Finite Group Databasebeta

← #13362272

Subgroups — #13362272

Order 1792.

1126 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×#124C211yesmaximal, characteristic, complemented
2C2×#89831C211yesmaximal, characteristic
3C2×#89798C211yesmaximal, characteristic, complemented
4C2×#89802C211yesmaximal, characteristic, complemented
5C2×#89786C211yesmaximal, characteristic
6C2×#89790C211yesmaximal, characteristic, complemented
7C4×#6438C211yesmaximal, characteristic, complemented
8#11729479C211yesmaximal, characteristic, complemented
9#11727433C211yesmaximal, characteristic, complemented
10#11727432C211yesmaximal, characteristic, complemented
11#11727403C211yesmaximal, characteristic, complemented
12#11727402C211yesmaximal, characteristic
13#11727305C211yesmaximal, characteristic, complemented
14#11727303C211yesmaximal, characteristic, complemented
15C4×#6377C211yesmaximal, characteristic, complemented
16C2×C7×#124C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1143C2211yescharacteristic
21C22×#1142C2211yescharacteristic
22C22×#1141C2211yescharacteristic
23C2×#6438C2211yescharacteristic
24C2×C4×D28C2211yescharacteristic
25C2×C4×Dic14C2211yescharacteristic
26C7×#391C2211yescharacteristic
27C7×#390C2211yescharacteristic
28C7×#388—22no—
29C7×#382C2211yescharacteristic
30C4×C7×C22⋊C4—22no—
31C43×C7C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36#89831C418yescomplemented
37#89802—24no—
38#89798—24no—
39#89790—24no—
40#89786—24no—
41C2×#6384C2211yescharacteristic
42C2×#6384C2211yescharacteristic
43C2×#6383C2211yescharacteristic
44C2×#6383C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6382C2211yescharacteristic
47C2×#6381C2211yescharacteristic
48C2×#6381C2211yescharacteristic
49#89712—22no—
50#89711C2211yescharacteristic
51C4×(C2×D7)⋊C4—22no—
52#89708C2211yescharacteristic
53#89701C2211yescharacteristic
54C2×#6377C2211yescharacteristic
55C2×#6377C2211yescharacteristic
56C2×#6377C2211yescharacteristic
57C2×#6377C2211yescharacteristic
58C2×C4×C7⋊C8C2211yescharacteristic
59C2×C4×C7⋊C8C2211yescharacteristic
60#21693—71nomaximal, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×C7×D4C2311yescharacteristic
63C23×C4×C7—21no—
64C22×D28C2311yescharacteristic
65C22×C4×D7—21no—
66C22×Dic14C2311yescharacteristic
67C7×#124—22no—
68C7×#124C2×C414yescomplemented
69C4×C7×Q8—22no—
70C4×C7×Q8—22no—
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—21no—
79C2×C42×C7—21no—
80C2×C42×C7D412yes—
81C2×C42×C7D412yes—
82C2×C42×C7C2311yescharacteristic
83C2×C42×C7C2311yescharacteristic
84C2×C42×C7C2311yescharacteristic
85C2×#1144—22no—
86C2×#1144—22no—
87C2×#1144C2×C414yescomplemented
88C2×#1143—22no—
89C2×#1143—22no—
90C2×#1143C2×C414yescomplemented
91C2×#1142—22no—
92C2×#1142—22no—
93C2×#1142C2×C414yescomplemented
94C2×#1141—22no—
95C2×#1141—22no—
96C2×#1141C2×C414yes—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—22no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×Dic7⋊C4—21no—
103C2×C4×Dic7—21no—
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108#6438—22no—
109#6438C2×C414yescomplemented
110C4×D28—22no—
111C4×D28—22no—
112C4×Dic14—22no—
113C4×Dic14—22no—
114C7×#95—22no—
115C7×#95—22no—
116#6409—22no—
117#6409—22no—
118#6406—22no—
119#6406—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122#6384—22no—
