Finite Group Databasebeta

← #13395068

Subgroups — #13395068

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
1C2×C7×#432C211yesmaximal, characteristic
2#11739519C211yesmaximal, characteristic
3C4×#6487C211yesmaximal, characteristic
4C2×#89601C211yesmaximal, characteristic, complemented
5#11728240C211yesmaximal, characteristic, complemented
6#11728215C211yesmaximal, characteristic, complemented
7#11728209C211yesmaximal, characteristic, complemented
8#11727694C211yesmaximal, characteristic
9#11727693C211yesmaximal, characteristic
10#11727691C211yesmaximal, characteristic
11#11727690C211yesmaximal, characteristic
12#11727574C211yesmaximal, characteristic, complemented
13#11727573C211yesmaximal, characteristic, complemented
14#11727571C211yesmaximal, characteristic, complemented
15#11727571C211yesmaximal, characteristic, complemented
16C22×C42×C7C2211yescharacteristic
17C2×#6487C2211yescharacteristic
18C2×#6433C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C7×#432—24no—
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C7×C22⋊C8C2211yescharacteristic
25C2×C7×#97C2211yescharacteristic
26C2×C7×#97C2211yescharacteristic
27#89984C2211yescharacteristic
28#89984C2211yescharacteristic
29#89984C2211yescharacteristic
30#89982—21no—
31#89982—21no—
32#89982—21no—
33C4×C22⋊Dic7—21no—
34C2×#6392C2211yescharacteristic
35C2×#6392C2211yescharacteristic
36C2×#6391C2211yescharacteristic
37C2×#6391C2211yescharacteristic
38C2×#6390C2211yescharacteristic
39C2×#6390C2211yescharacteristic
40C2×#6390C2211yescharacteristic
41C2×#6390C2211yescharacteristic
42#89708C2211yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44#89705—21no—
45#89705—21no—
46#89705—21no—
47C4×Dic7⋊C4—21no—
48#89701C2211yescharacteristic
49#89700C2211yescharacteristic
50#89700C2211yescharacteristic
51#89700C2211yescharacteristic
52#89601—24no—
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89346C2211yescharacteristic
61#24707—71nomaximal, Sylow
62C23×C4×C7D411yescharacteristic
63C23×C4×C7D411yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C22×Dic14C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7D411yescharacteristic
73C2×C42×C7D411yescharacteristic
74C2×C42×C7C2311yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C22⋊Dic7—21no—
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80C2×C4⋊Dic7C2311yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87#6487—22no—
88#6487—22no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—21no—
98#6433—22no—
99#6433—22no—
100C4×Dic14—22no—
101C4×Dic14—22no—
102C7×C4⋊C8—22no—
103C7×C4⋊C8D414yes—
104C7×C22⋊C8—22no—
105C7×C22⋊C8—22no—
106C7×#97—22no—
107C7×#97—22no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119#6392—22no—
120#6392—22no—
121#6391—22no—
122#6391—22no—
123#6390—22no—
124#6390—22no—
125#6390—22no—
126#6390—22no—
127C2×#479—71no—
128C2×#432D711yescharacteristic
129#2851—71no—
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—41no—
153C22×C4×C7—41no—
154C22×C4×C7—41no—
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2411yescharacteristic
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—21no—
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—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8—21no—
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8C2×D412yes—
186C2×C7×C8C2×D412yes—
187C42×C7—22no—
188C42×C7—22no—
189C42×C7—21no—
190C42×C7—21no—
191C42×C7C2×D412yes—
192C42×C7#4112yes—
193C22⋊Dic7—24no—
194C22⋊Dic7—42no—
195C22⋊Dic7—42no—
196C22⋊Dic7—42no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7#4112yes—
211Dic7⋊C4—24no—
212Dic7⋊C4—42no—
213Dic7⋊C4—42no—
214Dic7⋊C4—42no—
215Dic7⋊C4—42no—
216Dic7⋊C4—42no—
217Dic7⋊C4—42no—
218C4×Dic7—42no—
219C4×Dic7—42no—
220C2×#125—71no—
221C2×C22⋊Q8—71no—
222C2×C4×Q8—71no—
223C22×C42C2×D711yescharacteristic
224#479—144no—
225#432—24no—
226C2×#107—71no—
227C2×#107—71no—
228C2×#106—71no—
229C2×#106—71no—
230C2×C4⋊C8C2×D711yescharacteristic
231C2×C4⋊C8C2×D711yescharacteristic
232C2×#103—71no—
233C2×#103—71no—
234C2×#103—71no—
235C2×#103—71no—
236C2×C22⋊C8C2×D711yescharacteristic
237C2×C22⋊C8C2×D711yescharacteristic
238C2×#97C2×D711yescharacteristic
239C2×#97C2×D711yescharacteristic
240#391—71no—
241#389—71no—
242#389—71no—
243#389—71no—
244#387—141no—
245#387—141no—
246#387—141no—
247#385—141no—
248#385—141no—
249#385—141no—
250#382—71no—
251#380—71no—
252#380—71no—
253#380—71no—
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#12112yes—
293C2×C4×C7#12112yes—
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C2×C4×C7C2×#4111yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C2×C4×C72−1+411yescharacteristic
299C2×C4×C72−1+411yescharacteristic
