Finite Group Databasebeta

← #13277468

Subgroups — #13277468

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
1C2×C7×#385C211yesmaximal, characteristic
2C22×C7⋊#95C211yesmaximal, characteristic
3C2×C22⋊C4×Dic7C211yesmaximal, characteristic
4#11729881C211yesmaximal, characteristic
5#11729323C212yesmaximal, complemented
6#11729318C212yesmaximal, complemented
7#11729298C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11727170C212yesmaximal, complemented
11#11727155C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C7×#385C418yescomplemented
23C2×C7×#95C2212yes—
24C2×C7⋊#95—24no—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C22⋊C4×Dic7—24no—
38#14040—71nomaximal, Sylow
39C25×C7C2311yescharacteristic
40C23×C4×C7—22no—
41C23×C4×C7—22no—
42C23×C4×C7—42no—
43C23×C4×C7—42no—
44C23×C4×C7C2×C414yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C23×C4×C7C2312yes—
49C23×Dic7—22no—
50C23×Dic7—22no—
51C23×Dic7—22no—
52C23×Dic7—24no—
53C23×Dic7—24no—
54C23×Dic7—22no—
55C23×Dic7—22no—
56C23×Dic7—42no—
57C23×Dic7—42no—
58C23×Dic7D414yes—
59C23×Dic7C2312yes—
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2312yes—
64C23×Dic7C2311yescharacteristic
65C2×C7×C4⋊C4—42no—
66C2×C7×C4⋊C4—42no—
67C2×C7×C4⋊C4C2×C418yescomplemented
68C2×C7×C22⋊C4—22no—
69C2×C7×C22⋊C4—22no—
70C2×C7×C22⋊C4—22no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4C2×C414yes—
73C2×C7×C22⋊C4C2×C414yes—
74C2×C22⋊Dic7—22no—
75C2×C22⋊Dic7—22no—
76C2×C22⋊Dic7—22no—
77C2×C22⋊Dic7—22no—
78C2×C22⋊Dic7—22no—
79C2×C22⋊Dic7Q814yes—
80C2×C4×Dic7—22no—
81C2×C4×Dic7—22no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—42no—
84C7×#95C2×C418yescomplemented
85C7⋊#95—22no—
86C7⋊#95—22no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—24no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C7⋊#95—42no—
95C7⋊#95—42no—
96C7⋊#95—42no—
97C2×#385D711yescharacteristic
98C2×C4×C22⋊C4—71no—
99C22×#95—71no—
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—28no—
121C22×C4×C7—22no—
122C22×C4×C7—21no—
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—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—48no—
142C22×C4×C7—44no—
143C22×C4×C7—44no—
144C22×C4×C7—48no—
145C22×C4×C7C22×C412yes—
146C22×C4×C7C22×C414yes—
147C22×C4×C7C22×C414yes—
148C22×C4×C7C22×C412yes—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—22no—
152C22×Dic7—28no—
153C22×Dic7—28no—
154C22×Dic7—22no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—22no—
158C22×Dic7—22no—
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—22no—
172C22×Dic7—28no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—44no—
181C22×Dic7—48no—
182C22×Dic7—48no—
183C22×Dic7—48no—
184C22×Dic7—48no—
185C22×Dic7—44no—
186C22×Dic7—44no—
187C22×Dic7C2×D412yes—
188C22×Dic7C2×D412yes—
189C22×Dic7C2×Q812yes—
190C22×Dic7C2×Q812yes—
191C22×Dic7#4114yes—
192C22×Dic7#4114yes—
193C7×C4⋊C4—48no—
194C7×C22⋊C4—28no—
195C7×C22⋊C4—28no—
196C22⋊Dic7—28no—
197C22⋊Dic7—44no—
198C4×Dic7—44no—
199C4×Dic7—44no—
200C24×C4—71no—
201C24×C4—71no—
202C24×C4C2×D711yescharacteristic
203C22×C4⋊C4C2×D712yes—
204C22×C22⋊C4—71no—
205C22×C22⋊C4—71no—
206C22×C22⋊C4C2×D711yescharacteristic
207C22×C22⋊C4C2×D711yescharacteristic
208C22×C42—71no—
209C22×C42—71no—
210#385Dic718yescomplemented
211C4×C22⋊C4—144no—
