Finite Group Databasebeta

← #13275890

Subgroups — #13275890

Order 1792.

1746 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#89712C212yesmaximal
3C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
4C2×#89439C211yesmaximal, characteristic
5#11729324C212yesmaximal
6#11729322C212yesmaximal, complemented
7#11729290C212yesmaximal, complemented
8#11729288C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10Dic7⋊#95C211yesmaximal, characteristic, complemented
11#11727155C211yesmaximal, characteristic, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C42×C7C2212yes—
15C22×C42×C7C2211yescharacteristic
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2212yes—
21C22×Dic7⋊C4C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C4×C7×C4⋊C4—24no—
24C2×C7×#95C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36#89712—28no—
37C4×(C2×D7)⋊C4C418yescomplemented
38#89439—24no—
39#13891—71nomaximal, Sylow
40C24×D7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C22×C4×D7—22no—
52C22×C4×D7—22no—
53C22×C4×D7—24no—
54C22×C4×D7—42no—
55C22×C4×D7C2×C414yes—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—24no—
59C2×C42×C7—22no—
60C2×C42×C7—22no—
61C2×C42×C7—24no—
62C2×C42×C7—24no—
63C2×C42×C7—42no—
64C2×C42×C7C2×C414yes—
65C2×(C2×D7)⋊C4—24no—
66C2×(C2×D7)⋊C4—24no—
67C2×(C2×D7)⋊C4—24no—
68C2×(C2×D7)⋊C4—24no—
69C2×(C2×D7)⋊C4—24no—
70C2×(C2×D7)⋊C4—42no—
71C2×(C2×D7)⋊C4—42no—
72C2×(C2×D7)⋊C4C2×C414yes—
73C2×(C2×D7)⋊C4C2×C414yes—
74C2×(C2×D7)⋊C4D414yes—
75C2×(C2×D7)⋊C4Q814yes—
76C2×Dic7⋊C4—24no—
77C2×Dic7⋊C4—24no—
78C2×Dic7⋊C4—24no—
79C2×Dic7⋊C4—24no—
80C2×Dic7⋊C4—42no—
81C2×Dic7⋊C4—42no—
82C2×C4×Dic7—42no—
83C2×C4×Dic7C2×C414yes—
84C7×#95—22no—
85C7×#95D414yes—
86C7⋊#95—22no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—22no—
90C7⋊#95—24no—
91C7⋊#95—24no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C7⋊#95C2×C414yes—
95C7⋊#95C2×C414yes—
96C2×#388—72no—
97C2×#380—71no—
98C2×C4×C4⋊C4D711yescharacteristic, complemented
99C2×C4×C22⋊C4—71no—
100#1444—72no—
101#1439—72no—
102#1436—72no—
103C4⋊#95—71no—
104#1434—71no—
105#1434—71no—
106C22⋊#95—71no—
107C24×C7C2411yescharacteristic
108C23×D7—21no—
109C23×D7—22no—
110C23×D7—22no—
111C23×D7—22no—
112C23×D7—21no—
113C23×D7—21no—
114C23×D7—22no—
115C23×D7—21no—
116C23×D7C22×C412yes—
117C23×D7C2×D412yes—
118C23×D7C2×Q812yes—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
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×C7C22×C412yes—
141C22×C4×C7C22×C412yes—
142C22×C4×C7C22×C412yes—
143C22×C4×C7C2×D414yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×Q812yes—
147C22×C4×C7#4114yes—
148C22×C4×C7#4114yes—
149C22×C4×C7#4112yes—
150C22×Dic7—21no—
151C22×Dic7—22no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—21no—
157C22×Dic7—22no—
158C22×Dic7—21no—
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×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7C22×C412yes—
