Finite Group Databasebeta

← #13276410

Subgroups — #13276410

Order 1792.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic7C211yesmaximal, characteristic
2C7×C22⋊#95C211yesmaximal, characteristic
3#11729881C211yesmaximal, characteristic
4#11729303C212yesmaximal
5#11729299C212yesmaximal
6#11727171C212yesmaximal, complemented
7#11727157C211yesmaximal, characteristic, complemented
8#11727157C211yesmaximal, characteristic, complemented
9#11727156C212yesmaximal, 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
17C22×C4×Dic7C2212yes—
18C22×C4×Dic7C2211yescharacteristic
19C22×C4×Dic7C2211yescharacteristic
20C2×C7×#95C2211yescharacteristic
21C2×C7×#95C2211yescharacteristic
22C2×C7×#95C2212yes—
23C4×C22⋊Dic7C418yescomplemented
24C2×C7⋊#95C2211yescharacteristic
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36#13947—71nomaximal, Sylow
37C25×C7C2311yescharacteristic
38C23×C4×C7—22no—
39C23×C4×C7—22no—
40C23×C4×C7—42no—
41C23×C4×C7—42no—
42C23×C4×C7C2×C414yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2312yes—
52C23×Dic7C2311yescharacteristic
53C2×C7×C22⋊C4—24no—
54C2×C7×C22⋊C4—24no—
55C2×C7×C22⋊C4—42no—
56C2×C22⋊Dic7—22no—
57C2×C22⋊Dic7—22no—
58C2×C22⋊Dic7—22no—
59C2×C22⋊Dic7—22no—
60C2×C22⋊Dic7—24no—
61C2×C22⋊Dic7—24no—
62C2×C22⋊Dic7—42no—
63C2×C22⋊Dic7C2×C414yes—
64C2×C22⋊Dic7C2×C414yes—
65C2×C4×Dic7—24no—
66C2×C4×Dic7—24no—
67C2×C4×Dic7—42no—
68C2×C4×Dic7—42no—
69C2×C4×Dic7—42no—
70C2×C4×Dic7C2×C414yes—
71C2×C4×Dic7C2×C414yes—
72C7×#95—22no—
73C7×#95—22no—
74C7×#95—42no—
75C7⋊#95—24no—
76C7⋊#95—22no—
77C7⋊#95—22no—
78C7⋊#95—24no—
79C7⋊#95—24no—
80C7⋊#95—24no—
81C7⋊#95—42no—
82C7⋊#95—42no—
83C7⋊#95—42no—
84C7⋊#95—42no—
85C7⋊#95C2×C414yes—
86C7⋊#95C2×C414yes—
87C2×C4×C22⋊C4—71no—
88#1443—72no—
89#1440—72no—
90#1437—72no—
91#1434—71no—
92#1434—72no—
93#1434—71no—
94#1434—71no—
95C22⋊#95—71no—
96C22⋊#95D711yescharacteristic
97C4×#95—71no—
98C24×C7—21no—
99C24×C7—21no—
100C24×C7—22no—
101C24×C7—22no—
102C24×C7—21no—
103C24×C7—21no—
104C24×C7—22no—
105C24×C7—22no—
106C24×C7C22×C412yes—
107C24×C7#4112yes—
108C24×C7#4112yes—
109C24×C7C2411yescharacteristic
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—28no—
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—22no—
130C22×C4×C7—44no—
131C22×C4×C7—44no—
132C22×C4×C7—48no—
133C22×C4×C7—48no—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C22×C412yes—
136C22×C4×C7#4114yes—
137C22×C4×C7#4112yes—
138C22×C4×C7#4112yes—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
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×Dic7C22×C412yes—
167C22×Dic7C22×C412yes—
168C22×Dic7C22×C412yes—
169C22×Dic7C22×C412yes—
170C22×Dic7#4114yes—
171C22×Dic7#4112yes—
172C22×Dic7#4112yes—
173C7×C22⋊C4—48no—
174C22⋊Dic7—28no—
175C22⋊Dic7—28no—
176C22⋊Dic7—48no—
177C4×Dic7—44no—
178C4×Dic7—44no—
179C4×Dic7—48no—
180C24×C4C2×D711yescharacteristic
181C22×C22⋊C4—71no—
182C22×C22⋊C4—71no—
183C22×C22⋊C4—72no—
184C22×C22⋊C4C2×D712yes—
185C22×C42—71no—
186C22×C42—71no—
187C22×C42—72no—
188C4×C22⋊C4—78no—
189C2×#95—71no—
190C2×#95—71no—
191C2×#95—71no—
192C2×#95—72no—
193C2×#95—71no—
194C2×#95—72no—
195C2×#95—72no—
196C2×#95—72no—
197C2×#95—72no—
198C2×#95—72no—
199C2×#95—72no—
200C2×#95—72no—
201C2×#95C2×D711yescharacteristic
202C2×#95C2×D711yescharacteristic
203C2×#95C2×D712yes—
204C23×C7—22no—
205C23×C7—22no—
206C23×C7—22no—
207C23×C7—22no—
208C23×C7—22no—
209C23×C7—22no—
210C23×C7—22no—
