Finite Group Databasebeta

← #13285014

Subgroups — #13285014

Order 1792.

2430 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic7C211yesmaximal, characteristic
2C2×C7×#385C211yesmaximal, characteristic
3C2×#89750C212yesmaximal, complemented
4C2×#89718C211yesmaximal, characteristic
5#11729881C211yesmaximal, characteristic
6#11729318C212yesmaximal, complemented
7#11729298C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11727160C212yesmaximal, complemented
11#11727156C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×C4×Dic7—24no—
23C22×C4×Dic7—28no—
24C22×C4×Dic7C2212yes—
25C22×C4×Dic7C2212yes—
26C7×#385—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#89750—28no—
39#89718C418yescomplemented
40#14695—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—24no—
45C23×C4×C7—24no—
46C23×C4×C7D414yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×Dic7—22no—
54C23×Dic7—22no—
55C23×Dic7—22no—
56C23×Dic7—22no—
57C23×Dic7—24no—
58C23×Dic7—24no—
59C23×Dic7—24no—
60C23×Dic7—24no—
61C23×Dic7C2×C414yes—
62C23×Dic7Q814yes—
63C23×Dic7C2312yes—
64C23×Dic7C2312yes—
65C23×Dic7C2312yes—
66C23×Dic7C2312yes—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4C2×C414yes—
77C2×C22⋊Dic7—22no—
78C2×C22⋊Dic7—22no—
79C2×C22⋊Dic7—22no—
80C2×C22⋊Dic7—22no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7C2×C414yes—
83C2×Dic7⋊C4—24no—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4C2×C418yescomplemented
86C2×C4×Dic7—232no—
87C2×C4×Dic7—24no—
88C2×C4×Dic7—24no—
89C2×C4×Dic7—24no—
90C2×C4×Dic7—24no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7D418yes—
93C7×#95—22no—
94C7×#95—22no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95C2×C418yescomplemented
104C23×C42—71no—
105C2×#387—72no—
106C2×#385—71no—
107C2×#385D711yescharacteristic
108#1436—72no—
109#1436—72no—
110#1434—72no—
111C22⋊#95—71no—
112C22⋊#95—71no—
113C22⋊#95—71no—
114C22⋊#95—71no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—22no—
119C24×C7C22×C412yes—
120C24×C7C2×D412yes—
121C24×C7C2×Q812yes—
122C24×C7#4112yes—
123C24×C7#4112yes—
124C24×C7#4112yes—
125C24×C7#4112yes—
126C24×C7C2411yescharacteristic
127C22×C4×C7—216no—
128C22×C4×C7—216no—
129C22×C4×C7—28no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—28no—
137C22×C4×C7—28no—
138C22×C4×C7—22no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7C22×C412yes—
157C22×C4×C7C22×C412yes—
158C22×C4×C7C2×D414yes—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D412yes—
161C22×C4×C7#4114yes—
162C22×Dic7—28no—
163C22×Dic7—28no—
164C22×Dic7—216no—
165C22×Dic7—216no—
166C22×Dic7—28no—
167C22×Dic7—28no—
168C22×Dic7—28no—
169C22×Dic7—28no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—216no—
179C22×Dic7—216no—
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×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7C22×C414yes—
194C22×Dic7C22×C414yes—
195C22×Dic7C2×D414yes—
196C22×Dic7C2×D414yes—
197C22×Dic7C2×Q814yes—
198C22×Dic7#4114yes—
199C22×Dic7#4114yes—
200C7×C4⋊C4—44no—
201C7×C4⋊C4—44no—
202C7×C22⋊C4—28no—
203C7×C22⋊C4—44no—
204C22⋊Dic7—28no—
205C22⋊Dic7—44no—
206Dic7⋊C4—216no—
207C4×Dic7—216no—
208C4×Dic7—216no—
209C24×C4—71no—
210C24×C4—71no—
211C24×C4C2×D711yescharacteristic
212C22×C4⋊C4—72no—
213C22×C4⋊C4C2×D711yescharacteristic
214C22×C4⋊C4C2×D711yescharacteristic
215C22×C22⋊C4—71no—
216C22×C22⋊C4—71no—
217C22×C22⋊C4C2×D711yescharacteristic
218C22×C22⋊C4C2×D711yescharacteristic
219C22×C42—72no—
220C22×C42—72no—
221C22×C42—148no—
222C22×C42—144no—
223#387—148no—
224#385—24no—
225#385—78no—
226C2×#95—72no—
227C2×#95—72no—
228C2×#95—72no—
229C2×#95—72no—
230C2×#95—72no—
231C2×#95—72no—
232C2×#95—72no—
233C2×#95—72no—
234C2×#95—72no—
235C2×#95C2×D711yescharacteristic
236C2×#95C2×D711yescharacteristic
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—22no—