212C2×#95—72no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—71no—
217C2×#95—72no—
218C2×#95—71no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C2×#95—72no—
224C2×#95—144no—
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×#4111yescharacteristic
254C23×C7C2×#4111yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4112yes—
257C23×C7C2×#4112yes—
258C23×C7H(5,𝔽2)12yes—
259C23×C7H(5,𝔽2)12yes—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—24no—
268C2×C4×C7—24no—
269C2×C4×C7—24no—
270C2×C4×C7—416no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—42no—
274C2×C4×C7—41no—
275C2×C4×C7—42no—
276C2×C4×C7—41no—
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×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—24no—
288C2×Dic7—24no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—24no—
294C2×Dic7—22no—
295C2×Dic7—24no—
296C2×Dic7—24no—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—416no—
300C2×Dic7—416no—
301C2×Dic7—41no—
302C2×Dic7—42no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—42no—
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#12314yes—
321C25C22×D711yescharacteristic
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—42no—
325C23×C4—42no—
326C23×C4—71no—
327C23×C4—71no—
328C23×C4—71no—
329C23×C4—71no—
330C23×C4—72no—
331C23×C4—74no—
332C23×C4—72no—
333C23×C4—144no—
334C23×C4—144no—
335C23×C4—142no—
336C23×C4—142no—
337C23×C4—142no—
338C23×C4—142no—
339C23×C4—142no—
340C23×C4—282no—
341C23×C4—282no—
342C23×C4C2×Dic714yes—
343C23×C4C22×D711yescharacteristic
344C23×C4C22×D712yes—
345C23×C4C22×D711yescharacteristic
346C23×C4C22×D712yes—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4C2×Dic718yescomplemented
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—74no—
355C2×C22⋊C4—142no—
356C2×C22⋊C4—142no—
357C2×C22⋊C4—142no—
358C2×C22⋊C4—142no—
359C2×C22⋊C4—142no—
360C2×C22⋊C4C2×Dic714yes—
361C2×C22⋊C4C2×Dic714yes—
362C2×C42—142no—
363C2×C42—142no—
364C2×C42—144no—
365C2×C42—282no—
366#95—144no—
367#95—144no—
368#95—144no—
369#95—144no—
370#95—144no—
371#95—142no—
372#95—142no—
373#95—282no—
374#95—282no—
375#95—282no—
376#95—282no—
377#95—282no—
378#95C2×Dic718yescomplemented
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—42no—
414C4×C7—44no—
415C4×C7—44no—
416C4×C7—42no—
417Dic7—24no—
418Dic7—42no—
419Dic7—44no—
420Dic7—42no—
421Dic7—42no—
422Dic7—82no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24#115712yes—
428C24#115712yes—
429C24D4×D712yes—
430C24#115912yes—
431C24Q8×D712yes—
432C24#116112yes—
433C24C22×Dic712yes—
434C24C23×D711yescharacteristic
435C22×C4—28no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
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—48no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—72no—
461C22×C4—74no—
462C22×C4—72no—
463C22×C4—72no—
464C22×C4—72no—
465C22×C4—74no—
466C22×C4—148no—
467C22×C4—141no—
468C22×C4—142no—
469C22×C4—141no—
470C22×C4—148no—
471C22×C4—148no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—141no—
478C22×C4—141no—
479C22×C4—142no—
480C22×C4—142no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4—142no—
493C22×C4—142no—
494C22×C4—142no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—284no—
498C22×C4—288no—
499C22×C4—288no—
500C22×C4—288no—