211C23×C7—22no—
212C23×C7—22no—
213C23×C7—22no—
214C23×C7—24no—
215C23×C7—24no—
216C23×C7—24no—
217C23×C7—24no—
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#11714yes—
227C23×C7C23×C411yescharacteristic
228C23×C7C2×#4112yes—
229C23×C7C2×#4111yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4111yescharacteristic
233C23×C7C2×#4111yescharacteristic
234C23×C7C2×#4111yescharacteristic
235C23×C7C2×#4112yes—
236C23×C7H(5,𝔽2)12yes—
237C23×C7H(5,𝔽2)12yes—
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—416no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7#11714yes—
263C2×Dic7—22no—
264C2×Dic7—22no—
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—22no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—22no—
272C2×Dic7—22no—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—42no—
280C2×Dic7—42no—
281C2×Dic7—42no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—42no—
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#11714yes—
297C25C22×D711yescharacteristic
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—71no—
303C23×C4—71no—
304C23×C4—71no—
305C23×C4—71no—
306C23×C4—72no—
307C23×C4—72no—
308C23×C4C4×D714yes—
309C23×C4C22×D712yes—
310C23×C4C22×D711yescharacteristic
311C23×C4C22×D712yes—
312C23×C4C22×D711yescharacteristic
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—74no—
317C2×C22⋊C4—74no—
318C2×C22⋊C4—142no—
319C2×C22⋊C4—142no—
320C2×C22⋊C4—142no—
321C2×C22⋊C4—142no—
322C2×C22⋊C4—144no—
323C2×C22⋊C4—144no—
324C2×C22⋊C4—282no—
325C2×C42—74no—
326C2×C42—74no—
327C2×C42—144no—
328C2×C42—144no—
329C2×C42—282no—
330C2×C42—282no—
331C2×C42—282no—
332#95—22no—
333#95—22no—
334#95—42no—
335#95—74no—
336#95—74no—
337#95—144no—
338#95—144no—
339#95—144no—
340#95—144no—
341#95—142no—
342#95—142no—
343#95—282no—
344#95—282no—
345#95—282no—
346#95—282no—
347C22×C7—24no—
348C22×C7—24no—
349C22×C7—24no—
350C22×C7—42no—
351C22×C7—44no—
352C22×C7—44no—
353C22×C7—44no—
354C22×C7—44no—
355C22×C7—42no—
356C22×C7—42no—
357C22×C7—42no—
358C22×C7C2×#11711yescharacteristic
359C22×C7C2×#11711yescharacteristic
360C22×C7C2×#11711yescharacteristic
361C22×C7C4×#4111yescharacteristic
362C22×C7C4×#4111yescharacteristic
363C22×C7#51811yescharacteristic
364C22×C7#51811yescharacteristic
365C22×C7#52912yes—
366C22×C7#52912yes—
367C22×C7#52911yescharacteristic
368C22×C7#52911yescharacteristic
369C22×C7#52911yescharacteristic
370C22×C7#52911yescharacteristic
371C22×C7#53812yes—
372C22×C7#53812yes—
373C22×C7#55112yes—
374C22×C7#55112yes—
375C22×C7#55112yes—
376C22×C7#55312yes—
377C22×C7#55312yes—
378C22×C7#55312yes—
379C22×C7#55312yes—
380C22×C7#55912yes—
381C4×C7—24no—
382C4×C7—42no—
383C4×C7—44no—
384C4×C7—82no—
385Dic7—24no—
386Dic7—44no—
387Dic7—42no—
388Dic7—42no—
389Dic7—42no—
390Dic7—82no—
391C24—22no—
392C24—21no—
393C24—21no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24C2×C4×D712yes—
400C24#115912yes—
401C24#116112yes—
402C24C23×D711yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—28no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—48no—
426C22×C4—48no—
427C22×C4—72no—
428C22×C4—72no—
429C22×C4—72no—
430C22×C4—72no—
431C22×C4—72no—
432C22×C4—72no—
433C22×C4—74no—
434C22×C4—142no—
435C22×C4—142no—
436C22×C4—142no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—141no—
440C22×C4—141no—
441C22×C4—142no—
442C22×C4—142no—
443C22×C4—142no—
444C22×C4—142no—
445C22×C4—142no—
446C22×C4—141no—
