Finite Group Databasebeta

← #13275331

Subgroups — #13275331

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89762C212yesmaximal
2C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
3C2×#89438C211yesmaximal, characteristic
4C2×#89420C211yesmaximal, characteristic, complemented
5C7×C4⋊#95C211yesmaximal, characteristic, complemented
6#11729318C212yesmaximal, complemented
7C4×C7⋊#95C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic
9#11727162C212yesmaximal
10#11727156C211yesmaximal, characteristic, complemented
11Dic7×#95C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C42×C7C2211yescharacteristic
15C22×(C2×D7)⋊C4C2211yescharacteristic
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×C4×Dic7C2212yes—
20C22×C4×Dic7C2212yes—
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2212yes—
23C2×C7×#95C2212yes—
24C2×C7×#95C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
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⋊#95C2211yescharacteristic
35#89762C4116yescomplemented
36C4×(C2×D7)⋊C4C418yescomplemented
37#89438—24no—
38#89420—24no—
39#13816—71nomaximal, Sylow
40C24×D7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C22×C4×D7—22no—
52C22×C4×D7—22no—
53C22×C4×D7—24no—
54C22×C4×D7—42no—
55C22×C4×D7C2×C414yes—
56C2×C7×C4⋊C4—42no—
57C2×C7×C4⋊C4—42no—
58C2×C7×C4⋊C4C2×C418yescomplemented
59C2×C42×C7—42no—
60C2×C42×C7C2×C414yes—
61C2×(C2×D7)⋊C4—22no—
62C2×(C2×D7)⋊C4—22no—
63C2×(C2×D7)⋊C4—24no—
64C2×(C2×D7)⋊C4—24no—
65C2×(C2×D7)⋊C4—42no—
66C2×(C2×D7)⋊C4—42no—
67C2×(C2×D7)⋊C4C2×C414yes—
68C2×(C2×D7)⋊C4C2×C418yes—
69C2×(C2×D7)⋊C4C2×C418yes—
70C2×(C2×D7)⋊C4C2×C414yes—
71C2×(C2×D7)⋊C4C2×C418yes—
72C2×C4×Dic7—22no—
73C2×C4×Dic7—22no—
74C2×C4×Dic7—24no—
75C2×C4×Dic7—24no—
76C2×C4×Dic7—24no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—24no—
79C2×C4×Dic7—24no—
80C2×C4×Dic7—42no—
81C2×C4×Dic7—42no—
82C2×C4×Dic7C2×C414yes—
83C2×C4×Dic7C2×C418yescomplemented
84C7×#95—22no—
85C7×#95—22no—
86C7×#95—24no—
87C7⋊#95—22no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—42no—
91C7⋊#95C2×C414yes—
92C7⋊#95C2×C414yes—
93C7⋊#95C2×C418yescomplemented
94C7⋊#95C2×C418yescomplemented
95C7⋊#95D414yes—
96C2×#388—72no—
97C2×C4×C22⋊C4—71no—
98C2×C4×C22⋊C4—71no—
99C2×#376—71no—
100#1437—72no—
101#1436—72no—
102C4⋊#95D711yescharacteristic, complemented
103#1434—71no—
104C22⋊#95—71no—
105C4×#95—71no—
106C4×#95—72no—
107C24×C7C2411yescharacteristic
108C23×D7—21no—
109C23×D7—21no—
110C23×D7—21no—
111C23×D7—22no—
112C23×D7—22no—
113C23×D7—21no—
114C23×D7—21no—
115C23×D7—22no—
116C23×D7—21no—
117C23×D7C22×C414yes—
118C23×D7C22×C412yes—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
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×C414yes—
139C22×C4×C7C22×C414yes—
140C22×C4×C7C22×C412yes—
141C22×C4×C7C22×C414yes—
142C22×C4×C7C22×C412yes—
143C22×C4×C7C22×C412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7#4112yes—
146C22×C4×C7#4112yes—
147C22×C4×C7#4112yes—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—21no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—21no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—21no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—21no—
