Finite Group Databasebeta

← #13280783

Subgroups — #13280783

Order 1792.

1622 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#393C211yesmaximal, characteristic
2C2×#90002C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic7C211yesmaximal, characteristic
4#11729888C211yesmaximal, characteristic, complemented
5#11729300C212yesmaximal
6#11729300C211yesmaximal, characteristic
7#11729298C212yesmaximal
8#11727173C211yesmaximal, characteristic, complemented
9#11727170C212yesmaximal, complemented
10#11727161C212yesmaximal, complemented
11#11727155C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C22×C7×C22⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C4⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C7×#393C418yescomplemented
23C2×C7×#95C2211yescharacteristic
24C2×C7×#95C2212yes—
25#90002—24no—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C22⋊C4×Dic7—24no—
38#14319—71nomaximal, Sylow
39C25×C7C2311yescharacteristic
40C22×C7×Q8—22no—
41C22×C7×Q8—22no—
42C22×C7×Q8—42no—
43C22×C7×Q8—42no—
44C22×C7×Q8C2×C414yescomplemented
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×Dic7—22no—
50C23×Dic7—22no—
51C23×Dic7—42no—
52C23×Dic7—42no—
53C23×Dic7Q814yescomplemented
54C23×Dic7C2312yes—
55C23×Dic7C2312yes—
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2311yescharacteristic
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2311yescharacteristic
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—22no—
62C2×C7×C22⋊C4—42no—
63C2×C7×C22⋊C4—42no—
64C2×C7×C22⋊C4C2×C414yes—
65C2×C7×C22⋊C4C2×C418yes—
66C2×C22⋊Dic7—22no—
67C2×C22⋊Dic7—22no—
68C2×C22⋊Dic7—22no—
69C2×C22⋊Dic7—24no—
70C2×C22⋊Dic7—42no—
71C2×C22⋊Dic7—42no—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7—24no—
74C2×C4⋊Dic7—42no—
75C2×C4⋊Dic7—42no—
76C2×C4⋊Dic7—42no—
77C2×C4×Dic7—22no—
78C2×C4×Dic7—42no—
79C2×C4×Dic7—42no—
80C2×C4×Dic7D414yes—
81C7×#95C2×C418yescomplemented
82C7×#95C2×C414yescomplemented
83C7⋊#95—22no—
84C7⋊#95—22no—
85C7⋊#95—22no—
86C7⋊#95—24no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—42no—
90C7⋊#95—42no—
91C7⋊#95—42no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C2×#393D711yescharacteristic
95C2×#391—71no—
96C2×C4×C22⋊C4—71no—
97#1446—71no—
98#1444—71no—
99#1443—72no—
100#1439—72no—
101#1439—71no—
102#1436—72no—
103#1434—71no—
104C22⋊#95—72no—
105C24×C7—21no—
106C24×C7—21no—
107C24×C7—21no—
108C24×C7—21no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7—22no—
113C24×C7C22×C412yes—
114C24×C7C2×Q812yes—
115C24×C7#4112yes—
116C24×C7C2411yescharacteristic
117C2×C7×Q8—28no—
118C2×C7×Q8—48no—
119C2×C7×Q8—44no—
120C2×C7×Q8—44no—
121C2×C7×Q8—48no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—21no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
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×C7C22×C412yes—
141C22×C4×C7C22×C414yes—
142C22×C4×C7C22×C414yes—
143C22×C4×C7C22×C412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7#4112yes—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
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—28no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—48no—
176C22×Dic7—44no—
177C22×Dic7—44no—
178C22×Dic7—48no—
179C22×Dic7C2×D412yes—
180C22×Dic7C2×D412yes—
181C22×Dic7C2×Q812yes—
182C22×Dic7C2×Q812yes—
183C22×Dic7#4112yes—
184C22×Dic7#4112yes—
185C7×C22⋊C4—28no—
186C7×C22⋊C4—48no—
187C22⋊Dic7—28no—
188C22⋊Dic7—48no—
189C4⋊Dic7—48no—
190C4⋊Dic7—44no—
191C4×Dic7—44no—
192C4×Dic7—44no—
193C23×Q8C2×D711yescharacteristic
194C24×C4—71no—
195C22×C4⋊C4—72no—
196C22×C4⋊C4—71no—
197C22×C22⋊C4—71no—
198C22×C22⋊C4—72no—
199C22×C22⋊C4C2×D711yescharacteristic
200C22×C22⋊C4C2×D712yes—
201C22×C42—71no—
202C22×C42—71no—
203#393Dic718yescomplemented
204#391—144no—
205C4×C22⋊C4—144no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—71no—
209C2×#95—72no—
210C2×#95—71no—
211C2×#95—71no—
