Finite Group Databasebeta

← #13364923

Subgroups — #13364923

Order 1792.

1308 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×#121C211yesmaximal, characteristic, complemented
2C2×#89808C211yesmaximal, characteristic
3C2×#89711C211yesmaximal, characteristic, complemented
4#11729431C211yesmaximal, characteristic, complemented
5#11729367C212yesmaximal, complemented
6C4×C22⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
7#11727401C212yesmaximal, complemented
8#11727369C212yesmaximal, complemented
9#11727275C211yesmaximal, characteristic, complemented
10#11727258C211yesmaximal, characteristic, complemented
11#11727216C212yesmaximal, complemented
12C23×D28C2211yescharacteristic
13C2×C7×#121C2211yescharacteristic
14C2×C4×C7×D4—21no—
15C2×C4×C7×D4C2211yescharacteristic, complemented
16C22×C42×C7C2211yescharacteristic
17C22×#1141C2212yes—
18C22×(C2×D7)⋊C4—21no—
19C22×(C2×D7)⋊C4—21no—
20C22×C4⋊Dic7C2211yescharacteristic
21C7×#390C2211yescharacteristic, complemented
22C7×#389C2211yescharacteristic, complemented
23C7×#388—21no—
24C7×#386—21no—
25C7×#380C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic, complemented
27C4×C7×C22⋊C4—21no—
28C2×#6406C2212yescomplemented
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31#89808C418yescomplemented
32C2×#6383C2212yes—
33C2×#6383C2212yes—
34C2×#6383C2212yes—
35C2×#6381C2212yescomplemented
36#89711—21no—
37#89711—21no—
38#89711C2212yes—
39#89711C2212yes—
40C2×C4×C7⋊C8C2212yescomplemented
41#89324C2212yescomplemented
42#89324C2212yescomplemented
43#89319C2212yescomplemented
44#22040—71nomaximal, Sylow
45C24×D7—21no—
46C22×C7×D4—21no—
47C22×C7×D4C2311yescharacteristic
48C23×C4×C7—21no—
49C23×C4×C7D411yescharacteristic
50C23×C4×C7D411yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×Dic7—21no—
53C22×D28—21no—
54C22×D28—22no—
55C22×D28—42no—
56C22×D28—42no—
57C22×D28C2×C414yescomplemented
58C22×D28C2312yes—
59C7×#121—22no—
60C7×#121C2×C414yes—
61C4×C7×D4—42no—
62C4×C7×D4—44no—
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4C2311yescharacteristic
65C2×C7×C4⋊C4C2311yescharacteristic
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C22⋊C4—21no—
68C2×C7×C22⋊C4—21no—
69C2×C7×C22⋊C4—21no—
70C2×C7×C22⋊C4—21no—
71C2×C7×C22⋊C4—21no—
72C2×C42×C7—21no—
73C2×C42×C7—42no—
74C2×C42×C7D411yescharacteristic
75C2×C42×C7D411yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×C42×C7C2311yescharacteristic
78C2×#1141—42no—
79C2×#1141—42no—
80C2×#1141C2×C418yescomplemented
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—44no—
86C2×(C2×D7)⋊C4—44no—
87C2×C4⋊Dic7—21no—
88C2×C4⋊Dic7—42no—
89C2×C4⋊Dic7C2312yes—
90C22×C7⋊C8C2312yes—
91C22×C7⋊C8C2312yes—
92C7×#95—21no—
93C7×#95—21no—
94C7×#95—21no—
95#6406—42no—
96C22⋊(C7⋊C8)—22no—
97C22⋊(C7⋊C8)C2×C414yescomplemented
98#6383—42no—
99#6383—42no—
100#6383C2×C418yescomplemented
101#6381—42no—
102C4×C7⋊C8—42no—
103C2×#447—71no—
104C4×#121D711yescharacteristic, complemented
105C2×#390—71no—
106#1970—72no—
107#1934—72no—
108#1925—72no—
109#1879—72no—
110#1874—71no—
111#1852—71no—
112#1786—71no—
113C4×C22⋊C8—71no—
114C24×C7—21no—
115C24×C7C2×D411yescharacteristic
116C23×D7—24no—
117C23×D7—22no—
118C23×D7—42no—
119C23×D7—42no—
120C23×D7—42no—
121C23×D7—42no—
122C23×D7—42no—
123C23×D7—42no—
