Finite Group Databasebeta

← #13285809

Subgroups — #13285809

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89759C211yesmaximal, characteristic
2C2×#89759C212yesmaximal
3C2×#89440C211yesmaximal, characteristic
4C2×D7×#95C211yesmaximal, characteristic
5C2×#89433C211yesmaximal, characteristic, complemented
6C7×#1444C211yesmaximal, characteristic, complemented
7#11729320C211yesmaximal, characteristic, complemented
8#11729319C212yesmaximal, complemented
9(C2×D7)⋊#95C212yesmaximal
10#11727176C211yesmaximal, characteristic, complemented
11#11727166C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C23×C4×D7C2212yes—
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×(C2×D7)⋊C4C2211yescharacteristic
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2212yes—
21C22×C4⋊Dic7C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C2×C7×#95C2212yes—
24C2×C7×#95C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35#89759—24no—
36#89759—28no—
37#89440—24no—
38D7×#95—24no—
39#89433—24no—
40#14766—71nomaximal, Sylow
41C24×D7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2312yes—
52C22×C4×D7—24no—
53C22×C4×D7—24no—
54C22×C4×D7—24no—
55C22×C4×D7—22no—
56C22×C4×D7—24no—
57C22×C4×D7—22no—
58C22×C4×D7—24no—
59C22×C4×D7—42no—
60C22×C4×D7—42no—
61C22×C4×D7—42no—
62C22×C4×D7D414yes—
63C22×C4×D7Q818yes—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—42no—
68C2×C7×C4⋊C4—42no—
69C2×(C2×D7)⋊C4—22no—
70C2×(C2×D7)⋊C4—22no—
71C2×(C2×D7)⋊C4—22no—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—24no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—24no—
76C2×(C2×D7)⋊C4D414yes—
77C2×C4⋊Dic7—24no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—24no—
83C2×C4⋊Dic7—42no—
84C2×C4⋊Dic7—42no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C7×#95—22no—
89C7×#95—24no—
90C7×#95D414yes—
91C7⋊#95—24no—
92C7⋊#95—22no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—22no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—42no—
99C7⋊#95—42no—
100C2×#398—71no—
101C2×#385—71no—
102C2×#380—72no—
103C2×#380—71no—
104C22×#95—71no—
105#1445—71no—
106#1444D711yescharacteristic, complemented
107#1442—72no—
108#1441—72no—
109#1441—71no—
110C22⋊#95—72no—
111C24×C7C2411yescharacteristic
112C23×D7—21no—
113C23×D7—21no—
114C23×D7—22no—
115C23×D7—22no—
116C23×D7—21no—
117C23×D7—21no—
118C23×D7C2×D412yes—
119C23×D7C2×D412yes—
120C23×D7C2×Q814yes—
121C23×D7#4112yes—
122C23×D7#4114yes—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—21no—
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—21no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—21no—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×D412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D414yes—
149C22×C4×C7C2×Q814yes—
150C22×C4×C7#4112yes—
151C22×C4×C7#4114yes—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—21no—
166C22×Dic7—22no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7C2×D412yes—
181C22×Dic7C2×D412yes—
182C22×Dic7C2×Q814yes—
