Finite Group Databasebeta

← #13275615

Subgroups — #13275615

Order 1792.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89765C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
3C2×#89438C212yesmaximal
4C2×#89438C211yesmaximal, characteristic
5C7×#1445C211yesmaximal, characteristic, complemented
6#11727183C212yesmaximal
7#11727181C211yesmaximal, characteristic
8#11727172C212yesmaximal, complemented
9#11727169C211yesmaximal, characteristic, complemented
10Dic7×#95C212yesmaximal, complemented
11Dic7×#95C211yesmaximal, characteristic, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×(C2×D7)⋊C4C2212yes—
15C22×(C2×D7)⋊C4C2211yescharacteristic
16C22×(C2×D7)⋊C4C2211yescharacteristic
17C22×(C2×D7)⋊C4C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4×Dic7C2212yes—
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C2×C7×#95C2211yescharacteristic
24C2×C7×#95C2212yes—
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35#89765C418yescomplemented
36C4⋊C4×Dic7—24no—
37#89438—28no—
38#89438—24no—
39C4×#397—71nomaximal, Sylow
40C24×D7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
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—24no—
55C22×C4×D7D414yes—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4C2×C414yescomplemented
59C2×(C2×D7)⋊C4—24no—
60C2×(C2×D7)⋊C4—24no—
61C2×(C2×D7)⋊C4—22no—
62C2×(C2×D7)⋊C4—24no—
63C2×(C2×D7)⋊C4—22no—
64C2×(C2×D7)⋊C4—22no—
65C2×(C2×D7)⋊C4—22no—
66C2×(C2×D7)⋊C4—24no—
67C2×(C2×D7)⋊C4—22no—
68C2×(C2×D7)⋊C4—24no—
69C2×(C2×D7)⋊C4C2×C418yes—
70C2×(C2×D7)⋊C4C2×C414yes—
71C2×C4⋊Dic7—22no—
72C2×C4⋊Dic7—24no—
73C2×C4×Dic7—24no—
74C2×C4×Dic7—24no—
75C2×C4×Dic7—24no—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—24no—
79C2×C4×Dic7—24no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7—24no—
82C2×C4×Dic7D414yes—
83C7×#95—22no—
84C7×#95—24no—
85C7×#95—24no—
86C7×#95—22no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—22no—
91C7⋊#95—24no—
92C7⋊#95—24no—
93C7⋊#95C2×C418yescomplemented
94C7⋊#95C2×C414yescomplemented
95C2×#397—71no—
96C2×C4×C4⋊C4—71no—
97C2×C4×C22⋊C4—71no—
98C2×C4×C22⋊C4—72no—
99#1445D711yescharacteristic, complemented
100#1443—72no—
101#1442—71no—
102#1440—72no—
103#1439—71no—
104C4×#95—71no—
105C4×#95—72no—
106C24×C7C2411yescharacteristic
107C23×D7—21no—
108C23×D7—21no—
109C23×D7—22no—
110C23×D7—22no—
111C23×D7—21no—
112C23×D7—21no—
113C23×D7—22no—
114C23×D7—22no—
115C23×D7C22×C412yes—
116C23×D7C2×D412yes—
117C23×D7#4112yes—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
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—21no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7C22×C414yes—
141C22×C4×C7C22×C412yes—
142C22×C4×C7C2×D412yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7#4112yes—
145C22×C4×C7#4114yes—
146C22×C4×C7#4112yes—
147C22×Dic7—22no—
148C22×Dic7—22no—
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—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—22no—
167C22×Dic7C22×C412yes—
168C22×Dic7C22×C414yes—
169C22×Dic7C2×D412yes—
