Finite Group Databasebeta

← #13275320

Subgroups — #13275320

Order 1792.

1602 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic7C211yesmaximal, characteristic
2C2×#89426C212yesmaximal
3C2×#89421C211yesmaximal, characteristic
4C2×#89420C211yesmaximal, characteristic
5C7×#1434C211yesmaximal, characteristic
6C4×C7⋊#95C211yesmaximal, characteristic
7#11727161C212yesmaximal
8#11727160C212yesmaximal
9#11727156C211yesmaximal, characteristic
10#11727156C211yesmaximal, characteristic
11Dic7×#95C212yesmaximal
12C22×C42×C7C2211yescharacteristic
13C22×C4⋊Dic7C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×Dic7⋊C4C2212yes—
16C22×C4×Dic7C2212yes—
17C22×C4×Dic7C2212yes—
18C22×C4×Dic7C2212yes—
19C22×C4×Dic7C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C2×C7×#95C2212yes—
22C2×C7×#95C2211yescharacteristic
23C2×C7×#95C2211yescharacteristic
24C2×C7×#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C4×C4⋊Dic7C418yescomplemented
36#89426C4116yescomplemented
37#89421—24no—
38#89420—24no—
39#13815—71nomaximal, Sylow
40C23×C4×C7C2312yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×Dic7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C2×C42×C7—24no—
52C2×C42×C7C2×C414yes—
53C2×C4⋊Dic7—22no—
54C2×C4⋊Dic7—22no—
55C2×C4⋊Dic7C2×C414yes—
56C2×C4⋊Dic7C2×C418yes—
57C2×C4⋊Dic7C2×C414yes—
58C2×Dic7⋊C4—24no—
59C2×Dic7⋊C4—24no—
60C2×Dic7⋊C4C2×C418yes—
61C2×C4×Dic7—22no—
62C2×C4×Dic7—22no—
63C2×C4×Dic7—22no—
64C2×C4×Dic7—22no—
65C2×C4×Dic7—24no—
66C2×C4×Dic7—24no—
67C2×C4×Dic7—24no—
68C2×C4×Dic7—24no—
69C2×C4×Dic7—24no—
70C2×C4×Dic7—24no—
71C2×C4×Dic7—42no—
72C2×C4×Dic7—42no—
73C2×C4×Dic7C2×C418yes—
74C2×C4×Dic7C2×C414yes—
75C2×C4×Dic7C2×C414yes—
76C7×#95—22no—
77C7×#95—22no—
78C7×#95—24no—
79C7×#95C2×C418yes—
80C7⋊#95—22no—
81C7⋊#95—24no—
82C7⋊#95—24no—
83C7⋊#95—42no—
84C7⋊#95C2×C418yes—
85C7⋊#95C2×C418yes—
86C7⋊#95C2×C418yes—
87C7⋊#95C2×C414yes—
88C7⋊#95C2×C414yes—
89C7⋊#95D414yes—
90C2×#387—72no—
91C2×C4×C4⋊C4—71no—
92C2×C4×C4⋊C4—71no—
93C2×#376—71no—
94#1436—72no—
95#1436—72no—
96#1434—71no—
97#1434—71no—
98#1434D711yescharacteristic
99C4×#95—71no—
100C4×#95—72no—
101C24×C7C2411yescharacteristic
102C22×C4×C7—22no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—21no—
108C22×C4×C7—22no—
109C22×C4×C7—21no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7C22×C414yes—
123C22×C4×C7C22×C414yes—
124C22×C4×C7C22×C414yes—
125C22×C4×C7C22×C412yes—
126C22×C4×C7C22×C412yes—
127C22×C4×C7C22×C412yes—
128C22×C4×C7C2×D412yes—
129C22×C4×C7#4114yes—
130C22×C4×C7#4112yes—
131C22×Dic7—21no—
132C22×Dic7—21no—
133C22×Dic7—21no—
134C22×Dic7—21no—
135C22×Dic7—21no—
136C22×Dic7—22no—
137C22×Dic7—21no—
