Finite Group Databasebeta

← #13277465

Subgroups — #13277465

Order 1792.

1862 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#95C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4#11729881C211yesmaximal, characteristic
5#11729881C211yesmaximal, characteristic
6#11729881C211yesmaximal, characteristic
7#11729881C211yesmaximal, characteristic
8#11727175C212yesmaximal, complemented
9#11727172C212yesmaximal, complemented
10#11727160C212yesmaximal, complemented
11#11727156C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C22⋊Dic7C2211yescharacteristic
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C2×C7×#95—24no—
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25#89982C418yescomplemented
26C4×C22⋊Dic7—24no—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#14040—71nomaximal, Sylow
39C25×C7C2311yescharacteristic
40C23×C4×C7—22no—
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—24no—
46C23×C4×C7—24no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—42no—
50C23×C4×C7—42no—
51C23×C4×C7—42no—
52C23×C4×C7—42no—
53C23×C4×C7C2×C414yes—
54C23×C4×C7D414yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C23×Dic7C2312yes—
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2312yes—
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C2×C22⋊Dic7—22no—
66C2×C22⋊Dic7—22no—
67C2×C22⋊Dic7—22no—
68C2×C22⋊Dic7—22no—
69C2×C22⋊Dic7—22no—
70C2×C22⋊Dic7—22no—
71C2×C22⋊Dic7—22no—
72C2×C22⋊Dic7—22no—
73C2×C22⋊Dic7—22no—
74C2×C22⋊Dic7C2×C414yes—
75C2×C22⋊Dic7C2×C414yes—
76C2×C22⋊Dic7Q814yes—
77C2×Dic7⋊C4—42no—
78C2×Dic7⋊C4—42no—
79C2×Dic7⋊C4C2×C418yescomplemented
80C2×C4×Dic7—22no—
81C2×C4×Dic7—22no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—42no—
84C7×#95—24no—
85C7×#95—24no—
86C7⋊#95—22no—
87C7⋊#95—22no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—42no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C7⋊#95—42no—
95C7⋊#95—42no—
96C7⋊#95C2×C418yescomplemented
97C2×#385—71no—
98C2×C4×C22⋊C4—71no—
99C22×#95D711yescharacteristic
100#1445—72no—
101#1443—72no—
102#1436—72no—
103#1434—72no—
104C22⋊#95—71no—
105C22⋊#95—71no—
106C22⋊#95—71no—
107C22⋊#95—71no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7C22×C412yes—
113C24×C7C2×D412yes—
114C24×C7C2×Q812yes—
115C24×C7#4112yes—
116C24×C7#4112yes—
117C24×C7#4112yes—
118C24×C7#4112yes—
119C24×C7C2411yescharacteristic
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—22no—
123C22×C4×C7—28no—
124C22×C4×C7—28no—
125C22×C4×C7—28no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—28no—
143C22×C4×C7—48no—
144C22×C4×C7—44no—
145C22×C4×C7—48no—
146C22×C4×C7—48no—
147C22×C4×C7—48no—
148C22×C4×C7—48no—
149C22×C4×C7—44no—
150C22×C4×C7—44no—
151C22×C4×C7—44no—
152C22×C4×C7—48no—
153C22×C4×C7—44no—
154C22×C4×C7C22×C414yes—
155C22×C4×C7C2×D412yes—
156C22×C4×C7C2×D412yes—
157C22×C4×C7#4114yes—
158C22×C4×C7#4114yes—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7C22×C412yes—
189C22×Dic7C22×C414yes—
190C22×Dic7C22×C412yes—
191C22×Dic7C2×Q812yes—
192C22×Dic7C2×Q812yes—
193C22⋊Dic7—28no—
194C22⋊Dic7—28no—
195C22⋊Dic7—28no—
196C22⋊Dic7—44no—
197Dic7⋊C4—48no—
198C4×Dic7—44no—
199C4×Dic7—44no—
200C24×C4C2×D711yescharacteristic
201C24×C4C2×D711yescharacteristic
202C24×C4C2×D711yescharacteristic
203C22×C4⋊C4—72no—
204C22×C22⋊C4—71no—
205C22×C22⋊C4—71no—
206C22×C22⋊C4—71no—
207C22×C22⋊C4—71no—
208C22×C42—71no—
209C22×C42—71no—
210#385—78no—
211C4×C22⋊C4—144no—
212C2×#95—24no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—71no—
218C2×#95—71no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C2×#95—72no—
224C2×#95C2×D712yes—
225C2×#95C2×D712yes—
226C23×C7—24no—
227C23×C7—24no—
228C23×C7—22no—
