—144no—
350C2×C22⋊C4—144no—
351C2×C22⋊C4—144no—
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×C22⋊C4—282no—
359C2×C22⋊C4—282no—
360C2×C42—74no—
361C2×C42—281no—
362C2×C42—281no—
363#95—24no—
364#95—42no—
365#95—41no—
366#95—144no—
367#95—144no—
368#95—144no—
369#95—281no—
370#95—282no—
371#95—282no—
372#95—282no—
373C22×C7C22×C4⋊C411yescharacteristic
374C22×C7C4×#4112yes—
375C22×C7#51811yescharacteristic
376C22×C7#51811yescharacteristic
377C22×C7#51812yes—
378C22×C7#53411yescharacteristic
379C22×C7#53411yescharacteristic
380C22×C7#53812yes—
381C22×C7#53812yes—
382C22×C7#54012yes—
383C22×C7#54012yes—
384C22×C7#54311yescharacteristic
385C22×C7#54311yescharacteristic
386C22×C7#54612yes—
387C22×C7#54612yes—
388C22×C7#55112yes—
389C22×C7#55412yes—
390C22×C7#55412yes—
391C22×C7#55511yescharacteristic
392C22×C7#55511yescharacteristic
393C22×C7#56011yescharacteristic
394C22×C7#56012yes—
395C22×C7#56011yescharacteristic
396C2×D7—28no—
397C2×D7—28no—
398C2×D7—28no—
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—
410C2×D7—44no—
411C4×C7—24no—
412C4×C7—42no—
413C4×C7—42no—
414C4×C7—44no—
415C4×C7—82no—
416Dic7—44no—
417Dic7—44no—
418Dic7—82no—
419C24—74no—
420C24—74no—
421C24—74no—
422C24—142no—
423C24—142no—
424C24—142no—
425C24—142no—
426C24—142no—
427C24—142no—
428C24—142no—
429C24—142no—
430C24—142no—
431C24—142no—
432C24—142no—
433C24—142no—
434C24C23×D711yescharacteristic
435C2×D4—716no—
436C2×D4—284no—
437C2×D4—284no—
438C2×D4—284no—
439C2×D4—284no—
440C2×D4—284no—
441C2×D4—284no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
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—22no—
467C22×C4—74no—
468C22×C4—74no—
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—142no—
488C22×C4—288no—
489C22×C4—288no—
490C22×C4—288no—
491C22×C4—288no—
492C22×C4—288no—
493C22×C4—288no—
494C22×C4—288no—
495C22×C4C2×C4×D712yes—
496C22×C4C2×C4×D712yes—
497C22×C4C2×C4×D712yes—
498C22×C4D4×D712yes—
499C22×C4Q8×D712yes—
500C22×C4#116114yes—
501C4⋊C4—44no—
502C4⋊C4—44no—
503C4⋊C4—284no—
504C22⋊C4—288no—
505C22⋊C4—288no—
506C22⋊C4—288no—
507C22⋊C4—288no—
508C22⋊C4—288no—
509C42—284no—
510C2×C7#231511yescharacteristic
511C2×C7#233312yes—
512C2×C7#234912yes—
513C2×C7#237211yescharacteristic
514C2×C7#238011yescharacteristic
515C2×C7#269712yes—
516C2×C7#269911yescharacteristic
517C2×C7#269911yescharacteristic
518C2×C7#274812yes—
519C2×C7#278411yescharacteristic
520C2×C7#278411yescharacteristic
521D7—48no—
522C23—78no—
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—144no—
540C23—144no—
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—
555C23—282no—
556C23—282no—
557C23C22×C4×D711yescharacteristic
558C23C2×D4×D711yescharacteristic
559C23#654812yes—
560C23#654811yescharacteristic
561C23#654811yescharacteristic
562C23C2×Q8×D711yescharacteristic
563C23C2×#116112yes—
564C23D7×#4112yes—
565C23#655312yes—
566C23#655311yescharacteristic
567C23#655311yescharacteristic
568D4—2816no—
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—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—144no—
600C2×C4—144no—
601C2×C4—144no—
602C2×C4—144no—
603C2×C4—144no—
604C2×C4—144no—
605C2×C4—2832no—
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×C4—282no—
620C2×C4—282no—
621C2×C4D7×C4⋊C414yes—
622C7#1448611yescharacteristic, complemented, Sylow
623C22—148no—
624C22—148no—
625C22—148no—
626C22—284no—
627C22—284no—
628C22—284no—
629C22—284no—
630C22—284no—
631C22—284no—
632C22—284no—
633C22—284no—
634C22—284no—
635C22—284no—
636C22—284no—
637C22—284no—
638C22#9017711yescharacteristic
639C22C2×D7×C4⋊C411yescharacteristic
640C22#9021211yescharacteristic
641C22#9023612yes—
642C22C4×#116112yes—
643C22#9028611yescharacteristic
644C22#9029611yescharacteristic
645C22#9029611yescharacteristic
646C22#9030312yes—
647C22#9031112yes—
648C22#9032112yes—
649C22#9032511yescharacteristic
650C22#9032511yescharacteristic
651C22#9032812yes—
652C22#9033512yes—
653C22#9035412yes—
654C22#9035711yescharacteristic
655C22#9036111yescharacteristic
656C22#9038112yes—
657C22#9038912yes—
658C22#9039512yes—
659C22#9042112yes—
660C22#9042511yescharacteristic
661C4—24no—
662C4—44no—
663C4—42no—
664C4—42no—
665C4—82no—
666C4—284no—
667C4—284no—
668C4—562no—
669C2—288no—
670C2#1173145011yescharacteristic
671C2#1173213011yescharacteristic
672C2#1173239712yes—
673C2#1173364812yes—
674C2#1173394011yescharacteristic
675C2#1173459211yescharacteristic
676C2#1173471711yescharacteristic
677C2#1173488212yes—
678C2#1173542311yescharacteristic
679C2#1173544112yes—
680C2#1173573711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenter#1441D7
hypocenterC7#14486
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C7×#1441C2semidirect
4. #11729324C2semidirect
5. #11729319C2semidirect
6. #11727181C2semidirect
7. (C2×D7)⋊#95C2semidirect
8. (C2×D7)⋊#95C2semidirect
9. #11727157C2semidirect
31. #89760C4semidirect
61. C2×C7×C4⋊C4C2×C4semidirect
75. C2×(C2×D7)⋊C4C2×C4semidirect
76. C2×(C2×D7)⋊C4C2×C4semidirect
81. C2×C4×Dic7C2×C4semidirect
95. #1441D7semidirect
175. C2×D28C4⋊C4semidirect
344. C2×C4⋊C4C4×D7semidirect
622. C7#14486semidirect

Maximal subgroups

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

subgroupindex
C2×#897602
C2×#894372
C7×#14412
#117293242
#117293192
#117271812
(C2×D7)⋊#952
#117271572
#144867