124C2×C7×D4—24no—
125C2×C7×D4—21no—
126C2×C7×D4—22no—
127C2×C7×D4—22no—
128C2×C7×D4—42no—
129C2×C7×D4—42no—
130C2×C7×D4C22×C412yes—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—41no—
139C22×C4×C7—41no—
140C22×C4×C7—41no—
141C22×C4×C7—42no—
142C22×C4×C7—42no—
143C22×C4×C7—42no—
144C22×C4×C7D814yescomplemented
145C22×C4×C7C22×C412yes—
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2×D411yescharacteristic
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7#4112yes—
152C22×C4×C7C2411yescharacteristic
153C22×Dic7—22no—
154C22×Dic7—42no—
155C22×Dic7—42no—
156C22×Dic7—42no—
157C2×D28—22no—
158C2×D28—22no—
159C2×D28—22no—
160C2×D28—22no—
161C2×D28—24no—
162C2×D28—22no—
163C2×D28—48no—
164C2×D28—42no—
165C2×D28—42no—
166C2×D28—48no—
167C2×D28C22×C414yes—
168C7×C4⋊C4—21no—
169C7×C4⋊C4—22no—
170C7×C4⋊C4—22no—
171C7×C4⋊C4—42no—
172C7×C4⋊C4C22×C412yes—
173C7×C22⋊C4—24no—
174C7×C22⋊C4—42no—
175C7×C22⋊C4—42no—
176C7×C22⋊C4—42no—
177C7×C22⋊C4—42no—
178C42×C7—22no—
179C42×C7—22no—
180C42×C7—41no—
181C42×C7—41no—
182C42×C7—42no—
183#1141—48no—
184(C2×D7)⋊C4—44no—
185(C2×D7)⋊C4—44no—
186(C2×D7)⋊C4—44no—
187(C2×D7)⋊C4—44no—
188C4⋊Dic7—22no—
189C4⋊Dic7—22no—
190C4⋊Dic7—42no—
191C2×C7⋊C8—22no—
192C2×C7⋊C8—22no—
193C2×C7⋊C8—22no—
194C2×C7⋊C8—22no—
195C2×C7⋊C8—22no—
196C2×C7⋊C8C22×C414yes—
197C23×D4—71no—
198C22×D8—72no—
199C2×#121C2×D711yescharacteristic
200C2×C4×D4—21no—
201C2×C4×D4C2×D711yescharacteristic, complemented
202C22×C4⋊C4—71no—
203C22×C22⋊C4—141no—
204C22×C22⋊C4—141no—
205C22×C42C2×D711yescharacteristic
206#447—78no—
207C2×#107—72no—
208C2×#102—72no—
209C2×#102—72no—
210C2×#102—72no—
211C2×#102—72no—
212C2×C22⋊C8—71no—
213C2×C22⋊C8—71no—
214C2×C4×C8—72no—
215#390—72no—
216#390—72no—
217#390—141no—
218#390—141no—
219#390C2×D711yescharacteristic, complemented
220#389C2×D711yescharacteristic, complemented
221#388—21no—
222#386—21no—
223#380C2×D711yescharacteristic
224C4×C4⋊C4C2×D711yescharacteristic, complemented
225C4×C22⋊C4—21no—
226#340—72no—
227#340—72no—
228#336—72no—
229C23×C7—21no—
230C23×C7—21no—
231C23×C7—21no—
232C23×C7—21no—
233C23×C7—22no—
234C23×C7—41no—
235C23×C7—41no—
236C23×C7—41no—
237C23×C7—41no—
238C23×C7—41no—
239C23×C7—41no—
240C23×C7C4×D412yes—
241C23×C7C2×D812yes—
242C23×C7#13512yes—
243C23×C7C22×D411yescharacteristic
244C22×D7—24no—
245C22×D7—48no—
246C22×D7—48no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C22×D7—42no—
252C22×D7—42no—
253C22×D7—48no—
254C22×D7—84no—
255C22×D7—84no—
256C22×D7—84no—
257C22×D7—84no—
258C7×D4—24no—
259C7×D4—48no—
260C7×D4—42no—
261C2×C4×C7—21no—
262C2×C4×C7—21no—
263C2×C4×C7—21no—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—21no—
269C2×C4×C7—24no—
270C2×C4×C7—24no—
271C2×C4×C7—22no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—44no—
276C2×C4×C7—44no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
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—84no—
286C2×C4×C7C4×D412yes—
287C2×C4×C7C2×D812yes—
288C2×C4×C7C2×D812yes—
289C2×C4×C7AGL(1,ℤ/8)12yes—
290C2×C4×C7C23×C411yescharacteristic
291C2×C4×C7C2×#4111yescharacteristic
292C2×C4×C7H(5,𝔽2)12yes—
293C2×C4×C7H(5,𝔽2)12yes—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—84no—
298D28—24no—
299D28—24no—
300D28—48no—
301D28—42no—
302D28—42no—
303C7⋊C8—24no—