229C23×C7—22no—
230C23×C7—24no—
231C23×C7—22no—
232C23×C7—22no—
233C23×C7—24no—
234C23×C7—24no—
235C23×C7—24no—
236C23×C7—24no—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7#11714yes—
243C23×C7C4×D414yes—
244C23×C7C4×Q814yes—
245C23×C7C22⋊Q814yes—
246C23×C7#12314yes—
247C23×C7#12514yes—
248C23×C7#12614yes—
249C23×C7C23×C411yescharacteristic
250C23×C7C22×D411yescharacteristic
251C23×C7C22×Q811yescharacteristic
252C23×C7C2×#4111yescharacteristic
253C23×C7C2×#4112yes—
254C23×C7C2×#4112yes—
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7C2×#4111yescharacteristic
258C23×C7H(5,𝔽2)12yes—
259C23×C7H(5,𝔽2)12yes—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—24no—
270C2×C4×C7—22no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—416no—
274C2×C4×C7—416no—
275C2×C4×C7—416no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7#12314yes—
287C2×Dic7—24no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—24no—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—24no—
297C2×Dic7—24no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—42no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7—42no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C25C22×D711yescharacteristic
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—24no—
328C23×C4—24no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—42no—
335C23×C4—71no—
336C23×C4—72no—
337C23×C4—71no—
338C23×C4—71no—
339C23×C4—71no—
340C23×C4—72no—
341C23×C4C4×D714yes—
342C23×C4C22⋊D714yes—
343C23×C4C22×D712yes—
344C23×C4C22×D712yes—
345C23×C4C22×D711yescharacteristic
346C23×C4C22×D711yescharacteristic
347C2×C4⋊C4—78no—
348C2×C4⋊C4—282no—
349C2×C4⋊C4—282no—
350C2×C22⋊C4—74no—
351C2×C22⋊C4—74no—
352C2×C22⋊C4—74no—
353C2×C22⋊C4—142no—
354C2×C22⋊C4—142no—
355C2×C22⋊C4—142no—
356C2×C22⋊C4—142no—
357C2×C22⋊C4—142no—
358C2×C22⋊C4—142no—
359C2×C22⋊C4—142no—
360C2×C22⋊C4—142no—
361C2×C22⋊C4—142no—
362C2×C42—144no—
363C2×C42—142no—
364C2×C42—142no—
365C2×C42—282no—
366#95—24no—
367#95—24no—
368#95—78no—
369#95—144no—
370#95—144no—
371#95—144no—
372#95—142no—
373#95—142no—
374#95—282no—
375#95—282no—
376#95—282no—
377#95—282no—
378#95—282no—
379C22×C7—24no—
380C22×C7—24no—
381C22×C7—28no—
382C22×C7—28no—
383C22×C7—24no—
384C22×C7—24no—
385C22×C7—24no—
386C22×C7—28no—
387C22×C7—28no—
388C22×C7—24no—
389C22×C7#38718yes—
390C22×C7C2×#11711yescharacteristic
391C22×C7C2×C4×D411yescharacteristic
392C22×C7C2×C4×Q811yescharacteristic
393C22×C7C4×#4112yes—
394C22×C7#51812yes—
395C22×C7C2×C22⋊Q811yescharacteristic
396C22×C7C2×#12311yescharacteristic
397C22×C7C2×#12311yescharacteristic
398C22×C7#52511yescharacteristic
399C22×C7C2×#12511yescharacteristic
400C22×C7C2×#12611yescharacteristic
401C22×C7#52912yes—
402C22×C7#53411yescharacteristic
403C22×C7#53511yescharacteristic
404C22×C7#53812yes—
405C22×C7#55112yes—
406C22×C7#55112yes—
407C22×C7#55112yes—
408C22×C7#55112yes—
409C22×C7#55312yes—
410C22×C7#55312yes—
411C22×C7#55412yes—
412C22×C7#55412yes—
413C4×C7—24no—
414C4×C7—44no—
415C4×C7—44no—
416C4×C7—42no—
417Dic7—42no—
418Dic7—42no—
419Dic7—44no—
420Dic7—42no—
421Dic7—42no—
422Dic7—82no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24C2×C4×D712yes—
428C24#115712yes—
429C24#115912yes—
430C24#115912yes—
431C24Q8×D712yes—
432C24#116112yes—
433C24C2×C22⋊D712yes—
434C24C23×D711yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—28no—
458C22×C4—48no—
459C22×C4—44no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—72no—
470C22×C4—74no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—72no—
474C22×C4—142no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—141no—
481C22×C4—141no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—141no—
