Finite Group Databasebeta

← #13337746

Subgroups — #13337746

Order 1792.

722 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#486C211yesmaximal, characteristic, complemented
2#11740657C211yesmaximal, characteristic, complemented
3#11740610C211yesmaximal, characteristic
4C8×#1157C211yesmaximal, characteristic, complemented
5#11729528C211yesmaximal, characteristic, complemented
6#11729513C211yesmaximal, characteristic, complemented
7#11728962C214yesmaximal, complemented
8#11728954C214yesmaximal, complemented
9#11727484C211yesmaximal, characteristic, complemented
10C2×C7×C4⋊Q8C2211yescharacteristic
11C2×C7×#127C2211yescharacteristic
12C2×#6495—21no—
13C4×#1157C2211yescharacteristic
14C7×#486—21no—
15C7×#486—21no—
16C7×#486C2214yes—
17C2×C7×#102—22no—
18C2×C4×C7×C8C2211yescharacteristic
19#89987—21no—
20C8×C22⋊D7—22no—
21#89866—21no—
22#89863C2212yescomplemented
23#89859—21no—
24#89856C2212yescomplemented
25#89847—21no—
26#89847C2212yes—
27#89844—21no—
28#89844C2212yes—
29#89738—21no—
30#89736—21no—
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89696C2211yescharacteristic
34C8×D28C2212yescomplemented
35#89457—21no—
36C4×C8×D7—21no—
37C8×Dic14C2212yescomplemented
38#89341C2214yescomplemented
39#89339C2214yes—
40#89252C2214yescomplemented
41#19274—71nomaximal, Sylow
42C22×C7×Q8—21no—
43C22×C7×D4—21no—
44C22×C7×D4—21no—
45C22×C7×D4—21no—
46C2×#1157D411yescharacteristic
47C22×C7×C8D412yes—
48C7×C4⋊Q8—21no—
49C7×C4⋊Q8—21no—
50C7×C4⋊Q8—21no—
51C7×C4⋊Q8C2312yes—
52C7×#127—21no—
53C7×#127—21no—
54C7×#127—21no—
55C7×#127C2312yes—
56C2×C7×C4⋊C4—21no—
57C2×C7×C4⋊C4—21no—
58C2×C42×C7C2311yescharacteristic
59C2×#1142—22no—
60#6495—44no—
61C2×#1141—22no—
62C4×C22⋊D7—21no—
63C4×C22⋊D7—21no—
64#6489D411yescharacteristic
65C2×#1136—21no—
66C2×#1136—21no—
67C2×C8×D7—22no—
68C4×D28D411yescharacteristic
69C4×D28C2311yescharacteristic
70#6435—21no—
71C42×D7—21no—
72C4×Dic14D411yescharacteristic
73C4×Dic14C2311yescharacteristic
74C7×#102—24no—
75C7×#102—24no—
76C4×C7×C8D411yescharacteristic
77C4×C7×C8D411yescharacteristic
78C4×C7×C8C2312yes—
79#6406—22no—
80#6406—22no—
81C22⋊(C7⋊C8)—21no—
82(C2×D7)⋊C8—22no—
83Dic7⋊C8—22no—
84C8×Dic7—22no—
85#6384—22no—
86#6383—22no—
87#6382—22no—
88#6381—22no—
89C4⋊(C7⋊C8)—21no—
90C4⋊(C7⋊C8)—21no—
91C4⋊(C7⋊C8)C2312yes—
92C4⋊(C7⋊C8)C2312yes—
93C4⋊(C7⋊C8)C2312yes—
94C4×C7⋊C8—21no—
95C2×#486D711yescharacteristic, complemented
96#3079—71no—
97#3038—71no—
98C8×#41—71no—
99#1678—74no—
100#1677—74no—
101#1566—71no—
102#1548—71no—
103#1545—71no—
104C24×C7—41no—
105C2×C7×Q8—22no—
106C2×C7×Q8—41no—
107C2×C7×Q8—82no—
108C2×C7×D4—22no—
109C2×C7×D4—22no—
110C2×C7×D4—22no—
111C2×C7×D4—44no—
112C2×C7×D4—41no—
113C2×C7×D4—41no—
114C2×C7×D4—41no—
115C2×C7×D4—42no—
116C2×C7×D4—42no—
117C2×C7×D4—82no—
118C22×C4×C7—41no—
119C22×C4×C7C2×D411yescharacteristic
120C22×C4×C7C2×D411yescharacteristic
121C22×C4×C7#4111yescharacteristic
122C2×C22⋊D7—21no—
123#1157—22no—
124#1157SD1614yes—
125C2×D28C2×D411yescharacteristic
126C2×C4×D7—21no—
127C2×C4×D7—21no—
128C2×C4×D7—21no—
129C2×Dic14C2×D411yescharacteristic
130C2×C7×C8—42no—
131C2×C7×C8C2×D412yes—
132C2×C7×C8C2×D412yes—
133C7×C4⋊C4—22no—
134C7×C4⋊C4—22no—
