Finite Group Databasebeta

← #13275912

Subgroups — #13275912

Order 1792.

1298 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic
3C2×#89423C211yesmaximal, characteristic
4#11729321C212yesmaximal
5#11729320C212yesmaximal
6#11729290C212yesmaximal
7#11729288C211yesmaximal, characteristic
8#11729288C212yesmaximal
9#11727157C211yesmaximal, characteristic
10#11727156C211yesmaximal, characteristic
11#11727155C211yesmaximal, characteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C42×C7C2212yes—
14C22×C42×C7C2211yescharacteristic
15C22×Dic7⋊C4C2211yescharacteristic
16C22×Dic7⋊C4C2211yescharacteristic
17C22×C4×Dic7C2211yescharacteristic
18C22×C4×Dic7C2211yescharacteristic
19C4×C7×C4⋊C4—24no—
20C2×C7×#95C2211yescharacteristic
21C2×C7×#95C2211yescharacteristic
22C2×C7⋊#95C2211yescharacteristic
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2211yescharacteristic
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36C4×Dic7⋊C4C418yescomplemented
37#89423—24no—
38#13893—71nomaximal, Sylow
39C23×C4×C7C2312yes—
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2312yes—
45C23×Dic7C2312yes—
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C2×C7×C4⋊C4—24no—
51C2×C7×C4⋊C4—24no—
52C2×C7×C4⋊C4—24no—
53C2×C42×C7—22no—
54C2×C42×C7—22no—
55C2×C42×C7—24no—
56C2×C42×C7—24no—
57C2×C42×C7—42no—
58C2×C42×C7C2×C414yes—
59C2×Dic7⋊C4—24no—
60C2×Dic7⋊C4—22no—
61C2×Dic7⋊C4—22no—
62C2×Dic7⋊C4C2×C414yes—
63C2×Dic7⋊C4C2×C414yes—
64C2×C4×Dic7—22no—
65C2×C4×Dic7—22no—
66C2×C4×Dic7—24no—
67C2×C4×Dic7C2×C414yes—
68C2×C4×Dic7C2×C414yes—
69C7×#95—22no—
70C7×#95D414yes—
71C7⋊#95—24no—
72C7⋊#95—24no—
73C7⋊#95—22no—
74C7⋊#95—24no—
75C7⋊#95—24no—
76C7⋊#95—24no—
77C7⋊#95—22no—
78C7⋊#95—24no—
79C7⋊#95—24no—
80C7⋊#95—24no—
81C7⋊#95—42no—
82C7⋊#95—42no—
83C7⋊#95C2×C414yes—
84C7⋊#95C2×C414yes—
85C2×#383—71no—
86C2×C4×C4⋊C4—71no—
87C2×C4×C4⋊C4D711yescharacteristic
88#1442—72no—
89#1441—72no—
90#1436—72no—
91#1434—72no—
92#1434—71no—
93#1434—71no—
94#1434—71no—
95#1434—71no—
96C24×C7C2411yescharacteristic
97C22×C4×C7—21no—
98C22×C4×C7—21no—
99C22×C4×C7—22no—
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7—22no—
103C22×C4×C7—21no—
104C22×C4×C7—22no—
105C22×C4×C7—21no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
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×C7C22×C412yes—
119C22×C4×C7C22×C412yes—
120C22×C4×C7C22×C412yes—
121C22×C4×C7C2×D414yes—
122C22×C4×C7C2×D412yes—
123C22×C4×C7#4114yes—
124C22×C4×C7#4114yes—
125C22×C4×C7#4112yes—
126C22×C4×C7#4112yes—
127C22×C4×C7#4112yes—
128C22×Dic7—22no—
129C22×Dic7—21no—
130C22×Dic7—21no—
131C22×Dic7—21no—
132C22×Dic7—21no—
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7—21no—
137C22×Dic7—21no—
138C22×Dic7—22no—
139C22×Dic7—21no—
140C22×Dic7—21no—
141C22×Dic7—21no—
142C22×Dic7—21no—
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7C22×C412yes—
160C22×Dic7C22×C412yes—
161C22×Dic7C22×C412yes—
162C22×Dic7C22×C412yes—
163C22×Dic7#4114yes—
164C7×C4⋊C4—216no—
165C42×C7—28no—
166C42×C7—48no—
167Dic7⋊C4—28no—
168Dic7⋊C4—28no—
169C4×Dic7—28no—
170C4×Dic7—28no—
171C22×C4⋊C4—71no—
172C22×C4⋊C4—71no—
173C22×C4⋊C4C2×D712yes—
174C22×C42—71no—
175C22×C42—71no—
176C22×C42C2×D712yes—
177C22×C42C2×D711yescharacteristic
178#383—144no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4—78no—
181C2×#95—71no—
182C2×#95—71no—
183C2×#95—71no—
184C2×#95—72no—
185C2×#95—72no—
186C2×#95—72no—
187C2×#95—71no—
188C2×#95—72no—
189C2×#95—72no—