447C22×C4—141no—
448C22×C4—142no—
449C22×C4—142no—
450C22×C4—142no—
451C22×C4—142no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4C2×C4×D712yes—
462C22×C4C2×C4×D712yes—
463C22×C4#115714yes—
464C22×C4#115912yes—
465C22×C4#115912yes—
466C22⋊C4—48no—
467C22⋊C4—148no—
468C22⋊C4—148no—
469C22⋊C4—288no—
470C42—284no—
471C42—284no—
472C42—288no—
473C2×C7—44no—
474C2×C7#228311yescharacteristic
475C2×C7#229811yescharacteristic
476C2×C7#231211yescharacteristic
477C2×C7#235311yescharacteristic
478C2×C7#235311yescharacteristic
479C2×C7#235311yescharacteristic
480C2×C7#235711yescharacteristic
481C2×C7#257612yes—
482C2×C7#257812yes—
483C2×C7#259512yes—
484C2×C7#259712yes—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—24no—
490C23—24no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23#645514yes—
508C23C22×C4×D711yescharacteristic
509C23C2×#115712yes—
510C23C2×#115911yescharacteristic
511C23C2×#115911yescharacteristic
512C23C2×#115911yescharacteristic
513C23#654812yes—
514C23#654812yes—
515C23C2×#116111yescharacteristic
516C23D7×#4111yescharacteristic
517C23D7×#4111yescharacteristic
518C23D7×#4112yes—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—416no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—74no—
544C2×C4—142no—
545C2×C4—142no—
546C2×C4—144no—
547C2×C4—144no—
548C2×C4—142no—
549C2×C4—142no—
550C2×C4—142no—
551C2×C4—142no—
552C2×C4—142no—
553C2×C4—142no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—282no—
561C2×C4—282no—
562C2×C4—282no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4—282no—
567C2×C4—282no—
568C2×C4—282no—
569C2×C4—282no—
570C2×C4—282no—
571C2×C4—282no—
572C2×C4—282no—
573C2×C4—282no—
574C2×C4—282no—
575C2×C4—282no—
576C2×C4—282no—
577C2×C4#644014yes—
578C7#1394711yescharacteristic, complemented, Sylow
579C22—24no—
580C22—24no—
581C22—24no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22C4×#115711yescharacteristic
591C22C2×#644011yescharacteristic
592C22#9017711yescharacteristic
593C22#9017711yescharacteristic
594C22#9018612yes—
595C22C2×#645511yescharacteristic
596C22#9020512yes—
597C22D7×#11711yescharacteristic
598C22#9021311yescharacteristic
599C22#9022912yes—
600C22#9024712yes—
601C22#9024812yes—
602C22#9024912yes—
603C22#9028412yes—
604C22#9028412yes—
605C22#9029111yescharacteristic
606C22#9029111yescharacteristic
607C22#9029212yes—
608C22#9031511yescharacteristic
609C22#9031511yescharacteristic
610C22#9032812yes—
611C22#9035212yes—
612C22#9035512yes—
613C4—24no—
614C4—42no—
615C4—44no—
616C4—82no—
617C4—144no—
618C4—282no—
619C4—282no—
620C4—282no—
621C4—284no—
622C4—562no—
623C2—44no—
624C2#1173078111yescharacteristic
625C2#1173088511yescharacteristic
626C2#1173102111yescharacteristic
627C2#1173126511yescharacteristic
628C2#1173130811yescharacteristic
629C2#1173132911yescharacteristic
630C2#1173150611yescharacteristic
631C2#1173192912yes—
632C2#1173193912yes—
633C2#1173221112yes—
634C2#1173221912yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#13947
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. #11727171C2semidirect
7. #11727157C2semidirect
8. #11727157C2semidirect
9. #11727156C2semidirect
10. #11727155C2semidirect
11. Dic7×#95C2semidirect
23. C4×C22⋊Dic7C4semidirect
578. C7#13947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic72
C7×C22⋊#952
#117298812
#117293032
#117292992
#117271712
#117271572
#117271562
#117271552
Dic7×#952
#139477