Finite Group Databasebeta

← #13285085

Subgroups — #13285085

Order 1792.

2734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6509C211yesmaximal, characteristic
2C22×C42×D7C211yesmaximal, characteristic
3C2×C7×#391C211yesmaximal, characteristic, complemented
4C2×#90002C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic, complemented
7#11729289C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C214yesmaximal
9#11727160C214yesmaximal, complemented
10C23×C7×Q8C2211yescharacteristic
11C23×C4×D7C2212yes—
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C2×#6509—24no—
16C2×#6509—24no—
17C2×#6509C418yescomplemented
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×Dic7⋊C4C2212yes—
23C22×C4×Dic7C2212yes—
24C22×C4×Dic7C2211yescharacteristic
25C2×C42×D7—24no—
26C2×C42×D7—24no—
27C2×C42×D7—24no—
28C7×#391—24no—
29C2×C7×#95C2214yes—
30#90002—24no—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2214yes—
33C2×C7⋊#95C2214yes—
34C2×C7⋊#95C2214yes—
35#89759—24no—
36#14702—71nomaximal, Sylow
37C24×D7C2311yescharacteristic
38C22×C7×Q8—22no—
39C22×C7×Q8—22no—
40C22×C7×Q8—22no—
41C22×C7×Q8—22no—
42C22×C7×Q8—22no—
43C22×C7×Q8—22no—
44C22×C7×Q8C2×C414yescomplemented
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2312yes—
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2312yes—
53C22×C4×D7—24no—
54C22×C4×D7—24no—
55C22×C4×D7—24no—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7—24no—
59C22×C4×D7—22no—
60C22×C4×D7—22no—
61C22×C4×D7—24no—
62C22×C4×D7—24no—
63C22×C4×D7C2×C414yes—
64C22×C4×D7D414yes—
65C22×C4×D7D414yes—
66C22×C4×D7Q818yescomplemented
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7D414yes—
73#6509—232no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—24no—
76C2×(C2×D7)⋊C4—24no—
77C2×(C2×D7)⋊C4—28no—
78C2×(C2×D7)⋊C4C2×C418yes—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7C2×C414yescomplemented
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—24no—
87C2×Dic7⋊C4C2×C418yescomplemented
88C2×C4×Dic7—24no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7D414yes—
94C42×D7—232no—
95C7×#95—28no—
96C7⋊#95—28no—
97C7⋊#95—28no—
98C7⋊#95—24no—
99C7⋊#95—28no—
100C22×C22⋊Q8—71no—
101C23×C42—71no—
102C2×#391—71no—
103C2×#391D711yescharacteristic, complemented
104C2×#380—71no—
105#1436—74no—
106C4⋊#95—71no—
107C4⋊#95—71no—
108C22⋊#95—74no—
109C24×C7C2411yescharacteristic
110C23×D7—21no—
111C23×D7—21no—
112C23×D7—21no—
113C23×D7—21no—
114C23×D7—22no—
115C23×D7—22no—
116C23×D7C22×C412yes—
117C23×D7C2×D412yes—
118C23×D7C2×D412yes—
119C23×D7C2×Q814yes—
120C23×D7#4114yes—
121C2×C7×Q8—28no—
122C2×C7×Q8—28no—
123C2×C7×Q8—28no—
124C2×C7×Q8—44no—
125C2×C7×Q8—44no—
126C2×C7×Q8—44no—
127C2×C7×Q8—44no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
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—24no—
141C22×C4×C7—24no—
142C22×C4×C7—22no—
143C22×C4×C7C22×C414yes—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C2×D414yes—
146C22×C4×C7C2×D412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D412yes—
149C22×C4×C7C2×D412yes—
150C22×C4×C7C2×Q814yes—
151C22×C4×C7#4114yes—
152C22×C4×C7#4112yes—
153C22×C4×C7#4112yes—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—24no—
165C22×Dic7—24no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—24no—