304C7⋊C8—42no—
305C25—141no—
306C22×D4—21no—
307C22×D4—74no—
308C22×D4—72no—
309C22×D4—142no—
310C22×D4—141no—
311C22×D4—282no—
312C22×D4—282no—
313C22×D4C22×D711yescharacteristic
314C23×C4—21no—
315C23×C4—141no—
316C23×C4C22⋊D711yescharacteristic
317C23×C4C22⋊D711yescharacteristic
318C23×C4C22×D711yescharacteristic
319C2×D8—78no—
320C2×D8—282no—
321C2×D8—282no—
322C22×C8—72no—
323C22×C8—72no—
324#121—22no—
325#121C4×D714yes—
326C4×D4—42no—
327C4×D4—44no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—72no—
330C2×C4⋊C4—141no—
331C2×C4⋊C4—282no—
332C2×C4⋊C4C22×D711yescharacteristic
333C2×C4⋊C4C22×D711yescharacteristic
334C2×C4⋊C4C22×D711yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—142no—
341C2×C22⋊C4—142no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C22⋊C4—284no—
345C2×C22⋊C4—284no—
346C2×C42—21no—
347C2×C42—42no—
348C2×C42C22⋊D711yescharacteristic
349C2×C42C22⋊D711yescharacteristic
350C2×C42C22×D711yescharacteristic
351C2×C42C22×D711yescharacteristic
352#107—282no—
353#102—78no—
354#102—282no—
355#102—282no—
356#102—282no—
357C22⋊C8—74no—
358C22⋊C8—142no—
359C4×C8—282no—
360#95—21no—
361#95—21no—
362#95—21no—
363C22×C7—22no—
364C22×C7—22no—
365C22×C7—22no—
366C22×C7—22no—
367C22×C7—22no—
368C22×C7—22no—
369C22×C7—42no—
370C22×C7—42no—
371C22×C7—42no—
372C22×C7—81no—
373C22×C7—81no—
374C22×C7—81no—
375C22×C7—81no—
376C22×C7C4×D814yes—
377C22×C7C2×C4×D411yescharacteristic
378C22×C7#53411yescharacteristic
379C22×C7#53511yescharacteristic
380C22×C7C22×D811yescharacteristic
381C22×C7C2×#13511yescharacteristic
382C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C7#57511yescharacteristic
384C2×D7—44no—
385C2×D7—44no—
386C2×D7—44no—
387C2×D7—816no—
388C2×D7—82no—
389C2×D7—82no—
390C2×D7—82no—
391C2×D7—82no—
392C4×C7—22no—
393C4×C7—22no—
394C4×C7—22no—
395C4×C7—22no—
396C4×C7—41no—
397C4×C7—42no—
398C4×C7—81no—
399C4×C7—81no—
400C4×C7#51812yes—
401C4×C7#53812yes—
402Dic7—82no—
403C24—21no—
404C24—144no—
405C24—142no—
406C24—282no—
407C24—282no—
408C24—282no—
409C24—282no—
410C24—282no—
411C24—282no—
412C24C2×C22⋊D711yescharacteristic
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—74no—
420C2×D4—144no—
421C2×D4—142no—
422C2×D4—142no—
423C2×D4—142no—
424C2×D4—142no—
425C2×D4—142no—
426C2×D4—288no—
427C2×D4—282no—
428C2×D4—282no—
429C2×D4—288no—
430C2×D4C2×C4×D712yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—142no—
445C22×C4—282no—
446C22×C4—282no—
447C22×C4—282no—
448C22×C4#114114yescomplemented
449C22×C4C2×C4×D712yes—
450C22×C4#115712yes—
451C22×C4C2×C22⋊D711yescharacteristic
452C22×C4C2×C22⋊D711yescharacteristic
453C22×C4C2×C22⋊D711yescharacteristic
454C22×C4C2×C22⋊D711yescharacteristic
455C22×C4C2×C22⋊D711yescharacteristic
456C22×C4C23×D711yescharacteristic
457D8—288no—
458C2×C8—74no—
459C2×C8—142no—
460C2×C8—142no—
461C2×C8—142no—
462C2×C8—142no—
463C2×C8—142no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—142no—
469C4⋊C4—142no—
470C4⋊C4—282no—
471C4⋊C4C2×C4×D712yes—
472C22⋊C4—24no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—284no—
478C22⋊C4—284no—
479C22⋊C4—284no—
480C22⋊C4—284no—
481C42—22no—
482C42—22no—
483C42—41no—
484C42—41no—
485C42—42no—
486C2×C7—24no—
487C2×C7—82no—
488C2×C7#232111yescharacteristic
489C2×C7C2×C4×D811yescharacteristic
