Finite Group Databasebeta

← #13284074

Subgroups — #13284074

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89763C211yesmaximal, characteristic
2C2×#89762C212yesmaximal, complemented
3C7×C4⋊#95C211yesmaximal, characteristic, complemented
4#11729319C211yesmaximal, characteristic, complemented
5#11729291C212yesmaximal, complemented
6#11727181C212yesmaximal, complemented
7#11727180C212yesmaximal
8#11727162C212yesmaximal, complemented
9#11727156C212yesmaximal, complemented
10C23×D28C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×(C2×D7)⋊C4C2212yes—
15C22×(C2×D7)⋊C4C2212yes—
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C2×C7×#95C2212yes—
23C2×C7×#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2211yescharacteristic
31#89763C418yescomplemented
32#89762—28no—
33#14589—71nomaximal, Sylow
34C24×D7C2312yes—
35C23×C4×C7C2311yescharacteristic
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2312yes—
38C23×C4×C7C2312yes—
39C23×C4×C7C2311yescharacteristic
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C22×D28—42no—
44C22×D28—42no—
45C22×D28—41no—
46C22×D28—41no—
47C22×D28C2×C414yes—
48C2×C7×C4⋊C4—41no—
49C2×C7×C4⋊C4—41no—
50C2×C7×C4⋊C4—41no—
51C2×C7×C4⋊C4—41no—
52C2×C7×C4⋊C4C2×C414yes—
53C2×C7×C4⋊C4D414yescomplemented
54C2×C42×C7—22no—
55C2×C42×C7—41no—
56C2×C42×C7—41no—
57C2×(C2×D7)⋊C4—24no—
58C2×(C2×D7)⋊C4—24no—
59C2×(C2×D7)⋊C4—24no—
60C2×(C2×D7)⋊C4—24no—
61C2×(C2×D7)⋊C4—24no—
62C2×(C2×D7)⋊C4—24no—
63C2×(C2×D7)⋊C4—24no—
64C2×(C2×D7)⋊C4—24no—
65C2×(C2×D7)⋊C4—42no—
66C2×(C2×D7)⋊C4—42no—
67C2×(C2×D7)⋊C4—42no—
68C2×(C2×D7)⋊C4—42no—
69C2×(C2×D7)⋊C4—42no—
70C2×(C2×D7)⋊C4—42no—
71C2×(C2×D7)⋊C4—42no—
72C2×(C2×D7)⋊C4—42no—
73C2×(C2×D7)⋊C4C2×C418yes—
74C2×(C2×D7)⋊C4C2×C418yes—
75C2×C4⋊Dic7—42no—
76C2×C4⋊Dic7—41no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—24no—
79C2×C4×Dic7—42no—
80C7×#95—42no—
81C7×#95—42no—
82C7⋊#95—24no—
83C7⋊#95—24no—
84C7⋊#95—24no—
85C7⋊#95—42no—
86C7⋊#95—42no—
87C7⋊#95—41no—
88C7⋊#95C2×C414yes—
89C2×#394—71no—
90C2×#388—72no—
91#1441—71no—
92#1439—72no—
93#1438—72no—
94#1437—72no—
95#1437—72no—
96C4⋊#95D711yescharacteristic, complemented
97#1434—72no—
98C24×C7C2411yescharacteristic
99C23×D7—22no—
100C23×D7—22no—
101C23×D7—22no—
102C23×D7—22no—
103C23×D7—22no—
104C23×D7—22no—
105C23×D7—22no—
106C23×D7—22no—
107C23×D7—22no—
108C23×D7—22no—
109C23×D7—22no—
110C23×D7—22no—
111C23×D7—22no—
112C23×D7—22no—
113C23×D7C22×C414yes—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7C22×C412yes—
139C22×C4×C7C22×C412yes—
140C22×C4×C7C22×C412yes—
141C22×C4×C7C2×D414yes—
142C22×C4×C7C2×D412yes—
143C22×C4×C7#4114yes—
144C22×C4×C7#4112yes—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7C22×C414yes—
