Finite Group Databasebeta

← #13276058

Subgroups — #13276058

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89984C211yesmaximal, characteristic
2C22×C7⋊#95C211yesmaximal, characteristic
3C2×#89714C211yesmaximal, characteristic
4C2×#89714C211yesmaximal, characteristic
5C2×C22⋊C4×Dic7C211yesmaximal, characteristic
6C7×C22⋊#95C211yesmaximal, characteristic
7#11729298C211yesmaximal, characteristic
8#11727174C212yesmaximal, complemented
9#11727168C212yesmaximal, complemented
10#11727161C212yesmaximal, complemented
11#11727160C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C22×C7×C22⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2212yes—
20C22×Dic7⋊C4C2212yes—
21C22×Dic7⋊C4C2212yes—
22C22×C4×Dic7C2212yes—
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25#89984—24no—
26C2×C7⋊#95C418yescomplemented
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37#89714—24no—
38#89714—24no—
39C22⋊C4×Dic7—24no—
40#13908—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—24no—
45C23×C4×C7—42no—
46C23×C4×C7C2×C414yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×Dic7—22no—
52C23×Dic7—22no—
53C23×Dic7—24no—
54C23×Dic7—42no—
55C23×Dic7—42no—
56C23×Dic7—42no—
57C23×Dic7C2×C414yes—
58C23×Dic7C2×C414yes—
59C23×Dic7D414yes—
60C23×Dic7Q814yes—
61C23×Dic7C2312yes—
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2312yes—
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C2×C7×C22⋊C4—22no—
68C2×C7×C22⋊C4—22no—
69C2×C7×C22⋊C4—22no—
70C2×C7×C22⋊C4—22no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4Q814yes—
73C2×C22⋊Dic7—22no—
74C2×C22⋊Dic7—22no—
75C2×C22⋊Dic7—22no—
76C2×C22⋊Dic7—22no—
77C2×C22⋊Dic7—22no—
78C2×C22⋊Dic7D414yes—
79C2×C4⋊Dic7—24no—
80C2×C4⋊Dic7—24no—
81C2×C4⋊Dic7—42no—
82C2×Dic7⋊C4—24no—
83C2×Dic7⋊C4—24no—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4—42no—
86C2×Dic7⋊C4—42no—
87C2×Dic7⋊C4—42no—
88C2×C4×Dic7—24no—
89C2×C4×Dic7—42no—
90C2×C4×Dic7—42no—
91C7×#95—24no—
92C7×#95—42no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—42no—
99C7⋊#95C2×C414yes—
100C7⋊#95C2×C414yes—
101C7⋊#95C2×C414yes—
102C7⋊#95C2×C414yes—
103C2×#380—71no—
104C2×#380—71no—
105C2×#380—71no—
106C2×C4×C22⋊C4—71no—
107C22×#95—71no—
108#1444—72no—
109#1442—72no—
110#1436—72no—
111#1436—72no—
112C22⋊#95—71no—
113C22⋊#95D711yescharacteristic
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—21no—
127C22×C4×C7—21no—
128C22×C4×C7—22no—
129C22×C4×C7—28no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—28no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—44no—
149C22×C4×C7—48no—
150C22×C4×C7—48no—
151C22×C4×C7C22×C412yes—
152C22×C4×C7C22×C412yes—
153C22×C4×C7C2×Q814yes—
154C22×C4×C7#4114yes—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—28no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—21no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—28no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—44no—
182C22×Dic7—44no—
183C22×Dic7—44no—
184C22×Dic7—48no—
185C22×Dic7—48no—