183C2×C4×D7—216no—
184C2×C4×D7—28no—
185C2×C4×D7—28no—
186C2×C4×D7—216no—
187C2×C4×D7—44no—
188C2×C4×D7—48no—
189C2×C4×D7—48no—
190C2×C4×D7—48no—
191C2×C4×D7—48no—
192C2×C4×D7—48no—
193C2×C4×D7—48no—
194C2×C4×D7—48no—
195C7×C4⋊C4—48no—
196C7×C4⋊C4—44no—
197(C2×D7)⋊C4—28no—
198(C2×D7)⋊C4—48no—
199(C2×D7)⋊C4—44no—
200C4⋊Dic7—48no—
201C4⋊Dic7—44no—
202C4⋊Dic7—44no—
203Dic7⋊C4—44no—
204C24×C4—72no—
205C24×C4—71no—
206C22×C4⋊C4—71no—
207C22×C4⋊C4—71no—
208C22×C4⋊C4—72no—
209C22×C4⋊C4—71no—
210C22×C4⋊C4C2×D712yes—
211C22×C4⋊C4C2×D711yescharacteristic
212C22×C22⋊C4—71no—
213C22×C22⋊C4—71no—
214C22×C22⋊C4—72no—
215#398—144no—
216#385—144no—
217#380—148no—
218#380—144no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C2×#95—71no—
224C2×#95—72no—
225C2×#95—71no—
226C2×#95—72no—
227C2×#95—72no—
228C2×#95—144no—
229C2×#95C2×D712yes—
230C2×#95C2×D711yescharacteristic
231C2×#95C2×D711yescharacteristic
232C23×C7C22×D411yescharacteristic
233C23×C7C22×D411yescharacteristic
234C23×C7C22×D411yescharacteristic
235C23×C7C22×Q812yes—
236C23×C7C2×#4112yes—
237C23×C7C2×#4111yescharacteristic
238C23×C7C2×#4111yescharacteristic
239C23×C7C2×#4112yes—
240C23×C7H(5,𝔽2)12yes—
241C23×C7H(5,𝔽2)11yescharacteristic
242C23×C72−1+411yescharacteristic
243C22×D7—22no—
244C22×D7—24no—
245C22×D7—22no—
246C22×D7—24no—
247C22×D7—22no—
248C22×D7—22no—
249C22×D7—24no—
250C22×D7—24no—
251C22×D7—22no—
252C22×D7—24no—
253C22×D7—24no—
254C22×D7—22no—
255C22×D7—22no—
256C22×D7—24no—
257C22×D7—24no—
258C22×D7—24no—
259C22×D7—22no—
260C22×D7—24no—
261C22×D7#12114yes—
262C22×D7C22⋊Q818yes—
263C22×D7#12314yes—
264C22×D7#12518yes—
265C22×D7C4⋊Q814yes—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—24no—
270C2×C4×C7—24no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—24no—
276C2×C4×C7—22no—
277C2×C4×C7—24no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—41no—
287C2×C4×C7—42no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7—42no—
291C2×C4×C7—42no—
292C2×C4×C7—42no—
293C2×C4×C7#12114yes—
294C2×C4×C7C22⋊Q818yes—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—22no—
300C2×Dic7—22no—
301C2×Dic7—24no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—42no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—41no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C4×D7—416no—
327C4×D7—432no—
328C25—71no—
329C23×C4—71no—
330C23×C4—71no—
331C23×C4—72no—
332C23×C4—74no—
333C23×C4—78no—
334C23×C4—71no—
335C23×C4—72no—
336C23×C4—144no—
337C23×C4—144no—
338C23×C4—144no—
339C23×C4—142no—
340C23×C4—144no—
341C23×C4—144no—
342C23×C4—142no—
343C23×C4—282no—
344C23×C4—282no—
345C23×C4—282no—
346C23×C4C22×D712yes—
347C23×C4C22×D711yescharacteristic
348C23×C4C22×D711yescharacteristic
349C23×C4C22×D711yescharacteristic
350C23×C4C22×D712yes—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—144no—
357C2×C4⋊C4—142no—
358C2×C4⋊C4—142no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—142no—
362C2×C4⋊C4—142no—
363C2×C4⋊C4—142no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—282no—