135C7×C4⋊C4—41no—
136C7×C4⋊C4—41no—
137C42×C7C2×D411yescharacteristic
138C42×C7C2×D411yescharacteristic
139C42×C7#4111yescharacteristic
140C42×C7C2411yescharacteristic
141C22⋊Dic7—21no—
142#1142—44no—
143#1141—44no—
144(C2×D7)⋊C4—21no—
145(C2×D7)⋊C4—21no—
146C4⋊Dic7C2×D411yescharacteristic
147C4⋊Dic7C2×D411yescharacteristic
148Dic7⋊C4—21no—
149Dic7⋊C4—21no—
150C4×Dic7—21no—
151C4×Dic7—21no—
152C4×Dic7—21no—
153#1136—42no—
154#1136—42no—
155C2×C7⋊C8—22no—
156C2×C7⋊C8—22no—
157C2×C7⋊C8—22no—
158C8×D7—44no—
159C2×AGL(1,ℤ/8)—141no—
160C2×C4⋊Q8C2×D711yescharacteristic
161C2×#127C2×D711yescharacteristic
162C4×#41—71no—
163#486—21no—
164#486—21no—
165#486C2×D714yes—
166#477—72no—
167#476—72no—
168#475—141no—
169#474—141no—
170#460—72no—
171#460—141no—
172#459—72no—
173#459—141no—
174C8×Q8—72no—
175C8×D4—72no—
176C8×D4—142no—
177#431—71no—
178#431—141no—
179#428—141no—
180#423—71no—
181#423—71no—
182#418—141no—
183#417—141no—
184C2×#102—22no—
185C2×C4×C8—141no—
186C2×C4×C8C2×D711yescharacteristic
187#334—74no—
188#333—74no—
189#331—74no—
190C23×C7—42no—
191C23×C7—82no—
192C23×C7—82no—
193C23×C7—82no—
194C23×C7#12111yescharacteristic
195C22×D7—21no—
196C7×Q8—82no—
197C7×Q8—82no—
198C7×D4—42no—
199C7×D4—42no—
200C7×D4—44no—
201C7×D4—82no—
202C7×D4—82no—
203C7×D4—82no—
204C7×D4—82no—
205C2×C4×C7—22no—
206C2×C4×C7—22no—
207C2×C4×C7—42no—
208C2×C4×C7—82no—
209C2×C4×C7#12111yescharacteristic
210C2×C4×C7#12111yescharacteristic
211C2×C4×C7#12111yescharacteristic
212C2×C4×C7C2×SD1612yes—
213C2×C4×C7#13512yes—
214C2×C4×C7C22×D411yescharacteristic
215C2×C4×C7C22×D411yescharacteristic
216C2×C4×C7C2×#4111yescharacteristic
217C22⋊D7—24no—
218C2×Dic7—21no—
219C2×Dic7—21no—
220C2×Dic7—21no—
221D28—21no—
222D28C2×SD1612yes—
223C4×D7—24no—
224C4×D7—42no—
225C4×D7—42no—
226Dic14—21no—
227Dic14C2×SD1612yes—
228C7×C8—22no—
229C7×C8—22no—
230C7⋊C8—42no—
231C7⋊C8—42no—
232C7⋊C8—42no—
233C2×#41—71no—
234C22×Q8—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238AGL(1,ℤ/8)—284no—
239C2×SD16—142no—
240C2×D8—142no—
241C2×M16—141no—
242C2×M16—141no—
243C22×C8—142no—
244C22×C8C22⋊D712yes—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8C22×D712yes—
249#127—21no—
250#127—21no—
251#127—21no—
252#127C22×D712yes—
253C4×Q8—71no—
254C4×Q8—71no—
255C4×D4—71no—
256C4×D4—71no—
257C4×D4—141no—
258C4×D4—141no—
259#117—71no—
260#117—141no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C42—141no—
264C2×C42C22×D711yescharacteristic
265#107—142no—
266#106—142no—
267C4⋊C8—72no—
268C4⋊C8—72no—
269C4⋊C8—72no—
270C4⋊C8—142no—
271C4⋊C8—141no—
272C4⋊C8—141no—
273#103—142no—
274#102—24no—
275#102—24no—
276#102—142no—
277#102—142no—
278#102—142no—
279C22⋊C8—141no—
280C22⋊C8—142no—
281C4×C8—142no—
282C4×C8—141no—
283C4×C8C22⋊D711yescharacteristic
284C4×C8C22⋊D711yescharacteristic
285C4×C8C22×D712yes—
286C22×C7—21no—
287C22×C7—21no—
288C22×C7—82no—
289C22×C7—82no—
290C22×C7—82no—
291C22×C7—164no—
292C22×C7#46512yes—
293C22×C7C2×#12111yescharacteristic
294C2×D7—22no—
295C2×D7—41no—
296C2×D7—41no—
297C4×C7—21no—
298C4×C7—21no—
299C4×C7—82no—
300C4×C7#46512yes—
301C4×C7#47212yes—
302C4×C7C22×SD1611yescharacteristic
303C4×C7C2×#13511yescharacteristic
304C4×C7#57512yes—