165C22×Dic7#4114yes—
166C2×D28—44no—
167C2×D28—48no—
168C2×D28—44no—
169C2×D28—48no—
170C2×D28—44no—
171C7×C4⋊C4—44no—
172C7×C4⋊C4—44no—
173C42×C7—44no—
174(C2×D7)⋊C4—216no—
175(C2×D7)⋊C4—48no—
176(C2×D7)⋊C4—48no—
177(C2×D7)⋊C4—48no—
178(C2×D7)⋊C4—48no—
179(C2×D7)⋊C4—48no—
180C4⋊Dic7—44no—
181C4×Dic7—48no—
182C23×D4—71no—
183C22×C4⋊C4—71no—
184C22×C4⋊C4C2×D711yescharacteristic
185C22×C4⋊C4C2×D711yescharacteristic
186C22×C22⋊C4—72no—
187C22×C22⋊C4—72no—
188C22×C22⋊C4—72no—
189C22×C22⋊C4—72no—
190C22×C22⋊C4—72no—
191C22×C22⋊C4—72no—
192C22×C42—72no—
193C22×C42C2×D711yescharacteristic
194#394—78no—
195#388—148no—
196C2×#95—71no—
197C2×#95—72no—
198C2×#95—72no—
199C2×#95—72no—
200C2×#95—72no—
201C2×#95—72no—
202C2×#95—71no—
203C2×#95C2×D712yes—
204C2×#95C2×D712yes—
205C23×C7C23×C411yescharacteristic
206C23×C7C22×D411yescharacteristic
207C23×C7C2×#4111yescharacteristic
208C23×C7C2×#4112yes—
209C23×C7C2×#4112yes—
210C23×C7H(5,𝔽2)11yescharacteristic
211C23×C7H(5,𝔽2)11yescharacteristic
212C23×C7H(5,𝔽2)12yes—
213C23×C7H(5,𝔽2)11yescharacteristic
214C23×C7H(5,𝔽2)12yes—
215C23×C72−1+411yescharacteristic
216C22×D7—24no—
217C22×D7—24no—
218C22×D7—24no—
219C22×D7—24no—
220C22×D7—24no—
221C22×D7—24no—
222C22×D7—24no—
223C22×D7—42no—
224C22×D7—42no—
225C22×D7—42no—
226C22×D7—42no—
227C22×D7—42no—
228C22×D7—42no—
229C22×D7—42no—
230C22×D7—42no—
231C22×D7—42no—
232C22×D7—42no—
233C22×D7—42no—
234C22×D7—42no—
235C22×D7—42no—
236C22×D7—42no—
237C22×D7—42no—
238C22×D7—42no—
239C22×D7—42no—
240C22×D7—42no—
241C22×D7—42no—
242C22×D7—42no—
243C22×D7—42no—
244C22×D7—42no—
245C22×D7—42no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—41no—
274C2×C4×C7—42no—
275C2×C4×C7—41no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7C4×D414yes—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—24no—
287C2×Dic7—24no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303D28—416no—
304C25—72no—
305C22×D4—74no—
306C22×D4—282no—
307C22×D4—281no—
308C22×D4—281no—
309C22×D4—282no—
310C23×C4—72no—
311C23×C4—72no—
312C23×C4—72no—
313C23×C4C22×D711yescharacteristic
314C23×C4C22×D711yescharacteristic
315C23×C4C22×D712yes—
316C23×C4C22×D712yes—
317C23×C4C22×D711yescharacteristic
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—281no—
323C2×C4⋊C4—282no—
324C2×C4⋊C4C4×D714yes—
325C2×C4⋊C4D2814yescomplemented
326C2×C22⋊C4—78no—
327C2×C22⋊C4—78no—
328C2×C22⋊C4—144no—
329C2×C22⋊C4—144no—
330C2×C22⋊C4—144no—
331C2×C22⋊C4—144no—
332C2×C22⋊C4—144no—
333C2×C22⋊C4—144no—
334C2×C22⋊C4—144no—
335C2×C22⋊C4—144no—
336C2×C22⋊C4—282no—
337C2×C22⋊C4—282no—
338C2×C22⋊C4—282no—
339C2×C22⋊C4—282no—
340C2×C22⋊C4—282no—
341C2×C22⋊C4—282no—
342C2×C22⋊C4—282no—
343C2×C22⋊C4—282no—
344C2×C42—22no—