490C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
491C2×C7#318611yescharacteristic
492C2×C7#318811yescharacteristic
493C2×C7#320511yescharacteristic
494C2×C7#321111yescharacteristic
495D7—84no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—144no—
508C23—288no—
509C23—288no—
510C23—282no—
511C23—282no—
512C23—282no—
513C23—282no—
514C23—282no—
515C23—282no—
516C23—288no—
517C23—564no—
518C23—564no—
519C23—564no—
520C23—564no—
521C23C4×C22⋊D712yes—
522C23C2×#114112yes—
523C23#651312yes—
524C23C22×C22⋊D711yescharacteristic
525D4—24no—
526D4—48no—
527D4—42no—
528D4—144no—
529D4—144no—
530D4—288no—
531D4—282no—
532D4—282no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—44no—
548C2×C4—44no—
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—84no—
558C2×C4—282no—
559C2×C4—282no—
560C2×C4—282no—
561C2×C4—564no—
562C2×C4C4×C22⋊D712yes—
563C2×C4C2×#114112yes—
564C2×C4C2×#114112yes—
565C2×C4#651212yes—
566C2×C4C22×C4×D711yescharacteristic
567C2×C4C2×#115711yescharacteristic
568C2×C4#654812yes—
569C2×C4#655312yes—
570C8—144no—
571C8—282no—
572C7#2204011yescharacteristic, complemented, Sylow
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—284no—
587C22—284no—
588C22—284no—
589C22—5616no—
590C22—562no—
591C22—562no—
592C22—562no—
593C22—562no—
594C22C4×#114114yes—
595C22C2×C4×C22⋊D711yescharacteristic
596C22C22×#114111yescharacteristic
597C22#9049511yescharacteristic
598C22C2×#651211yescharacteristic
599C22C2×#651311yescharacteristic
600C22#9051311yescharacteristic
601C22#9052111yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—42no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—562no—
611C4#9023612yes—
612C4#9025112yes—
613C2—24no—
614C2—82no—
615C2—564no—
616C2C2×C4×#114111yescharacteristic
617C2#1173984011yescharacteristic
618C2C4×#651211yescharacteristic
619C2#1174007011yescharacteristic
620C2#1174037411yescharacteristic
621C2#1174058911yescharacteristic
622C2#1174074711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#121C2
socleC23×C7C22×D4
prime radicalC2×#89808C2
cosocleC22×C4×C7C24
hypercenterC4×#121D7
hypocenterC7#22040
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C4×C7×#121C2semidirect
3. C2×#89711C2semidirect
4. #11729431C2semidirect
5. #11729367C2semidirect
6. C4×C22⋊(C7⋊C8)C2semidirect
7. #11727401C2semidirect
8. #11727369C2semidirect
9. #11727275C2semidirect
10. #11727258C2semidirect
11. #11727216C2semidirect
15. C2×C4×C7×D4C22semidirect
21. C7×#390C22semidirect
22. C7×#389C22semidirect
26. C4×C7×C4⋊C4C22semidirect
28. C2×#6406C22semidirect
31. #89808C4semidirect
35. C2×#6381C22semidirect
40. C2×C4×C7⋊C8C22semidirect
41. #89324C22semidirect
42. #89324C22semidirect
43. #89319C22semidirect
57. C22×D28C2×C4semidirect
80. C2×#1141C2×C4semidirect
97. C22⋊(C7⋊C8)C2×C4semidirect
100. #6383C2×C4semidirect
104. C4×#121D7semidirect
144. C22×C4×C7D8semidirect
201. C2×C4×D4C2×D7semidirect
219. #390C2×D7semidirect
220. #389C2×D7semidirect
224. C4×C4⋊C4C2×D7semidirect
448. C22×C4#1141semidirect
572. C7#22040semidirect

Maximal subgroups

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

subgroupindex
C4×C7×#1212
C2×#898082
C2×#897112
#117294312
#117293672
C4×C22⋊(C7⋊C8)2
#117274012
#117273692
#117272752
#117272582
#117272162
#220407