Finite Group Databasebeta

← #13412604

Subgroups — #13412604

Order 1792.

774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#499C211yesmaximal, characteristic, complemented
2#11740503C211yesmaximal, characteristic
3#11740473C211yesmaximal, characteristic
4C2×#89653C211yesmaximal, characteristic
5#11729493C211yesmaximal, characteristic, complemented
6#11729493C211yesmaximal, characteristic, complemented
7#11728385C211yesmaximal, characteristic
8#11728367C211yesmaximal, characteristic, complemented
9#11728362C211yesmaximal, characteristic, complemented
10#11728334C211yesmaximal, characteristic
11#11728333C211yesmaximal, characteristic
12#11728325C211yesmaximal, characteristic, complemented
13#11728321C211yesmaximal, characteristic, complemented
14#11727535C211yesmaximal, characteristic
15#11727523C211yesmaximal, characteristic, complemented
16C2×C7×#125C2211yescharacteristic
17C2×C7×#125C2211yescharacteristic
18C22×#1131C2211yescharacteristic
19C2×#6455C2211yescharacteristic
20C2×D7×C4⋊C4C2211yescharacteristic
21C7×#499—24no—
22C2×C7×#107C2211yescharacteristic
23C2×C7×#107C2211yescharacteristic
24C2×C7×#106C2211yescharacteristic
25C2×C7×#106C2211yescharacteristic
26C2×C4×C7×C8C2211yescharacteristic
27C2×(C2×D7)⋊C8C2211yescharacteristic
28C2×#6391C2211yescharacteristic
29C2×#6391C2211yescharacteristic
30C2×#6389C2211yescharacteristic
31#89766—21no—
32#89764—21no—
33#89761—21no—
34#89759—21no—
35#89759C2211yescharacteristic
36#89759C2211yescharacteristic
37#89757C2211yescharacteristic
38#89757C2211yescharacteristic
39#89756—21no—
40#89754—21no—
41#89750—21no—
42#89749C2211yescharacteristic
43#89748C2211yescharacteristic
44#89745—21no—
45C2×#6382C2211yescharacteristic
46C2×#6382C2211yescharacteristic
47C2×#6381C2211yescharacteristic
48C2×#6381C2211yescharacteristic
49C4×(C2×D7)⋊C4C2211yescharacteristic
50#89700C2211yescharacteristic
51#89700C2211yescharacteristic
52#89653—24no—
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89345C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#26075—71nomaximal, Sylow
62C22×C4×D7—21no—
63C22×C4×D7C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C7×#125—22no—
67C7×#125—22no—
68C7×#125—41no—
69C7×#125—41no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C42×C7C2311yescharacteristic
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4D411yescharacteristic
83C2×(C2×D7)⋊C4D411yescharacteristic
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7—21no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2311yescharacteristic
99C2×#1131—22no—
100C2×#1131—22no—
101C2×#1131Q814yes—
102#6455—22no—
103#6455—41no—
104D7×C4⋊C4—22no—
105D7×C4⋊C4—41no—
106C7×#107—22no—
107C7×#107D414yes—
108C7×#106—22no—
109C7×#106—22no—
110C4×C7×C8—22no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119C7⋊#95D411yescharacteristic
120C7⋊#95D411yescharacteristic
121(C2×D7)⋊C8Q814yes—
122#6391—22no—
123#6391—22no—
124#6389—22no—
125#6382—22no—
126#6382—41no—
127#6381—22no—
128#6381—41no—
129C2×#499D711yescharacteristic, complemented
130C2×#428—71no—
131#2442—71no—
132#2441—71no—
133#2085—71no—
134#2084—71no—
135#2059—71no—
136#2059—71no—
137#1943—71no—
138#1941—71no—
139#1854—71no—
140#1853—71no—
141#1847—71no—
142#1809—71no—
143#1753—71no—
144C23×D7C2×D411yescharacteristic
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2411yescharacteristic
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7C2×D411yescharacteristic
157C22×Dic7C2×D411yescharacteristic
158C22×Dic7C2×D411yescharacteristic
159C2×C4×D7—21no—
160C2×C4×D7—21no—
161C2×C4×D7—21no—
162C2×C4×D7—21no—
163C2×C4×D7—42no—
164C2×C4×D7—42no—
165C2×C4×D7—81no—
166C2×C4×D7C2×Q812yes—
167C2×C4×D7C2×Q812yes—
168C2×C7×C8—21no—
169C2×C7×C8—21no—
170C2×C7×C8C2×D412yes—
