Finite Group Databasebeta

← #13395076

Subgroups — #13395076

Order 1792.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2851C211yesmaximal, characteristic
2C2×#89835C211yesmaximal, characteristic, complemented
3C4×#6487C211yesmaximal, characteristic
4C2×#89698C211yesmaximal, characteristic
5#11729492C211yesmaximal, characteristic, complemented
6#11727375C211yesmaximal, characteristic, complemented
7#11727374C211yesmaximal, characteristic, complemented
8#11727370C211yesmaximal, characteristic, complemented
9#11727370C211yesmaximal, characteristic, complemented
10#11727313C211yesmaximal, characteristic, complemented
11#11727294C211yesmaximal, characteristic, complemented
12#11727281C211yesmaximal, characteristic
13#11727280C211yesmaximal, characteristic
14#11727274C211yesmaximal, characteristic
15#11727273C211yesmaximal, characteristic
16C2×C7×#125C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C2×#6487C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C7×#389C2211yescharacteristic
21C7×#389C2211yescharacteristic
22C7×#387—21no—
23C7×#387—21no—
24C7×#385—21no—
25C7×#385—21no—
26C7×#382C2211yescharacteristic
27C7×#380C2211yescharacteristic
28C7×#380C2211yescharacteristic
29#89984C2211yescharacteristic
30#89982—21no—
31C4×C22⋊Dic7—21no—
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2211yescharacteristic
34#89835—24no—
35C2×#6384C2211yescharacteristic
36C2×#6384C2211yescharacteristic
37C2×#6384C2211yescharacteristic
38C2×#6384C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40C2×#6382C2211yescharacteristic
41C2×#6381C2211yescharacteristic
42C2×#6381C2211yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44#89705—21no—
45C4×Dic7⋊C4—21no—
46#89701C2211yescharacteristic
47#89700C2211yescharacteristic
48#89698—24no—
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51C2×#6377C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#24707—71nomaximal, Sylow
62C23×C4×C7D411yescharacteristic
63C23×C4×C7D411yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C22×Dic14C2311yescharacteristic
66C7×#125—22no—
67C7×#125—22no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C22⋊C4—21no—
77C2×C7×C22⋊C4—21no—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7D411yescharacteristic
81C2×C42×C7D411yescharacteristic
82C2×C42×C7C2311yescharacteristic
83C2×C42×C7C2311yescharacteristic
84C2×C22⋊Dic7—21no—
85C2×C22⋊Dic7—21no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89#6487—22no—
90#6487—22no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2311yescharacteristic
99C22×C7⋊C8C2311yescharacteristic
100C4×Dic14—22no—
101C4×Dic14—22no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95—21no—
105C7×#95—21no—
106C7×#95—21no—
107C7×#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C22⋊(C7⋊C8)—22no—
114C22⋊(C7⋊C8)—22no—
115#6384—22no—
116#6384—22no—
117#6384—22no—
118#6384—22no—
119#6382—22no—
120#6382—22no—
121#6381—22no—
122#6381—22no—
123C4⋊(C7⋊C8)—22no—
124C4⋊(C7⋊C8)D414yes—
125#6377—22no—
126#6377—22no—
127C2×#479—71no—
128C2×#432—71no—
129#2851D711yescharacteristic
130C4×C22⋊Q8—71no—
131#2077—71no—
132#2076—71no—
133#2036—71no—
134#2035—71no—
135#1989—71no—
136#1949—71no—
137#1944—71no—
138#1943—71no—
139#1935—71no—
140#1935—71no—
141#1805—71no—
142C24×C7C2×D411yescharacteristic
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—41no—
157C22×C4×C7—41no—
158C22×C4×C7—41no—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C2×Dic14—21no—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14#4112yes—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—42no—