169C22×Dic7—22no—
170C22×Dic7—24no—
171C22×Dic7C22×C414yes—
172C22×Dic7C22×C412yes—
173C22×Dic7C2×D412yes—
174C22×Dic7C2×D412yes—
175C22×Dic7C2×D414yes—
176C22×Dic7C2×Q814yes—
177C22×Dic7#4114yes—
178C2×C4×D7—216no—
179C2×C4×D7—216no—
180C2×C4×D7—216no—
181C2×C4×D7—216no—
182C2×C4×D7—216no—
183C2×C4×D7—28no—
184C2×C4×D7—28no—
185C2×C4×D7—28no—
186C2×C4×D7—28no—
187C2×C4×D7—28no—
188C2×C4×D7—216no—
189C2×C4×D7—28no—
190C2×C4×D7—216no—
191C2×C4×D7C22⋊C4116yes—
192C7×C4⋊C4—44no—
193C42×C7—28no—
194(C2×D7)⋊C4—216no—
195(C2×D7)⋊C4—48no—
196C4⋊Dic7—28no—
197C4⋊Dic7—44no—
198Dic7⋊C4—216no—
199C4×Dic7—216no—
200C4×Dic7—28no—
201C23×Q8C2×D711yescharacteristic
202C24×C4—71no—
203C24×C4—72no—
204C2×C22⋊Q8—78no—
205C2×C22⋊Q8—144no—
206C2×C22⋊Q8—144no—
207C22×C4⋊C4—72no—
208C22×C4⋊C4—71no—
209C22×C4⋊C4—71no—
210C22×C4⋊C4C2×D711yescharacteristic
211C22×C22⋊C4—72no—
212C22×C22⋊C4—72no—
213C22×C42—71no—
214C22×C42—72no—
215C22×C42—144no—
216C22×C42—144no—
217C22×C42—144no—
218C22×C42C2×D711yescharacteristic
219#391—24no—
220#391—144no—
221#380—144no—
222C2×#95—74no—
223C2×#95—74no—
224C2×#95—74no—
225C2×#95—72no—
226C2×#95C2×D714yes—
227C23×C7C23×C411yescharacteristic
228C23×C7C22×D411yescharacteristic
229C23×C7C22×D411yescharacteristic
230C23×C7C22×D411yescharacteristic
231C23×C7C22×D411yescharacteristic
232C23×C7C22×Q812yes—
233C23×C7C2×#4111yescharacteristic
234C23×C7C2×#4111yescharacteristic
235C23×C7C2×#4112yes—
236C23×C7C2×#4112yes—
237C23×C7C2×#4112yes—
238C22×D7—22no—
239C22×D7—22no—
240C22×D7—24no—
241C22×D7—22no—
242C22×D7—22no—
243C22×D7—22no—
244C22×D7—24no—
245C22×D7—24no—
246C22×D7—22no—
247C22×D7—24no—
248C22×D7—24no—
249C22×D7—24no—
250C22×D7—24no—
251C22×D7—24no—
252C22×D7—22no—
253C22×D7—22no—
254C22×D7—24no—
255C22×D7—24no—
256C22×D7C2×C22⋊C414yes—
257C22×D7C4×Q818yes—
258C22×D7C22⋊Q818yes—
259C22×D7#12414yes—
260C22×D7C4⋊Q814yes—
261C7×Q8—416no—
262C2×C4×C7—24no—
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—24no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—44no—
277C2×C4×C7—42no—
278C2×C4×C7—44no—
279C2×C4×C7—42no—
280C2×C4×C7C2×C22⋊C414yes—
281C2×C4×C7C4×D414yes—
282C2×C4×C7C4×D414yes—
283C2×C4×C7#12014yes—
284C2×C4×C7#12114yes—
285C2×C4×C7#12114yes—
286C2×C4×C7C22⋊Q818yescomplemented
287C2×C4×C7#12314yes—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—24no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—22no—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—24no—
300C2×Dic7—24no—
301C2×Dic7—28no—
302C2×Dic7—44no—
303C2×Dic7—42no—
304C2×Dic7—42no—
305C2×Dic7—42no—
306C2×Dic7—44no—
307C2×Dic7—42no—
308C2×Dic7—44no—
309C2×Dic7—42no—
310C2×Dic7C2×C22⋊C414yes—
311C2×Dic7C22⋊Q818yescomplemented
312C4×D7—264no—
313C4×D7—232no—
314C25—71no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8C4×D714yescomplemented
322C23×C4—71no—
323C23×C4—72no—
324C23×C4—74no—
325C23×C4—74no—
326C23×C4—74no—
327C23×C4—72no—
328C23×C4—78no—
329C23×C4—72no—
330C23×C4—144no—
331C23×C4—144no—
332C23×C4—144no—
333C23×C4—144no—
334C23×C4—142no—
335C23×C4—142no—
336C23×C4—142no—
337C23×C4—144no—
338C23×C4—144no—
339C23×C4—142no—
340C23×C4C22×D712yes—
341C23×C4C22×D712yes—
342C23×C4C22×D712yes—
343C23×C4C22×D711yescharacteristic