123#6384—22no—
124#6383—22no—
125#6383—22no—
126#6382—22no—
127#6382—22no—
128#6381—22no—
129#6381—22no—
130#6377—22no—
131#6377—22no—
132#6377D414yes—
133#6377D414yes—
134C4×C7⋊C8—22no—
135C4×C7⋊C8C2×C414yescomplemented
136C2×#495—71no—
137C2×#442—71no—
138C2×#441—71no—
139C2×#440—71no—
140C2×#440—71no—
141C4×#124—71no—
142C4×#124D711yescharacteristic, complemented
143#1973—71no—
144#1973—71no—
145#1972—71no—
146#1971—71no—
147#1958—71no—
148#1958—71no—
149#1846—71no—
150C4×#97—71no—
151C24×C7—21no—
152C23×D7—21no—
153C2×C7×Q8—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8C22×C412yes—
159C2×C7×D4—21no—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4C22×C412yes—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—44no—
169C22×C4×C7—42no—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2411yescharacteristic
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C2×D28—21no—
179C2×D28—21no—
180C2×D28—21no—
181C2×D28—21no—
182C2×D28—21no—
183C2×D28C22×C412yes—
184C2×C4×D7—44no—
185C2×C4×D7—42no—
186C2×Dic14—21no—
187C2×Dic14—21no—
188C2×Dic14—21no—
189C2×Dic14—21no—
190C2×Dic14—21no—
191C2×Dic14C22×C412yes—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—42no—
197C7×C22⋊C4—28no—
198C7×C22⋊C4—44no—
199C7×C22⋊C4—42no—
200C42×C7—21no—
201C42×C7—21no—
202C42×C7—42no—
203C42×C7—42no—
204C42×C7—42no—
205C42×C7C22×C412yes—
206C42×C7C2×D412yes—
207C42×C7C2×D412yes—
208C42×C7#4112yes—
209#1144—28no—
210#1143—28no—
211#1142—28no—
212#1141—28no—
213(C2×D7)⋊C4—28no—
214(C2×D7)⋊C4—44no—
215(C2×D7)⋊C4—42no—
216C4⋊Dic7—21no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7—21no—
220Dic7⋊C4—42no—
221C4×Dic7—42no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8C22×C412yes—
227C2×C7⋊C8C22×C412yes—
228C2×C7⋊C8C2×D412yes—
229C2×C7⋊C8C2×D412yes—
230C2×C7⋊C8C2×D412yes—
231C2×C7⋊C8C2×D412yes—
232C2×C7⋊C8#4112yes—
233C2×C7⋊C8#4112yes—
234C22×Q16—71no—
235C22×SD16—71no—
236C22×SD16—71no—
237C22×D8—71no—
238C2×#124—71no—
239C2×#124C2×D711yescharacteristic
240C2×C4×Q8—71no—
241C2×C4×Q8C2×D711yescharacteristic
242C2×C4×D4—71no—
243C2×C4×D4C2×D711yescharacteristic
244#495—78no—
245#442—144no—
246#441—144no—
247#440—144no—
248#440—144no—
249C2×#107—71no—
250C2×#107—71no—
251C2×#106—71no—
252C2×#106—71no—
253C2×#103—71no—
254C2×#103—71no—
255C2×#103—71no—
256C2×#103—71no—
257C2×#102—71no—
258C2×#102—71no—
259C2×#102—71no—
260C2×#102—71no—
261C2×#97—71no—
262C2×#97—71no—
263C2×#97—71no—
264C2×#97—71no—
265C2×C4×C8—71no—
266C2×C4×C8—71no—
267#391—71no—
268#391C2×D711yescharacteristic
269#390—71no—
270#390C2×D711yescharacteristic
271#388—22no—
272#388—142no—
273#382—71no—
274#382C2×D711yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4—142no—
277C43C2×D711yescharacteristic
278C23×C7—22no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7C22×D411yescharacteristic
284C22×D7—22no—
285C22×D7—41no—
286C22×D7—41no—
287C22×D7—42no—
288C22×D7—42no—
289C7×Q8—22no—
290C7×Q8—22no—
291C7×Q8—41no—
292C7×Q8—41no—
293C7×D4—22no—
294C7×D4—22no—
295C7×D4—41no—
296C7×D4—41no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—84no—
312C2×C4×C7C4×D414yes—
313C2×C4×C7#12712yes—
314C2×C4×C7#12712yes—
315C2×C4×C7C23×C411yescharacteristic
316C2×C4×C7C22×D411yescharacteristic
