Finite Group Databasebeta

← #13277513

Subgroups — #13277513

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 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×#89722C211yesmaximal, characteristic
4C2×#89722C211yesmaximal, characteristic
5C2×C22⋊C4×Dic7C211yesmaximal, characteristic
6#11729881C211yesmaximal, characteristic
7#11729319C212yesmaximal, complemented
8#11729317C212yesmaximal, complemented
9#11729298C211yesmaximal, characteristic
10#11727166C212yesmaximal, complemented
11#11727161C212yesmaximal, 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⋊Dic7C2212yes—
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C7×#385C418yescomplemented
25C2×C7×#95C2212yes—
26C2×C7⋊#95—24no—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37#89722—24no—
38#89722—24no—
39C22⋊C4×Dic7—24no—
40#14044—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—42no—
45C23×C4×C7—42no—
46C23×C4×C7C2×C414yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×Dic7—22no—
52C23×Dic7—22no—
53C23×Dic7—22no—
54C23×Dic7—24no—
55C23×Dic7—24no—
56C23×Dic7—22no—
57C23×Dic7—22no—
58C23×Dic7—42no—
59C23×Dic7—42no—
60C23×Dic7D414yes—
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2312yes—
65C23×Dic7C2312yes—
66C23×Dic7C2311yescharacteristic
67C2×C7×C4⋊C4—42no—
68C2×C7×C4⋊C4—42no—
69C2×C7×C4⋊C4C2×C418yescomplemented
70C2×C7×C22⋊C4—22no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4C2×C414yes—
73C2×C7×C22⋊C4C2×C414yes—
74C2×C7×C22⋊C4D414yes—
75C2×C7×C22⋊C4Q814yes—
76C2×C22⋊Dic7—22no—
77C2×C22⋊Dic7—22no—
78C2×C22⋊Dic7—22no—
79C2×C22⋊Dic7—22no—
80C2×C22⋊Dic7—22no—
81C2×C22⋊Dic7Q814yes—
82C2×C4⋊Dic7—24no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—24no—
86C2×C4⋊Dic7—24no—
87C2×C4⋊Dic7—42no—
88C2×C4⋊Dic7—42no—
89C2×C4×Dic7—24no—
90C2×C4×Dic7—24no—
91C2×C4×Dic7—42no—
92C7×#95C2×C418yescomplemented
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—22no—
96C7⋊#95—22no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—42no—
101C7⋊#95—42no—
102C7⋊#95—42no—
103C2×#385—71no—
104C2×#385—71no—
105C2×#385D711yescharacteristic
106C2×C4×C22⋊C4—71no—
107C22×#95—71no—
108#1442—72no—
109#1441—72no—
110#1436—72no—
111C4⋊#95—72no—
112C22⋊#95—71no—
113C22⋊#95—71no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7C22×C412yes—
119C24×C7C2×D412yes—
120C24×C7C2×D412yes—
121C24×C7C2×Q812yes—
122C24×C7C2×Q812yes—
123C24×C7#4112yes—
124C24×C7#4112yes—
125C24×C7C2411yescharacteristic
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—28no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—48no—
146C22×C4×C7—44no—
147C22×C4×C7—44no—
148C22×C4×C7—48no—
149C22×C4×C7C22×C412yes—
150C22×C4×C7C22×C414yes—
151C22×C4×C7C22×C412yes—
152C22×C4×C7C22×C414yes—
153C22×C4×C7C2×D414yes—
154C22×C4×C7C2×Q814yes—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—22no—
158C22×Dic7—28no—
159C22×Dic7—28no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—21no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—28no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—44no—
188C22×Dic7—48no—
189C22×Dic7—48no—
190C22×Dic7—48no—
191C22×Dic7—48no—