240C23×C7—24no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7—22no—
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×C7—24no—
253C23×C7#11714yes—
254C23×C7C4×D414yes—
255C23×C7C4×Q814yes—
256C23×C7C22⋊Q814yes—
257C23×C7#12314yes—
258C23×C7#12514yes—
259C23×C7#12614yes—
260C23×C7C23×C411yescharacteristic
261C23×C7C22×D412yes—
262C23×C7C22×D411yescharacteristic
263C23×C7C22×Q811yescharacteristic
264C23×C7C2×#4111yescharacteristic
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4111yescharacteristic
267C23×C7C2×#4112yes—
268C23×C7C2×#4111yescharacteristic
269C23×C7C2×#4112yes—
270C23×C7C2×#4112yes—
271C2×C4×C7—232no—
272C2×C4×C7—22no—
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—24no—
280C2×C4×C7—24no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—24no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—42no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—42no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7—42no—
299C2×C4×C7—42no—
300C2×C4×C7#12014yes—
301C2×C4×C7#12314yes—
302C2×Dic7—232no—
303C2×Dic7—232no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—24no—
310C2×Dic7—24no—
311C2×Dic7—24no—
312C2×Dic7—24no—
313C2×Dic7—24no—
314C2×Dic7—24no—
315C2×Dic7—24no—
316C2×Dic7—24no—
317C2×Dic7—24no—
318C2×Dic7—24no—
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×Dic7—42no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7C4×D418yes—
331C2×Dic7C22⋊Q818yes—
332C25C22×D711yescharacteristic
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—72no—
338C23×C4—72no—
339C23×C4—74no—
340C23×C4—74no—
341C23×C4—72no—
342C23×C4—72no—
343C23×C4—144no—
344C23×C4—144no—
345C23×C4—144no—
346C23×C4—144no—
347C23×C4—142no—
348C23×C4—142no—
349C23×C4—142no—
350C23×C4—142no—
351C23×C4C22⋊D714yes—
352C23×C4C22×D711yescharacteristic
353C23×C4C22×D711yescharacteristic
354C23×C4C22×D711yescharacteristic
355C23×C4C22×D711yescharacteristic
356C23×C4C22×D711yescharacteristic
357C23×C4C22×D711yescharacteristic
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—78no—
363C2×C4⋊C4—144no—
364C2×C4⋊C4—144no—
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⋊C4C4×D714yes—
377C2×C42—78no—
378C2×C42—144no—
379C2×C42—144no—
380C2×C42—1432no—
381C2×C42—144no—
382C2×C42—144no—
383C2×C42—144no—
384#95—22no—
385#95—22no—
386#95—78no—
387#95—144no—
388#95—144no—
389#95—144no—
390#95—144no—
391#95—144no—
392#95—144no—
393#95—144no—
394#95—144no—
395C22×C7—24no—
396C22×C7—24no—
397C22×C7—28no—
398C22×C7—28no—
399C22×C7—24no—
400C22×C7—24no—
401C22×C7—28no—
402C22×C7—24no—
403C22×C7—24no—
404C22×C7—28no—
405C22×C7#38718yescomplemented
406C22×C7C2×#11711yescharacteristic
407C22×C7C2×C4×D411yescharacteristic
408C22×C7C2×C4×D412yes—
409C22×C7C2×C4×Q811yescharacteristic
410C22×C7C4×#4112yes—
411C22×C7C2×#12011yescharacteristic
412C22×C7C2×C22⋊Q811yescharacteristic
413C22×C7C2×C22⋊Q812yes—
414C22×C7C2×#12311yescharacteristic
415C22×C7C2×#12311yescharacteristic
416C22×C7#52512yes—
417C22×C7#52511yescharacteristic
418C22×C7#52511yescharacteristic
419C22×C7#52512yes—
420C22×C7#52512yes—
421C22×C7#52512yes—
422C22×C7C2×#12511yescharacteristic
423C22×C7C2×#12611yescharacteristic
424C22×C7#52912yes—
425C22×C7#52912yes—
426C22×C7#52912yes—
427C22×C7#52912yes—
428C22×C7#53312yes—
429C4×C7—24no—
430C4×C7—24no—
431C4×C7—42no—
432C4×C7—42no—
433C4×C7—81no—
434C4×C7—81no—
435Dic7—28no—
436Dic7—28no—
437Dic7—44no—
438Dic7—82no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24C2×C4×D712yes—
444C24#115712yes—
445C24#115912yes—
446C24#115912yes—
447C24Q8×D712yes—
448C24#116112yes—
449C24C2×C22⋊D712yes—
450C24C23×D711yescharacteristic
451C22×C4—216no—
452C22×C4—216no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—74no—
481C22×C4—74no—
482C22×C4—74no—
483C22×C4—74no—
484C22×C4—74no—
485C22×C4—74no—
486C22×C4—74no—
487C22×C4—1416no—
488C22×C4—1416no—
489C22×C4—148no—
490C22×C4—148no—