345C2×C42—41no—
346C2×C42—41no—
347C2×C42—144no—
348C2×C42—144no—
349C2×C42—282no—
350#95—42no—
351#95—42no—
352#95—74no—
353#95—144no—
354#95—144no—
355#95—144no—
356#95—281no—
357#95—282no—
358#95—282no—
359C22×C7C2×C4×D411yescharacteristic
360C22×C7C4×#4112yes—
361C22×C7#51811yescharacteristic
362C22×C7#51812yes—
363C22×C7#52011yescharacteristic
364C22×C7#53411yescharacteristic
365C22×C7#53711yescharacteristic
366C22×C7#53811yescharacteristic
367C22×C7#53812yes—
368C22×C7#53912yes—
369C22×C7#53911yescharacteristic
370C22×C7#54012yes—
371C22×C7#54212yes—
372C22×C7#54612yes—
373C22×C7#55012yes—
374C22×C7#55112yes—
375C22×C7#55312yes—
376C22×C7#55511yescharacteristic
377C22×C7#55512yes—
378C22×C7#55511yescharacteristic
379C22×C7#56011yescharacteristic
380C22×C7#56012yes—
381C22×C7H(3,𝔽4)11yescharacteristic
382C2×D7—44no—
383C2×D7—44no—
384C2×D7—44no—
385C2×D7—44no—
386C2×D7—44no—
387C2×D7—44no—
388C2×D7—44no—
389C2×D7—82no—
390C2×D7—82no—
391C2×D7—82no—
392C2×D7—82no—
393C2×D7—82no—
394C2×D7—82no—
395C2×D7—82no—
396C2×D7—82no—
397C4×C7—24no—
398C4×C7—42no—
399C4×C7—42no—
400C4×C7—44no—
401C4×C7—44no—
402Dic7—44no—
403Dic7—44no—
404Dic7—82no—
405C24—74no—
406C24—142no—
407C24—142no—
408C24—142no—
409C24—142no—
410C24—142no—
411C24—142no—
412C24—142no—
413C24—142no—
414C24—142no—
415C24—142no—
416C24—142no—
417C24—142no—
418C24—142no—
419C24—142no—
420C24C23×D711yescharacteristic
421C2×D4—284no—
422C2×D4—288no—
423C2×D4—284no—
424C2×D4—284no—
425C2×D4—288no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—74no—
451C22×C4—74no—
452C22×C4—142no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4C2×C4×D712yes—
472C22×C4C2×C4×D712yes—
473C22×C4C2×C4×D712yes—
474C22×C4C2×D2814yes—
475C22×C4C2×D2812yes—
476C22×C4#115712yes—
477C22×C4#116114yes—
478C4⋊C4—44no—
479C4⋊C4—44no—
480C4⋊C4—284no—
481C22⋊C4—1416no—
482C22⋊C4—288no—
483C22⋊C4—288no—
484C22⋊C4—288no—
485C22⋊C4—288no—
486C22⋊C4—288no—
487C42—44no—
488C42—288no—
489C2×C7#232511yescharacteristic
490C2×C7#233512yes—
491C2×C7#236312yes—
492C2×C7#237211yescharacteristic
493C2×C7#237511yescharacteristic
494C2×C7#269911yescharacteristic
495C2×C7#270512yes—
496C2×C7#273311yescharacteristic
497C2×C7#275612yes—
498C2×C7#278511yescharacteristic
499C2×C7#279511yescharacteristic
500D7—84no—
501C23—144no—
502C23—144no—
503C23—144no—
504C23—144no—
505C23—144no—
506C23—144no—
507C23—144no—
508C23—282no—
509C23—282no—
510C23—282no—
511C23—282no—
512C23—282no—
513C23—282no—
514C23—282no—
515C23—282no—
516C23—282no—
517C23—282no—
518C23—282no—
519C23—282no—
520C23—282no—
521C23—282no—
522C23—282no—
523C23—282no—
524C23—282no—
525C23—282no—
526C23—282no—
527C23—282no—
528C23—282no—
529C23—282no—
530C23—282no—