170C22×Dic7C2×D412yes—
171C22×Dic7C2×D412yes—
172C22×Dic7#4114yes—
173C22×Dic7#4112yes—
174C22×Dic7#4114yes—
175C22×Dic7#4114yes—
176C2×C4×D7—28no—
177C2×C4×D7—216no—
178C2×C4×D7—44no—
179C2×C4×D7—44no—
180C2×C4×D7—48no—
181C7×C4⋊C4—28no—
182(C2×D7)⋊C4—28no—
183(C2×D7)⋊C4—216no—
184(C2×D7)⋊C4—216no—
185(C2×D7)⋊C4—28no—
186C4⋊Dic7—28no—
187C4×Dic7—28no—
188C4×Dic7—48no—
189C4×Dic7—48no—
190C4×Dic7—44no—
191C24×C4—71no—
192C22×C4⋊C4—71no—
193C22×C4⋊C4C2×D711yescharacteristic
194C22×C22⋊C4—71no—
195C22×C22⋊C4—72no—
196C22×C22⋊C4—72no—
197C22×C22⋊C4—71no—
198C22×C42—71no—
199C22×C42—71no—
200C22×C42—72no—
201C22×C42—72no—
202#397—78no—
203C4×C4⋊C4—144no—
204C4×C22⋊C4—144no—
205C4×C22⋊C4—148no—
206C2×#95—71no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—72no—
210C2×#95—72no—
211C2×#95—72no—
212C2×#95—72no—
213C2×#95—71no—
214C2×#95C2×D711yescharacteristic
215C2×#95C2×D712yes—
216C2×#95C2×D711yescharacteristic
217C2×#95C2×D712yes—
218C23×C7C23×C411yescharacteristic
219C23×C7C22×D411yescharacteristic
220C23×C7C22×D411yescharacteristic
221C23×C7C2×#4111yescharacteristic
222C23×C7C2×#4111yescharacteristic
223C23×C7C2×#4112yes—
224C23×C7C2×#4111yescharacteristic
225C23×C7C2×#4111yescharacteristic
226C23×C7C2×#4112yes—
227C23×C7C2×#4112yes—
228C23×C7C2×#4112yes—
229C22×D7—22no—
230C22×D7—24no—
231C22×D7—22no—
232C22×D7—24no—
233C22×D7—22no—
234C22×D7—24no—
235C22×D7—24no—
236C22×D7—22no—
237C22×D7—22no—
238C22×D7—24no—
239C22×D7—24no—
240C22×D7—22no—
241C22×D7—41no—
242C22×D7—41no—
243C22×D7—41no—
244C22×D7—42no—
245C22×D7—42no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—41no—
251C22×D7C4×D414yes—
252C2×C4×C7—24no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
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—42no—
267C2×C4×C7—42no—
268C2×C4×C7—41no—
269C2×C4×C7—42no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
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×C7C4×D414yes—
281C2×Dic7—22no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—22no—
287C2×Dic7—24no—
288C2×Dic7—22no—
289C2×Dic7—24no—
290C2×Dic7—24no—
291C2×Dic7—22no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—41no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303C2×Dic7—42no—
304C2×Dic7—41no—
305C2×Dic7#12114yes—
306C2×Dic7#12314yes—
307C2×Dic7#12318yes—
308C2×Dic7#12414yes—
309C2×Dic7#12618yes—
310C4×D7—416no—
311C25—71no—
312C23×C4—71no—
313C23×C4—72no—
314C23×C4—71no—
315C23×C4—72no—
316C23×C4—71no—
317C23×C4—74no—
318C23×C4—142no—
319C23×C4—142no—
320C23×C4—144no—
321C23×C4—144no—
322C23×C4C22×D712yes—
323C23×C4C22×D711yescharacteristic
324C23×C4C22×D711yescharacteristic
325C23×C4C22×D712yes—
326C23×C4C22×D711yescharacteristic
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—144no—
330C2×C4⋊C4—142no—
331C2×C4⋊C4C4×D714yescomplemented
332C2×C22⋊C4—78no—
333C2×C22⋊C4—74no—
334C2×C22⋊C4—144no—
335C2×C22⋊C4—142no—
336C2×C22⋊C4—144no—
337C2×C22⋊C4—142no—
338C2×C22⋊C4—144no—
339C2×C22⋊C4—144no—
340C2×C22⋊C4—142no—