317C2×C4×C7C22×D411yescharacteristic
318C2×C4×C7C2×#4111yescharacteristic
319C2×C4×C7C2×#4111yescharacteristic
320C2×C4×C7C2×#4111yescharacteristic
321C2×Dic7—22no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328D28—22no—
329D28—22no—
330D28—41no—
331D28—41no—
332C4×D7—84no—
333Dic14—22no—
334Dic14—22no—
335Dic14—41no—
336Dic14—41no—
337C7⋊C8—22no—
338C7⋊C8—22no—
339C7⋊C8C4×D414yes—
340C7⋊C8C4×D414yes—
341C22×Q8—71no—
342C22×Q8C22×D711yescharacteristic
343C22×D4—71no—
344C22×D4C22×D711yescharacteristic
345C23×C4—21no—
346C23×C4—141no—
347C2×Q16—74no—
348C2×Q16—142no—
349C2×Q16—142no—
350C2×SD16—74no—
351C2×SD16—74no—
352C2×SD16—142no—
353C2×SD16—142no—
354C2×SD16—142no—
355C2×SD16—142no—
356C2×D8—74no—
357C2×D8—142no—
358C2×D8—142no—
359C22×C8—71no—
360C22×C8—71no—
361C22×C8—71no—
362C22×C8—71no—
363#124—22no—
364#124—74no—
365#124—142no—
366#124C4×D714yescomplemented
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—142no—
370C4×Q8—142no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—142no—
374C4×D4—142no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—71no—
377C2×C4⋊C4—71no—
378C2×C4⋊C4—141no—
379C2×C4⋊C4C22×D711yescharacteristic
380C2×C4⋊C4C22×D711yescharacteristic
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—142no—
385C2×C22⋊C4—141no—
386C2×C22⋊C4—142no—
387C2×C42—21no—
388C2×C42—141no—
389C2×C42C22⋊D712yes—
390C2×C42C22⋊D712yes—
391C2×C42C22×D711yescharacteristic
392C2×C42C22×D711yescharacteristic
393C2×C42C22×D711yescharacteristic
394#107—142no—
395#107—142no—
396#106—142no—
397#106—142no—
398#103—142no—
399#103—142no—
400#103—142no—
401#103—142no—
402#102—142no—
403#102—142no—
404#102—142no—
405#102—142no—
406#97—74no—
407#97—74no—
408#97—142no—
409#97—142no—
410C4×C8—74no—
411C4×C8—142no—
412#95—22no—
413#95—22no—
414#95—142no—
415#95—142no—
416C22×C7—42no—
417C22×C7—44no—
418C22×C7—81no—
419C22×C7—81no—
420C22×C7—82no—
421C22×C7C2×C4×D411yescharacteristic
422C22×C7C2×#12711yescharacteristic
423C22×C7#53211yescharacteristic
424C22×C7#57512yes—
425C22×C7#57512yes—
426C2×D7—42no—
427C2×D7—44no—
428C2×D7—81no—
429C2×D7—81no—
430C2×D7—82no—
431C4×C7—22no—
432C4×C7—22no—
433C4×C7—24no—
434C4×C7—42no—
435C4×C7—42no—
436C4×C7—81no—
437C4×C7—81no—
438C4×C7C2×C4×D411yescharacteristic
439C4×C7C2×C4×D411yescharacteristic
440C4×C7#53211yescharacteristic
441C4×C7#53211yescharacteristic
442Dic7—42no—
443Dic7—81no—
444Dic7—81no—
445C24—21no—
446C24—141no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—72no—
453C2×Q8—141no—
454C2×Q8—141no—
455C2×Q8—141no—
456C2×Q8—141no—
457C2×Q8—141no—
458C2×Q8C2×C4×D712yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—72no—
465C2×D4—141no—
466C2×D4—141no—
467C2×D4—141no—
468C2×D4—141no—
469C2×D4—141no—
470C2×D4C2×C4×D712yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—44no—
475C22×C4—42no—
476C22×C4—141no—
477C22×C4—141no—
478C22×C4—141no—
479C22×C4—284no—
480C22×C4—282no—
481C22×C4C2×C22⋊D712yes—
482C22×C4C2×C22⋊D712yes—
483C22×C4C2×C22⋊D711yescharacteristic
484C22×C4C2×C22⋊D711yescharacteristic
485C22×C4C23×D711yescharacteristic
486Q16—148no—
487SD16—148no—
488SD16—148no—
489D8—148no—
490C2×C8—72no—
491C2×C8—72no—
492C2×C8—72no—
493C2×C8—72no—
494C2×C8—72no—
495C2×C8—72no—
496C2×C8—72no—
497C2×C8—72no—
498C2×C8—141no—