192C22×Dic7—44no—
193C22×Dic7—44no—
194C22×Dic7C2×D412yes—
195C22×Dic7C2×D412yes—
196C22×Dic7C2×Q814yes—
197C22×Dic7#4114yes—
198C22×Dic7#4114yes—
199C7×C4⋊C4—48no—
200C7×C22⋊C4—28no—
201C7×C22⋊C4C4⋊C4116yescomplemented
202C22⋊Dic7—28no—
203C22⋊Dic7—44no—
204C4⋊Dic7—48no—
205C4⋊Dic7—44no—
206C4⋊Dic7—44no—
207C4×Dic7—48no—
208C24×C4—71no—
209C24×C4—71no—
210C24×C4C2×D711yescharacteristic
211C22×C4⋊C4—71no—
212C22×C4⋊C4—72no—
213C22×C4⋊C4—71no—
214C22×C4⋊C4C2×D712yes—
215C22×C22⋊C4—71no—
216C22×C22⋊C4—71no—
217C22×C22⋊C4C2×D711yescharacteristic
218C22×C22⋊C4C2×D711yescharacteristic
219C22×C42—72no—
220#385—144no—
221#385—144no—
222#385Dic718yescomplemented
223C4×C22⋊C4—144no—
224C2×#95—72no—
225C2×#95—71no—
226C2×#95—72no—
227C2×#95—72no—
228C2×#95—72no—
229C2×#95—72no—
230C2×#95—71no—
231C2×#95—72no—
232C2×#95—72no—
233C2×#95—72no—
234C2×#95—144no—
235C2×#95C2×D712yes—
236C23×C7—24no—
237C23×C7—24no—
238C23×C7—22no—
239C23×C7—22no—
240C23×C7—24no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7—24no—
244C23×C7—24no—
245C23×C7—24no—
246C23×C7—24no—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7—24no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7C2×C4⋊C414yes—
253C23×C7C4×D414yes—
254C23×C7C4×Q814yes—
255C23×C7#12114yes—
256C23×C7C22⋊Q814yes—
257C23×C7#12514yes—
258C23×C7C4⋊Q814yes—
259C23×C7C23×C411yescharacteristic
260C23×C7C22×D411yescharacteristic
261C23×C7C22×D411yescharacteristic
262C23×C7C22×Q811yescharacteristic
263C23×C7C22×Q811yescharacteristic
264C23×C7C2×#4111yescharacteristic
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4112yes—
267C23×C7C2×#4112yes—
268C23×C7H(5,𝔽2)12yes—
269C23×C7H(5,𝔽2)12yes—
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—22no—
278C2×C4×C7—24no—
279C2×C4×C7—24no—
280C2×C4×C7—24no—
281C2×C4×C7—24no—
282C2×C4×C7—24no—
283C2×C4×C7—416no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—42no—
287C2×C4×C7—41no—
288C2×C4×C7—42no—
289C2×C4×C7—41no—
290C2×C4×C7—42no—
291C2×C4×C7—42no—
292C2×C4×C7—42no—
293C2×C4×C7—42no—
294C2×C4×C7C2×C4⋊C418yes—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—22no—
300C2×Dic7—24no—
301C2×Dic7—22no—
302C2×Dic7—24no—
303C2×Dic7—22no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—416no—
309C2×Dic7—416no—
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—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7#12314yes—
331C25C22×D711yescharacteristic
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4—71no—
337C23×C4—72no—
338C23×C4—71no—
339C23×C4—72no—
340C23×C4—74no—
341C23×C4—71no—
342C23×C4—71no—
343C23×C4—144no—
344C23×C4—144no—
345C23×C4—142no—
346C23×C4—142no—
347C23×C4—142no—
348C23×C4—142no—
349C23×C4—142no—
350C23×C4—282no—
351C23×C4—282no—
352C23×C4C2×Dic714yes—
353C23×C4C22×D711yescharacteristic
354C23×C4C22×D711yescharacteristic
355C23×C4C22×D712yes—
356C23×C4C22×D712yes—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—144no—
361C2×C4⋊C4—142no—
362C2×C4⋊C4—142no—
363C2×C4⋊C4—144no—
364C2×C4⋊C4—282no—
365C2×C4⋊C4—282no—
366C2×C4⋊C4C2×Dic718yescomplemented
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—74no—