184C7×C4⋊C4—42no—
185C7×C4⋊C4—42no—
186C7×C4⋊C4—42no—
187C7×C22⋊C4—42no—
188C7×C22⋊C4—42no—
189C42×C7—22no—
190C42×C7—22no—
191C42×C7—21no—
192C42×C7—21no—
193C42×C7C2×D412yes—
194C42×C7#4112yes—
195C22⋊Dic7—24no—
196C22⋊Dic7—42no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7#4112yes—
203Dic7⋊C4—24no—
204Dic7⋊C4—42no—
205Dic7⋊C4—42no—
206C4×Dic7—42no—
207C4×Dic7—42no—
208C2×C7⋊C8—21no—
209C2×C7⋊C8—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8C2×D412yes—
219C2×C7⋊C8C2×D412yes—
220C2×#125C2×D711yescharacteristic
221C2×C22⋊Q8—71no—
222C2×C4×Q8—71no—
223C22×C42C2×D711yescharacteristic
224#479—144no—
225#432—144no—
226C2×#107—71no—
227C2×#107—71no—
228C2×#106—71no—
229C2×#106—71no—
230C2×C4⋊C8—71no—
231C2×C4⋊C8—71no—
232C2×#103—71no—
233C2×#103—71no—
234C2×#103—71no—
235C2×#103—71no—
236C2×C22⋊C8—71no—
237C2×C22⋊C8—71no—
238C2×#97—71no—
239C2×#97—71no—
240#391—71no—
241#389—71no—
242#389C2×D711yescharacteristic
243#389C2×D711yescharacteristic
244#387—21no—
245#387—21no—
246#387—141no—
247#385—21no—
248#385—21no—
249#385—141no—
250#382C2×D711yescharacteristic
251#380—71no—
252#380C2×D711yescharacteristic
253#380C2×D711yescharacteristic
254C4×C4⋊C4—71no—
255C4×C4⋊C4—141no—
256C4×C22⋊C4—141no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#340—71no—
265C23×C7—21no—
266C23×C7—21no—
267C23×C7—21no—
268C23×C7—21no—
269C23×C7—21no—
270C23×C7—21no—
271C23×C7#13712yes—
272C23×C7C22×D411yescharacteristic
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—44no—
287C2×C4×C7—44no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7#12112yes—
305C2×C4×C7#12112yes—
306C2×C4×C7C22×D411yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C2×C4×C7C2×#4111yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C72−1+411yescharacteristic
311C2×C4×C72−1+411yescharacteristic
312C2×Dic7—22no—
313C2×Dic7—22no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324Dic14—22no—
325Dic14—22no—
326Dic14—41no—
327Dic14—41no—
328C7⋊C8—22no—
329C7⋊C8—22no—
330C7⋊C8—41no—
331C7⋊C8—41no—
332C22×Q8—71no—
333C23×C4C22⋊D711yescharacteristic
334C23×C4C22⋊D711yescharacteristic
335C23×C4C22×D711yescharacteristic
336C22×C8—71no—
337C22×C8—71no—
338C22×C8—71no—
339C22×C8—71no—
340#125—22no—
341#125—22no—
342C22⋊Q8—142no—
343C22⋊Q8—142no—
344C4×Q8—142no—
345C4×Q8—142no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—71no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4C22×D711yescharacteristic
357C2×C4⋊C4C22×D711yescharacteristic
358C2×C4⋊C4C22×D711yescharacteristic
359C2×C4⋊C4C22×D711yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—141no—
363C2×C22⋊C4—141no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—141no—
367C2×C42—141no—
368C2×C42C22⋊D711yescharacteristic
369C2×C42C22⋊D711yescharacteristic
370C2×C42C22×D711yescharacteristic
371C2×C42C22×D711yescharacteristic
372#107—142no—
373#107—142no—
374#106—142no—
375#106—142no—
376C4⋊C8—74no—
377C4⋊C8—142no—
378#103—142no—
379#103—142no—
380#103—142no—
381#103—142no—
382C22⋊C8—142no—
383C22⋊C8—142no—
384#97—142no—
385#97—142no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—141no—
393#95—141no—
394#95—141no—
395#95—141no—
396#95—141no—
397C22×C7—22no—
398C22×C7—22no—
399C22×C7—22no—
400C22×C7—41no—
401C22×C7—41no—
402C22×C7—41no—
403C22×C7—41no—
404C22×C7C2×#12111yescharacteristic
405C22×C7#52511yescharacteristic
406C22×C7#53611yescharacteristic
407C22×C7C2×#13711yescharacteristic
408C22×C7#57511yescharacteristic
409C22×C7#57511yescharacteristic