138C22×Dic7—22no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—21no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—21no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—22no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7C22×C414yes—
158C22×Dic7C22×C412yes—
159C22×Dic7C22×C412yes—
160C22×Dic7C22×C412yes—
161C22×Dic7C22×C414yes—
162C22×Dic7C22×C414yes—
163C22×Dic7C22×C412yes—
164C22×Dic7C22×C414yes—
165C22×Dic7C2×D414yes—
166C22×Dic7#4112yes—
167C22×Dic7#4112yes—
168C22×Dic7#4114yes—
169C42×C7—28no—
170C4⋊Dic7—28no—
171C4⋊Dic7C42116yescomplemented
172Dic7⋊C4—216no—
173C4×Dic7—28no—
174C4×Dic7—28no—
175C4×Dic7—216no—
176C4×Dic7—48no—
177C4×Dic7—48no—
178C22×C4⋊C4—71no—
179C22×C4⋊C4—72no—
180C22×C4⋊C4—71no—
181C22×C42—72no—
182C22×C42—71no—
183C22×C42—71no—
184C22×C42—72no—
185C22×C42—72no—
186C22×C42C2×D711yescharacteristic
187#387—716no—
188C4×C4⋊C4—78no—
189C4×C4⋊C4—144no—
190#376—144no—
191C2×#95—71no—
192C2×#95—72no—
193C2×#95—72no—
194C2×#95—71no—
195C2×#95—72no—
196C2×#95—71no—
197C2×#95—71no—
198C2×#95—72no—
199C2×#95—72no—
200C2×#95—72no—
201C2×#95C2×D712yes—
202C2×#95C2×D711yescharacteristic
203C2×#95C2×D711yescharacteristic
204C2×#95C2×D712yes—
205C23×C7C23×C411yescharacteristic
206C23×C7C23×C412yes—
207C23×C7C22×D411yescharacteristic
208C23×C7C2×#4112yes—
209C23×C7C2×#4111yescharacteristic
210C23×C7C2×#4111yescharacteristic
211C23×C7C2×#4111yescharacteristic
212C23×C7C2×#4112yes—
213C23×C7H(5,𝔽2)11yescharacteristic
214C23×C72−1+412yes—
215C23×C72−1+411yescharacteristic
216C2×C4×C7—22no—
217C2×C4×C7—22no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—24no—
221C2×C4×C7—24no—
222C2×C4×C7—22no—
223C2×C4×C7—22no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7C2×C4214yes—
243C2×C4×C7#11714yes—
244C2×C4×C7C4×D414yes—
245C2×Dic7—22no—
246C2×Dic7—22no—
247C2×Dic7—22no—
248C2×Dic7—24no—
249C2×Dic7—24no—
250C2×Dic7—22no—
251C2×Dic7—22no—
252C2×Dic7—24no—
253C2×Dic7—24no—
254C2×Dic7—24no—
255C2×Dic7—22no—
256C2×Dic7—24no—
257C2×Dic7—22no—
258C2×Dic7—24no—
259C2×Dic7—24no—
260C2×Dic7—22no—
261C2×Dic7—24no—
262C2×Dic7—22no—
263C2×Dic7—24no—
264C2×Dic7—22no—
265C2×Dic7—22no—
266C2×Dic7—22no—
267C2×Dic7—24no—
268C2×Dic7—24no—
269C2×Dic7—22no—
270C2×Dic7—24no—
271C2×Dic7—41no—
272C2×Dic7—41no—
273C2×Dic7—42no—
274C2×Dic7—41no—
275C2×Dic7—42no—
276C2×Dic7—41no—
277C2×Dic7—42no—
278C2×Dic7—42no—
279C2×Dic7C2×C4214yes—
280C2×Dic7C2×C4214yes—
281C2×Dic7#11714yes—
282C2×Dic7C4×D418yes—
283C23×C4—71no—
284C23×C4—71no—
285C23×C4—72no—
286C23×C4—71no—
287C23×C4—71no—
288C23×C4—72no—
289C23×C4C22×D712yes—
290C23×C4C22×D712yes—
291C23×C4C22×D711yescharacteristic
292C23×C4C22×D711yescharacteristic
293C23×C4C22×D711yescharacteristic