499C2×C8—141no—
500C2×C8—141no—
501C2×C8—141no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—141no—
508C4⋊C4—141no—
509C4⋊C4—141no—
510C4⋊C4—141no—
511C4⋊C4—282no—
512C22⋊C4—28no—
513C22⋊C4—44no—
514C22⋊C4—42no—
515C22⋊C4—148no—
516C22⋊C4—284no—
517C22⋊C4—282no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—42no—
522C42—42no—
523C42—282no—
524C42C2×C4×D712yes—
525C42#115712yes—
526C42D4×D712yes—
527C42D4×D712yes—
528C2×C7—82no—
529C2×C7C4×#12711yescharacteristic
530C2×C7#294312yes—
531C2×C7#315311yescharacteristic
532C2×C7#315311yescharacteristic
533C2×C7#318312yes—
534D7—82no—
535C23—22no—
536C23—41no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—142no—
541C23—281no—
542C23—282no—
543C23—282no—
544C23—281no—
545C23C22×C22⋊D711yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—142no—
551Q8—142no—
552Q8—281no—
553Q8—281no—
554D4—22no—
555D4—22no—
556D4—41no—
557D4—41no—
558D4—142no—
559D4—142no—
560D4—281no—
561D4—281no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—84no—
577C2×C4—142no—
578C2×C4—281no—
579C2×C4—281no—
580C2×C4—281no—
581C2×C4—281no—
582C2×C4—282no—
583C2×C4—282no—
584C2×C4—564no—
585C2×C4C4×C22⋊D714yes—
586C2×C4#650312yes—
587C2×C4#650312yes—
588C2×C4C22×C4×D711yescharacteristic
589C2×C4C2×#115711yescharacteristic
590C2×C4C2×D4×D711yescharacteristic
591C2×C4C2×D4×D711yescharacteristic
592C2×C4D7×#4111yescharacteristic
593C2×C4D7×#4111yescharacteristic
594C8—74no—
595C8—74no—
596C8—142no—
597C8—142no—
598C7#2169311yescharacteristic, complemented, Sylow
599C22—44no—
600C22—42no—
601C22—81no—
602C22—82no—
603C22—81no—
604C22—284no—
605C22—282no—
606C22—561no—
607C22—562no—
608C22—561no—
609C22C2×C4×C22⋊D711yescharacteristic
610C22C2×#650311yescharacteristic
611C22#9051312yes—
612C22#9051312yes—
613C22#9052311yescharacteristic
614C4—24no—
615C4—22no—
616C4—22no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—282no—
622C4—561no—
623C4—561no—
624C4C4×D4×D711yescharacteristic
625C4C4×D4×D711yescharacteristic
626C4#9023911yescharacteristic
627C4#9023911yescharacteristic
628C2—82no—
629C2—562no—
630C2C4×#650311yescharacteristic
631C2#1173995112yes—
632C2#1174038811yescharacteristic
633C2#1174058412yes—
634C2#1174073411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#124C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
cosocleC22×C4×C7C24
hypercenterC4×#124D7
hypocenterC7#21693
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. C4×C7×#124C2semidirect
3. C2×#89798C2semidirect
4. C2×#89802C2semidirect
6. C2×#89790C2semidirect
7. C4×#6438C2semidirect
8. #11729479C2semidirect
9. #11727433C2semidirect
10. #11727432C2semidirect
11. #11727403C2semidirect
13. #11727305C2semidirect
14. #11727303C2semidirect
15. C4×#6377C2semidirect
36. #89831C4semidirect
68. C7×#124C2×C4semidirect
87. C2×#1144C2×C4semidirect
90. C2×#1143C2×C4semidirect
93. C2×#1142C2×C4semidirect
109. #6438C2×C4semidirect
135. C4×C7⋊C8C2×C4semidirect
142. C4×#124D7semidirect
366. #124C4×D7semidirect
598. C7#21693semidirect

Maximal subgroups

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

subgroupindex
C4×C7×#1242
C2×#898312
C2×#897982
C2×#898022
C2×#897862
C2×#897902
C4×#64382
#117294792
#117274332
#117274322
#117274032
#117274022
#117273052
#117273032
C4×#63772
#216937