344C22⋊Q8—1432no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—78no—
349C2×C4⋊C4—74no—
350C2×C4⋊C4—144no—
351C2×C4⋊C4—144no—
352C2×C4⋊C4—142no—
353C2×C4⋊C4—142no—
354C2×C4⋊C4—142no—
355C2×C4⋊C4—142no—
356C2×C4⋊C4—142no—
357C2×C22⋊C4—78no—
358C2×C22⋊C4—144no—
359C2×C22⋊C4—144no—
360C2×C22⋊C4—148no—
361C2×C22⋊C4—144no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—74no—
365C2×C42—1432no—
366C2×C42—144no—
367C2×C42—144no—
368C2×C42—142no—
369C2×C42—144no—
370C2×C42—142no—
371C2×C42C22⋊D714yes—
372#95—28no—
373#95—148no—
374#95—144no—
375#95—148no—
376#95—148no—
377C22×C7C22×C22⋊C411yescharacteristic
378C22×C7C2×C4×D411yescharacteristic
379C22×C7C2×C4×D411yescharacteristic
380C22×C7C2×C4×Q812yes—
381C22×C7C4×#4112yes—
382C22×C7C2×#12011yescharacteristic
383C22×C7C2×#12111yescharacteristic
384C22×C7C2×#12111yescharacteristic
385C22×C7C2×C22⋊Q812yes—
386C22×C7C2×C22⋊Q812yes—
387C22×C7C2×C22⋊Q812yes—
388C22×C7C2×#12311yescharacteristic
389C22×C7#52512yes—
390C22×C7#52512yes—
391C22×C7#52512yes—
392C22×C7C2×#12411yescharacteristic
393C22×C7#52912yes—
394C22×C7#52912yes—
395C22×C7C2×C4⋊Q811yescharacteristic
396C22×C7#53211yescharacteristic
397C22×C7#53211yescharacteristic
398C22×C7#53312yes—
399C22×C7#53312yes—
400C2×D7—28no—
401C2×D7—24no—
402C2×D7—24no—
403C2×D7—28no—
404C2×D7—24no—
405C2×D7—24no—
406C2×D7—24no—
407C2×D7—24no—
408C2×D7—28no—
409C2×D7—28no—
410C2×D7#39118yescomplemented
411C4×C7—28no—
412C4×C7—44no—
413C4×C7—82no—
414C4×C7#38618yes—
415Dic7—28no—
416Dic7—24no—
417Dic7—44no—
418Dic7—82no—
419C24—72no—
420C24—72no—
421C24—72no—
422C24—74no—
423C24—74no—
424C24—141no—
425C24—141no—
426C24—141no—
427C24—142no—
428C24—142no—
429C24—141no—
430C24C23×D711yescharacteristic
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—72no—
454C22×C4—74no—
455C22×C4—72no—
456C22×C4—72no—
457C22×C4—74no—
458C22×C4—74no—
459C22×C4—716no—
460C22×C4—74no—
461C22×C4—1416no—
462C22×C4—1416no—
463C22×C4—1416no—
464C22×C4—1416no—
465C22×C4—1416no—
466C22×C4—1416no—
467C22×C4—141no—
468C22×C4—141no—
469C22×C4—142no—
470C22×C4—141no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—148no—
476C22×C4—148no—
477C22×C4—148no—
478C22×C4—148no—
479C22×C4—148no—
480C22×C4—148no—
481C22×C4—1416no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—144no—
485C22×C4—144no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—144no—
490C22×C4—144no—
491C22×C4C2×C4×D714yes—
492C22×C4C2×C4×D712yes—
493C22×C4#115712yes—
494C22×C4D4×D712yes—
495C22×C4D4×D712yes—
496C22×C4D4×D712yes—
497C22×C4#115912yes—
498C22×C4Q8×D714yes—
499C22×C4#116114yes—
500C22×C4C2×C22⋊D714yes—
501C22×C4C2×C22⋊D712yes—
502C4⋊C4—44no—
503C4⋊C4—1416no—
504C4⋊C4—148no—
505C4⋊C4—284no—
506C22⋊C4—1416no—
507C22⋊C4—288no—
508C42—28no—
509C42—1416no—
510C42—148no—
511C2×C7C2×#38611yescharacteristic
512C2×C7C2×#39111yescharacteristic
513C2×C7#229711yescharacteristic
514C2×C7C4×C22⋊Q812yes—
515C2×C7C4×C22⋊Q812yes—
516C2×C7#284812yes—
517C2×C7#285011yescharacteristic
518C2×C7#285011yescharacteristic
519C2×C7#285512yes—
520C2×C7#285711yescharacteristic
521C2×C7#285711yescharacteristic
522D7—28no—
523C23—74no—
524C23—74no—
525C23—78no—
526C23—78no—
527C23—74no—
528C23—144no—
529C23—142no—
530C23—144no—