186C22×Dic7—48no—
187C22×Dic7—48no—
188C22×Dic7C4⋊C4116yescomplemented
189C22×Dic7C22×C412yes—
190C22×Dic7C22×C412yes—
191C22×Dic7C22×C412yes—
192C22×Dic7C22×C412yes—
193C22×Dic7C2×D414yes—
194C22×Dic7C2×D412yes—
195C22×Dic7C2×D412yes—
196C22×Dic7C2×Q812yes—
197C22×Dic7C2×Q812yes—
198C22×Dic7#4114yes—
199C7×C22⋊C4—28no—
200C7×C22⋊C4—44no—
201C22⋊Dic7—28no—
202C22⋊Dic7—44no—
203C4⋊Dic7—48no—
204Dic7⋊C4—48no—
205Dic7⋊C4—48no—
206C4×Dic7—48no—
207C24×C4—71no—
208C24×C4—71no—
209C24×C4C2×D711yescharacteristic
210C22×C4⋊C4—72no—
211C22×C4⋊C4—72no—
212C22×C4⋊C4—72no—
213C22×C22⋊C4—71no—
214C22×C22⋊C4—71no—
215C22×C22⋊C4C2×D711yescharacteristic
216C22×C22⋊C4C2×D711yescharacteristic
217C22×C42—72no—
218#380—144no—
219#380—144no—
220#380—144no—
221C4×C22⋊C4—144no—
222C2×#95—78no—
223C2×#95—71no—
224C2×#95—71no—
225C2×#95—71no—
226C2×#95—71no—
227C2×#95—72no—
228C2×#95—72no—
229C2×#95—72no—
230C2×#95—72no—
231C2×#95—72no—
232C2×#95—72no—
233C2×#95C2×D712yes—
234C2×#95C2×D712yes—
235C23×C7—22no—
236C23×C7—22no—
237C23×C7—22no—
238C23×C7—22no—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7—24no—
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×C7C2×C4⋊C414yes—
252C23×C7C4×D414yes—
253C23×C7C4×Q814yes—
254C23×C7#12114yes—
255C23×C7C22⋊Q814yes—
256C23×C7#12514yes—
257C23×C7C4⋊Q814yes—
258C23×C7C23×C411yescharacteristic
259C23×C7C22×D411yescharacteristic
260C23×C7C22×D411yescharacteristic
261C23×C7C22×Q811yescharacteristic
262C23×C7C22×Q811yescharacteristic
263C23×C7C2×#4111yescharacteristic
264C23×C7C2×#4112yes—
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4112yes—
267C23×C7H(5,𝔽2)12yes—
268C23×C7H(5,𝔽2)12yes—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—24no—
277C2×C4×C7—24no—
278C2×C4×C7—24no—
279C2×C4×C7—416no—
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—42no—
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#11714yes—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—24no—
301C2×Dic7—24no—
302C2×Dic7—24no—
303C2×Dic7—24no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—22no—
307C2×Dic7—22no—
308C2×Dic7—22no—
309C2×Dic7—24no—
310C2×Dic7—24no—
311C2×Dic7—24no—
312C2×Dic7—416no—
313C2×Dic7—416no—
314C2×Dic7—42no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7C2×C4⋊C414yes—
328C2×Dic7C2×C4⋊C414yes—
329C2×Dic7#11714yes—
330C25C22×D711yescharacteristic
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—24no—
334C23×C4—42no—
335C23×C4—71no—
336C23×C4—71no—
337C23×C4—71no—
338C23×C4—74no—
339C23×C4—74no—
340C23×C4—74no—
341C23×C4—72no—
342C23×C4—71no—
343C23×C4—74no—
344C23×C4—72no—
345C23×C4—144no—
346C23×C4—142no—
347C23×C4—142no—
348C23×C4—282no—
349C23×C4—282no—
350C23×C4—282no—
351C23×C4C4×D714yes—
352C23×C4C22×D712yes—
353C23×C4C22×D712yes—
354C23×C4C22×D711yescharacteristic
355C23×C4C22×D711yescharacteristic
356C2×C4⋊C4—144no—
357C2×C4⋊C4—144no—
358C2×C4⋊C4—144no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—144no—
361C2×C4⋊C4—282no—
362C2×C4⋊C4—282no—
363C2×C4⋊C4—282no—