174C22×Dic7C22×C412yes—
175C22×Dic7C22×C412yes—
176C22×Dic7C2×D412yes—
177C22×Dic7C2×Q812yes—
178C22×Dic7#4114yes—
179C2×C4×D7—28no—
180C2×C4×D7—28no—
181C2×C4×D7—44no—
182C2×C4×D7—48no—
183C2×C4×D7—48no—
184C7×C4⋊C4—216no—
185C42×C7—28no—
186C42×C7—48no—
187(C2×D7)⋊C4—28no—
188(C2×D7)⋊C4—48no—
189(C2×D7)⋊C4—48no—
190(C2×D7)⋊C4C4⋊C4116yescomplemented
191Dic7⋊C4—48no—
192Dic7⋊C4—48no—
193C4×Dic7—44no—
194C24×C4—71no—
195C22×C4⋊C4—72no—
196C22×C4⋊C4—72no—
197C22×C4⋊C4C2×D712yes—
198C22×C22⋊C4—71no—
199C22×C22⋊C4—71no—
200C22×C22⋊C4—72no—
201C22×C22⋊C4—72no—
202C22×C42—71no—
203C22×C42C2×D712yes—
204C22×C42C2×D711yescharacteristic
205#388—148no—
206#380—144no—
207C4×C4⋊C4—24no—
208C4×C22⋊C4—78no—
209C2×#95—71no—
210C2×#95—71no—
211C2×#95—71no—
212C2×#95—72no—
213C2×#95—71no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—72no—
219C2×#95C2×D711yescharacteristic
220C2×#95C2×D711yescharacteristic
221C23×C7C23×C411yescharacteristic
222C23×C7C22×D411yescharacteristic
223C23×C7C22×D411yescharacteristic
224C23×C7C22×Q811yescharacteristic
225C23×C7C2×#4112yes—
226C23×C7C2×#4111yescharacteristic
227C23×C7C2×#4112yes—
228C23×C7C2×#4112yes—
229C23×C7H(5,𝔽2)11yescharacteristic
230C23×C7H(5,𝔽2)12yes—
231C23×C72−1+411yescharacteristic
232C22×D7—22no—
233C22×D7—22no—
234C22×D7—22no—
235C22×D7—22no—
236C22×D7—22no—
237C22×D7—22no—
238C22×D7—24no—
239C22×D7—24no—
240C22×D7—22no—
241C22×D7—24no—
242C22×D7—22no—
243C22×D7—22no—
244C22×D7—22no—
245C22×D7—24no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C22×D7—42no—
252C22×D7—42no—
253C22×D7—42no—
254C22×D7C2×C4⋊C414yes—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—22no—
264C2×C4×C7—24no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—24no—
268C2×C4×C7—22no—
269C2×C4×C7—24no—
270C2×C4×C7—24no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7C2×C4⋊C414yes—
284C2×C4×C7#11714yes—
285C2×C4×C7C4×D414yes—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—24no—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303C2×Dic7—42no—
304C2×Dic7—42no—
305C2×Dic7—42no—
306C2×Dic7—42no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7C2×C4⋊C414yes—
314C2×Dic7#11714yes—
315C4×D7—416no—
316C25—71no—
317C23×C4—71no—
318C23×C4—71no—
319C23×C4—71no—
320C23×C4—74no—
321C23×C4—72no—
322C23×C4—72no—
323C23×C4—144no—
324C23×C4—142no—
325C23×C4—142no—
326C23×C4—282no—
327C23×C4C22×D712yes—
328C23×C4C22×D712yes—
329C23×C4C22×D711yescharacteristic
330C23×C4C22×D711yescharacteristic
331C23×C4C22×D711yescharacteristic
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—144no—
336C2×C4⋊C4—144no—
337C2×C4⋊C4—144no—
338C2×C4⋊C4—144no—
339C2×C4⋊C4—282no—
340C2×C4⋊C4—282no—
341C2×C22⋊C4—74no—
342C2×C22⋊C4—74no—
343C2×C22⋊C4—74no—
344C2×C22⋊C4—74no—
345C2×C22⋊C4—144no—
346C2×C22⋊C4—144no—
347C2×C22⋊C4—144no—