294C2×C4⋊C4—74no—
295C2×C4⋊C4—78no—
296C2×C4⋊C4—78no—
297C2×C4⋊C4—74no—
298C2×C4⋊C4—144no—
299C2×C4⋊C4—144no—
300C2×C4⋊C4—142no—
301C2×C4⋊C4—142no—
302C2×C42—24no—
303C2×C42—74no—
304C2×C42—74no—
305C2×C42—78no—
306C2×C42—144no—
307C2×C42—144no—
308C2×C42—142no—
309C2×C42—142no—
310C2×C42—142no—
311C2×C42—142no—
312C2×C42—144no—
313C2×C42—144no—
314C2×C42—144no—
315C2×C42—144no—
316C2×C42—282no—
317C2×C42—282no—
318C2×C42C4×D714yes—
319#95—22no—
320#95—22no—
321#95—24no—
322#95—74no—
323#95—74no—
324#95—78no—
325#95—78no—
326#95—78no—
327#95—74no—
328#95—144no—
329#95—144no—
330#95—142no—
331#95—282no—
332#95C4×D718yes—
333C22×C7C22×C4211yescharacteristic
334C22×C7C2×#11711yescharacteristic
335C22×C7C2×#11711yescharacteristic
336C22×C7C2×C4×D411yescharacteristic
337C22×C7C2×C4×D412yes—
338C22×C7C4×#4111yescharacteristic
339C22×C7C4×#4112yes—
340C22×C7C4×#4112yes—
341C22×C7C4×#4112yes—
342C22×C7#51911yescharacteristic
343C22×C7#51912yes—
344C22×C7#52011yescharacteristic
345C22×C7#52012yes—
346C22×C7#54611yescharacteristic
347C22×C7#54712yes—
348C22×C7#54811yescharacteristic
349C22×C7#55112yes—
350C22×C7#55211yescharacteristic
351C22×C7#55212yes—
352C22×C7#55212yes—
353C22×C7#55212yes—
354C22×C7#55311yescharacteristic
355C22×C7#55612yes—
356C4×C7—24no—
357C4×C7—24no—
358C4×C7—24no—
359C4×C7—44no—
360C4×C7—44no—
361Dic7—24no—
362Dic7—28no—
363Dic7—24no—
364Dic7—24no—
365Dic7—42no—
366Dic7—44no—
367C24C23×D711yescharacteristic
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—72no—
389C22×C4—72no—
390C22×C4—74no—
391C22×C4—72no—
392C22×C4—74no—
393C22×C4—74no—
394C22×C4—74no—
395C22×C4—72no—
396C22×C4—72no—
397C22×C4—74no—
398C22×C4—74no—
399C22×C4—72no—
400C22×C4—141no—
401C22×C4—141no—
402C22×C4—141no—
403C22×C4—142no—
404C22×C4—141no—
405C22×C4—141no—
406C22×C4—141no—
407C22×C4—142no—
408C22×C4—142no—
409C22×C4—142no—
410C22×C4—141no—
411C22×C4—142no—
412C22×C4—141no—
413C22×C4—142no—
414C22×C4—141no—
415C22×C4—142no—
416C22×C4—142no—
417C22×C4—141no—
418C22×C4—142no—
419C22×C4—142no—
420C22×C4—141no—
421C22×C4—141no—
422C22×C4—141no—
423C22×C4—142no—
424C22×C4—141no—
425C22×C4—142no—
426C22×C4C2×C4×D714yes—
427C22×C4C2×C4×D714yes—
428C22×C4C2×C4×D714yes—
429C22×C4C2×C4×D712yes—
430C22×C4C2×C4×D712yes—
431C22×C4C2×C4×D712yes—
432C22×C4D4×D712yes—
433C22×C4#115914yes—
434C22×C4#116112yes—
435C4⋊C4—716no—
436C4⋊C4—1416no—
437C4⋊C4—148no—
438C42—28no—
439C42—1416no—
440C42—148no—
441C42—148no—
442C42—288no—
443C42—288no—
444C2×C7C4×#11711yescharacteristic
445C2×C7C42×D411yescharacteristic
446C2×C7#227611yescharacteristic
447C2×C7#234311yescharacteristic
448C2×C7#234411yescharacteristic
449C2×C7#235211yescharacteristic