364C2×C4⋊C4—282no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—74no—
371C2×C22⋊C4—142no—
372C2×C22⋊C4—142no—
373C2×C22⋊C4—142no—
374C2×C22⋊C4—142no—
375C2×C22⋊C4—142no—
376C2×C22⋊C4Dic1414yes—
377C2×C42—144no—
378C2×C42—282no—
379C2×C42—282no—
380#95—24no—
381#95—42no—
382#95—74no—
383#95—74no—
384#95—74no—
385#95—74no—
386#95—144no—
387#95—144no—
388#95—144no—
389#95—144no—
390#95—144no—
391#95—282no—
392C22×C7—28no—
393C22×C7—28no—
394C22×C7—24no—
395C22×C7—24no—
396C22×C7—24no—
397C22×C7—24no—
398C22×C7—24no—
399C22×C7—24no—
400C22×C7—28no—
401C22×C7—28no—
402C22×C7#38918yes—
403C22×C7C22×C4⋊C411yescharacteristic
404C22×C7C2×#11711yescharacteristic
405C22×C7C2×#11711yescharacteristic
406C22×C7C2×C4×D411yescharacteristic
407C22×C7C2×C4×Q811yescharacteristic
408C22×C7#51811yescharacteristic
409C22×C7#51811yescharacteristic
410C22×C7C2×#12111yescharacteristic
411C22×C7C2×C22⋊Q811yescharacteristic
412C22×C7C2×#12511yescharacteristic
413C22×C7C2×C4⋊Q811yescharacteristic
414C22×C7#53212yes—
415C22×C7#53312yes—
416C22×C7#53412yes—
417C22×C7#54312yes—
418C22×C7#54612yes—
419C22×C7#54612yes—
420C22×C7#55112yes—
421C22×C7#55112yes—
422C22×C7#55312yes—
423C22×C7#55312yes—
424C22×C7#55412yes—
425C22×C7#55412yes—
426C4×C7—24no—
427C4×C7—44no—
428C4×C7—42no—
429C4×C7—82no—
430Dic7—24no—
431Dic7—24no—
432Dic7—24no—
433Dic7—42no—
434Dic7—44no—
435Dic7—82no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24C2×Dic1412yes—
441C24C2×C4×D712yes—
442C24#115712yes—
443C24D4×D712yes—
444C24D4×D712yes—
445C24#115912yes—
446C24Q8×D712yes—
447C24C23×D711yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—28no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—44no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—72no—
474C22×C4—72no—
475C22×C4—72no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—74no—
481C22×C4—716no—
482C22×C4—72no—
483C22×C4—74no—
484C22×C4—148no—
485C22×C4—141no—
486C22×C4—141no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4—148no—
493C22×C4—142no—
494C22×C4—141no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—141no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—142no—
502C22×C4—142no—
503C22×C4—142no—
504C22×C4—142no—
505C22×C4—142no—
506C22×C4—142no—
507C22×C4—142no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—284no—
511C22×C4—284no—
512C22×C4—284no—
513C22×C4—288no—
514C22×C4—288no—
515C22×C4—288no—
516C22×C4—288no—
517C22×C4C2×Dic1414yes—
518C22×C4C2×C4×D712yes—
519C22×C4C2×C4×D712yes—
520C22×C4#115914yes—
521C4⋊C4—288no—
522C4⋊C4—288no—
523C4⋊C4—288no—
524C22⋊C4—28no—
525C22⋊C4—44no—
526C22⋊C4—148no—
527C22⋊C4—284no—
528C42—288no—
529C2×C7—28no—
530C2×C7#228511yescharacteristic
531C2×C7C2×#38911yescharacteristic
532C2×C7#231511yescharacteristic
533C2×C7#234211yescharacteristic
534C2×C7#234211yescharacteristic
535C2×C7#234511yescharacteristic
536C2×C7#234511yescharacteristic
537C2×C7#254312yes—
538C2×C7#254912yes—
539C2×C7#256412yes—