531C23—282no—
532C23—282no—
533C23—282no—
534C23—282no—
535C23—282no—
536C23C22×C4×D711yescharacteristic
537C23C22×D2811yescharacteristic
538C23C2×#115711yescharacteristic
539C23#654811yescharacteristic
540C23#654812yes—
541C23#654811yescharacteristic
542C23#654811yescharacteristic
543C23C2×#116112yes—
544C23#655111yescharacteristic
545C23D7×#4112yes—
546C23#655312yes—
547D4—2816no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—144no—
579C2×C4—144no—
580C2×C4—144no—
581C2×C4—144no—
582C2×C4—144no—
583C2×C4—144no—
584C2×C4—282no—
585C2×C4—282no—
586C2×C4—282no—
587C2×C4—282no—
588C2×C4—282no—
589C2×C4—282no—
590C2×C4—282no—
591C2×C4—282no—
592C2×C4—282no—
593C2×C4—282no—
594C2×C4—282no—
595C2×C4—282no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—282no—
599C2×C4C4×D2814yes—
600C7#1458911yescharacteristic, complemented, Sylow
601C22—284no—
602C22—284no—
603C22—284no—
604C22—284no—
605C22—284no—
606C22—284no—
607C22—284no—
608C22—562no—
609C22—562no—
610C22—562no—
611C22—562no—
612C22—562no—
613C22—562no—
614C22—562no—
615C22—562no—
616C22C2×C4×D2811yescharacteristic
617C22#9017711yescharacteristic
618C22#9018411yescharacteristic
619C22#9018511yescharacteristic
620C22#9019511yescharacteristic
621C22#9020111yescharacteristic
622C22#9020512yes—
623C22#9020611yescharacteristic
624C22#9022312yes—
625C22#9023612yes—
626C22#9024512yes—
627C22C4×#116112yes—
628C22#9026812yes—
629C22#9030612yes—
630C22#9031112yes—
631C22#9032812yes—
632C22#9033512yes—
633C22#9036111yescharacteristic
634C22#9037411yescharacteristic
635C22#9038312yes—
636C22#9041111yescharacteristic
637C22#9042412yes—
638C22#9042511yescharacteristic
639C4—24no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—284no—
645C4—284no—
646C4—562no—
647C2—564no—
648C2#1173077811yescharacteristic
649C2#1173109412yes—
650C2#1173143212yes—
651C2#1173166011yescharacteristic
652C2#1173179811yescharacteristic
653C2#1173342212yes—
654C2#1173355812yes—
655C2#1173383011yescharacteristic
656C2#1173387911yescharacteristic
657C2#1173394011yescharacteristic
658C2#1173401811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenterC4⋊#95D7
hypocenterC7#14589
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#89762C2semidirect
3. C7×C4⋊#95C2semidirect
4. #11729319C2semidirect
5. #11729291C2semidirect
6. #11727181C2semidirect
8. #11727162C2semidirect
9. #11727156C2semidirect
31. #89763C4semidirect
53. C2×C7×C4⋊C4D4semidirect
96. C4⋊#95D7semidirect
325. C2×C4⋊C4D28semidirect
600. C7#14589semidirect

Maximal subgroups

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

subgroupindex
C2×#897632
C2×#897622
C7×C4⋊#952
#117293192
#117292912
#117271812
#117271802
#117271622
#117271562
#145897