348C2×C22⋊C4—144no—
349C2×C22⋊C4—144no—
350C2×C22⋊C4—282no—
351C2×C22⋊C4—282no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—42no—
357C2×C42—74no—
358C2×C42—282no—
359C2×C42C4×D714yes—
360#95—22no—
361#95—74no—
362#95—74no—
363#95—144no—
364#95—144no—
365#95—144no—
366#95—142no—
367#95—144no—
368#95—142no—
369#95—282no—
370#95—282no—
371#95C22⋊D714yes—
372C22×C7C22×C4⋊C411yescharacteristic
373C22×C7C2×#11711yescharacteristic
374C22×C7C2×#11711yescharacteristic
375C22×C7C2×C4×D411yescharacteristic
376C22×C7C4×#4111yescharacteristic
377C22×C7#51811yescharacteristic
378C22×C7#52011yescharacteristic
379C22×C7#52512yes—
380C22×C7#52912yes—
381C22×C7#53212yes—
382C22×C7#53312yes—
383C22×C7#54012yes—
384C22×C7#54212yes—
385C22×C7D4211yescharacteristic
386C22×C7#54612yes—
387C22×C7#54612yes—
388C22×C7#54711yescharacteristic
389C22×C7D4×Q811yescharacteristic
390C22×C7#55112yes—
391C22×C7#55312yes—
392C22×C7#55411yescharacteristic
393C22×C7#55412yes—
394C22×C7#55612yes—
395C2×D7—24no—
396C2×D7—24no—
397C2×D7—24no—
398C2×D7—42no—
399C2×D7—42no—
400C2×D7—42no—
401C2×D7—44no—
402C2×D7—44no—
403C2×D7—44no—
404C2×D7—44no—
405C2×D7—42no—
406C4×C7—24no—
407C4×C7—24no—
408C4×C7—24no—
409C4×C7—44no—
410C4×C7—44no—
411Dic7—24no—
412Dic7—24no—
413Dic7—42no—
414Dic7—82no—
415Dic7—82no—
416C24—72no—
417C24—72no—
418C24—72no—
419C24—142no—
420C24—142no—
421C24—141no—
422C24—141no—
423C24—141no—
424C24—142no—
425C24—142no—
426C24—141no—
427C24C23×D711yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
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—72no—
450C22×C4—72no—
451C22×C4—72no—
452C22×C4—72no—
453C22×C4—74no—
454C22×C4—72no—
455C22×C4—148no—
456C22×C4—142no—
457C22×C4—141no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—141no—
461C22×C4—142no—
462C22×C4—141no—
463C22×C4—141no—
464C22×C4—142no—
465C22×C4—148no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—284no—
481C22×C4—288no—
482C22×C4—288no—
483C22×C4C2×C4×D712yes—
484C22×C4C2×C4×D712yes—
485C22×C4C2×C4×D712yes—
486C22×C4#115714yes—
487C22×C4#115714yes—
488C22×C4#115712yes—
489C22×C4D4×D712yes—
490C22×C4Q8×D712yes—
491C22×C4C2×C22⋊D714yes—
492C22×C4C2×C22⋊D712yes—
493C4⋊C4—216no—
494C4⋊C4—288no—
495C4⋊C4—288no—
496C22⋊C4—716no—
497C22⋊C4—148no—
498C22⋊C4—288no—
499C22⋊C4—288no—
500C42—28no—
501C42—48no—
502C42—284no—
503C2×C7#228511yescharacteristic
504C2×C7#229011yescharacteristic
505C2×C7#231911yescharacteristic
506C2×C7#234211yescharacteristic
507C2×C7#234711yescharacteristic
508C2×C7D4×C4⋊C411yescharacteristic
509C2×C7#234911yescharacteristic
510C2×C7#246412yes—
511C2×C7#246512yes—
512C2×C7#252112yes—
513C2×C7#252212yes—
514D7—44no—
515C23—74no—
516C23—142no—
517C23—142no—
518C23—142no—
519C23—142no—
520C23—142no—
521C23—142no—
522C23—142no—
523C23—142no—
524C23—142no—
525C23—144no—
526C23—144no—
527C23—142no—
528C23—144no—
529C23—144no—