190C2×#95—72no—
191C2×#95—72no—
192C2×#95—72no—
193C2×#95—72no—
194C2×#95—72no—
195C2×#95C2×D711yescharacteristic
196C2×#95C2×D711yescharacteristic
197C23×C7C23×C411yescharacteristic
198C23×C7C22×D411yescharacteristic
199C23×C7C2×#4112yes—
200C23×C7C2×#4111yescharacteristic
201C23×C7C2×#4112yes—
202C23×C7C2×#4111yescharacteristic
203C23×C7C2×#4111yescharacteristic
204C23×C7C2×#4112yes—
205C23×C7H(5,𝔽2)11yescharacteristic
206C23×C72−1+411yescharacteristic
207C23×C72−1+412yes—
208C2×C4×C7—22no—
209C2×C4×C7—22no—
210C2×C4×C7—22no—
211C2×C4×C7—22no—
212C2×C4×C7—22no—
213C2×C4×C7—22no—
214C2×C4×C7—24no—
215C2×C4×C7—24no—
216C2×C4×C7—22no—
217C2×C4×C7—24no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—24no—
221C2×C4×C7—22no—
222C2×C4×C7—24no—
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—42no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7#11714yes—
237C2×C4×C7#11714yes—
238C2×C4×C7C4×D414yes—
239C2×Dic7—22no—
240C2×Dic7—22no—
241C2×Dic7—24no—
242C2×Dic7—24no—
243C2×Dic7—22no—
244C2×Dic7—22no—
245C2×Dic7—22no—
246C2×Dic7—22no—
247C2×Dic7—22no—
248C2×Dic7—22no—
249C2×Dic7—22no—
250C2×Dic7—22no—
251C2×Dic7—22no—
252C2×Dic7—42no—
253C2×Dic7—42no—
254C2×Dic7—41no—
255C2×Dic7—41no—
256C2×Dic7—41no—
257C2×Dic7—41no—
258C2×Dic7—42no—
259C2×Dic7—42no—
260C2×Dic7—42no—
261C2×Dic7—42no—
262C2×Dic7—42no—
263C2×Dic7—42no—
264C2×Dic7—42no—
265C2×Dic7—42no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—42no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7—42no—
272C2×Dic7—42no—
273C2×Dic7—42no—
274C2×Dic7#11714yes—
275C23×C4—71no—
276C23×C4—71no—
277C23×C4—71no—
278C23×C4—71no—
279C23×C4—72no—
280C23×C4—72no—
281C23×C4C22×D712yes—
282C23×C4C22×D712yes—
283C23×C4C22×D711yescharacteristic
284C23×C4C22×D711yescharacteristic
285C23×C4C22×D711yescharacteristic
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—74no—
290C2×C4⋊C4—74no—
291C2×C4⋊C4—144no—
292C2×C4⋊C4—142no—
293C2×C4⋊C4—142no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—24no—
297C2×C42—24no—
298C2×C42—42no—
299C2×C42—74no—
300C2×C42—74no—
301C2×C42—144no—
302C2×C42—142no—
303C2×C42—142no—
304C2×C42C4×D714yes—
305#95—22no—
306#95—74no—
307#95—74no—
308#95—144no—
309#95—144no—
310#95—144no—
311#95—144no—
312#95—144no—
313#95—142no—
314#95—144no—
315#95—144no—
316#95—144no—
317#95—142no—
318#95—282no—
319#95—282no—
320#95C22⋊D714yes—
321C22×C7C2×#11711yescharacteristic
322C22×C7C2×#11711yescharacteristic
323C22×C7C2×#11711yescharacteristic
324C22×C7C2×C4×D411yescharacteristic
325C22×C7C4×#4111yescharacteristic
326C22×C7#51911yescharacteristic
327C22×C7#52011yescharacteristic
328C22×C7#52512yes—
329C22×C7#52912yes—
330C22×C7#52912yes—
331C22×C7#52912yes—
332C22×C7#54112yes—
333C22×C7#54212yes—
334C22×C7#54611yescharacteristic
335C22×C7#54712yes—
336C22×C7#54811yescharacteristic
337C22×C7#55211yescharacteristic
338C22×C7#55212yes—
339C22×C7#55212yes—
340C22×C7#55311yescharacteristic
341C22×C7#55312yes—
342C22×C7#55612yes—
343C22×C7#55612yes—
344C4×C7—24no—
345C4×C7—24no—
346C4×C7—24no—
347C4×C7—44no—
348C4×C7—44no—
349Dic7—24no—
350Dic7—42no—
351Dic7—42no—
352Dic7—42no—
353Dic7—82no—
354Dic7—82no—
355C24C23×D711yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—72no—
378C22×C4—74no—
379C22×C4—72no—
380C22×C4—72no—
381C22×C4—72no—
382C22×C4—142no—
383C22×C4—141no—
384C22×C4—141no—
385C22×C4—142no—
386C22×C4—142no—
387C22×C4—141no—
388C22×C4—141no—
389C22×C4—142no—
390C22×C4—141no—
391C22×C4—141no—