171C2×C7×C8C2×Q812yes—
172C2×C7×C8C2×Q812yes—
173C2×C7×C8#4112yes—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—42no—
181C7×C4⋊C4—42no—
182C7×C4⋊C4—42no—
183C7×C4⋊C4—42no—
184C7×C4⋊C4C2×D412yes—
185C7×C4⋊C4C2×D412yes—
186C42×C7—21no—
187C42×C7—21no—
188(C2×D7)⋊C4—41no—
189(C2×D7)⋊C4—41no—
190(C2×D7)⋊C4—42no—
191(C2×D7)⋊C4—42no—
192(C2×D7)⋊C4—81no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—42no—
202C4⋊Dic7—81no—
203Dic7⋊C4—42no—
204Dic7⋊C4—42no—
205Dic7⋊C4—81no—
206Dic7⋊C4—81no—
207Dic7⋊C4—81no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C4×Dic7—42no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8C2×Q812yes—
216C2×C7⋊C8C2×Q812yes—
217#1131—28no—
218C22×M16—71no—
219C2×#125C2×D711yescharacteristic
220C2×#125C2×D711yescharacteristic
221C2×#117—71no—
222C22×C4⋊C4—71no—
223#499—24no—
224#428—144no—
225C2×#107—71no—
226C2×#107—71no—
227C2×#107C2×D711yescharacteristic
228C2×#107C2×D711yescharacteristic
229C2×#106—71no—
230C2×#106—71no—
231C2×#106—71no—
232C2×#106—71no—
233C2×#106C2×D711yescharacteristic
234C2×#106C2×D711yescharacteristic
235C2×C22⋊C8—71no—
236C2×#97—71no—
237C2×C4×C8C2×D711yescharacteristic
238#400—141no—
239#399—141no—
240#398—141no—
241#396—141no—
242#389—71no—
243#389—71no—
244#389—71no—
245#389—71no—
246#389—141no—
247#387—141no—
248#385—141no—
249#384—71no—
250#382—71no—
251#380—71no—
252#380—71no—
253#380—141no—
254C4×C22⋊C4—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#336—71no—
262#336—71no—
263C23×C7C22×D411yescharacteristic
264C22×D7—21no—
265C22×D7—21no—
266C22×D7—21no—
267C22×D7—21no—
268C22×D7—21no—
269C22×D7—21no—
270C22×D7C4⋊Q812yes—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
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—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7C22×D411yescharacteristic
290C2×C4×C7C22×Q811yescharacteristic
291C2×C4×C7C22×Q811yescharacteristic
292C2×C4×C7C2×#4111yescharacteristic
293C2×C4×C7H(5,𝔽2)11yescharacteristic
294C2×C4×C72−1+411yescharacteristic
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301C2×Dic7—21no—
302C2×Dic7—21no—
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×Dic7C4⋊Q812yes—
316C4×D7—22no—
317C4×D7—22no—
318C4×D7—22no—
319C4×D7—22no—
320C4×D7—84no—
321C7×C8—22no—
322C7×C8C22⋊Q814yes—
323C7⋊C8—22no—
324C7⋊C8—22no—
325C23×C4—71no—
326C23×C4—141no—
327C2×M16—74no—
328C2×M16—142no—
329C2×M16—142no—
330C22×C8—71no—
331C22×C8—71no—
332C22×C8C22×D711yescharacteristic
333C22×C8C22×D711yescharacteristic
334#125—22no—
335#125—22no—
336#125—41no—
337#125—41no—
338#117—142no—
339#117—281no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—142no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4—281no—
357C2×C4⋊C4C22×D711yescharacteristic
358C2×C4⋊C4C22×D711yescharacteristic
359C2×C4⋊C4C22×D711yescharacteristic
360C2×C4⋊C4C22×D711yescharacteristic
361C2×C22⋊C4—71no—
362C2×C22⋊C4—71no—
363C2×C22⋊C4—141no—
364C2×C22⋊C4—141no—
365C2×C22⋊C4—141no—
366C2×C42—71no—
367C2×C42—141no—
368C2×C42C22×D711yescharacteristic
369#107—22no—
370#107—142no—
371#107—281no—
372#107C22⋊D714yes—
373#106—22no—
374#106—22no—
375#106—142no—
376#106—142no—
377#106—142no—
378#106—281no—
379C22⋊C8—74no—
380#97—142no—
381C4×C8—22no—
382#95—71no—
383#95—71no—
384#95—141no—
385#95—141no—
386#95—141no—
387#95—141no—
388#95—141no—
389#95—141no—
390#95—141no—
391#95—141no—
392C22×C7C2×C4⋊Q811yescharacteristic
393C22×C7D4211yescharacteristic
394C22×C7#54711yescharacteristic
395C22×C7#57511yescharacteristic
396C22×C7#57511yescharacteristic
397C22×C7#57711yescharacteristic
398C22×C7#57711yescharacteristic
399C2×D7—22no—
400C2×D7—22no—
401C2×D7—22no—
402C2×D7—41no—
403C2×D7—41no—
404C2×D7—41no—
405C2×D7—41no—
406C4×C7—42no—
407C4×C7—41no—
408C4×C7—42no—
