Finite Group Databasebeta

← #13283880

Subgroups — #13283880

Order 1792.

1358 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89751C211yesmaximal, characteristic
2C2×#89705C212yesmaximal
3C2×#89418C212yesmaximal
4C7×#1436C211yesmaximal, characteristic
5#11729323C211yesmaximal, characteristic
6#11727172C212yesmaximal
7#11727167C212yesmaximal
8#11727160C212yesmaximal
9#11727157C212yesmaximal
10C23×Dic14C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C42×C7C2211yescharacteristic
13C22×Dic7⋊C4C2212yes—
14C22×Dic7⋊C4C2212yes—
15C22×C4×Dic7C2212yes—
16C2×C7×#95C2212yes—
17C2×C7×#95C2212yes—
18C2×C7×#95C2211yescharacteristic
19C2×C7⋊#95C2212yes—
20C2×C7⋊#95C2212yes—
21C2×C7⋊#95C2212yes—
22C2×C7⋊#95C2212yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31#89751C418yescomplemented
32#89705—28no—
33#89418—28no—
34#14574—71nomaximal, Sylow
35C23×C4×C7C2311yescharacteristic
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2312yes—
39C23×C4×C7C2312yes—
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C23×Dic7C2312yes—
44C22×Dic14—24no—
45C22×Dic14—24no—
46C22×Dic14—41no—
47C22×Dic14—41no—
48C22×Dic14C2×C414yes—
49C2×C7×C4⋊C4—41no—
50C2×C7×C4⋊C4—41no—
51C2×C7×C4⋊C4C2×C414yes—
52C2×C42×C7—24no—
53C2×C42×C7—41no—
54C2×Dic7⋊C4—24no—
55C2×Dic7⋊C4—24no—
56C2×Dic7⋊C4—24no—
57C2×Dic7⋊C4—24no—
58C2×Dic7⋊C4—42no—
59C2×Dic7⋊C4C2×C418yes—
60C2×C4×Dic7—24no—
61C2×C4×Dic7—24no—
62C2×C4×Dic7—42no—
63C7×#95—24no—
64C7×#95—24no—
65C7×#95—41no—
66C7⋊#95—24no—
67C7⋊#95—24no—
68C7⋊#95—24no—
69C7⋊#95—24no—
70C7⋊#95—24no—
71C7⋊#95—24no—
72C7⋊#95—24no—
73C7⋊#95—41no—
74C7⋊#95—41no—
75C7⋊#95C2×C414yes—
76C7⋊#95C2×C418yes—
77C7⋊#95D418yes—
78C2×#395—71no—
79C2×#391—72no—
80C2×#387—72no—
81#1445—71no—
82#1443—72no—
83#1442—72no—
84#1436—72no—
85#1436D711yescharacteristic
86#1434—72no—
87C24×C7C2411yescharacteristic
88C22×C4×C7—22no—
89C22×C4×C7—22no—
90C22×C4×C7—22no—
91C22×C4×C7—22no—
92C22×C4×C7—22no—
93C22×C4×C7—22no—
94C22×C4×C7—22no—
95C22×C4×C7—22no—
96C22×C4×C7—22no—
97C22×C4×C7—21no—
98C22×C4×C7—21no—
99C22×C4×C7—22no—
100C22×C4×C7—21no—
101C22×C4×C7—22no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—22no—
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×C7C22×C412yes—
113C22×C4×C7C22×C412yes—
114C22×C4×C7C22×C412yes—
115C22×C4×C7C2×D414yes—
116C22×C4×C7#4114yes—
117C22×Dic7—22no—
118C22×Dic7—22no—
119C22×Dic7—22no—
120C22×Dic7—22no—
121C22×Dic7—22no—
122C22×Dic7—22no—
123C22×Dic7—22no—
124C22×Dic7—22no—
125C22×Dic7—22no—
126C22×Dic7—22no—
127C22×Dic7—22no—
128C22×Dic7—22no—
129C22×Dic7—22no—
130C22×Dic7—22no—
131C22×Dic7—22no—
132C22×Dic7—22no—
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7—22no—
137C22×Dic7—22no—
138C22×Dic7—22no—
139C22×Dic7—22no—
140C22×Dic7C22×C414yes—
141C22×Dic7C22×C414yes—
142C22×Dic7C2×D414yes—
143C22×Dic7C2×D414yes—
144C22×Dic7#4114yes—
145C2×Dic14—216no—
146C2×Dic14—44no—
147C2×Dic14—44no—
148C2×Dic14—48no—
149C2×Dic14—44no—
150C7×C4⋊C4—44no—
151C42×C7—44no—
152Dic7⋊C4—216no—
153Dic7⋊C4—48no—
154C4×Dic7—48no—
155C23×Q8—71no—
