Finite Group Databasebeta

← #13276366

Subgroups — #13276366

Order 1792.

1846 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6489C211yesmaximal, characteristic
2C2×#89716C212yesmaximal
3C7×C22⋊#95C211yesmaximal, characteristic
4#11729881C211yesmaximal, characteristic
5#11729303C212yesmaximal
6#11727165C212yesmaximal, complemented
7#11727161C212yesmaximal, complemented
8Dic7⋊#95C211yesmaximal, characteristic, complemented
9#11727157C211yesmaximal, characteristic, complemented
10#11727155C211yesmaximal, characteristic, complemented
11Dic7×#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C22⋊C4C2212yes—
14C22×C22⋊Dic7C2212yes—
15C22×C22⋊Dic7C2211yescharacteristic
16C22×C22⋊Dic7C2211yescharacteristic
17C2×#6489—28no—
18C2×#6489C418yescomplemented
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×C4×Dic7C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37#89716—28no—
38#13943—71nomaximal, Sylow
39C25×C7C2311yescharacteristic
40C23×C4×C7—24no—
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—24no—
44C23×C4×C7C2×C414yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2312yes—
53C23×Dic7C2311yescharacteristic
54C23×Dic7C2311yescharacteristic
55C2×C7×C22⋊C4—24no—
56C2×C7×C22⋊C4—24no—
57C2×C7×C22⋊C4—42no—
58C2×C22⋊Dic7—24no—
59C2×C22⋊Dic7—24no—
60C2×C22⋊Dic7—24no—
61C2×C22⋊Dic7—42no—
62C2×C22⋊Dic7C2×C414yes—
63C2×C22⋊Dic7C2×C414yes—
64C2×C22⋊Dic7D418yes—
65#6489—232no—
66C2×C4⋊Dic7—24no—
67C2×C4⋊Dic7—24no—
68C2×C4⋊Dic7C2×C414yes—
69C2×C4⋊Dic7C2×C414yes—
70C2×Dic7⋊C4—24no—
71C2×Dic7⋊C4—24no—
72C2×Dic7⋊C4—42no—
73C2×C4×Dic7—24no—
74C2×C4×Dic7—24no—
75C2×C4×Dic7—24no—
76C2×C4×Dic7—24no—
77C2×C4×Dic7—42no—
78C2×C4×Dic7C2×C414yes—
79C2×C4×Dic7C2×C414yes—
80C7×#95—22no—
81C7×#95—24no—
82C7×#95—22no—
83C7⋊#95—24no—
84C7⋊#95—22no—
85C7⋊#95—24no—
86C7⋊#95—22no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—42no—
91C7⋊#95—42no—
92C22×#117—71no—
93C2×#388—72no—
94#1441—72no—
95#1440—72no—
96#1436—72no—
97C4⋊#95—71no—
98#1434—71no—
99#1434—71no—
100C22⋊#95—71no—
101C22⋊#95D711yescharacteristic
102C4×#95—71no—
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—21no—
106C24×C7—21no—
107C24×C7—22no—
108C24×C7—21no—
109C24×C7—21no—
110C24×C7—21no—
111C24×C7—21no—
112C24×C7C22×C412yes—
113C24×C7C2×D414yes—
114C24×C7C2411yescharacteristic
115C22×C4×C7—216no—
116C22×C4×C7—216no—
117C22×C4×C7—28no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—22no—
123C22×C4×C7—28no—
124C22×C4×C7—28no—
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—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7C22×C412yes—
139C22×C4×C7C22×C412yes—
140C22×C4×C7#4114yes—
141C22×C4×C7#4112yes—
142C22×C4×C7#4112yes—
143C22×C4×C7#4114yes—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—21no—
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
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—21no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7C22×C412yes—
172C22×Dic7C22×C412yes—
173C22×Dic7C22×C412yes—
174C22×Dic7C22×C412yes—
175C22×Dic7C2×D414yes—
176C22×Dic7C2×D414yes—
177C22×Dic7#4114yes—
178C7×C22⋊C4—48no—
179C22⋊Dic7—28no—
180C22⋊Dic7—48no—
181C22⋊Dic7C22⋊C4116yes—
182C4⋊Dic7—28no—
183C4⋊Dic7—28no—
184Dic7⋊C4—48no—
185C4×Dic7—28no—
186C4×Dic7—28no—
187C4×Dic7—48no—
188C24×C4C2×D711yescharacteristic
189C2×#117—78no—
190C2×#117—148no—
191C22×C4⋊C4—71no—
192C22×C4⋊C4—71no—
193C22×C4⋊C4—72no—
194C22×C22⋊C4—71no—
195C22×C22⋊C4—71no—
196C22×C22⋊C4—72no—
197C22×C22⋊C4C2×D712yes—
198C22×C42—71no—
199C22×C42—71no—
200C22×C42—72no—
201#388—148no—
202C2×#95—71no—
203C2×#95—72no—
204C2×#95—71no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—72no—
210C2×#95—72no—