531C23—142no—
532C23—142no—
533C23—142no—
534C23—142no—
535C23—142no—
536C23—142no—
537C23—144no—
538C23—144no—
539C23—144no—
540C23—144no—
541C23—144no—
542C23—144no—
543C23—144no—
544C23—144no—
545C23—142no—
546C23C22×C4×D711yescharacteristic
547C23C2×#115711yescharacteristic
548C23C2×D4×D711yescharacteristic
549C23C2×D4×D711yescharacteristic
550C23C2×D4×D711yescharacteristic
551C23C2×#115911yescharacteristic
552C23C2×Q8×D712yes—
553C23C2×#116112yes—
554C23D7×#4112yes—
555C23D7×#4112yes—
556C23C22×C22⋊D711yescharacteristic
557Q8—416no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—74no—
577C2×C4—78no—
578C2×C4—1464no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—144no—
584C2×C4—142no—
585C2×C4—142no—
586C2×C4—144no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—144no—
590C2×C4—144no—
591C2×C4—1432no—
592C2×C4—144no—
593C2×C4—148no—
594C2×C4—282no—
595C2×C4—284no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—282no—
599C2×C4—284no—
600C2×C4—284no—
601C2×C4—282no—
602C2×C4D7×C22⋊C414yes—
603C2×C4(C22⋊D7)⋊C414yes—
604C2×C4#644614yes—
605C2×C4#644714yes—
606C2×C4C4×C22⋊D714yes—
607C2×C4#650014yes—
608C2×C4#650114yes—
609C2×C4#650918yescomplemented
610C7#1470211yescharacteristic, complemented, Sylow
611C22—78no—
612C22—148no—
613C22—144no—
614C22—144no—
615C22—144no—
616C22—148no—
617C22—144no—
618C22—148no—
619C22—144no—
620C22—148no—
621C22—144no—
622C22C2×D7×C22⋊C411yescharacteristic
623C22C2×(C22⋊D7)⋊C411yescharacteristic
624C22C2×#644611yescharacteristic
625C22C2×#644711yescharacteristic
626C22C4×Q8×D712yes—
627C22C4×#116112yes—
628C22#9026912yes—
629C22#9027112yes—
630C22D7×C22⋊Q812yes—
631C22D7×C22⋊Q812yes—
632C22#9031812yes—
633C22#9031812yes—
634C22#9035911yescharacteristic
635C22D7×#12411yescharacteristic
636C22#9037112yes—
637C22D7×C4⋊Q811yescharacteristic
638C22#9041611yescharacteristic
639C22#9041912yes—
640C22C2×C4×C22⋊D711yescharacteristic
641C22C2×#650011yescharacteristic
642C22C2×#650111yescharacteristic
643C22C2×#650912yes—
644C22#9051912yes—
645C4—28no—
646C4—44no—
647C4—82no—
648C4—148no—
649C4—144no—
650C4—284no—
651C4—562no—
652C4#8972818yes—
653C2—148no—
654C2#1173392311yescharacteristic
655C2#1173392412yes—
656C2D7×#39111yescharacteristic
657C2#1173410711yescharacteristic
658C2#1173410812yes—
659C2#1173410911yescharacteristic
660C2C2×#8972811yescharacteristic
661C2C4×#650912yes—
662C2#1174027912yes—
663C2#1174045311yescharacteristic
664C2#1174071411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#391D7
hypocenterC7#14702
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. C2×C7×#391C2semidirect
4. C2×#90002C2semidirect
6. #11729317C2semidirect
7. #11729289C2semidirect
9. #11727160C2semidirect
17. C2×#6509C4semidirect
44. C22×C7×Q8C2×C4semidirect
66. C22×C4×D7Q8semidirect
84. C2×C4⋊Dic7C2×C4semidirect
87. C2×Dic7⋊C4C2×C4semidirect
103. C2×#391D7semidirect
286. C2×C4×C7C22⋊Q8semidirect
311. C2×Dic7C22⋊Q8semidirect
321. C22×Q8C4×D7semidirect
410. C2×D7#391semidirect
609. C2×C4#6509semidirect
610. C7#14702semidirect

Maximal subgroups

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

subgroupindex
C22×#65092
C22×C42×D72
C2×C7×#3912
C2×#900022
C2×#897592
#117293172
#117292892
(C2×D7)⋊#952
#117271602
#147027