370C2×C22⋊C4—142no—
371C2×C22⋊C4—142no—
372C2×C22⋊C4—142no—
373C2×C22⋊C4—142no—
374C2×C22⋊C4—142no—
375C2×C22⋊C4Dic1414yes—
376C2×C22⋊C4D2814yes—
377C2×C22⋊C4C2×Dic714yes—
378C2×C22⋊C4C2×Dic714yes—
379C2×C42—144no—
380C2×C42—144no—
381C2×C42—282no—
382#95—144no—
383#95—144no—
384#95—144no—
385#95—142no—
386#95—142no—
387#95—144no—
388#95—144no—
389#95—282no—
390#95—282no—
391#95—282no—
392#95C2×Dic718yescomplemented
393C22×C7—24no—
394C22×C7—24no—
395C22×C7—28no—
396C22×C7—28no—
397C22×C7—24no—
398C22×C7—24no—
399C22×C7—28no—
400C22×C7—24no—
401C22×C7—28no—
402C22×C7—24no—
403C22×C7#38918yes—
404C22×C7C22×C4⋊C411yescharacteristic
405C22×C7C2×C4×D411yescharacteristic
406C22×C7C2×C4×Q811yescharacteristic
407C22×C7C4×#4112yes—
408C22×C7#51812yes—
409C22×C7C2×#12111yescharacteristic
410C22×C7C2×C22⋊Q811yescharacteristic
411C22×C7C2×#12311yescharacteristic
412C22×C7#52511yescharacteristic
413C22×C7C2×#12511yescharacteristic
414C22×C7#52912yes—
415C22×C7C2×C4⋊Q811yescharacteristic
416C22×C7#53411yescharacteristic
417C22×C7#53511yescharacteristic
418C22×C7#53812yes—
419C22×C7#54612yes—
420C22×C7#54612yes—
421C22×C7#55112yes—
422C22×C7#55112yes—
423C22×C7#55412yes—
424C22×C7#55412yes—
425C22×C7#55412yes—
426C22×C7#55412yes—
427C4×C7—28no—
428C4×C7—42no—
429C4×C7—44no—
430C4×C7—42no—
431Dic7—24no—
432Dic7—44no—
433Dic7—42no—
434Dic7—44no—
435Dic7—81no—
436Dic7—81no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24C2×Dic1412yes—
442C24C2×D2812yes—
443C24D4×D712yes—
444C24#115912yes—
445C24Q8×D712yes—
446C24#116112yes—
447C24C22×Dic712yes—
448C24C23×D711yescharacteristic
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—48no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—48no—
472C22×C4—72no—
473C22×C4—74no—
474C22×C4—72no—
475C22×C4—74no—
476C22×C4—74no—
477C22×C4—148no—
478C22×C4—141no—
479C22×C4—142no—
480C22×C4—141no—
481C22×C4—148no—
482C22×C4—148no—
483C22×C4—141no—
484C22×C4—142no—
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—141no—
494C22×C4—142no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—141no—
500C22×C4—141no—
501C22×C4—141no—
502C22×C4—141no—
503C22×C4—142no—
504C22×C4—142no—
505C22×C4—141no—
506C22×C4—141no—
507C22×C4—142no—
508C22×C4—142no—
509C22×C4—284no—
510C22×C4—288no—
511C22×C4—288no—
512C22×C4—288no—
513C22×C4—288no—
514C22×C4—284no—
515C22×C4—284no—
516C22×C4C2×Dic1414yes—
517C22×C4C2×D2814yes—
518C22×C4C22×Dic712yes—
519C22×C4C22×Dic714yes—
520C22×C4C22×Dic712yes—
521C22×C4C22×Dic714yes—
522C4⋊C4—48no—
523C4⋊C4—288no—
524C4⋊C4—284no—
525C4⋊C4—284no—
526C22⋊C4—28no—
527C22⋊C4—148no—
528C22⋊C4—284no—
529C22⋊C4C4⋊Dic7116yescomplemented
530C42—288no—
531C2×C7—28no—
532C2×C7C2×#38911yescharacteristic
533C2×C7C4×#12311yescharacteristic
534C2×C7#232111yescharacteristic
535C2×C7#234912yes—
536C2×C7#236812yes—
537C2×C7#241111yescharacteristic
538C2×C7#241211yescharacteristic
539C2×C7#245012yes—
540C2×C7#250211yescharacteristic
541C2×C7#250512yes—
542C2×C7#258311yescharacteristic
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—22no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—22no—