341C2×C22⋊C4—142no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—144no—
344C2×C42—74no—
345C2×C42—144no—
346C2×C42—142no—
347C2×C42—144no—
348C2×C42—144no—
349C2×C42—144no—
350C2×C42—144no—
351C2×C42—144no—
352C2×C42—144no—
353C2×C42—144no—
354#95—22no—
355#95—24no—
356#95—24no—
357#95—22no—
358#95—78no—
359#95—74no—
360#95—144no—
361#95—142no—
362#95—144no—
363#95—144no—
364#95—144no—
365#95—144no—
366C22×C7C2×C4×D411yescharacteristic
367C22×C7C2×C4×D411yescharacteristic
368C22×C7C4×#4112yes—
369C22×C7C4×#4111yescharacteristic
370C22×C7C4×#4112yes—
371C22×C7C2×#12111yescharacteristic
372C22×C7C2×#12311yescharacteristic
373C22×C7C2×#12312yes—
374C22×C7#52511yescharacteristic
375C22×C7#52512yes—
376C22×C7#52511yescharacteristic
377C22×C7C2×#12411yescharacteristic
378C22×C7C2×#12612yes—
379C22×C7#52911yescharacteristic
380C22×C7#52912yes—
381C22×C7#52912yes—
382C22×C7#52912yes—
383C22×C7#52912yes—
384C22×C7#52912yes—
385C22×C7#52912yes—
386C22×C7#52912yes—
387C22×C7#53211yescharacteristic
388C22×C7#53211yescharacteristic
389C2×D7—24no—
390C2×D7—28no—
391C2×D7—44no—
392C2×D7—42no—
393C2×D7—42no—
394C2×D7—42no—
395C2×D7—44no—
396C2×D7—42no—
397C2×D7—44no—
398C2×D7—42no—
399C2×D7—42no—
400C4×C7—24no—
401C4×C7—42no—
402C4×C7—44no—
403C4×C7—42no—
404C4×C7—44no—
405Dic7—44no—
406Dic7—42no—
407Dic7—44no—
408Dic7—42no—
409Dic7#39718yescomplemented
410C24—72no—
411C24—72no—
412C24—72no—
413C24—141no—
414C24—141no—
415C24—141no—
416C24—142no—
417C24—142no—
418C24—141no—
419C24—142no—
420C24—142no—
421C24C23×D711yescharacteristic
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
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—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—72no—
445C22×C4—72no—
446C22×C4—72no—
447C22×C4—74no—
448C22×C4—74no—
449C22×C4—72no—
450C22×C4—74no—
451C22×C4—72no—
452C22×C4—74no—
453C22×C4—148no—
454C22×C4—1416no—
455C22×C4—141no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—141no—
460C22×C4—141no—
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×C4—142no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—288no—
476C22×C4—284no—
477C22×C4—284no—
478C22×C4C2×C4×D714yes—
479C22×C4C2×C4×D712yes—
480C22×C4D4×D712yes—
481C22×C4D4×D712yes—
482C22×C4#115912yes—
483C22×C4#115912yes—
484C22×C4#116114yes—
485C4⋊C4—28no—
486C4⋊C4—148no—
487C22⋊C4—1416no—
488C22⋊C4—148no—
489C22⋊C4—1416no—
490C22⋊C4—148no—
491C42—148no—
492C42—288no—
493C42—288no—
494C42—284no—
495C2×C7C4×#12111yescharacteristic
496C2×C7C4×#12311yescharacteristic
497C2×C7C4×#12312yes—
498C2×C7C4×#12411yescharacteristic
499C2×C7C4×#12612yes—
500C2×C7C2×#39711yescharacteristic
501C2×C7#239211yescharacteristic
502C2×C7#239511yescharacteristic
503C2×C7#239512yes—
504C2×C7#239811yescharacteristic
505C2×C7#240112yes—
506D7—44no—
507C23—74no—
508C23—142no—
509C23—144no—
510C23—144no—
511C23—142no—
512C23—142no—
513C23—144no—
514C23—142no—
515C23—144no—
516C23—142no—
517C23—142no—
518C23—144no—
519C23—144no—
520C23—282no—
521C23—282no—
