Finite Group Databasebeta

← #13284078

Subgroups — #13284078

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#394C211yesmaximal, characteristic
2C2×#89723C212yesmaximal, complemented
3#11729885C212yesmaximal
4#11729319C211yesmaximal, characteristic, complemented
5#11729317C211yesmaximal, characteristic, complemented
6#11729300C212yesmaximal, complemented
7#11729299C212yesmaximal, complemented
8#11729299C212yesmaximal, complemented
9#11727155C212yesmaximal, complemented
10C23×C7×D4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C22⋊C4C2212yes—
13C22×C7×C22⋊C4C2212yes—
14C22×C22⋊Dic7C2212yes—
15C22×C22⋊Dic7C2212yes—
16C22×C22⋊Dic7C2212yes—
17C22×C22⋊Dic7C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4×Dic7C2212yes—
21C22×C4×Dic7C2211yescharacteristic
22C7×#394C418yescomplemented
23C2×C7×#95C2211yescharacteristic
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32#89723—28no—
33#14589—71nomaximal, Sylow
34C25×C7C2312yes—
35C22×C7×D4—42no—
36C22×C7×D4—42no—
37C22×C7×D4—41no—
38C22×C7×D4—41no—
39C22×C7×D4C2×C414yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2312yes—
45C23×Dic7C2312yes—
46C23×Dic7C2312yes—
47C23×Dic7C2312yes—
48C2×C7×C4⋊C4—41no—
49C2×C7×C4⋊C4—41no—
50C2×C7×C4⋊C4C2×C414yes—
51C2×C7×C22⋊C4—24no—
52C2×C7×C22⋊C4—24no—
53C2×C7×C22⋊C4—42no—
54C2×C7×C22⋊C4—42no—
55C2×C7×C22⋊C4C2×C418yes—
56C2×C7×C22⋊C4C2×C418yes—
57C2×C22⋊Dic7—24no—
58C2×C22⋊Dic7—24no—
59C2×C22⋊Dic7—24no—
60C2×C22⋊Dic7—24no—
61C2×C22⋊Dic7—24no—
62C2×C22⋊Dic7—24no—
63C2×C22⋊Dic7—42no—
64C2×C22⋊Dic7—42no—
65C2×C22⋊Dic7—42no—
66C2×C22⋊Dic7—42no—
67C2×C22⋊Dic7—42no—
68C2×C22⋊Dic7—42no—
69C2×C4⋊Dic7—41no—
70C2×C4⋊Dic7—41no—
71C2×C4⋊Dic7—42no—
72C2×C4⋊Dic7—41no—
73C2×C4⋊Dic7D414yescomplemented
74C2×C4×Dic7—22no—
75C2×C4×Dic7—24no—
76C2×C4×Dic7—24no—
77C2×C4×Dic7—42no—
78C2×C4×Dic7—41no—
79C2×C4×Dic7—41no—
80C7×#95C2×C414yes—
81C7⋊#95—24no—
82C7⋊#95—24no—
83C7⋊#95—24no—
84C7⋊#95—42no—
85C7⋊#95—42no—
86C7⋊#95—42no—
87C7⋊#95—42no—
88C7⋊#95—41no—
89C2×#394D711yescharacteristic
90C2×#388—72no—
91#1441—71no—
92#1439—72no—
93#1438—72no—
94#1437—72no—
95#1437—72no—
96C4⋊#95—71no—
97#1434—72no—
98C24×C7—22no—
99C24×C7—22no—
100C24×C7—22no—
101C24×C7—22no—
102C24×C7—22no—
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—22no—
106C24×C7—22no—
107C24×C7—22no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7C22×C414yes—
113C24×C7C2411yescharacteristic
114C2×C7×D4—44no—
115C2×C7×D4—48no—
116C2×C7×D4—44no—
117C2×C7×D4—48no—
118C2×C7×D4—44no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—21no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7C22×C414yes—
138C22×C4×C7C22×C412yes—
139C22×C4×C7C22×C412yes—
140C22×C4×C7C22×C412yes—
141C22×C4×C7C2×D412yes—
142C22×C4×C7#4112yes—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
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×Dic7—22no—
168C22×Dic7C2×D414yes—
169C22×Dic7#4114yes—
170C22×Dic7#4114yes—
171C7×C4⋊C4—44no—
172C7×C22⋊C4—216no—
173C7×C22⋊C4—48no—
174C22⋊Dic7—48no—
175C22⋊Dic7—48no—
176C22⋊Dic7—48no—
177C22⋊Dic7—48no—
178C4⋊Dic7—44no—
179C4⋊Dic7—44no—
180C4×Dic7—48no—
181C4×Dic7—44no—
182C23×D4C2×D711yescharacteristic
183C22×C4⋊C4—71no—
184C22×C4⋊C4—71no—
185C22×C4⋊C4C2×D711yescharacteristic
186C22×C22⋊C4—72no—
187C22×C22⋊C4—72no—
188C22×C22⋊C4—72no—
189C22×C22⋊C4—72no—
190C22×C22⋊C4C2×D712yes—
191C22×C22⋊C4C2×D712yes—
192C22×C42—72no—
193C22×C42—71no—
194#394Dic718yescomplemented
195#388—148no—
196C2×#95—72no—
197C2×#95—72no—
198C2×#95—72no—