366C2×C4⋊C4—282no—
367C2×C22⋊C4—74no—
368C2×C22⋊C4—142no—
369C2×C22⋊C4—142no—
370C2×C22⋊C4—144no—
371C2×C22⋊C4—144no—
372C2×C22⋊C4—144no—
373C2×C22⋊C4—144no—
374C2×C22⋊C4—142no—
375#95—22no—
376#95—24no—
377#95—144no—
378#95—144no—
379#95—142no—
380#95—142no—
381#95—144no—
382#95—144no—
383#95—144no—
384#95—282no—
385#95—282no—
386#95D2814yes—
387C22×C7C2×#12111yescharacteristic
388C22×C7C2×#12111yescharacteristic
389C22×C7C2×C22⋊Q812yes—
390C22×C7C2×C22⋊Q812yes—
391C22×C7C2×#12311yescharacteristic
392C22×C7C2×#12512yes—
393C22×C7C2×C4⋊Q811yescharacteristic
394C22×C7#53211yescharacteristic
395C22×C7#53312yes—
396C22×C7#53411yescharacteristic
397C22×C7#53711yescharacteristic
398C22×C7#54312yes—
399C22×C7#54412yes—
400C22×C7D4211yescharacteristic
401C22×C7#54612yes—
402C22×C7#54612yes—
403C22×C7#54711yescharacteristic
404C22×C7#54811yescharacteristic
405C22×C7#55112yes—
406C22×C7#55112yes—
407C22×C7#55212yes—
408C22×C7#55311yescharacteristic
409C22×C7#55312yes—
410C2×D7—28no—
411C2×D7—24no—
412C2×D7—24no—
413C2×D7—24no—
414C2×D7—24no—
415C2×D7—28no—
416C2×D7—28no—
417C2×D7—28no—
418C2×D7—24no—
419C2×D7—24no—
420C2×D7#39818yescomplemented
421C4×C7—24no—
422C4×C7—28no—
423C4×C7—42no—
424C4×C7—81no—
425C4×C7—82no—
426Dic7—42no—
427Dic7—42no—
428Dic7—44no—
429Dic7—81no—
430Dic7—82no—
431C24—72no—
432C24—72no—
433C24—74no—
434C24—72no—
435C24—74no—
436C24—141no—
437C24—142no—
438C24—142no—
439C24—141no—
440C24—141no—
441C24—141no—
442C24C23×D711yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—72no—
466C22×C4—72no—
467C22×C4—74no—
468C22×C4—1416no—
469C22×C4—148no—
470C22×C4—141no—
471C22×C4—142no—
472C22×C4—141no—
473C22×C4—142no—
474C22×C4—141no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—141no—
479C22×C4—141no—
480C22×C4—141no—
481C22×C4—141no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4—141no—
486C22×C4—148no—
487C22×C4—1416no—
488C22×C4—141no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4—141no—
493C22×C4—142no—
494C22×C4—142no—
495C22×C4—141no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—284no—
501C22×C4—288no—
502C22×C4—288no—
503C22×C4—288no—
504C22×C4—288no—
505C22×C4—288no—
506C22×C4—288no—
507C22×C4—288no—
508C22×C4C2×D2812yes—
509C22×C4C2×D2814yes—
510C22×C4D4×D712yes—
511C22×C4D4×D712yes—
512C22×C4#115914yes—
513C22×C4Q8×D714yes—
514C22×C4#116112yes—
515C4⋊C4—48no—
516C4⋊C4—44no—
517C4⋊C4—288no—
518C4⋊C4—284no—
519C4⋊C4—284no—
520C4⋊C4—284no—
521C22⋊C4—148no—
522C22⋊C4—288no—
523C22⋊C4—284no—
524C2×C7C2×#39811yescharacteristic
525C2×C7#241211yescharacteristic
526C2×C7#241611yescharacteristic
527C2×C7#243712yes—
528C2×C7#243812yes—
529C2×C7#244212yes—
530C2×C7#249811yescharacteristic
531C2×C7#254311yescharacteristic
532C2×C7#256912yes—
533C2×C7#265911yescharacteristic
534C2×C7#285711yescharacteristic
535D7—28no—
536C23—78no—
537C23—74no—
538C23—74no—
539C23—78no—
540C23—74no—
541C23—142no—
542C23—142no—
543C23—142no—
544C23—144no—
545C23—144no—