522C23—281no—
523C23—282no—
524C23—282no—
525C23—282no—
526C23—282no—
527C23—281no—
528C23—281no—
529C23—281no—
530C23C22×C4×D711yescharacteristic
531C23C2×D4×D711yescharacteristic
532C23C2×D4×D711yescharacteristic
533C23C2×#115911yescharacteristic
534C23C2×#115911yescharacteristic
535C23C2×#116112yes—
536C23D7×#4111yescharacteristic
537C23D7×#4111yescharacteristic
538C23D7×#4112yes—
539C23D7×#4112yes—
540C23D7×#4112yes—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—78no—
570C2×C4—74no—
571C2×C4—74no—
572C2×C4—78no—
573C2×C4—74no—
574C2×C4—144no—
575C2×C4—142no—
576C2×C4—142no—
577C2×C4—144no—
578C2×C4—144no—
579C2×C4—144no—
580C2×C4—144no—
581C2×C4—142no—
582C2×C4—144no—
583C2×C4—142no—
584C2×C4—144no—
585C2×C4—2816no—
586C2×C4—282no—
587C2×C4—282no—
588C2×C4—282no—
589C2×C4—282no—
590C2×C4—282no—
591C2×C4—281no—
592C2×C4—282no—
593C2×C4—282no—
594C2×C4—282no—
595C2×C4—282no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—281no—
599C2×C4(C22⋊D7)⋊C414yes—
600C7C4×#39711yescharacteristic, complemented, Sylow
601C22—148no—
602C22—144no—
603C22—284no—
604C22—282no—
605C22—282no—
606C22—282no—
607C22—282no—
608C22—282no—
609C22—284no—
610C22—282no—
611C22—284no—
612C22C2×(C22⋊D7)⋊C411yescharacteristic
613C22#9021312yes—
614C22C4×#115911yescharacteristic
615C22C4×D4×D711yescharacteristic
616C22C4×#116112yes—
617C22D7×#12111yescharacteristic
618C22#9029711yescharacteristic
619C22#9031512yes—
620C22#9031512yes—
621C22#9031812yes—
622C22#9034012yes—
623C22#9034012yes—
624C22D7×#12311yescharacteristic
625C22D7×#12312yes—
626C22#9034711yescharacteristic
627C22D7×#12411yescharacteristic
628C22#9037111yescharacteristic
629C22#9038212yes—
630C22#9038212yes—
631C22D7×#12612yes—
632C22#9039712yes—
633C22#9040711yescharacteristic
634C22#9041611yescharacteristic
635C4—24no—
636C4—42no—
637C4—42no—
638C4—44no—
639C4—44no—
640C4—78no—
641C4—284no—
642C4—282no—
643C4—284no—
644C4—282no—
645C2—284no—
646C2#1173149711yescharacteristic
647C2#1173238512yes—
648C2#1173238712yes—
649C2#1173373611yescharacteristic
650C2#1173392511yescharacteristic
651C2#1173490511yescharacteristic
652C2D7×#39711yescharacteristic
653C2#1173518211yescharacteristic
654C2#1173518311yescharacteristic
655C2#1173546212yes—
656C2#1173557712yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1445C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1445D7
hypocenterC7C4×#397
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic7C2semidirect
5. C7×#1445C2semidirect
8. #11727172C2semidirect
9. #11727169C2semidirect
10. Dic7×#95C2semidirect
11. Dic7×#95C2semidirect
35. #89765C4semidirect
58. C2×C7×C4⋊C4C2×C4semidirect
93. C7⋊#95C2×C4semidirect
94. C7⋊#95C2×C4semidirect
99. #1445D7semidirect
331. C2×C4⋊C4C4×D7semidirect
409. Dic7#397semidirect
600. C7C4×#397semidirect

Maximal subgroups

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

subgroupindex
C2×#897652
C2×C4⋊C4×Dic72
C2×#894382
C7×#14452
#117271832
#117271812
#117271722
#117271692
Dic7×#952
C4×#3977