170C22×Dic7C22×C412yes—
171C22×Dic7C22×C414yes—
172C22×Dic7C22×C412yes—
173C22×Dic7C22×C414yes—
174C22×Dic7C22×C412yes—
175C22×Dic7C22×C414yes—
176C22×Dic7C2×D414yes—
177C22×Dic7#4114yes—
178C22×Dic7#4114yes—
179C2×C4×D7—28no—
180C2×C4×D7—28no—
181C2×C4×D7—44no—
182C2×C4×D7—48no—
183C2×C4×D7—48no—
184C7×C4⋊C4—48no—
185C42×C7—44no—
186(C2×D7)⋊C4—28no—
187(C2×D7)⋊C4—216no—
188(C2×D7)⋊C4—48no—
189(C2×D7)⋊C4C42116yescomplemented
190C4×Dic7—28no—
191C4×Dic7—216no—
192C4×Dic7—48no—
193C4×Dic7—48no—
194C24×C4—71no—
195C22×C4⋊C4C2×D712yes—
196C22×C22⋊C4—71no—
197C22×C22⋊C4—71no—
198C22×C22⋊C4—72no—
199C22×C22⋊C4—72no—
200C22×C42—72no—
201C22×C42—71no—
202C22×C42—72no—
203C22×C42—72no—
204C22×C42C2×D711yescharacteristic
205#388—716no—
206C4×C22⋊C4—78no—
207C4×C22⋊C4—144no—
208#376—144no—
209C2×#95—71no—
210C2×#95—72no—
211C2×#95—72no—
212C2×#95—71no—
213C2×#95—71no—
214C2×#95—71no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95C2×D712yes—
219C2×#95C2×D711yescharacteristic
220C2×#95C2×D711yescharacteristic
221C23×C7C23×C411yescharacteristic
222C23×C7C23×C412yes—
223C23×C7C22×D411yescharacteristic
224C23×C7C2×#4111yescharacteristic
225C23×C7C2×#4111yescharacteristic
226C23×C7C2×#4111yescharacteristic
227C23×C7C2×#4112yes—
228C23×C7C2×#4112yes—
229C23×C7H(5,𝔽2)12yes—
230C23×C7H(5,𝔽2)11yescharacteristic
231C23×C72−1+411yescharacteristic
232C22×D7—22no—
233C22×D7—22no—
234C22×D7—24no—
235C22×D7—22no—
236C22×D7—22no—
237C22×D7—24no—
238C22×D7—24no—
239C22×D7—24no—
240C22×D7—24no—
241C22×D7—22no—
242C22×D7—22no—
243C22×D7—24no—
244C22×D7—42no—
245C22×D7—41no—
246C22×D7—41no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C22×D7—41no—
252C22×D7—42no—
253C22×D7—41no—
254C22×D7C2×C4214yes—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—24no—
268C2×C4×C7—24no—
269C2×C4×C7—24no—
270C2×C4×C7—24no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7C2×C4214yes—
282C2×C4×C7#11714yes—
283C2×C4×C7C4×D414yes—
284C2×Dic7—22no—
285C2×Dic7—24no—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—24no—
289C2×Dic7—24no—
290C2×Dic7—22no—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—24no—
297C2×Dic7—24no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—24no—
301C2×Dic7—24no—
302C2×Dic7—24no—
303C2×Dic7—22no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—42no—
307C2×Dic7—42no—
308C2×Dic7—41no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—41no—
312C2×Dic7C2×C4214yes—
313C2×Dic7#11714yes—
314C2×Dic7C4×D418yes—
315C4×D7—416no—
316C25—71no—
317C23×C4—71no—
318C23×C4—72no—
319C23×C4—71no—
320C23×C4—72no—
321C23×C4—71no—
322C23×C4—74no—
323C23×C4—144no—
324C23×C4—142no—
325C23×C4—142no—
326C23×C4—282no—
327C23×C4C22×D712yes—
328C23×C4C22×D712yes—
329C23×C4C22×D711yescharacteristic
330C23×C4C22×D711yescharacteristic
331C23×C4C22×D711yescharacteristic
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4C4×D718yescomplemented
335C2×C22⋊C4—74no—
336C2×C22⋊C4—78no—
337C2×C22⋊C4—74no—
338C2×C22⋊C4—78no—
339C2×C22⋊C4—78no—
340C2×C22⋊C4—144no—
