Finite Group Databasebeta

← #13276352

Subgroups — #13276352

Order 1792.

1766 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic14C211yesmaximal, characteristic
2C2×#89418C212yesmaximal
3C2×#89422C211yesmaximal, characteristic
4C2×#89421C211yesmaximal, characteristic
5C7×#1434C211yesmaximal, characteristic
6#11729288C211yesmaximal, characteristic
7#11727165C212yesmaximal
8#11727163C212yesmaximal
9Dic7⋊#95C212yesmaximal
10#11727156C211yesmaximal, characteristic
11#11727156C211yesmaximal, characteristic
12C23×Dic14C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×Dic7⋊C4C2212yes—
16C22×Dic7⋊C4C2212yes—
17C22×Dic7⋊C4C2211yescharacteristic
18C22×Dic7⋊C4C2211yescharacteristic
19C22×C4×Dic7C2212yes—
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C2×C4×Dic14—24no—
23C2×C4×Dic14—24no—
24C2×C4×Dic14C418yescomplemented
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
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⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89422—24no—
39#89421—24no—
40#89418—28no—
41#13942—71nomaximal, Sylow
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×Dic14—22no—
54C22×Dic14—22no—
55C22×Dic14—22no—
56C22×Dic14—22no—
57C22×Dic14C2×C414yes—
58C22×Dic14D414yes—
59C22×Dic14Q814yes—
60C2×C42×C7—22no—
61C2×C42×C7—22no—
62C2×C42×C7C2×C414yes—
63C2×C4⋊Dic7—22no—
64C2×C4⋊Dic7—22no—
65C2×C4⋊Dic7C2×C414yes—
66C2×Dic7⋊C4—24no—
67C2×Dic7⋊C4—22no—
68C2×Dic7⋊C4—22no—
69C2×Dic7⋊C4—22no—
70C2×Dic7⋊C4—22no—
71C2×Dic7⋊C4—24no—
72C2×Dic7⋊C4—24no—
73C2×Dic7⋊C4—24no—
74C2×Dic7⋊C4—24no—
75C2×Dic7⋊C4—24no—
76C2×Dic7⋊C4C2×C414yes—
77C2×Dic7⋊C4C2×C414yes—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7—24no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7C2×C414yes—
84C2×C4×Dic7C2×C414yes—
85C2×C4×Dic7D414yes—
86C2×C4×Dic7D414yes—
87C4×Dic14—232no—
88C7×#95—24no—
89C7×#95—22no—
90C7×#95—22no—
91C7×#95—24no—
92C7⋊#95—24no—
93C7⋊#95—22no—
94C7⋊#95—22no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C22×C4×Q8—71no—
102C2×#391—72no—
103C2×#382—71no—
104C2×C4×C4⋊C4—71no—
105#1441—72no—
106#1441—72no—
107C4⋊#95—72no—
108#1434—71no—
109#1434—71no—
110#1434—71no—
111#1434D711yescharacteristic
112C24×C7C2411yescharacteristic
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
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—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7C22×C412yes—
137C22×C4×C7C22×C412yes—
138C22×C4×C7C22×C412yes—
139C22×C4×C7C2×D412yes—
140C22×C4×C7C2×D412yes—
141C22×C4×C7C2×D412yes—
142C22×C4×C7C2×Q812yes—
143C22×C4×C7#4114yes—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7C22×C412yes—
168C22×Dic7C22×C412yes—
169C22×Dic7C22×C412yes—
170C22×Dic7C22×C412yes—
171C22×Dic7C2×D412yes—
172C22×Dic7C2×D412yes—
173C22×Dic7C2×D412yes—
174C22×Dic7C2×D412yes—
175C22×Dic7C2×D412yes—
176C22×Dic7C2×D412yes—
177C22×Dic7C2×Q812yes—
178C22×Dic7C2×Q812yes—
179C22×Dic7#4114yes—
180C22×Dic7#4112yes—
181C22×Dic7#4112yes—
182C2×Dic14—28no—
183C2×Dic14—28no—
184C2×Dic14—28no—
185C2×Dic14—28no—
186C2×Dic14—28no—
187C2×Dic14—28no—
188C2×Dic14C4⋊C4116yescomplemented
189C42×C7—28no—
190C4⋊Dic7—28no—
191Dic7⋊C4—216no—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194Dic7⋊C4—48no—
195C4×Dic7—28no—
196C4×Dic7—48no—
197C4×Dic7C22⋊C4116yes—
198C23×Q8—71no—
199C2×C4×Q8—78no—
200C2×C4×Q8—144no—
201C2×C4×Q8—144no—
202C22×C4⋊C4—71no—
203C22×C4⋊C4—71no—
204C22×C4⋊C4—71no—