546C23—142no—
547C23—144no—
548C23—142no—
549C23—144no—
550C23—142no—
551C23—142no—
552C23—144no—
553C23—144no—
554C23—142no—
555C23—144no—
556C23—144no—
557C23—144no—
558C23—144no—
559C23C22×D2811yescharacteristic
560C23C2×D4×D711yescharacteristic
561C23C2×D4×D711yescharacteristic
562C23C2×#115912yes—
563C23#654812yes—
564C23C2×Q8×D712yes—
565C23C2×#116111yescharacteristic
566C23#655111yescharacteristic
567C23D7×#4111yescharacteristic
568C23D7×#4112yes—
569C23#655311yescharacteristic
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—142no—
598C2×C4—142no—
599C2×C4—144no—
600C2×C4—142no—
601C2×C4—142no—
602C2×C4—142no—
603C2×C4—144no—
604C2×C4—144no—
605C2×C4—142no—
606C2×C4—2816no—
607C2×C4—2832no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4—282no—
611C2×C4—282no—
612C2×C4—282no—
613C2×C4—281no—
614C2×C4—282no—
615C2×C4—281no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4—282no—
620C2×C4—281no—
621C2×C4—282no—
622C2×C4—282no—
623C2×C4—282no—
624C2×C4—282no—
625C2×C4—281no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—282no—
629C2×C4—281no—
630C2×C4#645814yes—
631C2×C4#646018yes—
632C7#1476611yescharacteristic, complemented, Sylow
633C22—78no—
634C22—148no—
635C22—144no—
636C22—144no—
637C22—148no—
638C22—144no—
639C22—148no—
640C22—144no—
641C22—144no—
642C22—148no—
643C22—144no—
644C22C2×#645811yescharacteristic
645C22C2×#646012yes—
646C22D4×D2811yescharacteristic
647C22#9024512yes—
648C22#9026711yescharacteristic
649C22#9028011yescharacteristic
650C22#9028212yes—
651C22D7×#12111yescharacteristic
652C22#9030512yes—
653C22D7×C22⋊Q812yes—
654C22#9032011yescharacteristic
655C22#9032512yes—
656C22#9032812yes—
657C22#9033012yes—
658C22D7×#12311yescharacteristic
659C22#9034912yes—
660C22D7×#12512yes—
661C22#9038611yescharacteristic
662C22#9040711yescharacteristic
663C22D7×C4⋊Q811yescharacteristic
664C22#9041711yescharacteristic
665C22#9041912yes—
666C22#9042012yes—
667C4—24no—
668C4—28no—
669C4—42no—
670C4—82no—
671C4—81no—
672C4—282no—
673C4—284no—
674C4—282no—
675C4—561no—
676C4—562no—
677C2—148no—
678C2#1173182111yescharacteristic
679C2#1173185111yescharacteristic
680C2#1173185812yes—
681C2#1173344812yes—
682C2#1173365611yescharacteristic
683C2#1173420411yescharacteristic
684C2#1173469612yes—
685C2#1173470311yescharacteristic
686C2D7×#39811yescharacteristic
687C2#1173540412yes—
688C2#1173555111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC7×#1444C2
prime radicalC24×D7C23
hypercenter#1444D7
hypocenterC7#14766
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
5. C2×#89433C2semidirect
6. C7×#1444C2semidirect
7. #11729320C2semidirect
8. #11729319C2semidirect
10. #11727176C2semidirect
11. #11727166C2semidirect
106. #1444D7semidirect
420. C2×D7#398semidirect
632. C7#14766semidirect

Maximal subgroups

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

subgroupindex
C2×#897592
C2×#894402
C2×D7×#952
C2×#894332
C7×#14442
#117293202
#117293192
(C2×D7)⋊#952
#117271762
#117271662
#147667