305Dic7—22no—
306Dic7—41no—
307Dic7—41no—
308C24—41no—
309#41—74no—
310#41—142no—
311C2×Q8—22no—
312C2×Q8—41no—
313C2×Q8—71no—
314C2×Q8—82no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—44no—
319C2×D4—42no—
320C2×D4—42no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—71no—
325C2×D4—82no—
326C2×D4—141no—
327C22×C4—41no—
328C22×C4—141no—
329C22×C4—141no—
330C22×C4—141no—
331C22×C4D4×D711yescharacteristic
332C22×C4#115911yescharacteristic
333C22×C4C2×C22⋊D711yescharacteristic
334SD16—284no—
335D8—284no—
336M16—282no—
337M16—282no—
338C2×C8—42no—
339C2×C8—142no—
340C2×C8—142no—
341C2×C8—142no—
342C2×C8—284no—
343C2×C8C2×C22⋊D712yes—
344C2×C8C2×C22⋊D712yes—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—71no—
350C4⋊C4—71no—
351C4⋊C4—141no—
352C4⋊C4—141no—
353C22⋊C4—141no—
354C22⋊C4—141no—
355C22⋊C4—141no—
356C42—141no—
357C42—141no—
358C42—141no—
359C42D4×D711yescharacteristic
360C42#115911yescharacteristic
361C42C2×C22⋊D711yescharacteristic
362C42C23×D711yescharacteristic
363C2×C7—22no—
364C2×C7—162no—
365C2×C7#304011yescharacteristic
366C2×C7C2×#46511yescharacteristic
367C2×C7C2×#47211yescharacteristic
368D7—42no—
369C23—42no—
370C23—82no—
371C23—82no—
372C23—82no—
373C23—141no—
374C23#650111yescharacteristic
375Q8—72no—
376Q8—82no—
377Q8—82no—
378Q8—141no—
379D4—42no—
380D4—42no—
381D4—44no—
382D4—72no—
383D4—82no—
384D4—82no—
385D4—82no—
386D4—82no—
387D4—144no—
388D4—141no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—141no—
394C2×C4—144no—
395C2×C4—141no—
396C2×C4—141no—
397C2×C4—282no—
398C2×C4—282no—
399C2×C4D7×SD1612yes—
400C2×C4#647912yes—
401C2×C4#650111yescharacteristic
402C2×C4#650111yescharacteristic
403C2×C4#650111yescharacteristic
404C2×C4C2×D4×D711yescharacteristic
405C2×C4C2×#115911yescharacteristic
406C2×C4C22×C22⋊D711yescharacteristic
407C8—22no—
408C8—22no—
409C8—282no—
410C8—282no—
411C8—282no—
412C7#1927411yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—82no—
416C22—82no—
417C22—82no—
418C22—142no—
419C22—164no—
420C22—281no—
421C22—281no—
422C22#8994312yes—
423C22C2×#650111yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—142no—
428C4—281no—
429C4—281no—
430C4#8993212yes—
431C4#8994312yes—
432C4C2×D7×SD1611yescharacteristic
433C4C2×#647911yescharacteristic
434C4#9051312yes—
435C2—22no—
436C2—162no—
437C2—282no—
438C2#1174039011yescharacteristic
439C2C2×#8993211yescharacteristic
440C2C2×#8994311yescharacteristic
subgroupG/H
centerC22C2×#6501
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#486C2
socleC22×C7C2×#121
prime radical#11740610C2
hypercenterC2×#486D7
hypocenterC7#19274
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×C7×#486C2semidirect
2. #11740657C2semidirect
4. C8×#1157C2semidirect
5. #11729528C2semidirect
6. #11729513C2semidirect
7. #11728962C2semidirect
8. #11728954C2semidirect
9. #11727484C2semidirect
22. #89863C22semidirect
24. #89856C22semidirect
34. C8×D28C22semidirect
37. C8×Dic14C22semidirect
38. #89341C22semidirect
40. #89252C22semidirect
95. C2×#486D7semidirect
412. C7#19274semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4862
#117406572
#117406102
C8×#11572
#117295282
#117295132
#117289622
#117289542
#117274842
#192747