199C2×#95—72no—
200C2×#95—72no—
201C2×#95—72no—
202C2×#95—72no—
203C2×#95—71no—
204C2×#95C2×D711yescharacteristic
205C23×C7—24no—
206C23×C7—24no—
207C23×C7—24no—
208C23×C7—24no—
209C23×C7—24no—
210C23×C7—24no—
211C23×C7—24no—
212C23×C7—42no—
213C23×C7—42no—
214C23×C7—42no—
215C23×C7—42no—
216C23×C7—42no—
217C23×C7—42no—
218C23×C7—42no—
219C23×C7—42no—
220C23×C7—42no—
221C23×C7—42no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—42no—
229C23×C7—42no—
230C23×C7—42no—
231C23×C7—42no—
232C23×C7—42no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7C23×C411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C2×#4111yescharacteristic
243C23×C7C2×#4112yes—
244C23×C7C2×#4112yes—
245C23×C7H(5,𝔽2)11yescharacteristic
246C23×C7H(5,𝔽2)11yescharacteristic
247C23×C7H(5,𝔽2)12yes—
248C23×C7H(5,𝔽2)12yes—
249C23×C7H(5,𝔽2)11yescharacteristic
250C23×C72−1+411yescharacteristic
251C7×D4—416no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—24no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—41no—
270C2×C4×C7—42no—
271C2×C4×C7—41no—
272C2×C4×C7—42no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7C4×D414yes—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—24no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
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×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303C2×Dic7—42no—
304C25C22×D712yes—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4—41no—
308C22×D4—41no—
309C22×D4C2×Dic714yes—
310C23×C4—72no—
311C23×C4—72no—
312C23×C4—72no—
313C23×C4—72no—
314C23×C4C22×D711yescharacteristic
315C23×C4C22×D712yes—
316C23×C4C22×D711yescharacteristic
317C23×C4C22×D711yescharacteristic
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—74no—
321C2×C4⋊C4—281no—
322C2×C4⋊C4—281no—
323C2×C4⋊C4—282no—
324C2×C4⋊C4—281no—
325C2×C4⋊C4C2×Dic714yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—144no—
331C2×C22⋊C4—144no—
332C2×C22⋊C4—144no—
333C2×C22⋊C4—144no—
334C2×C22⋊C4—144no—
335C2×C22⋊C4—144no—
336C2×C22⋊C4—282no—
337C2×C22⋊C4—282no—
338C2×C22⋊C4—282no—
339C2×C22⋊C4—282no—
340C2×C22⋊C4—282no—
341C2×C22⋊C4—282no—
342C2×C22⋊C4C2×Dic718yes—
343C2×C22⋊C4C2×Dic718yes—
344C2×C42—144no—
345C2×C42—144no—
346C2×C42—142no—
347C2×C42—281no—
348C2×C42—281no—
349C2×C42—282no—
350#95—144no—
351#95—144no—
352#95—144no—
353#95—282no—
354#95—282no—
355#95—281no—
356#95—282no—
357#95—282no—
358#95C2×Dic714yes—
359C22×C7—44no—
360C22×C7—44no—
361C22×C7—44no—
362C22×C7—44no—
363C22×C7—44no—
364C22×C7—44no—
365C22×C7—44no—
366C22×C7—82no—
367C22×C7—82no—
368C22×C7—82no—
369C22×C7—82no—
370C22×C7—82no—
371C22×C7—82no—
372C22×C7—82no—
373C22×C7—82no—
374C22×C7C2×C4×D411yescharacteristic
375C22×C7C4×#4112yes—
376C22×C7#51811yescharacteristic
377C22×C7#51812yes—
378C22×C7#52011yescharacteristic
379C22×C7#53411yescharacteristic
380C22×C7#53711yescharacteristic
381C22×C7#53811yescharacteristic
382C22×C7#53812yes—
383C22×C7#53911yescharacteristic
384C22×C7#53912yes—
385C22×C7#54012yes—
386C22×C7#54212yes—
387C22×C7#54612yes—
388C22×C7#55012yes—
389C22×C7#55112yes—
390C22×C7#55312yes—
391C22×C7#55512yes—
392C22×C7#55511yescharacteristic
393C22×C7#55511yescharacteristic
394C22×C7#56011yescharacteristic
395C22×C7#56012yes—
396C22×C7H(3,𝔽4)11yescharacteristic
397C4×C7—24no—
398C4×C7—44no—
399C4×C7—42no—
400C4×C7—42no—
401Dic7—44no—
402Dic7—44no—
403Dic7—44no—
404Dic7—82no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24C22×Dic714yes—
420C24C23×D711yescharacteristic