205C22×C4⋊C4—72no—
206C22×C4⋊C4—72no—
207C22×C42—71no—
208C22×C42—71no—
209C22×C42—72no—
210C22×C42C2×D711yescharacteristic
211#391—148no—
212#382—144no—
213C4×C4⋊C4—144no—
214C2×#95—71no—
215C2×#95—71no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—72no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C2×#95C2×D711yescharacteristic
224C2×#95C2×D711yescharacteristic
225C2×#95C2×D712yes—
226C2×#95C2×D712yes—
227C23×C7C23×C411yescharacteristic
228C23×C7C22×D411yescharacteristic
229C23×C7C22×D411yescharacteristic
230C23×C7C22×D411yescharacteristic
231C23×C7C22×Q811yescharacteristic
232C23×C7C2×#4112yes—
233C23×C7C2×#4111yescharacteristic
234C23×C7C2×#4111yescharacteristic
235C23×C7C2×#4112yes—
236C23×C72−1+412yes—
237C23×C72−1+412yes—
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7C2×C22⋊C414yes—
268C2×C4×C7C2×C4⋊C414yes—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—22no—
272C2×Dic7—22no—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—22no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7C2×C22⋊C414yes—
299C2×Dic7C2×C22⋊C414yes—
300C2×Dic7C2×C4⋊C414yes—
301C2×Dic7C2×C4⋊C414yes—
302C2×Dic7#11714yes—
303C2×Dic7#12114yes—
304C2×Dic7#12114yes—
305C2×Dic7C22⋊Q814yes—
306C2×Dic7C22⋊Q814yes—
307Dic14—232no—
308C22×Q8—74no—
309C22×Q8—74no—
310C22×Q8—74no—
311C22×Q8—142no—
312C22×Q8—142no—
313C22×Q8—142no—
314C22×Q8—142no—
315C23×C4—71no—
316C23×C4—71no—
317C23×C4—71no—
318C23×C4—71no—
319C23×C4—72no—
320C23×C4—72no—
321C23×C4C22×D712yes—
322C23×C4C22×D711yescharacteristic
323C23×C4C22×D712yes—
324C23×C4C22×D711yescharacteristic
325C23×C4C22×D711yescharacteristic
326C4×Q8—1432no—
327C2×C4⋊C4—74no—
328C2×C4⋊C4—74no—
329C2×C4⋊C4—74no—
330C2×C4⋊C4—142no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—142no—
336C2×C4⋊C4—144no—
337C2×C4⋊C4—144no—
338C2×C4⋊C4—144no—
339C2×C4⋊C4—144no—
340C2×C4⋊C4—144no—
341C2×C4⋊C4—144no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—74no—
345C2×C42—74no—
346C2×C42—74no—
347C2×C42—74no—
348C2×C42—142no—
349C2×C42—142no—
350C2×C42—144no—
351C2×C42—144no—
352C2×C42—144no—
353C2×C42C4×D714yes—
354#95—24no—
355#95—22no—
356#95—22no—
357#95—24no—
358#95—144no—
359#95—144no—
360#95—144no—
361#95—144no—
362#95—144no—
363#95—144no—
364#95—142no—
365#95—142no—
366#95—144no—
367C22×C7C22×C22⋊C411yescharacteristic
368C22×C7C22×C4⋊C411yescharacteristic
369C22×C7C2×#11711yescharacteristic
370C22×C7C4×#4111yescharacteristic
371C22×C7C4×#4111yescharacteristic
372C22×C7#51911yescharacteristic
373C22×C7#51911yescharacteristic
374C22×C7C2×#12111yescharacteristic
375C22×C7C2×#12111yescharacteristic
376C22×C7C2×C22⋊Q811yescharacteristic
377C22×C7C2×C22⋊Q811yescharacteristic
378C22×C7#52512yes—
379C22×C7#53212yes—
380C22×C7#53612yes—
381C22×C7#53612yes—
382C22×C7#54812yes—
383C22×C7#54812yes—
384C22×C7#55212yes—
385C22×C7#55212yes—
386C22×C7#55612yes—
387C22×C7#55612yes—
388C22×C7#55712yes—
389C22×C7#55712yes—
390C4×C7—24no—
391C4×C7—24no—
392C4×C7—44no—
393C4×C7—42no—
394C4×C7—82no—
395Dic7—24no—
396Dic7—24no—
397Dic7—44no—
398Dic7—42no—
399Dic7—82no—
400Dic7#38018yes—
401C24C23×D711yescharacteristic
402C2×Q8—716no—
403C2×Q8—148no—
404C2×Q8—148no—
405C2×Q8—148no—
406C2×Q8—148no—
407C2×Q8—148no—
408C2×Q8—148no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—72no—
433C22×C4—72no—
434C22×C4—72no—
435C22×C4—72no—
436C22×C4—72no—
437C22×C4—72no—
438C22×C4—72no—