156C22×C4⋊C4—72no—
157C22×C4⋊C4—72no—
158C22×C4⋊C4C2×D711yescharacteristic
159C22×C42—72no—
160C22×C42C2×D711yescharacteristic
161#395—78no—
162#391—148no—
163#387—148no—
164C2×#95—72no—
165C2×#95—71no—
166C2×#95—72no—
167C2×#95—72no—
168C2×#95—72no—
169C2×#95—72no—
170C2×#95—72no—
171C2×#95—72no—
172C2×#95—72no—
173C2×#95—72no—
174C2×#95—71no—
175C2×#95—71no—
176C2×#95C2×D712yes—
177C2×#95C2×D712yes—
178C2×#95C2×D711yescharacteristic
179C23×C7C23×C411yescharacteristic
180C23×C7C22×D412yes—
181C23×C7C2×#4112yes—
182C23×C7C2×#4112yes—
183C23×C7H(5,𝔽2)11yescharacteristic
184C23×C7H(5,𝔽2)11yescharacteristic
185C23×C72−1+412yes—
186C23×C72−1+412yes—
187C23×C72−1+412yes—
188C2×C4×C7—24no—
189C2×C4×C7—24no—
190C2×C4×C7—22no—
191C2×C4×C7—22no—
192C2×C4×C7—22no—
193C2×C4×C7—22no—
194C2×C4×C7—22no—
195C2×C4×C7—24no—
196C2×C4×C7—24no—
197C2×C4×C7—24no—
198C2×C4×C7—24no—
199C2×C4×C7—24no—
200C2×C4×C7—24no—
201C2×C4×C7—42no—
202C2×C4×C7—42no—
203C2×C4×C7—42no—
204C2×C4×C7—42no—
205C2×C4×C7—42no—
206C2×C4×C7—42no—
207C2×C4×C7—41no—
208C2×C4×C7—41no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—42no—
213C2×C4×C7—41no—
214C2×C4×C7—41no—
215C2×C4×C7—42no—
216C2×C4×C7—42no—
217C2×Dic7—24no—
218C2×Dic7—24no—
219C2×Dic7—24no—
220C2×Dic7—24no—
221C2×Dic7—24no—
222C2×Dic7—24no—
223C2×Dic7—24no—
224C2×Dic7—24no—
225C2×Dic7—24no—
226C2×Dic7—24no—
227C2×Dic7—24no—
228C2×Dic7—24no—
229C2×Dic7—42no—
230C2×Dic7—42no—
231C2×Dic7—42no—
232C2×Dic7—42no—
233C2×Dic7—42no—
234C2×Dic7—42no—
235C2×Dic7—42no—
236C2×Dic7—42no—
237C2×Dic7—42no—
238C2×Dic7—42no—
239C2×Dic7—42no—
240C2×Dic7—42no—
241C2×Dic7—42no—
242C2×Dic7—42no—
243C2×Dic7—42no—
244C2×Dic7C4×D418yes—
245Dic14—416no—
246C22×Q8—74no—
247C22×Q8—144no—
248C22×Q8—144no—
249C22×Q8—281no—
250C22×Q8—281no—
251C23×C4—72no—
252C23×C4—72no—
253C23×C4—72no—
254C23×C4—72no—
255C23×C4C22×D711yescharacteristic
256C23×C4C22×D711yescharacteristic
257C23×C4C22×D711yescharacteristic
258C23×C4C22×D712yes—
259C23×C4C22×D712yes—
260C2×C4⋊C4—41no—
261C2×C4⋊C4—41no—
262C2×C4⋊C4—78no—
263C2×C4⋊C4—144no—
264C2×C4⋊C4—144no—
265C2×C4⋊C4—144no—
266C2×C4⋊C4—144no—
267C2×C4⋊C4—282no—
268C2×C4⋊C4C4×D714yes—
269C2×C42—24no—
270C2×C42—41no—
271C2×C42—144no—
272C2×C42—144no—
273C2×C42—282no—
274#95—24no—
275#95—24no—
276#95—41no—
277#95—78no—
278#95—74no—
279#95—78no—
280#95—144no—
281#95—144no—
282#95—144no—
283#95—144no—
284#95—144no—
285#95—144no—
286#95—144no—
287#95—281no—
288#95—281no—
289C22×C7C2×C4×D412yes—
290C22×C7C4×#4111yescharacteristic
291C22×C7#51811yescharacteristic
292C22×C7#51911yescharacteristic
293C22×C7#51912yes—
294C22×C7#53612yes—
295C22×C7#53612yes—
296C22×C7#53912yes—
297C22×C7#54112yes—
298C22×C7#54112yes—
299C22×C7#54212yes—
300C22×C7D4211yescharacteristic
301C22×C7#54612yes—
302C22×C7#54712yes—
303C22×C7#54812yes—
304C22×C7#55111yescharacteristic
305C22×C7#55212yes—
306C22×C7#55612yes—
307C22×C7#56311yescharacteristic
308C22×C7#56312yes—
309C22×C7#56311yescharacteristic
310C4×C7—42no—
311C4×C7—42no—
312C4×C7—42no—
313C4×C7—44no—
314C4×C7—44no—
315Dic7—28no—