540C2×C7#256912yes—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23C4×Dic1414yes—
558C23#644114yes—
559C23(C22⋊D7)⋊C414yes—
560C23#644714yes—
561C23#645114yes—
562C23#645214yes—
563C23D7×C4⋊C414yes—
564C23C22×Dic1411yescharacteristic
565C23C22×C4×D711yescharacteristic
566C23C2×#115711yescharacteristic
567C23C2×D4×D711yescharacteristic
568C23C2×D4×D711yescharacteristic
569C23C2×#115912yes—
570C23C2×#115911yescharacteristic
571C23#654812yes—
572C23C2×Q8×D711yescharacteristic
573C23D7×#4112yes—
574C23#655312yes—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—416no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—74no—
600C2×C4—74no—
601C2×C4—74no—
602C2×C4—142no—
603C2×C4—142no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—142no—
608C2×C4—144no—
609C2×C4—144no—
610C2×C4—144no—
611C2×C4—144no—
612C2×C4—144no—
613C2×C4—144no—
614C2×C4—142no—
615C2×C4—144no—
616C2×C4—142no—
617C2×C4—142no—
618C2×C4—144no—
619C2×C4—144no—
620C2×C4—2816no—
621C2×C4—2816no—
622C2×C4—282no—
623C2×C4—282no—
624C2×C4—282no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—282no—
629C2×C4—282no—
630C2×C4—282no—
631C2×C4—282no—
632C2×C4—282no—
633C2×C4—282no—
634C2×C4—282no—
635C2×C4#644014yes—
636C7#1390811yescharacteristic, complemented, Sylow
637C22—24no—
638C22—24no—
639C22—24no—
640C22—28no—
641C22—28no—
642C22—24no—
643C22—24no—
644C22—28no—
645C22—28no—
646C22—24no—
647C22#8941918yes—
648C22C2×C4×Dic1411yescharacteristic
649C22C2×#644011yescharacteristic
650C22C2×#644111yescharacteristic
651C22C2×(C22⋊D7)⋊C411yescharacteristic
652C22#9017711yescharacteristic
653C22C2×#644711yescharacteristic
654C22C2×#645111yescharacteristic
655C22C2×#645211yescharacteristic
656C22C2×D7×C4⋊C411yescharacteristic
657C22D7×#11711yescharacteristic
658C22#9021211yescharacteristic
659C22#9023012yes—
660C22#9023112yes—
661C22#9023412yes—
662C22#9025612yes—
663C22#9027812yes—
664C22#9028212yes—
665C22#9028712yes—
666C22#9029612yes—
667C22#9031312yes—
668C22#9032512yes—
669C22#9034512yes—
670C22#9034912yes—
671C4—24no—
672C4—42no—
673C4—44no—
674C4—82no—
675C4—144no—
676C4—144no—
677C4—144no—
678C4—282no—
679C4—284no—
680C4—562no—
681C2—28no—
682C2C2×#8941911yescharacteristic
683C2#1173090211yescharacteristic
684C2#1173090311yescharacteristic
685C2#1173126711yescharacteristic
686C2#1173130911yescharacteristic
687C2#1173145011yescharacteristic
688C2#1173156711yescharacteristic
689C2#1173191712yes—
690C2#1173192312yes—
691C2#1173219712yes—
692C2#1173220812yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#13908
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
8. #11727174C2semidirect
9. #11727168C2semidirect
10. #11727161C2semidirect
11. #11727160C2semidirect
26. C2×C7⋊#95C4semidirect
188. C22×Dic7C4⋊C4semidirect
636. C7#13908semidirect

Maximal subgroups

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

subgroupindex
C2×#899842
C22×C7⋊#952
C2×#897142
C2×C22⋊C4×Dic72
C7×C22⋊#952
#117292982
#117271742
#117271682
#117271612
#117271602
#139087