Finite Group Databasebeta

← #13281997

Subgroups — #13281997

Order 1792.

1302 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89748C211yesmaximal, characteristic
2C2×#89705C212yesmaximal
3C2×#89424C212yesmaximal
4C7×#1436C211yesmaximal, characteristic
5#11729318C211yesmaximal, characteristic
6#11727175C212yesmaximal
7#11727175C212yesmaximal
8#11727165C212yesmaximal
9#11727156C212yesmaximal
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C42×C7C2211yescharacteristic
12C22×C4⋊Dic7C2211yescharacteristic
13C22×Dic7⋊C4C2212yes—
14C22×Dic7⋊C4C2212yes—
15C22×Dic7⋊C4C2212yes—
16C22×C4×Dic7C2211yescharacteristic
17C22×C4×Dic7C2211yescharacteristic
18C2×C7×#95C2212yes—
19C2×C7×#95C2212yes—
20C2×C7×#95C2211yescharacteristic
21C2×C7⋊#95C2212yes—
22C2×C7⋊#95C2212yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31#89748C418yescomplemented
32#89705—28no—
33#89424—28no—
34#14424—71nomaximal, Sylow
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2312yes—
39C23×C4×C7C2311yescharacteristic
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C23×Dic7C2312yes—
44C2×C7×C4⋊C4—41no—
45C2×C7×C4⋊C4—41no—
46C2×C7×C4⋊C4C2×C414yes—
47C2×C42×C7—24no—
48C2×C42×C7—41no—
49C2×C4⋊Dic7—41no—
50C2×C4⋊Dic7—41no—
51C2×C4⋊Dic7C2×C414yes—
52C2×Dic7⋊C4—24no—
53C2×Dic7⋊C4—24no—
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×Dic7⋊C4C2×C418yes—
61C2×C4×Dic7—24no—
62C2×C4×Dic7—24no—
63C2×C4×Dic7—41no—
64C2×C4×Dic7C2×C414yes—
65C7×#95—24no—
66C7×#95—24no—
67C7×#95—41no—
68C7⋊#95—24no—
69C7⋊#95—24no—
70C7⋊#95—24no—
71C7⋊#95—24no—
72C7⋊#95—24no—
73C7⋊#95—24no—
74C7⋊#95—24no—
75C7⋊#95—42no—
76C7⋊#95—41no—
77C7⋊#95D418yes—
78C2×#387—72no—
79C2×#387—72no—
80C2×#384—71no—
81#1445—72no—
82#1445—72no—
83#1441—72no—
84#1436—71no—
85#1436D711yescharacteristic
86#1434—72no—
87C24×C7C2411yescharacteristic
88C22×C4×C7—21no—
89C22×C4×C7—21no—
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—21no—
100C22×C4×C7—22no—
101C22×C4×C7—21no—
102C22×C4×C7—22no—
103C22×C4×C7—22no—
104C22×C4×C7—22no—
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—
145C7×C4⋊C4—44no—
146C42×C7—44no—
147C4⋊Dic7—44no—
148Dic7⋊C4—216no—
149Dic7⋊C4—216no—
150Dic7⋊C4—48no—
151C4×Dic7—28no—
152C4×Dic7—44no—
153C22×C4⋊C4—72no—
154C22×C4⋊C4—72no—
155C22×C4⋊C4—71no—
156C22×C4⋊C4—72no—
157C22×C4⋊C4C2×D711yescharacteristic
158C22×C42—71no—
159C22×C42—71no—
160C22×C42C2×D711yescharacteristic
161#387—148no—
162#387—148no—
163#384—78no—
164C2×#95—72no—
165C2×#95—72no—
166C2×#95—72no—
167C2×#95—72no—
168C2×#95—72no—
169C2×#95—72no—
170C2×#95—72no—
171C2×#95—72no—
172C2×#95—71no—
173C2×#95—72no—
174C2×#95C2×D712yes—
175C2×#95C2×D712yes—
176C2×#95C2×D711yescharacteristic
177C23×C7C23×C411yescharacteristic
178C23×C7C22×D412yes—
179C23×C7C2×#4112yes—
180C23×C7C2×#4112yes—
181C23×C7H(5,𝔽2)11yescharacteristic
182C23×C7H(5,𝔽2)11yescharacteristic
183C23×C72−1+412yes—
184C23×C72−1+412yes—
185C23×C72−1+412yes—
186C2×C4×C7—22no—
187C2×C4×C7—22no—
188C2×C4×C7—24no—
189C2×C4×C7—24no—
190C2×C4×C7—24no—
191C2×C4×C7—24no—
192C2×C4×C7—22no—
193C2×C4×C7—22no—
194C2×C4×C7—24no—
195C2×C4×C7—24no—
196C2×C4×C7—24no—
197C2×C4×C7—42no—
198C2×C4×C7—42no—
199C2×C4×C7—41no—
200C2×C4×C7—41no—
201C2×C4×C7—42no—
202C2×C4×C7—42no—
203C2×C4×C7—42no—
204C2×C4×C7—41no—
205C2×C4×C7—41no—
206C2×C4×C7—42no—
207C2×C4×C7—42no—
208C2×C4×C7—42no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—42no—
213C2×C4×C7—42no—
214C2×C4×C7#11714yes—
215C2×Dic7—24no—
216C2×Dic7—24no—
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—42no—
228C2×Dic7—42no—
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×Dic7C4×D418yes—
243C23×C4—72no—
244C23×C4—72no—
245C23×C4—72no—
246C23×C4—72no—
247C23×C4C22×D712yes—
248C23×C4C22×D711yescharacteristic
249C23×C4C22×D711yescharacteristic
250C23×C4C22×D712yes—
251C23×C4C22×D711yescharacteristic
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—78no—