558C23—22no—
559C23#645114yes—
560C23#645314yes—
561C23#645814yes—
562C23#646014yes—
563C23C2×C4⋊Dic714yes—
564C23D4×Dic714yes—
565C23Q8×Dic714yes—
566C23C22×Dic1411yescharacteristic
567C23C22×D2811yescharacteristic
568C23C2×D4×D711yescharacteristic
569C23C2×#115911yescharacteristic
570C23#654812yes—
571C23#654812yes—
572C23C2×Q8×D711yescharacteristic
573C23C2×#116111yescharacteristic
574C23D7×#4112yes—
575C23D7×#4112yes—
576C23C23×Dic711yescharacteristic
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—416no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—74no—
602C2×C4—142no—
603C2×C4—144no—
604C2×C4—142no—
605C2×C4—144no—
606C2×C4—142no—
607C2×C4—144no—
608C2×C4—144no—
609C2×C4—142no—
610C2×C4—144no—
611C2×C4—144no—
612C2×C4—144no—
613C2×C4—142no—
614C2×C4—144no—
615C2×C4—2816no—
616C2×C4—2816no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4—282no—
620C2×C4—282no—
621C2×C4—282no—
622C2×C4—282no—
623C2×C4—282no—
624C2×C4—282no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—281no—
628C2×C4—281no—
629C2×C4—282no—
630C2×C4—282no—
631C2×C4—281no—
632C2×C4—281no—
633C2×C4—282no—
634C2×C4—282no—
635C2×C4—281no—
636C2×C4—281no—
637C2×C4C2×C4⋊Dic718yes—
638C7#1404411yescharacteristic, complemented, Sylow
639C22—28no—
640C22—24no—
641C22—24no—
642C22—24no—
643C22—28no—
644C22—24no—
645C22—28no—
646C22—24no—
647C22—28no—
648C22—24no—
649C22#8975718yes—
650C22C2×#645111yescharacteristic
651C22C2×#645311yescharacteristic
652C22C2×#645811yescharacteristic
653C22C2×#646011yescharacteristic
654C22#9023012yes—
655C22#9023012yes—
656C22#9024512yes—
657C22#9024512yes—
658C22#9028011yescharacteristic
659C22#9028311yescharacteristic
660C22#9028412yes—
661C22#9032712yes—
662C22#9032712yes—
663C22#9032812yes—
664C22#9032812yes—
665C22#9034012yes—
666C22D7×#12311yescharacteristic
667C22#9034711yescharacteristic
668C22C22×C4⋊Dic711yescharacteristic
669C22C2×D4×Dic711yescharacteristic
670C22#9048912yes—
671C22C2×Q8×Dic711yescharacteristic
672C22#41×Dic712yes—
673C4—28no—
674C4—44no—
675C4—42no—
676C4—42no—
677C4—144no—
678C4—284no—
679C4—282no—
680C4—284no—
681C4—561no—
682C4—561no—
683C2—28no—
684C2#1173185111yescharacteristic
685C2#1173186912yes—
686C2#1173190511yescharacteristic
687C2#1173190912yes—
688C2#1173193411yescharacteristic
689C2#1173204711yescharacteristic
690C2C2×#8975711yescharacteristic
691C2#1173977812yes—
692C2#1174002311yescharacteristic
693C2#1174019412yes—
694C2Dic7×#12311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14044
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
7. #11729319C2semidirect
8. #11729317C2semidirect
10. #11727166C2semidirect
11. #11727161C2semidirect
24. C7×#385C4semidirect
69. C2×C7×C4⋊C4C2×C4semidirect
92. C7×#95C2×C4semidirect
201. C7×C22⋊C4C4⋊C4semidirect
222. #385Dic7semidirect
366. C2×C4⋊C4C2×Dic7semidirect
392. #95C2×Dic7semidirect
529. C22⋊C4C4⋊Dic7semidirect
638. C7#14044semidirect

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×#897222
C2×C22⋊C4×Dic72
#117298812
#117293192
#117293172
#117292982
#117271662
#117271612
#140447