211C2×#95C2×D711yescharacteristic
212C2×#95C2×D711yescharacteristic
213C2×#95C2×D712yes—
214C23×C7—22no—
215C23×C7—22no—
216C23×C7—22no—
217C23×C7—22no—
218C23×C7—22no—
219C23×C7—22no—
220C23×C7—24no—
221C23×C7—24no—
222C23×C7—24no—
223C23×C7—24no—
224C23×C7—24no—
225C23×C7—24no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—41no—
229C23×C7—41no—
230C23×C7—41no—
231C23×C7—41no—
232C23×C7—42no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7C2×C22⋊C414yes—
237C23×C7C23×C411yescharacteristic
238C23×C7C22×D412yes—
239C23×C7C2×#4112yes—
240C23×C7C2×#4111yescharacteristic
241C23×C7C2×#4111yescharacteristic
242C23×C7C2×#4112yes—
243C23×C7C2×#4112yes—
244C23×C7H(5,𝔽2)11yescharacteristic
245C23×C7H(5,𝔽2)11yescharacteristic
246C23×C72−1+411yescharacteristic
247C23×C72−1+411yescharacteristic
248C2×C4×C7—232no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—42no—
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×C7#11714yes—
272C2×C4×C7#11714yes—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—24no—
280C2×Dic7—24no—
281C2×Dic7—22no—
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—24no—
288C2×Dic7—24no—
289C2×Dic7—24no—
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—
304C2×Dic7—42no—
305C2×Dic7C2×C22⋊C414yes—
306C2×Dic7C2×C22⋊C414yes—
307C25C22×D711yescharacteristic
308C23×C4—24no—
309C23×C4—22no—
310C23×C4—24no—
311C23×C4—22no—
312C23×C4—71no—
313C23×C4—71no—
314C23×C4—71no—
315C23×C4—71no—
316C23×C4—72no—
317C23×C4—72no—
318C23×C4C4×D714yes—
319C23×C4C22×D712yes—
320C23×C4C22×D712yes—
321C23×C4C22×D711yescharacteristic
322C23×C4C22×D711yescharacteristic
323#117—1432no—
324C2×C4⋊C4—74no—
325C2×C4⋊C4—74no—
326C2×C4⋊C4—144no—
327C2×C4⋊C4—144no—
328C2×C4⋊C4—144no—
329C2×C4⋊C4—144no—
330C2×C4⋊C4—282no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—74no—
335C2×C22⋊C4—78no—
336C2×C22⋊C4—74no—
337C2×C22⋊C4—144no—
338C2×C22⋊C4—144no—
339C2×C22⋊C4—144no—
340C2×C22⋊C4—282no—
341C2×C42—74no—
342C2×C42—74no—
343C2×C42—144no—
344C2×C42—144no—
345C2×C42—144no—
346C2×C42—144no—
347C2×C42—282no—
348#95—22no—
349#95—24no—
350#95—22no—
351#95—144no—
352#95—144no—
353#95—144no—
354#95—144no—
355#95—142no—
356#95—144no—
357#95—142no—
358#95—282no—
359#95—282no—
360C22×C7—24no—
361C22×C7—24no—
362C22×C7—24no—
363C22×C7—42no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7—44no—
367C22×C7—44no—
368C22×C7—44no—
369C22×C7—44no—
370C22×C7—42no—
371C22×C7C22×C22⋊C411yescharacteristic
372C22×C7C2×#11711yescharacteristic
373C22×C7C2×#11711yescharacteristic
374C22×C7C4×#4111yescharacteristic
375C22×C7C4×#4111yescharacteristic
376C22×C7#52011yescharacteristic
377C22×C7#52011yescharacteristic
378C22×C7#52512yes—
379C22×C7#52512yes—
380C22×C7#52912yes—
381C22×C7#52912yes—
382C22×C7#54011yescharacteristic
383C22×C7#54111yescharacteristic
384C22×C7#54211yescharacteristic
385C22×C7#54211yescharacteristic
386C22×C7#54612yes—
387C22×C7#54612yes—
388C22×C7#54712yes—
389C22×C7#54712yes—
390C22×C7#55212yes—
391C22×C7#55312yes—
392C22×C7#55512yes—
393C22×C7#55612yes—
394C4×C7—24no—
395C4×C7—24no—
396C4×C7—44no—
397C4×C7—82no—
398Dic7—24no—
399Dic7—24no—
400Dic7—42no—
401Dic7—42no—
402Dic7—44no—
403Dic7—82no—
404C24—22no—
405C24—21no—
406C24—22no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24C2×C4×D712yes—
414C24D4×D714yes—
415C24C23×D711yescharacteristic
416C22×C4—216no—
417C22×C4—216no—
418C22×C4—28no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—72no—
440C22×C4—72no—
441C22×C4—74no—
442C22×C4—74no—
443C22×C4—72no—
444C22×C4—72no—
445C22×C4—74no—
446C22×C4—142no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—142no—
450C22×C4—141no—