530C23—282no—
531C23—282no—
532C23—282no—
533C23—282no—
534C23—282no—
535C23—282no—
536C23—282no—
537C23—282no—
538C23C22×C4×D711yescharacteristic
539C23C2×#115712yes—
540C23C2×#115712yes—
541C23C2×#115711yescharacteristic
542C23C2×D4×D711yescharacteristic
543C23#654811yescharacteristic
544C23C2×Q8×D711yescharacteristic
545C23#655111yescharacteristic
546C23D7×#4112yes—
547C23#655312yes—
548C23C22×C22⋊D711yescharacteristic
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—74no—
578C2×C4—74no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—144no—
583C2×C4—142no—
584C2×C4—144no—
585C2×C4—144no—
586C2×C4—144no—
587C2×C4—142no—
588C2×C4—142no—
589C2×C4—142no—
590C2×C4—2816no—
591C2×C4—282no—
592C2×C4—282no—
593C2×C4—282no—
594C2×C4—282no—
595C2×C4—282no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—282no—
599C2×C4—282no—
600C2×C4—282no—
601C2×C4—282no—
602C2×C4—282no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4—282no—
606C2×C4—282no—
607C2×C4#643514yes—
608C2×C4D7×C4⋊C414yes—
609C2×C4C4×C22⋊D714yes—
610C7#1389111yescharacteristic, complemented, Sylow
611C22—144no—
612C22—144no—
613C22—144no—
614C22—282no—
615C22—284no—
616C22—284no—
617C22—284no—
618C22—282no—
619C22—282no—
620C22—282no—
621C22—284no—
622C22C2×#643511yescharacteristic
623C22C4×#115711yescharacteristic
624C22#9017012yes—
625C22C2×D7×C4⋊C411yescharacteristic
626C22#9019511yescharacteristic
627C22#9019811yescharacteristic
628C22#9020211yescharacteristic
629C22D7×#11711yescharacteristic
630C22#9021211yescharacteristic
631C22#9021812yes—
632C22#9023112yes—
633C22#9023912yes—
634C22#9024112yes—
635C22#9025312yes—
636C22#9025912yes—
637C22#9026912yes—
638C22#9027012yes—
639C22#9027312yes—
640C22C2×C4×C22⋊D711yescharacteristic
641C22#9048212yes—
642C22D4×C22⋊D711yescharacteristic
643C22Q8×C22⋊D711yescharacteristic
644C22#9052012yes—
645C4—24no—
646C4—24no—
647C4—24no—
648C4—44no—
649C4—44no—
650C4—144no—
651C4—144no—
652C4—282no—
653C4—562no—
654C4—562no—
655C2—284no—
656C2#1173108011yescharacteristic
657C2#1173119811yescharacteristic
658C2#1173120611yescharacteristic
659C2#1173121511yescharacteristic
660C2#1173124112yes—
661C2#1173124212yes—
662C2#1173951011yescharacteristic
663C2C4⋊C4×C22⋊D711yescharacteristic
664C2#1173971611yescharacteristic
665C2#1173985812yes—
666C2#1173994312yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#13891
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C4⋊C4C2semidirect
6. #11729322C2semidirect
7. #11729290C2semidirect
8. #11729288C2semidirect
10. Dic7⋊#95C2semidirect
11. #11727155C2semidirect
37. C4×(C2×D7)⋊C4C4semidirect
98. C2×C4×C4⋊C4D7semidirect
190. (C2×D7)⋊C4C4⋊C4semidirect
610. C7#13891semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897122
C2×C4×(C2×D7)⋊C42
C2×#894392
#117293242
#117293222
#117292902
#117292882
(C2×D7)⋊#952
Dic7⋊#952
#117271552
#138917