421C2×D4—44no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—48no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—74no—
445C22×C4—74no—
446C22×C4—74no—
447C22×C4—142no—
448C22×C4—142no—
449C22×C4—142no—
450C22×C4—142no—
451C22×C4—142no—
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—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4D4×D712yes—
473C22×C4#115912yes—
474C22×C4C22×Dic714yes—
475C22×C4C22×Dic712yes—
476C22×C4C22×Dic712yes—
477C22×C4C22×Dic712yes—
478C4⋊C4—44no—
479C4⋊C4—284no—
480C4⋊C4—284no—
481C22⋊C4—216no—
482C22⋊C4—48no—
483C22⋊C4—288no—
484C22⋊C4—288no—
485C22⋊C4—288no—
486C22⋊C4—288no—
487C42—284no—
488C42—288no—
489C2×C7—84no—
490C2×C7#232511yescharacteristic
491C2×C7#233512yes—
492C2×C7#236312yes—
493C2×C7#237211yescharacteristic
494C2×C7#237511yescharacteristic
495C2×C7#269911yescharacteristic
496C2×C7#270512yes—
497C2×C7#273311yescharacteristic
498C2×C7#275612yes—
499C2×C7#278511yescharacteristic
500C2×C7#279511yescharacteristic
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23C2×D4×D711yescharacteristic
537C23C2×#115911yescharacteristic
538C23#654811yescharacteristic
539C23#654812yes—
540C23#654811yescharacteristic
541C23#654812yes—
542C23D7×#4112yes—
543C23D7×#4112yes—
544C23#655311yescharacteristic
545C23#655411yescharacteristic
546C23C23×Dic711yescharacteristic
547D4—416no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—144no—
572C2×C4—144no—
573C2×C4—144no—
574C2×C4—144no—
575C2×C4—144no—
576C2×C4—144no—
577C2×C4—144no—
578C2×C4—144no—
579C2×C4—144no—
580C2×C4—282no—
581C2×C4—282no—
582C2×C4—282no—
583C2×C4—282no—
584C2×C4—282no—
585C2×C4—282no—
586C2×C4—282no—
587C2×C4—282no—
588C2×C4—282no—
589C2×C4—282no—
590C2×C4—282no—
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×C4D4×Dic714yes—
600C7#1458911yescharacteristic, complemented, Sylow
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22#9028511yescharacteristic
617C22#9028611yescharacteristic
618C22#9028612yes—
619C22#9028811yescharacteristic
620C22#9029012yes—
621C22#9029311yescharacteristic
622C22#9029611yescharacteristic
623C22#9030312yes—
624C22#9030512yes—
625C22#9030712yes—
626C22#9030811yescharacteristic
627C22#9034812yes—
628C22#9035112yes—
629C22#9035312yes—
630C22#9035412yes—
631C22#9036111yescharacteristic
632C22#9036111yescharacteristic
633C22#9037012yes—
634C22C2×D4×Dic711yescharacteristic
635C22#9048912yes—
636C22#9048911yescharacteristic
637C22#41×Dic712yes—
638C22#9051811yescharacteristic
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—284no—
644C4—284no—
645C4—284no—
646C4—562no—
647C2—84no—
648C2#1173447012yes—
649C2#1173449211yescharacteristic
650C2#1173450612yes—
651C2#1173451511yescharacteristic
652C2#1173451711yescharacteristic
653C2#1173459211yescharacteristic
654C2#1174002511yescharacteristic
655C2#1174007911yescharacteristic
656C2#1174008212yes—
657C2#1174028212yes—
658C2#1174040111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#394C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#394D7
hypocenterC7#14589
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#89723C2semidirect
4. #11729319C2semidirect
5. #11729317C2semidirect
6. #11729300C2semidirect
7. #11729299C2semidirect
8. #11729299C2semidirect
9. #11727155C2semidirect
22. C7×#394C4semidirect
73. C2×C4⋊Dic7D4semidirect
194. #394Dic7semidirect
600. C7#14589semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×#897232
#117298852
#117293192
#117293172
#117293002
#117292992
#117271552
#145897