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
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×C4D2811yescharacteristic
334C23×C4D2811yescharacteristic
335C23×C4C22×D711yescharacteristic
336C22×C8C22×D711yescharacteristic
337C22×C8C22×D711yescharacteristic
338C22×C8C22×D711yescharacteristic
339C22×C8C22×D711yescharacteristic
340#125—142no—
341#125—142no—
342C22⋊Q8—142no—
343C22⋊Q8—142no—
344C4×Q8—142no—
345C4×Q8—142no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—71no—
349C2×C4⋊C4—71no—
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⋊C4—141no—
357C2×C4⋊C4—141no—
358C2×C4⋊C4—141no—
359C2×C4⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C22⋊C4—141no—
362C2×C22⋊C4—141no—
363C2×C22⋊C4—141no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—141no—
367C2×C42—141no—
368C2×C42D2811yescharacteristic
369C2×C42D2811yescharacteristic
370C2×C42C22×D711yescharacteristic
371C2×C42C22×D711yescharacteristic
372#107—142no—
373#107—142no—
374#106—142no—
375#106—142no—
376C4⋊C8—22no—
377C4⋊C8C22⋊D714yes—
378#103—142no—
379#103—142no—
380#103—142no—
381#103—142no—
382C22⋊C8—22no—
383C22⋊C8—22no—
384#97—22no—
385#97—22no—
386#95—141no—
387#95—141no—
388#95—141no—
389#95—141no—
390#95—141no—
391#95—141no—
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#54711yescharacteristic
417C4×C7#54811yescharacteristic
418C4×C7#55211yescharacteristic
419C4×C7#55611yescharacteristic
420Dic7—42no—
421Dic7—42no—
422Dic7—81no—
423Dic7—81no—
424Dic7—81no—
425Dic7—81no—
426Dic7—81no—
427Dic7—81no—
428C24C2×D2811yescharacteristic
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—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4—141no—
455C22×C4C2×D2811yescharacteristic
456C22×C4C2×D2811yescharacteristic
457C22×C4C2×D2811yescharacteristic
458C22×C4C2×D2811yescharacteristic
459C22×C4C2×D2811yescharacteristic
460C22×C4C23×D711yescharacteristic
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×C22⋊D712yes—
472C2×C8C2×C22⋊D712yes—
473C4⋊C4—72no—
474C4⋊C4—144no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—141no—
481C4⋊C4—141no—
482C4⋊C4—141no—
483C4⋊C4—141no—
484C4⋊C4—141no—
485C4⋊C4—141no—
486C4⋊C4—141no—
487C4⋊C4—141no—
488C4⋊C4—282no—
489C4⋊C4—282no—
490C4⋊C4—282no—
491C4⋊C4—282no—
492C4⋊C4—282no—
493C4⋊C4—282no—
494C22⋊C4—144no—
495C22⋊C4—282no—
496C22⋊C4—282no—
497C22⋊C4—282no—
498C42—22no—
499C42—22no—
500C42—21no—
501C42—21no—
502C42—282no—
503C42—282no—
504C42#115712yes—
505C42C2×C22⋊D712yes—
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#647212yes—
521C23C22×D2811yescharacteristic
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—142no—
546C2×C4—142no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—281no—
550C2×C4—281no—
551C2×C4—281no—
552C2×C4—281no—
553C2×C4—281no—
554C2×C4—281no—
555C2×C4—281no—
556C2×C4—281no—
557C2×C4—281no—
558C2×C4—281no—
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#649312yes—
570C2×C4#649312yes—
571C2×C4C2×#115711yescharacteristic
572C2×C4D7×#4111yescharacteristic
573C2×C4D7×#4111yescharacteristic
574C2×C4#655411yescharacteristic
575C2×C4#655411yescharacteristic
576C2×C4C22×C22⋊D711yescharacteristic
577C8—22no—
578C8—22no—
579C8—41no—
580C8—41no—
581C7#2470711yescharacteristic, complemented, Sylow
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22#9021511yescharacteristic
590C22#9021711yescharacteristic
591C22C2×#647211yescharacteristic
592C22#9043911yescharacteristic
593C22#9043911yescharacteristic
594C22#9043911yescharacteristic
595C22C2×#649311yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—282no—
602C4—282no—
603C4—561no—
604C4—561no—
605C4—561no—
606C4—561no—
607C4—561no—
608C4—561no—
609C4#9022011yescharacteristic
610C4#9022411yescharacteristic
611C4#9051511yescharacteristic
612C4#9052211yescharacteristic
613C2—42no—
614C2#1173676511yescharacteristic
615C2#1173676911yescharacteristic
616C2#1173679011yescharacteristic
617C2#1173680211yescharacteristic
618C2#1173972211yescharacteristic
619C2#1174121611yescharacteristic
620C2#1174122111yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#432C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenterC2×#432D7
hypocenterC7#24707
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
4. C2×#89601C2semidirect
5. #11728240C2semidirect
6. #11728215C2semidirect
7. #11728209C2semidirect
12. #11727574C2semidirect
13. #11727573C2semidirect
14. #11727571C2semidirect
15. #11727571C2semidirect
581. C7#24707semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4322
#117395192
C4×#64872
C2×#896012
#117282402
#117282152
#117282092
#117276942
#117276932
#117276912
#117276902
#117275742
#117275732
#117275712
#247077