212C2×#95—72no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95C2×D711yescharacteristic
218C2×#95C2×D712yes—
219C23×C7—22no—
220C23×C7—22no—
221C23×C7—24no—
222C23×C7—24no—
223C23×C7—22no—
224C23×C7—22no—
225C23×C7—22no—
226C23×C7—22no—
227C23×C7—24no—
228C23×C7—24no—
229C23×C7—24no—
230C23×C7—24no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—41no—
234C23×C7—41no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7—42no—
241C23×C7C4×Q814yes—
242C23×C7C23×C411yescharacteristic
243C23×C7C22×D411yescharacteristic
244C23×C7C22×Q811yescharacteristic
245C23×C7C2×#4111yescharacteristic
246C23×C7C2×#4111yescharacteristic
247C23×C7C2×#4111yescharacteristic
248C23×C7C2×#4111yescharacteristic
249C23×C7H(5,𝔽2)12yes—
250C23×C7H(5,𝔽2)12yes—
251C23×C7H(5,𝔽2)12yes—
252C23×C72−1+412yes—
253C7×Q8—416no—
254C2×C4×C7—24no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—42no—
267C2×C4×C7—41no—
268C2×C4×C7—42no—
269C2×C4×C7—41no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7C4×D414yes—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—24no—
288C2×Dic7—24no—
289C2×Dic7—416no—
290C2×Dic7—41no—
291C2×Dic7—41no—
292C2×Dic7—41no—
293C2×Dic7—41no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
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—
312C2×Dic7C22⋊Q814yes—
313C25C22×D711yescharacteristic
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—42no—
317C22×Q8—42no—
318C22×Q8C2×Dic714yescomplemented
319C23×C4—71no—
320C23×C4—71no—
321C23×C4—71no—
322C23×C4—71no—
323C23×C4—74no—
324C23×C4—72no—
325C23×C4—72no—
326C23×C4—142no—
327C23×C4—142no—
328C23×C4—282no—
329C23×C4—282no—
330C23×C4C22×D712yes—
331C23×C4C22×D712yes—
332C23×C4C22×D711yescharacteristic
333C23×C4C22×D711yescharacteristic
334C2×C4⋊C4—144no—
335C2×C4⋊C4—142no—
336C2×C4⋊C4—282no—
337C2×C4⋊C4—282no—
338C2×C4⋊C4—282no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—142no—
344C2×C22⋊C4—142no—
345C2×C22⋊C4—142no—
346C2×C22⋊C4—144no—
347C2×C22⋊C4—282no—
348C2×C22⋊C4—282no—
349C2×C22⋊C4C2×Dic714yes—
350C2×C22⋊C4C2×Dic718yes—
351C2×C42—74no—
352C2×C42—142no—
353C2×C42—282no—
354C2×C42—282no—
355#95—144no—
356#95—142no—
357#95—144no—
358#95—144no—
359#95—142no—
360#95—142no—
361#95—282no—
362#95—282no—
363#95—282no—
364#95—282no—
365#95—282no—
366#95C2×Dic718yescomplemented
367#95C2×Dic714yescomplemented
368C22×C7—28no—
369C22×C7—24no—
370C22×C7—42no—
371C22×C7—42no—
372C22×C7—44no—
373C22×C7—42no—
374C22×C7—42no—
375C22×C7—42no—
376C22×C7—42no—
377C22×C7—44no—
378C22×C7—44no—
379C22×C7C2×C4×D411yescharacteristic
380C22×C7C2×C4×Q811yescharacteristic
381C22×C7C4×#4111yescharacteristic
382C22×C7#51812yes—
383C22×C7#52012yes—
384C22×C7C2×C22⋊Q811yescharacteristic
385C22×C7#52511yescharacteristic
386C22×C7#52911yescharacteristic
387C22×C7#53311yescharacteristic
388C22×C7#53411yescharacteristic
389C22×C7#53511yescharacteristic
390C22×C7#53511yescharacteristic
391C22×C7#53611yescharacteristic
392C22×C7#53812yes—
393C22×C7#53812yes—
394C22×C7#53812yes—
395C22×C7#53812yes—
396C22×C7#53912yes—
397C22×C7#54212yes—
398C22×C7#54212yes—
399C22×C7#54212yes—
400C22×C7#54312yes—
401C22×C7#54412yes—
402C4×C7—24no—
403C4×C7—44no—
404C4×C7—42no—
405C4×C7—44no—
406Dic7—24no—
407Dic7—42no—
408Dic7—42no—
409Dic7—42no—
410Dic7—82no—
411Dic7—82no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24Q8×D712yes—
421C24#116112yes—
422C24C22×Dic712yes—
423C24C23×D711yescharacteristic
424C2×Q8—28no—
425C2×Q8—48no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—48no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—72no—
448C22×C4—72no—
449C22×C4—72no—
450C22×C4—72no—
451C22×C4—72no—
452C22×C4—72no—
453C22×C4—148no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—141no—
457C22×C4—141no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—141no—
462C22×C4—141no—
463C22×C4—141no—