341C2×C22⋊C4—144no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C22⋊C4—282no—
345C2×C22⋊C4—282no—
346C2×C42—42no—
347C2×C42—74no—
348C2×C42—78no—
349C2×C42—144no—
350C2×C42—144no—
351C2×C42—142no—
352C2×C42—142no—
353C2×C42—144no—
354C2×C42—144no—
355C2×C42—144no—
356C2×C42—144no—
357C2×C42—282no—
358C2×C42—282no—
359C2×C42C4×D714yes—
360#95—22no—
361#95—22no—
362#95—24no—
363#95—74no—
364#95—74no—
365#95—78no—
366#95—78no—
367#95—74no—
368#95—144no—
369#95—144no—
370#95—142no—
371#95—282no—
372C22×C7C22×C4211yescharacteristic
373C22×C7C2×#11711yescharacteristic
374C22×C7C2×#11711yescharacteristic
375C22×C7C2×C4×D411yescharacteristic
376C22×C7C2×C4×D412yes—
377C22×C7C4×#4111yescharacteristic
378C22×C7C4×#4112yes—
379C22×C7C4×#4112yes—
380C22×C7C4×#4112yes—
381C22×C7#51811yescharacteristic
382C22×C7#51812yes—
383C22×C7#52011yescharacteristic
384C22×C7#52012yes—
385C22×C7#54612yes—
386C22×C7#54711yescharacteristic
387C22×C7#55011yescharacteristic
388C22×C7#55112yes—
389C22×C7#55112yes—
390C22×C7#55212yes—
391C22×C7#55312yes—
392C22×C7#55511yescharacteristic
393C22×C7#55512yes—
394C22×C7#55611yescharacteristic
395C2×D7—24no—
396C2×D7—24no—
397C2×D7—24no—
398C2×D7—42no—
399C2×D7—42no—
400C2×D7—42no—
401C2×D7—42no—
402C2×D7—44no—
403C2×D7—44no—
404C2×D7—44no—
405C2×D7—44no—
406C4×C7—24no—
407C4×C7—24no—
408C4×C7—24no—
409C4×C7—44no—
410C4×C7—44no—
411Dic7—24no—
412Dic7—28no—
413Dic7—24no—
414Dic7—42no—
415Dic7—44no—
416C24—74no—
417C24—72no—
418C24—141no—
419C24—141no—
420C24—141no—
421C24—142no—
422C24—141no—
423C24—141no—
424C24—141no—
425C24—142no—
426C24—142no—
427C24C23×D711yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
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—74no—
450C22×C4—74no—
451C22×C4—74no—
452C22×C4—74no—
453C22×C4—74no—
454C22×C4—74no—
455C22×C4—72no—
456C22×C4—148no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—141no—
463C22×C4—141no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—141no—
468C22×C4—141no—
469C22×C4—141no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—141no—
476C22×C4—141no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—148no—
480C22×C4—284no—
481C22×C4—288no—
482C22×C4—288no—
483C22×C4C2×C4×D714yes—
484C22×C4C2×C4×D714yes—
485C22×C4C2×C4×D712yes—
486C22×C4C2×C4×D714yes—
487C22×C4C2×C4×D712yes—
488C22×C4C2×C4×D712yes—
489C22×C4D4×D712yes—
490C22×C4#115912yes—
491C22×C4#116112yes—
492C22×C4#116112yes—
493C4⋊C4—48no—
494C22⋊C4—716no—
495C22⋊C4—1416no—
496C22⋊C4—148no—
497C22⋊C4—288no—
498C42—44no—
499C42—1416no—
500C42—148no—
501C42—288no—
502C42—288no—
503C2×C7C4×#11711yescharacteristic
504C2×C7C42×D411yescharacteristic
505C2×C7#227511yescharacteristic
506C2×C7#234211yescharacteristic
507C2×C7#234611yescharacteristic
508C2×C7#235311yescharacteristic
509C2×C7#235411yescharacteristic
510C2×C7#235912yes—
511C2×C7#236312yes—
512C2×C7#237212yes—
513C2×C7#237312yes—
514D7—44no—
515C23—74no—
516C23—144no—
517C23—142no—
518C23—142no—
519C23—142no—
520C23—142no—
521C23—144no—
522C23—142no—
523C23—142no—
524C23—144no—
525C23—144no—
526C23—144no—
527C23—144no—
528C23—282no—
529C23—281no—