439C22×C4—72no—
440C22×C4—72no—
441C22×C4—72no—
442C22×C4—72no—
443C22×C4—72no—
444C22×C4—72no—
445C22×C4—72no—
446C22×C4—74no—
447C22×C4—142no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—142no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4C2×C4×D712yes—
471C22×C4C2×C4×D712yes—
472C22×C4C2×C4×D712yes—
473C22×C4#115714yes—
474C22×C4D4×D712yes—
475C22×C4D4×D712yes—
476C22×C4D4×D712yes—
477C22×C4Q8×D712yes—
478C4⋊C4—148no—
479C4⋊C4—148no—
480C4⋊C4—148no—
481C4⋊C4—1416no—
482C4⋊C4—288no—
483C42—28no—
484C42—716no—
485C42—148no—
486C42—288no—
487C2×C7C2×#38011yescharacteristic
488C2×C7#229711yescharacteristic
489C2×C7#231011yescharacteristic
490C2×C7#235111yescharacteristic
491C2×C7#235111yescharacteristic
492C2×C7#235611yescharacteristic
493C2×C7#235611yescharacteristic
494C2×C7#253612yes—
495C2×C7#254512yes—
496C2×C7#256512yes—
497C2×C7#258112yes—
498C23C22×C4×D711yescharacteristic
499C23C2×#115712yes—
500C23C2×D4×D711yescharacteristic
501C23C2×D4×D711yescharacteristic
502C23C2×D4×D711yescharacteristic
503C23C2×Q8×D711yescharacteristic
504C23D7×#4112yes—
505C23D7×#4111yescharacteristic
506C23D7×#4111yescharacteristic
507C23#655412yes—
508C23#655412yes—
509Q8—1432no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—74no—
540C2×C4—74no—
541C2×C4—74no—
542C2×C4—74no—
543C2×C4—74no—
544C2×C4—74no—
545C2×C4—74no—
546C2×C4—74no—
547C2×C4—74no—
548C2×C4—142no—
549C2×C4—142no—
550C2×C4—142no—
551C2×C4—142no—
552C2×C4—144no—
553C2×C4—144no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—142no—
561C2×C4—142no—
562C2×C4—142no—
563C2×C4—144no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4—282no—
567C2×C4—282no—
568C2×C4—282no—
569C2×C4—282no—
570C2×C4—282no—
571C2×C4—282no—
572C2×C4—282no—
573C2×C4—282no—
574C2×C4—282no—
575C2×C4—282no—
576C2×C4—282no—
577C2×C4D7×C22⋊C414yes—
578C2×C4D7×C4⋊C414yes—
579C7#1394211yescharacteristic, complemented, Sylow
580C22C4×#115711yescharacteristic
581C22C2×D7×C22⋊C411yescharacteristic
582C22C2×D7×C4⋊C411yescharacteristic
583C22#9020711yescharacteristic
584C22#9020711yescharacteristic
585C22D7×#11711yescharacteristic
586C22#9021311yescharacteristic
587C22#9022212yes—
588C22#9022412yes—
589C22#9023812yes—
590C22#9023912yes—
591C22#9024312yes—
592C22#9025812yes—
593C22D7×#12111yescharacteristic
594C22D7×#12111yescharacteristic
595C22D7×C22⋊Q811yescharacteristic
596C22D7×C22⋊Q811yescharacteristic
597C22#9033912yes—
598C22#9033912yes—
599C22#9036812yes—
600C22#9037612yes—
601C22#9039312yes—
602C22#9039912yes—
603C4—24no—
604C4—24no—
605C4—44no—
606C4—42no—
607C4—78no—
608C4—82no—
609C4—144no—
610C4—144no—
611C4—284no—
612C4—282no—
613C4—562no—
614C2#1173083811yescharacteristic
615C2#1173100811yescharacteristic
616C2#1173108211yescharacteristic
617C2D7×#38011yescharacteristic
618C2#1173149811yescharacteristic
619C2#1173160211yescharacteristic
620C2#1173170911yescharacteristic
621C2#1173252112yes—
622C2#1173253512yes—
623C2#1173303712yes—
624C2#1173303812yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1434C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1434D7
hypocenterC7#13942
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
24. C2×C4×Dic14C4semidirect
188. C2×Dic14C4⋊C4semidirect
579. C7#13942semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic142
C2×#894182
C2×#894222
C2×#894212
C7×#14342
#117292882
#117271652
#117271632
Dic7⋊#952
#117271562
#139427