464C22×C4—141no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—142no—
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—288no—
483C22×C4—288no—
484C22×C4—284no—
485C22×C4—284no—
486C22×C4D4×D712yes—
487C22×C4#115912yes—
488C22×C4C22×Dic712yes—
489C22×C4C22×Dic714yes—
490C22×C4C22×Dic714yes—
491C22×C4C22×Dic712yes—
492C4⋊C4—284no—
493C4⋊C4—288no—
494C22⋊C4—28no—
495C22⋊C4—48no—
496C22⋊C4—148no—
497C22⋊C4—288no—
498C42—284no—
499C42—284no—
500C2×C7—44no—
501C2×C7C4×C22⋊Q811yescharacteristic
502C2×C7#232111yescharacteristic
503C2×C7#232611yescharacteristic
504C2×C7#232912yes—
505C2×C7#233712yes—
506C2×C7#262611yescharacteristic
507C2×C7#262811yescharacteristic
508C2×C7#263111yescharacteristic
509C2×C7#263811yescharacteristic
510C2×C7#265312yes—
511C2×C7#266512yes—
512C23—22no—
513C23—24no—
514C23—22no—
515C23—24no—
516C23—22no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23Q8×Dic714yes—
535C23C2×D4×D711yescharacteristic
536C23C2×#115911yescharacteristic
537C23#654812yes—
538C23#654812yes—
539C23C2×Q8×D711yescharacteristic
540C23C2×#116111yescharacteristic
541C23D7×#4111yescharacteristic
542C23D7×#4111yescharacteristic
543C23#655312yes—
544C23#655412yes—
545C23C23×Dic711yescharacteristic
546Q8—416no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—74no—
571C2×C4—144no—
572C2×C4—142no—
573C2×C4—144no—
574C2×C4—142no—
575C2×C4—144no—
576C2×C4—142no—
577C2×C4—142no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—144no—
581C2×C4—142no—
582C2×C4—2816no—
583C2×C4—282no—
584C2×C4—281no—
585C2×C4—281no—
586C2×C4—282no—
587C2×C4—282no—
588C2×C4—282no—
589C2×C4—281no—
590C2×C4—281no—
591C2×C4—282no—
592C2×C4—282no—
593C2×C4—282no—
594C2×C4—282no—
595C2×C4—282no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—282no—
599C2×C4—282no—
600C2×C4—282no—
601C2×C4—282no—
602C2×C4—282no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4D4×Dic714yes—
606C7#1431911yescharacteristic, complemented, Sylow
607C22—24no—
608C22—28no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22—44no—
617C22—44no—
618C22#9028011yescharacteristic
619C22#9028311yescharacteristic
620C22#9028412yes—
621C22#9031311yescharacteristic
622C22#9031412yes—
623C22#9031511yescharacteristic
624C22D7×C22⋊Q811yescharacteristic
625C22#9031811yescharacteristic
626C22#9032512yes—
627C22#9033512yes—
628C22#9033612yes—
629C22#9036012yes—
630C22#9036012yes—
631C22#9036511yescharacteristic
632C22#9036611yescharacteristic
633C22#9036912yes—
634C22#9036912yes—
635C22#9037312yes—
636C22C2×D4×Dic711yescharacteristic
637C22#9048912yes—
638C22C2×Q8×Dic711yescharacteristic
639C22#41×Dic711yescharacteristic
640C22#9051812yes—
641C4—24no—
642C4—44no—
643C4—42no—
644C4—44no—
645C4—144no—
646C4—282no—
647C4—282no—
648C4—282no—
649C4—562no—
650C4—562no—
651C2—44no—
652C2#1173425511yescharacteristic
653C2#1173425611yescharacteristic
654C2#1173425911yescharacteristic
655C2#1173426312yes—
656C2#1173426612yes—
657C2#1173431611yescharacteristic
658C2#1174002311yescharacteristic
659C2Dic7×C22⋊Q811yescharacteristic
660C2#1174019012yes—
661C2#1174039811yescharacteristic
662C2#1174039912yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#393C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#393D7
hypocenterC7#14319
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
2. C2×#90002C2semidirect
4. #11729888C2semidirect
8. #11727173C2semidirect
9. #11727170C2semidirect
10. #11727161C2semidirect
11. #11727155C2semidirect
22. C7×#393C4semidirect
44. C22×C7×Q8C2×C4semidirect
53. C23×Dic7Q8semidirect
81. C7×#95C2×C4semidirect
82. C7×#95C2×C4semidirect
203. #393Dic7semidirect
318. C22×Q8C2×Dic7semidirect
366. #95C2×Dic7semidirect
367. #95C2×Dic7semidirect
606. C7#14319semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3932
C2×#900022
C2×C22⋊C4×Dic72
#117298882
#117293002
#117292982
#117271732
#117271702
#117271612
#117271552
#143197