392C22×C4—141no—
393C22×C4—141no—
394C22×C4—141no—
395C22×C4—141no—
396C22×C4—142no—
397C22×C4—141no—
398C22×C4—141no—
399C22×C4—142no—
400C22×C4—142no—
401C22×C4—142no—
402C22×C4—142no—
403C22×C4—142no—
404C22×C4—142no—
405C22×C4—142no—
406C22×C4—142no—
407C22×C4—142no—
408C22×C4—142no—
409C22×C4—142no—
410C22×C4—142no—
411C22×C4—142no—
412C22×C4—142no—
413C22×C4C2×C4×D712yes—
414C22×C4C2×C4×D712yes—
415C22×C4C2×C4×D712yes—
416C22×C4#115714yes—
417C22×C4#115714yes—
418C22×C4#115712yes—
419C22×C4#115912yes—
420C22×C4#116112yes—
421C22×C4C2×C22⋊D714yes—
422C22×C4C2×C22⋊D712yes—
423C4⋊C4—216no—
424C4⋊C4—148no—
425C4⋊C4—148no—
426C42—28no—
427C42—48no—
428C42—148no—
429C42—148no—
430C2×C7#228311yescharacteristic
431C2×C7#229011yescharacteristic
432C2×C7#232011yescharacteristic
433C2×C7#234411yescharacteristic
434C2×C7#234711yescharacteristic
435C2×C7#235211yescharacteristic
436C2×C7#235611yescharacteristic
437C2×C7#246812yes—
438C2×C7#246912yes—
439C2×C7#252412yes—
440C2×C7#252512yes—
441C23C22×C4×D711yescharacteristic
442C23C2×#115712yes—
443C23C2×#115712yes—
444C23C2×#115711yescharacteristic
445C23C2×#115911yescharacteristic
446C23#654811yescharacteristic
447C23C2×#116111yescharacteristic
448C23#655111yescharacteristic
449C23D7×#4112yes—
450C23#655412yes—
451C23C22×C22⋊D711yescharacteristic
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—74no—
481C2×C4—142no—
482C2×C4—142no—
483C2×C4—144no—
484C2×C4—144no—
485C2×C4—142no—
486C2×C4—142no—
487C2×C4—142no—
488C2×C4—142no—
489C2×C4—142no—
490C2×C4—142no—
491C2×C4—142no—
492C2×C4—142no—
493C2×C4—142no—
494C2×C4—282no—
495C2×C4—281no—
496C2×C4—281no—
497C2×C4—282no—
498C2×C4—282no—
499C2×C4—281no—
500C2×C4—281no—
501C2×C4—282no—
502C2×C4—282no—
503C2×C4—282no—
504C2×C4—282no—
505C2×C4—282no—
506C2×C4—282no—
507C2×C4—282no—
508C2×C4—282no—
509C2×C4—282no—
510C2×C4—282no—
511C2×C4—282no—
512C2×C4—282no—
513C2×C4—282no—
514C2×C4—282no—
515C2×C4—282no—
516C2×C4#643514yes—
517C2×C4#645514yes—
518C2×C4C4×C22⋊D714yes—
519C7#1389311yescharacteristic, complemented, Sylow
520C22C2×#643511yescharacteristic
521C22C4×#115711yescharacteristic
522C22#9017012yes—
523C22C2×#645511yescharacteristic
524C22#9019511yescharacteristic
525C22#9020411yescharacteristic
526C22#9020511yescharacteristic
527C22#9020711yescharacteristic
528C22D7×#11711yescharacteristic
529C22#9022212yes—
530C22#9023112yes—
531C22#9023212yes—
532C22#9024812yes—
533C22#9025212yes—
534C22#9025912yes—
535C22#9027112yes—
536C22#9027412yes—
537C22#9027512yes—
538C22C2×C4×C22⋊D711yescharacteristic
539C22#9048212yes—
540C22#9049711yescharacteristic
541C22#9050811yescharacteristic
542C22#9051512yes—
543C4—24no—
544C4—24no—
545C4—24no—
546C4—44no—
547C4—44no—
548C4—144no—
549C4—282no—
550C4—282no—
551C4—282no—
552C4—562no—
553C4—562no—
554C2#1173107011yescharacteristic
555C2#1173108011yescharacteristic
556C2#1173108811yescharacteristic
557C2#1173114812yes—
558C2#1173115012yes—
559C2#1173119711yescharacteristic
560C2#1173951011yescharacteristic
561C2#1173960611yescharacteristic
562C2#1173968311yescharacteristic
563C2#1173981612yes—
564C2#1173991812yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#13893
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. C4×Dic7⋊C4C4semidirect
519. C7#13893semidirect

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×C4×Dic7⋊C42
C2×#894232
#117293212
#117293202
#117292902
#117292882
#117271572
#117271562
#117271552
#138937