410C22×C7#57511yescharacteristic
411C4×C7—22no—
412C4×C7—22no—
413C4×C7—41no—
414C4×C7—41no—
415C4×C7—41no—
416C4×C7—81no—
417C4×C7—81no—
418C4×C7—81no—
419C4×C7—81no—
420C4×C7#54711yescharacteristic
421C4×C7#54811yescharacteristic
422C4×C7#55211yescharacteristic
423C4×C7#55611yescharacteristic
424Dic7—42no—
425Dic7—42no—
426Dic7—81no—
427Dic7—81no—
428C24C2×C22⋊D711yescharacteristic
429C2×Q8—72no—
430C2×Q8—141no—
431C2×Q8—141no—
432C2×Q8—141no—
433C2×Q8—141no—
434C2×Q8—141no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4—141no—
455C22×C4C2×C22⋊D711yescharacteristic
456C22×C4C2×C22⋊D711yescharacteristic
457C22×C4C2×C22⋊D711yescharacteristic
458C22×C4C2×C22⋊D711yescharacteristic
459C22×C4C2×C22⋊D711yescharacteristic
460C22×C4C23×D711yescharacteristic
461C2×C8—72no—
462C2×C8—72no—
463C2×C8—141no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8—141no—
470C2×C8—141no—
471C2×C8—141no—
472C2×C8—141no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—72no—
486C4⋊C4—144no—
487C4⋊C4—141no—
488C4⋊C4—141no—
489C4⋊C4—141no—
490C4⋊C4—141no—
491C4⋊C4—141no—
492C4⋊C4—282no—
493C4⋊C4—282no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—144no—
497C22⋊C4—282no—
498C42—22no—
499C42—22no—
500C42—21no—
501C42—21no—
502C42—282no—
503C42—282no—
504C42D4×D712yes—
505C42#115912yes—
506C2×C7—42no—
507C2×C7#241511yescharacteristic
508C2×C7#305411yescharacteristic
509C2×C7#305611yescharacteristic
510C2×C7#311111yescharacteristic
511C2×C7#311711yescharacteristic
512C2×C7#323611yescharacteristic
513C2×C7#324011yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23#651412yes—
521C23C22×C22⋊D711yescharacteristic
522Q8—142no—
523Q8—142no—
524Q8—281no—
525Q8—281no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—281no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4#650212yes—
570C2×C4#650212yes—
571C2×C4C2×D4×D711yescharacteristic
572C2×C4C2×#115911yescharacteristic
573C2×C4#655111yescharacteristic
574C2×C4#655111yescharacteristic
575C2×C4D7×#4111yescharacteristic
576C2×C4D7×#4111yescharacteristic
577C8—142no—
578C8—142no—
579C8—281no—
580C8—281no—
581C7#2470711yescharacteristic, complemented, Sylow
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×#650211yescharacteristic
590C22#9050711yescharacteristic
591C22#9051311yescharacteristic
592C22#9051311yescharacteristic
593C22#9051311yescharacteristic
594C22C2×#651411yescharacteristic
595C22#9051911yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—282no—
606C4—282no—
607C4—561no—
608C4—561no—
609C4#9032211yescharacteristic
610C4#9032411yescharacteristic
611C4#9033011yescharacteristic
612C4#9033211yescharacteristic
613C2—42no—
614C2#1174025911yescharacteristic
615C2#1174036811yescharacteristic
616C2#1174037011yescharacteristic
617C2#1174046611yescharacteristic
618C2#1174058711yescharacteristic
619C2#1174059811yescharacteristic
620C2#1174080711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2851C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenter#2851D7
hypocenterC7#24707
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
2. C2×#89835C2semidirect
5. #11729492C2semidirect
6. #11727375C2semidirect
7. #11727374C2semidirect
8. #11727370C2semidirect
9. #11727370C2semidirect
10. #11727313C2semidirect
11. #11727294C2semidirect
581. C7#24707semidirect

Maximal subgroups

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

subgroupindex
C7×#28512
C2×#898352
C4×#64872
C2×#896982
#117294922
#117273752
#117273742
#117273702
#117273132
#117272942
#117272812
#117272802
#117272742
#117272732
#247077