530C23—281no—
531C23—281no—
532C23—281no—
533C23—282no—
534C23—282no—
535C23—282no—
536C23—282no—
537C23—282no—
538C23C22×C4×D711yescharacteristic
539C23C22×C4×D712yes—
540C23C2×D4×D711yescharacteristic
541C23C2×#115911yescharacteristic
542C23#654811yescharacteristic
543C23#654812yes—
544C23C2×#116111yescharacteristic
545C23C2×#116111yescharacteristic
546C23#655111yescharacteristic
547C23D7×#4112yes—
548C23D7×#4112yes—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—74no—
576C2×C4—74no—
577C2×C4—78no—
578C2×C4—144no—
579C2×C4—144no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—144no—
584C2×C4—142no—
585C2×C4—144no—
586C2×C4—144no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—144no—
590C2×C4—144no—
591C2×C4—144no—
592C2×C4—144no—
593C2×C4—142no—
594C2×C4—142no—
595C2×C4—142no—
596C2×C4—144no—
597C2×C4—144no—
598C2×C4—2816no—
599C2×C4—281no—
600C2×C4—281no—
601C2×C4—281no—
602C2×C4—281no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4—282no—
606C2×C4—282no—
607C2×C4C42×D714yes—
608C2×C4#645514yes—
609C2×C4#645614yes—
610C7#1381611yescharacteristic, complemented, Sylow
611C22—144no—
612C22—144no—
613C22—144no—
614C22—282no—
615C22—282no—
616C22—282no—
617C22—284no—
618C22—284no—
619C22—284no—
620C22—284no—
621C22—282no—
622C22C2×C42×D711yescharacteristic
623C22#9017711yescharacteristic
624C22#9017712yes—
625C22C2×#645511yescharacteristic
626C22C2×#645611yescharacteristic
627C22#9019511yescharacteristic
628C22#9019512yes—
629C22D7×#11711yescharacteristic
630C22#9021311yescharacteristic
631C22C4×#115912yes—
632C22C4×D4×D712yes—
633C22C4×#116112yes—
634C22C4×#116112yes—
635C22#9029212yes—
636C22#9030112yes—
637C22#9032812yes—
638C22#9032812yes—
639C22#9036112yes—
640C22#9038412yes—
641C22#9040911yescharacteristic
642C22#9041711yescharacteristic
643C22#9042311yescharacteristic
644C22#9042511yescharacteristic
645C4—24no—
646C4—24no—
647C4—24no—
648C4—44no—
649C4—44no—
650C4—144no—
651C4—148no—
652C4—144no—
653C4—282no—
654C4—284no—
655C2—284no—
656C2#1173076711yescharacteristic
657C2C4×#645511yescharacteristic
658C2C4×#645611yescharacteristic
659C2#1173132911yescharacteristic
660C2#1173145411yescharacteristic
661C2#1173160111yescharacteristic
662C2#1173176911yescharacteristic
663C2#1173343612yes—
664C2#1173364912yes—
665C2#1173375012yes—
666C2#1173394012yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4⋊#95D7
hypocenterC7#13816
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#89420C2semidirect
5. C7×C4⋊#95C2semidirect
6. #11729318C2semidirect
7. C4×C7⋊#95C2semidirect
10. #11727156C2semidirect
11. Dic7×#95C2semidirect
35. #89762C4semidirect
36. C4×(C2×D7)⋊C4C4semidirect
58. C2×C7×C4⋊C4C2×C4semidirect
83. C2×C4×Dic7C2×C4semidirect
93. C7⋊#95C2×C4semidirect
94. C7⋊#95C2×C4semidirect
102. C4⋊#95D7semidirect
189. (C2×D7)⋊C4C42semidirect
334. C2×C4⋊C4C4×D7semidirect
610. C7#13816semidirect

Maximal subgroups

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

subgroupindex
C2×#897622
C2×C4×(C2×D7)⋊C42
C2×#894382
C2×#894202
C7×C4⋊#952
#117293182
C4×C7⋊#952
(C2×D7)⋊#952
#117271622
#117271562
Dic7×#952
#138167