450C2×C7#235611yescharacteristic
451C2×C7#235912yes—
452C2×C7#236212yes—
453C2×C7#237112yes—
454C2×C7#237312yes—
455C23C22×C4×D711yescharacteristic
456C23C22×C4×D712yes—
457C23C2×D4×D711yescharacteristic
458C23C2×#115912yes—
459C23C2×#116111yescharacteristic
460C23D7×#4111yescharacteristic
461C23D7×#4111yescharacteristic
462C23D7×#4112yes—
463C23#655311yescharacteristic
464C23#655411yescharacteristic
465C23#655412yes—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—74no—
493C2×C4—74no—
494C2×C4—74no—
495C2×C4—78no—
496C2×C4—142no—
497C2×C4—142no—
498C2×C4—142no—
499C2×C4—144no—
500C2×C4—142no—
501C2×C4—142no—
502C2×C4—142no—
503C2×C4—142no—
504C2×C4—142no—
505C2×C4—144no—
506C2×C4—142no—
507C2×C4—144no—
508C2×C4—144no—
509C2×C4—144no—
510C2×C4—144no—
511C2×C4—144no—
512C2×C4—144no—
513C2×C4—144no—
514C2×C4—142no—
515C2×C4—144no—
516C2×C4—142no—
517C2×C4—142no—
518C2×C4—144no—
519C2×C4—142no—
520C2×C4—144no—
521C2×C4—144no—
522C2×C4—281no—
523C2×C4—281no—
524C2×C4—282no—
525C2×C4—281no—
526C2×C4—282no—
527C2×C4—282no—
528C2×C4—282no—
529C2×C4—281no—
530C2×C4C42×D714yes—
531C2×C4#644014yes—
532C2×C4#645614yes—
533C7#1381511yescharacteristic, complemented, Sylow
534C22C2×C42×D711yescharacteristic
535C22C2×#644011yescharacteristic
536C22C2×#645611yescharacteristic
537C22#9020711yescharacteristic
538C22#9020712yes—
539C22D7×#11711yescharacteristic
540C22#9021311yescharacteristic
541C22#9021412yes—
542C22#9021411yescharacteristic
543C22C4×#115912yes—
544C22C4×#115912yes—
545C22C4×D4×D712yes—
546C22C4×#116112yes—
547C22#9030212yes—
548C22#9033312yes—
549C22#9034112yes—
550C22#9034912yes—
551C22#9036711yescharacteristic
552C22#9036811yescharacteristic
553C22#9038511yescharacteristic
554C22#9038611yescharacteristic
555C22#9039312yes—
556C22#9039912yes—
557C4—24no—
558C4—24no—
559C4—24no—
560C4—44no—
561C4—44no—
562C4—148no—
563C4—144no—
564C4—144no—
565C4—144no—
566C4—284no—
567C4—282no—
568C2#1173082811yescharacteristic
569C2C4×#644011yescharacteristic
570C2C4×#645611yescharacteristic
571C2#1173132311yescharacteristic
572C2#1173150411yescharacteristic
573C2#1173167411yescharacteristic
574C2#1173170911yescharacteristic
575C2#1173241612yes—
576C2#1173241912yes—
577C2#1173292312yes—
578C2#1173328312yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×#1434C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1434D7
hypocenterC7#13815
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
35. C4×C4⋊Dic7C4semidirect
36. #89426C4semidirect
171. C4⋊Dic7C42semidirect
533. C7#13815semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic72
C2×#894262
C2×#894212
C2×#894202
C7×#14342
C4×C7⋊#952
#117271612
#117271602
#117271562
Dic7×#952
#138157