501C22×C4—288no—
502C22×C4—284no—
503C22×C4—284no—
504C22×C4C22×Dic712yes—
505C22×C4C22×Dic714yes—
506C22×C4C22×Dic714yes—
507C22×C4C22×Dic712yes—
508C4⋊C4—48no—
509C22⋊C4—28no—
510C22⋊C4—28no—
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—22no—
534C23—22no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—22no—
542C23—22no—
543C23#645214yes—
544C23#645714yes—
545C23#645914yes—
546C23#646114yes—
547C23#648914yes—
548C23D4×Dic714yes—
549C23Q8×Dic714yes—
550C23C2×#115711yescharacteristic
551C23C2×#115711yescharacteristic
552C23C2×D4×D711yescharacteristic
553C23C2×#115911yescharacteristic
554C23#654812yes—
555C23#654812yes—
556C23C2×Q8×D711yescharacteristic
557C23C2×#116111yescharacteristic
558C23D7×#4112yes—
559C23D7×#4112yes—
560C23C23×Dic711yescharacteristic
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—416no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—74no—
587C2×C4—142no—
588C2×C4—144no—
589C2×C4—142no—
590C2×C4—144no—
591C2×C4—142no—
592C2×C4—142no—
593C2×C4—142no—
594C2×C4—144no—
595C2×C4—142no—
596C2×C4—144no—
597C2×C4—144no—
598C2×C4—144no—
599C2×C4—142no—
600C2×C4—144no—
601C2×C4—2816no—
602C2×C4—2816no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4—282no—
606C2×C4—282no—
607C2×C4—282no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4—282no—
611C2×C4—282no—
612C2×C4—282no—
613C2×C4—281no—
614C2×C4—281no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4—282no—
620C2×C4—282no—
621C2×C4—282no—
622C7#1404011yescharacteristic, complemented, Sylow
623C22—28no—
624C22—24no—
625C22—24no—
626C22—24no—
627C22—28no—
628C22—24no—
629C22—24no—
630C22—28no—
631C22—28no—
632C22—24no—
633C22#8975318yes—
634C22C2×#645211yescharacteristic
635C22C2×#645711yescharacteristic
636C22C2×#645911yescharacteristic
637C22C2×#646111yescharacteristic
638C22#9023112yes—
639C22#9023112yes—
640C22#9024712yes—
641C22#9024712yes—
642C22#9028011yescharacteristic
643C22#9028311yescharacteristic
644C22#9028412yes—
645C22#9032712yes—
646C22#9032712yes—
647C22#9032812yes—
648C22#9032812yes—
649C22#9034012yes—
650C22D7×#12311yescharacteristic
651C22#9034711yescharacteristic
652C22C2×#648911yescharacteristic
653C22C2×D4×Dic711yescharacteristic
654C22#9048912yes—
655C22C2×Q8×Dic711yescharacteristic
656C22#41×Dic712yes—
657C4—44no—
658C4—42no—
659C4—42no—
660C4—44no—
661C4—144no—
662C4—284no—
663C4—282no—
664C4—282no—
665C4—282no—
666C4—562no—
667C2—28no—
668C2#1173190011yescharacteristic
669C2#1173190211yescharacteristic
670C2#1173190812yes—
671C2#1173191012yes—
672C2#1173193111yescharacteristic
673C2#1173205911yescharacteristic
674C2C2×#8975311yescharacteristic
675C2#1173978112yes—
676C2#1174002311yescharacteristic
677C2#1174019412yes—
678C2Dic7×#12311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14040
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. #11729323C2semidirect
6. #11729318C2semidirect
10. #11727170C2semidirect
11. #11727155C2semidirect
22. C7×#385C4semidirect
67. C2×C7×C4⋊C4C2×C4semidirect
84. C7×#95C2×C4semidirect
210. #385Dic7semidirect
349. C2×C4⋊C4C2×Dic7semidirect
378. #95C2×Dic7semidirect
622. C7#14040semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3852
C22×C7⋊#952
C2×C22⋊C4×Dic72
#117298812
#117293232
#117293182
#117292982
#117271702
#117271552
#140407