409C4×C7—41no—
410C4×C7—81no—
411C4×C7—81no—
412C4×C7C2×C22⋊Q811yescharacteristic
413C4×C7#54411yescharacteristic
414C4×C7D4×Q811yescharacteristic
415C4×C7#55411yescharacteristic
416Dic7—22no—
417Dic7—41no—
418Dic7—41no—
419Dic7—81no—
420Dic7—81no—
421Dic7—81no—
422Dic7—81no—
423C24—71no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—71no—
429C22×C4—72no—
430C22×C4—72no—
431C22×C4—71no—
432C22×C4—71no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4—141no—
441C22×C4—282no—
442C22×C4—282no—
443C22×C4—561no—
444C22×C4D4×D711yescharacteristic
445C22×C4D4×D711yescharacteristic
446C22×C4C23×D711yescharacteristic
447M16—148no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—72no—
451C2×C8—72no—
452C2×C8—141no—
453C2×C8—141no—
454C2×C8—141no—
455C2×C8—141no—
456C2×C8Q8×D712yes—
457C2×C8Q8×D712yes—
458C2×C8#116112yes—
459C2×C8C2×C22⋊D712yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—282no—
479C4⋊C4—282no—
480C4⋊C4—282no—
481C4⋊C4—561no—
482C4⋊C4—561no—
483C4⋊C4—561no—
484C4⋊C4—561no—
485C4⋊C4C2×C22⋊D712yes—
486C4⋊C4C2×C22⋊D712yes—
487C22⋊C4—281no—
488C22⋊C4—281no—
489C22⋊C4—282no—
490C22⋊C4—282no—
491C22⋊C4—561no—
492C42—21no—
493C42—21no—
494C42—141no—
495C42—141no—
496C42—282no—
497C2×C7#244011yescharacteristic
498C2×C7#316311yescharacteristic
499C2×C7#316611yescharacteristic
500C2×C7#326711yescharacteristic
501C2×C7#327111yescharacteristic
502C2×C7#335111yescharacteristic
503C2×C7#335111yescharacteristic
504D7—42no—
505C23—72no—
506C23—141no—
507C23—141no—
508C23—141no—
509C23—141no—
510C23—141no—
511C23—141no—
512C23C2×D4×D711yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—72no—
532C2×C4—141no—
533C2×C4—141no—
534C2×C4—142no—
535C2×C4—142no—
536C2×C4—142no—
537C2×C4—142no—
538C2×C4—141no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—141no—
543C2×C4—141no—
544C2×C4—281no—
545C2×C4—281no—
546C2×C4—281no—
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—564no—
557C2×C4#654811yescharacteristic
558C2×C4C2×Q8×D711yescharacteristic
559C2×C4C2×Q8×D711yescharacteristic
560C2×C4C2×#116111yescharacteristic
561C2×C4#655111yescharacteristic
562C2×C4C22×C22⋊D711yescharacteristic
563C8—22no—
564C8—142no—
565C8—142no—
566C8#650914yes—
567C7#2607511yescharacteristic, complemented, Sylow
568C22—142no—
569C22—142no—
570C22—142no—
571C22—281no—
572C22—281no—
573C22—281no—
574C22—281no—
575C22D7×C4⋊Q811yescharacteristic
576C22#9041711yescharacteristic
577C22#9045911yescharacteristic
578C22#9045911yescharacteristic
579C22#9046111yescharacteristic
580C22#9046111yescharacteristic
581C22D4×C22⋊D711yescharacteristic
582C4—41no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—142no—
589C4—281no—
590C4—281no—
591C4—561no—
592C4—561no—
593C4—561no—
594C4—561no—
595C4#9042011yescharacteristic
596C4#9042111yescharacteristic
597C4C2×#650911yescharacteristic
598C4Q8×C22⋊D711yescharacteristic
599C2—282no—
600C2#1173936211yescharacteristic
601C2#1173936411yescharacteristic
602C2#1173937211yescharacteristic
603C2#1173937211yescharacteristic
604C2#1174067811yescharacteristic
605C2#1174136611yescharacteristic
606C2#1174136811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#499C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#499D7
hypocenterC7#26075
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
1. C2×C7×#499C2semidirect
5. #11729493C2semidirect
6. #11729493C2semidirect
8. #11728367C2semidirect
9. #11728362C2semidirect
12. #11728325C2semidirect
13. #11728321C2semidirect
15. #11727523C2semidirect
129. C2×#499D7semidirect
567. C7#26075semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4992
#117405032
#117404732
C2×#896532
#117294932
#117283852
#117283672
#117283622
#117283342
#117283332
#117283252
#117283212
#117275352
#117275232
#260757