491C22×C4—1416no—
492C22×C4—148no—
493C22×C4—148no—
494C22×C4—1416no—
495C22×C4—148no—
496C22×C4—148no—
497C22×C4—142no—
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—142no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4—142no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—142no—
518C22×C4C2×C4×D712yes—
519C22×C4C2×C4×D712yes—
520C22×C4D4×D714yes—
521C22×C4#115914yes—
522C22×C4C2×C22⋊D712yes—
523C22×C4C2×C22⋊D712yes—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—1416no—
527C22⋊C4—28no—
528C22⋊C4—44no—
529C22⋊C4—148no—
530C22⋊C4—284no—
531C42—1416no—
532C42—1416no—
533C2×C7—28no—
534C2×C7C2×#38711yescharacteristic
535C2×C7#229012yes—
536C2×C7C4×#12011yescharacteristic
537C2×C7C4×#12311yescharacteristic
538C2×C7C4×C22⋊Q812yes—
539C2×C7#284811yescharacteristic
540C2×C7#284911yescharacteristic
541C2×C7#285112yes—
542C2×C7#285212yes—
543C2×C7#285311yescharacteristic
544C2×C7#285511yescharacteristic
545C23—24no—
546C23—24no—
547C23—22no—
548C23—22no—
549C23—24no—
550C23—24no—
551C23—22no—
552C23—22no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23#645014yes—
562C23#645214yes—
563C23#645514yes—
564C23#646114yes—
565C23C4×C22⋊D714yes—
566C23#649814yes—
567C23#650914yes—
568C23C22×C4×D711yescharacteristic
569C23C2×#115711yescharacteristic
570C23C2×D4×D712yes—
571C23C2×#115911yescharacteristic
572C23C2×#115911yescharacteristic
573C23C2×#115912yes—
574C23C2×Q8×D711yescharacteristic
575C23C2×#116111yescharacteristic
576C23D7×#4112yes—
577C23D7×#4112yes—
578C23C22×C22⋊D711yescharacteristic
579C2×C4—232no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—78no—
609C2×C4—78no—
610C2×C4—1432no—
611C2×C4—1432no—
612C2×C4—144no—
613C2×C4—144no—
614C2×C4—144no—
615C2×C4—144no—
616C2×C4—144no—
617C2×C4—144no—
618C2×C4—144no—
619C2×C4—144no—
620C2×C4—144no—
621C2×C4—144no—
622C2×C4—144no—
623C2×C4—144no—
624C2×C4—144no—
625C2×C4—144no—
626C2×C4—144no—
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—282no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4#649814yes—
639C2×C4#650014yes—
640C7#1469511yescharacteristic, complemented, Sylow
641C22—28no—
642C22—28no—
643C22—24no—
644C22—28no—
645C22—28no—
646C22—24no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22#8975018yescomplemented
652C22C2×#645011yescharacteristic
653C22C2×#645211yescharacteristic
654C22C2×#645511yescharacteristic
655C22C2×#646111yescharacteristic
656C22C4×#115912yes—
657C22#9022912yes—
658C22C4×D4×D712yes—
659C22#9023812yes—
660C22#9027712yes—
661C22#9027712yes—
662C22#9031312yes—
663C22#9031512yes—
664C22D7×C22⋊Q812yes—
665C22#9031812yes—
666C22#9034012yes—
667C22#9034012yes—
668C22C2×C4×C22⋊D711yescharacteristic
669C22C2×#649811yescharacteristic
670C22C2×#649811yescharacteristic
671C22C2×#650011yescharacteristic
672C22C2×#650911yescharacteristic
673C22#9051911yescharacteristic
674C22#9051911yescharacteristic
675C4—24no—
676C4—24no—
677C4—42no—
678C4—42no—
679C4—81no—
680C4—81no—
681C4—148no—
682C4—148no—
683C4—284no—
684C4—562no—
685C2—28no—
686C2#1173182212yes—
687C2#1173182612yes—
688C2#1173203112yes—
689C2#1173203212yes—
690C2C2×#8975011yescharacteristic
691C2C4×#649811yescharacteristic
692C2C4×#650011yescharacteristic
693C2#1174004711yescharacteristic
694C2#1174025511yescharacteristic
695C2#1174027911yescharacteristic
696C2#1174033511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14695
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×#89750C2semidirect
6. #11729318C2semidirect
10. #11727160C2semidirect
11. #11727156C2semidirect
39. #89718C4semidirect
85. C2×Dic7⋊C4C2×C4semidirect
103. C7⋊#95C2×C4semidirect
405. C22×C7#387semidirect
640. C7#14695semidirect
651. C22#89750semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic72
C2×C7×#3852
C2×#897502
C2×#897182
#117298812
#117293182
#117292982
#117271602
#117271562
#146957