316Dic7—44no—
317Dic7—44no—
318Dic7—82no—
319C24C23×D711yescharacteristic
320C2×Q8—1416no—
321C2×Q8—284no—
322C2×Q8—284no—
323C2×Q8—288no—
324C2×Q8—284no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—74no—
350C22×C4—74no—
351C22×C4—74no—
352C22×C4—74no—
353C22×C4—74no—
354C22×C4—142no—
355C22×C4—142no—
356C22×C4—142no—
357C22×C4—142no—
358C22×C4—142no—
359C22×C4—142no—
360C22×C4—142no—
361C22×C4—142no—
362C22×C4—142no—
363C22×C4—142no—
364C22×C4—142no—
365C22×C4—142no—
366C22×C4—142no—
367C22×C4—142no—
368C22×C4—142no—
369C22×C4—142no—
370C22×C4—142no—
371C22×C4—142no—
372C22×C4—142no—
373C22×C4—142no—
374C22×C4—142no—
375C22×C4—142no—
376C22×C4—142no—
377C22×C4C2×C4×D712yes—
378C22×C4C2×C4×D712yes—
379C22×C4C2×C4×D712yes—
380C22×C4#115714yes—
381C22×C4D4×D714yes—
382C4⋊C4—44no—
383C4⋊C4—1416no—
384C4⋊C4—288no—
385C42—44no—
386C42—288no—
387C2×C7#232712yes—
388C2×C7#233211yescharacteristic
389C2×C7#235811yescharacteristic
390C2×C7#236212yes—
391C2×C7#238111yescharacteristic
392C2×C7#267412yes—
393C2×C7#268912yes—
394C2×C7#269012yes—
395C2×C7#276212yes—
396C23C22×C4×D711yescharacteristic
397C23C2×#115712yes—
398C23C2×D4×D712yes—
399C23#654811yescharacteristic
400C23#654811yescharacteristic
401C23#655112yes—
402C23D7×#4112yes—
403C23#655412yes—
404C23#655412yes—
405Q8—2816no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—78no—
436C2×C4—144no—
437C2×C4—144no—
438C2×C4—144no—
439C2×C4—144no—
440C2×C4—144no—
441C2×C4—144no—
442C2×C4—144no—
443C2×C4—144no—
444C2×C4—144no—
445C2×C4—144no—
446C2×C4—144no—
447C2×C4—144no—
448C2×C4—282no—
449C2×C4—282no—
450C2×C4—282no—
451C2×C4—282no—
452C2×C4—282no—
453C2×C4—282no—
454C2×C4—282no—
455C2×C4—282no—
456C2×C4—282no—
457C2×C4—282no—
458C2×C4—282no—
459C2×C4—282no—
460C2×C4—282no—
461C2×C4—282no—
462C2×C4—282no—
463C7#1457411yescharacteristic, complemented, Sylow
464C22C4×#115711yescharacteristic
465C22#9017711yescharacteristic
466C22#9019812yes—
467C22#9020711yescharacteristic
468C22#9022212yes—
469C22C4×D4×D712yes—
470C22#9024312yes—
471C22#9025212yes—
472C22#9025512yes—
473C22#9025912yes—
474C22#9026312yes—
475C22#9028111yescharacteristic
476C22#9030312yes—
477C22#9031912yes—
478C22#9033712yes—
479C22#9033912yes—
480C22#9035011yescharacteristic
481C22#9036311yescharacteristic
482C22#9038712yes—
483C22#9039212yes—
484C22#9042611yescharacteristic
485C4—42no—
486C4—42no—
487C4—44no—
488C4—42no—
489C4—44no—
490C4—148no—
491C4—284no—
492C4—284no—
493C4—562no—
494C2#1173089311yescharacteristic
495C2#1173109312yes—
496C2#1173195312yes—
497C2#1173232511yescharacteristic
498C2#1173239312yes—
499C2#1173264412yes—
500C2#1173311712yes—
501C2#1173370712yes—
502C2#1173394211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1436D7
hypocenterC7#14574
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #89751C4semidirect
463. C7#14574semidirect

Maximal subgroups

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

subgroupindex
C2×#897512
C2×#897052
C2×#894182
C7×#14362
#117293232
#117271722
#117271672
#117271602
#117271572
#145747