255C2×C4⋊C4—78no—
256C2×C4⋊C4—74no—
257C2×C4⋊C4—144no—
258C2×C4⋊C4—144no—
259C2×C4⋊C4—144no—
260C2×C4⋊C4—144no—
261C2×C4⋊C4—144no—
262C2×C4⋊C4—144no—
263C2×C4⋊C4—282no—
264C2×C4⋊C4—281no—
265C2×C4⋊C4—281no—
266C2×C4⋊C4C4×D714yes—
267C2×C42—24no—
268C2×C42—41no—
269C2×C42—74no—
270C2×C42—144no—
271C2×C42—144no—
272C2×C42—281no—
273#95—24no—
274#95—24no—
275#95—41no—
276#95—78no—
277#95—144no—
278#95—144no—
279#95—144no—
280#95—144no—
281#95—144no—
282#95—144no—
283#95—144no—
284#95—281no—
285#95—282no—
286C22×C7C2×#11711yescharacteristic
287C22×C7C2×C4×D412yes—
288C22×C7#51811yescharacteristic
289C22×C7#51911yescharacteristic
290C22×C7#51912yes—
291C22×C7#53612yes—
292C22×C7#53612yes—
293C22×C7#53912yes—
294C22×C7#53912yes—
295C22×C7#54112yes—
296C22×C7#54112yes—
297C22×C7D4211yescharacteristic
298C22×C7#54712yes—
299C22×C7#54712yes—
300C22×C7#55012yes—
301C22×C7#55212yes—
302C22×C7#55212yes—
303C22×C7#55911yescharacteristic
304C22×C7#56311yescharacteristic
305C22×C7#56312yes—
306C22×C7#56311yescharacteristic
307C4×C7—24no—
308C4×C7—42no—
309C4×C7—42no—
310C4×C7—44no—
311C4×C7—82no—
312Dic7—28no—
313Dic7—44no—
314Dic7—44no—
315Dic7—82no—
316C24C23×D711yescharacteristic
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—74no—
342C22×C4—74no—
343C22×C4—74no—
344C22×C4—74no—
345C22×C4—74no—
346C22×C4—142no—
347C22×C4—142no—
348C22×C4—142no—
349C22×C4—142no—
350C22×C4—142no—
351C22×C4—142no—
352C22×C4—142no—
353C22×C4—142no—
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×C4C2×C4×D712yes—
370C22×C4C2×C4×D712yes—
371C22×C4C2×C4×D712yes—
372C22×C4#115714yes—
373C22×C4D4×D714yes—
374C4⋊C4—44no—
375C4⋊C4—1416no—
376C4⋊C4—1416no—
377C4⋊C4—284no—
378C4⋊C4—288no—
379C42—44no—
380C42—148no—
381C42—284no—
382C2×C7#231311yescharacteristic
383C2×C7#232712yes—
384C2×C7#234412yes—
385C2×C7#236611yescharacteristic
386C2×C7#238111yescharacteristic
387C2×C7#268012yes—
388C2×C7#272112yes—
389C2×C7#272112yes—
390C2×C7#279412yes—
391C23C22×C4×D711yescharacteristic
392C23C2×#115712yes—
393C23C2×D4×D712yes—
394C23#654811yescharacteristic
395C23#654811yescharacteristic
396C23#655112yes—
397C23D7×#4112yes—
398C23#655412yes—
399C23#655412yes—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—78no—
429C2×C4—144no—
430C2×C4—144no—
431C2×C4—144no—
432C2×C4—144no—
433C2×C4—144no—
434C2×C4—144no—
435C2×C4—144no—
436C2×C4—144no—
437C2×C4—144no—
438C2×C4—144no—
439C2×C4—144no—
440C2×C4—144no—
441C2×C4—282no—
442C2×C4—282no—
443C2×C4—282no—
444C2×C4—282no—
445C2×C4—282no—
446C2×C4—282no—
447C2×C4—282no—
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#643514yes—
457C7#1442411yescharacteristic, complemented, Sylow
458C22C2×#643511yescharacteristic
459C22#9017711yescharacteristic
460C22#9019812yes—
461C22#9020711yescharacteristic
462C22#9022012yes—
463C22C4×D4×D712yes—
464C22#9024212yes—
465C22#9025512yes—
466C22#9025512yes—
467C22#9026312yes—
468C22#9027212yes—
469C22#9028111yescharacteristic
470C22#9029012yes—
471C22#9031912yes—
472C22#9033712yes—
473C22#9033912yes—
474C22#9035511yescharacteristic
475C22#9036311yescharacteristic
476C22#9038712yes—
477C22#9039212yes—
478C22#9042611yescharacteristic
479C4—24no—
480C4—44no—
481C4—42no—
482C4—42no—
483C4—82no—
484C4—148no—
485C4—284no—
486C4—284no—
487C4—562no—
488C2#1173089011yescharacteristic
489C2#1173121212yes—
490C2#1173207612yes—
491C2#1173212411yescharacteristic
492C2#1173239312yes—
493C2#1173270812yes—
494C2#1173314512yes—
495C2#1173356512yes—
496C2#1173394211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1436D7
hypocenterC7#14424
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #89748C4semidirect
457. C7#14424semidirect

Maximal subgroups

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

subgroupindex
C2×#897482
C2×#897052
C2×#894242
C7×#14362
#117293182
#117271752
#117271652
#117271562
#144247