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—141no—
460C22×C4—142no—
461C22×C4—141no—
462C22×C4—142no—
463C22×C4—141no—
464C22×C4—142no—
465C22×C4—141no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4C2×C4×D712yes—
474C22×C4C2×C4×D712yes—
475C22×C4#115714yes—
476C22×C4#115912yes—
477C22×C4#115914yes—
478C22×C4#115912yes—
479C4⋊C4—148no—
480C4⋊C4—148no—
481C4⋊C4—288no—
482C22⋊C4—48no—
483C22⋊C4—716no—
484C22⋊C4—148no—
485C22⋊C4—288no—
486C42—148no—
487C42—148no—
488C42—288no—
489C2×C7—44no—
490C2×C7#228011yescharacteristic
491C2×C7#229811yescharacteristic
492C2×C7#231411yescharacteristic
493C2×C7#233911yescharacteristic
494C2×C7#233911yescharacteristic
495C2×C7#234611yescharacteristic
496C2×C7#234711yescharacteristic
497C2×C7#247012yes—
498C2×C7#247412yes—
499C2×C7#247612yes—
500C2×C7#247812yes—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—41no—
523C23D7×C22⋊C414yes—
524C23C22×C4×D711yescharacteristic
525C23C2×#115712yes—
526C23C2×D4×D712yes—
527C23C2×#115911yescharacteristic
528C23C2×#115912yes—
529C23C2×#115911yescharacteristic
530C23#654811yescharacteristic
531C23#655111yescharacteristic
532C23D7×#4112yes—
533C23#655311yescharacteristic
534C23#655411yescharacteristic
535C2×C4—232no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
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—42no—
557C2×C4—42no—
558C2×C4—74no—
559C2×C4—74no—
560C2×C4—142no—
561C2×C4—144no—
562C2×C4—142no—
563C2×C4—144no—
564C2×C4—142no—
565C2×C4—142no—
566C2×C4—144no—
567C2×C4—144no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—142no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—142no—
574C2×C4—144no—
575C2×C4—144no—
576C2×C4—144no—
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×C4—282no—
587C2×C4—282no—
588C2×C4—282no—
589C2×C4—282no—
590C2×C4—282no—
591C2×C4—282no—
592C2×C4#644014yes—
593C2×C4#644014yes—
594C7#1394311yescharacteristic, complemented, Sylow
595C22—24no—
596C22—24no—
597C22—24no—
598C22—42no—
599C22—42no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—44no—
604C22—44no—
605C22—42no—
606C22C4×#115711yescharacteristic
607C22C2×#644011yescharacteristic
608C22C2×#644011yescharacteristic
609C22C2×D7×C22⋊C411yescharacteristic
610C22#9018112yes—
611C22#9019511yescharacteristic
612C22#9019812yes—
613C22#9021311yescharacteristic
614C22#9021411yescharacteristic
615C22#9022912yes—
616C22#9023212yes—
617C22#9024812yes—
618C22#9025412yes—
619C22#9027712yes—
620C22#9027712yes—
621C22#9029411yescharacteristic
622C22#9030512yes—
623C22#9031011yescharacteristic
624C22#9031611yescharacteristic
625C22#9033212yes—
626C22#9033411yescharacteristic
627C22#9034512yes—
628C22#9034612yes—
629C4—24no—
630C4—24no—
631C4—44no—
632C4—82no—
633C4—144no—
634C4—144no—
635C4—282no—
636C4—282no—
637C4—284no—
638C4—562no—
639C2—44no—
640C2#1173081311yescharacteristic
641C2#1173088511yescharacteristic
642C2#1173090411yescharacteristic
643C2#1173126211yescharacteristic
644C2#1173131311yescharacteristic
645C2#1173132711yescharacteristic
646C2#1173156611yescharacteristic
647C2#1173188912yes—
648C2#1173189512yes—
649C2#1173216812yes—
650C2#1173217612yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#13943
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. #11727165C2semidirect
7. #11727161C2semidirect
8. Dic7⋊#95C2semidirect
9. #11727157C2semidirect
10. #11727155C2semidirect
11. Dic7×#95C2semidirect
18. C2×#6489C4semidirect
594. C7#13943semidirect

Maximal subgroups

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

subgroupindex
C22×#64892
C2×#897162
C7×C22⋊#952
#117298812
#117293032
#117271652
#117271612
Dic7⋊#952
#117271572
#117271552
Dic7×#952
#139437