491C22×C4—141no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—141no—
495C22×C4—141no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—142no—
502C22×C4—142no—
503C22×C4C2×C4×D714yes—
504C22×C4#115714yes—
505C22×C4#115714yes—
506C22×C4C2×C22⋊D712yes—
507C22×C4C2×C22⋊D712yes—
508C4⋊C4—288no—
509C22⋊C4—148no—
510C22⋊C4—148no—
511C22⋊C4—148no—
512C22⋊C4—284no—
513C42—284no—
514C42—284no—
515C2×C7—28no—
516C2×C7C2×#38711yescharacteristic
517C2×C7C4×#12311yescharacteristic
518C2×C7#232111yescharacteristic
519C2×C7#235312yes—
520C2×C7#236812yes—
521C2×C7#248211yescharacteristic
522C2×C7#248311yescharacteristic
523C2×C7#248711yescharacteristic
524C2×C7#250512yes—
525C2×C7#251012yes—
526C2×C7#257911yescharacteristic
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23#645014yes—
544C23#645214yes—
545C23#645514yes—
546C23#646114yes—
547C23C4×C22⋊D714yes—
548C23#649814yes—
549C23#650914yes—
550C23C22×C4×D711yescharacteristic
551C23C2×#115712yes—
552C23C2×#115712yes—
553C23C2×#115711yescharacteristic
554C23C2×#115911yescharacteristic
555C23C2×#115911yescharacteristic
556C23#654812yes—
557C23#654812yes—
558C23C2×Q8×D711yescharacteristic
559C23C2×#116111yescharacteristic
560C23C22×C22⋊D711yescharacteristic
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—416no—
575C2×C4—416no—
576C2×C4—416no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—144no—
590C2×C4—144no—
591C2×C4—144no—
592C2×C4—144no—
593C2×C4—144no—
594C2×C4—142no—
595C2×C4—142no—
596C2×C4—142no—
597C2×C4—142no—
598C2×C4—282no—
599C2×C4—282no—
600C2×C4—282no—
601C2×C4—282no—
602C2×C4—282no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4—282no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4—281no—
611C2×C4—281no—
612C2×C4—281no—
613C2×C4—281no—
614C2×C4—282no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4—282no—
620C2×C4—282no—
621C2×C4#649214yes—
622C7#1404011yescharacteristic, complemented, Sylow
623C22—28no—
624C22—28no—
625C22—28no—
626C22—28no—
627C22—24no—
628C22—24no—
629C22—24no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22#8975018yes—
634C22C4×#115712yes—
635C22#9017012yes—
636C22#9017712yes—
637C22#9018512yes—
638C22#9018612yes—
639C22#9018612yes—
640C22#9018612yes—
641C22#9018612yes—
642C22C2×#645011yescharacteristic
643C22C2×#645211yescharacteristic
644C22C2×#645511yescharacteristic
645C22#9020212yes—
646C22#9020212yes—
647C22C2×#646111yescharacteristic
648C22#9020512yes—
649C22#9020512yes—
650C22C2×C4×C22⋊D711yescharacteristic
651C22C2×#649211yescharacteristic
652C22#9048211yescharacteristic
653C22C2×#649811yescharacteristic
654C22#9049511yescharacteristic
655C22#9049611yescharacteristic
656C22C2×#650911yescharacteristic
657C4—24no—
658C4—44no—
659C4—44no—
660C4—42no—
661C4—284no—
662C4—282no—
663C4—282no—
664C4—282no—
665C4—282no—
666C4—562no—
667C2—28no—
668C2#1173078112yes—
669C2#1173078412yes—
670C2#1173080012yes—
671C2#1173080112yes—
672C2C4×#649211yescharacteristic
673C2#1173954111yescharacteristic
674C2#1173955811yescharacteristic
675C2#1173955911yescharacteristic
676C2C2×#8975011yescharacteristic
677C2#1173964211yescharacteristic
678C2#1173964311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22×#95D7
hypocenterC7#14040
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
8. #11727175C2semidirect
9. #11727172C2semidirect
10. #11727160C2semidirect
11. #11727156C2semidirect
25. #89982C4semidirect
79. C2×Dic7⋊C4C2×C4semidirect
96. C7⋊#95C2×C4semidirect
622. C7#14040semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#952
C2×#899822
C2×C4×C22⋊Dic72
#117298812
#117271752
#117271722
#117271602
#117271562
#140407