Finite Group Databasebeta

← #13337755

Subgroups — #13337755

Order 1792.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#487C211yesmaximal, characteristic, complemented
2#11740657C211yesmaximal, characteristic
3#11740654C211yesmaximal, characteristic
4C8×#1157C211yesmaximal, characteristic
5#11729529C211yesmaximal, characteristic, complemented
6#11729527C211yesmaximal, characteristic, complemented
7#11728994C214yesmaximal, complemented
8#11728986C214yesmaximal, complemented
9#11727484C211yesmaximal, characteristic, complemented
10C2×C7×C4⋊Q8C2211yescharacteristic
11C2×C7×C4⋊Q8C2211yescharacteristic
12C2×#6505—21no—
13C4×#1157C2211yescharacteristic
14C7×#487—21no—
15C7×#487—21no—
16C7×#487C2214yes—
17C2×C7×#103—22no—
18C2×C4×C7×C8C2211yescharacteristic
19#89997—21no—
20C8×C22⋊D7—22no—
21#89866C2212yes—
22#89863—21no—
23#89862—21no—
24#89862C2212yes—
25#89859C2212yes—
26#89856—21no—
27#89855—21no—
28#89855C2212yes—
29#89738—21no—
30#89736—21no—
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89696C2211yescharacteristic
34C8×D28C2212yes—
35#89457—21no—
36C4×C8×D7—21no—
37C8×Dic14C2212yes—
38#89342C2214yes—
39#89342C2214yes—
40#89252C2214yes—
41#19275—71nomaximal, Sylow
42C22×C7×Q8—21no—
43C22×C7×Q8—21no—
44C2×#1157D411yescharacteristic
45C22×C7×C8D412yes—
46C7×C4⋊Q8—21no—
47C7×C4⋊Q8—21no—
48C7×C4⋊Q8—21no—
49C7×C4⋊Q8—21no—
50C7×C4⋊Q8—21no—
51C7×C4⋊Q8—21no—
52C7×C4⋊Q8C2312yes—
53C7×C4⋊Q8C2312yes—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4—21no—
57C2×C7×C4⋊C4—21no—
58C2×C42×C7C2311yescharacteristic
59C2×#1144—22no—
60#6505—44no—
61C2×#1143—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×#103—24no—
75C7×#103—24no—
76C4×C7×C8D411yescharacteristic
77C4×C7×C8D411yescharacteristic
78C4×C7×C8C2312yes—
79#6409—22no—
80#6409—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×#487D711yescharacteristic, complemented
96#3079—71no—
97#3039—71no—
98C8×#41—71no—
99#1680—74no—
100#1679—74no—
101#1566—71no—
102#1549—71no—
103#1546—71no—
104C2×C7×Q8—22no—
105C2×C7×Q8—22no—
106C2×C7×Q8—44no—
107C2×C7×Q8—41no—
108C2×C7×Q8—41no—
109C2×C7×Q8—42no—
110C2×C7×Q8—42no—
111C22×C4×C7—41no—
112C22×C4×C7—41no—
113C22×C4×C7C2×D411yescharacteristic
114C22×C4×C7C2×D411yescharacteristic
115C22×C4×C7#4111yescharacteristic
116C2×C22⋊D7—21no—
117#1157—22no—
118#1157SD1614yes—
119C2×D28C2×D411yescharacteristic
120C2×C4×D7—21no—
121C2×C4×D7—21no—
122C2×C4×D7—21no—
123C2×Dic14C2×D411yescharacteristic
124C2×C7×C8—42no—
125C2×C7×C8C2×D412yes—
126C2×C7×C8C2×D412yes—
127C7×C4⋊C4—22no—
128C7×C4⋊C4—22no—
129C7×C4⋊C4—22no—
130C7×C4⋊C4—22no—
131C7×C4⋊C4—41no—
132C7×C4⋊C4—41no—
133C7×C4⋊C4—41no—
134C7×C4⋊C4—41no—
135C42×C7C2×D411yescharacteristic
136C42×C7C2×D411yescharacteristic
137C42×C7#4111yescharacteristic
138C42×C7C2411yescharacteristic
139C22⋊Dic7—21no—
140#1144—44no—
141#1143—44no—
142(C2×D7)⋊C4—21no—
143(C2×D7)⋊C4—21no—
144C4⋊Dic7C2×D411yescharacteristic
145C4⋊Dic7C2×D411yescharacteristic
146Dic7⋊C4—21no—
147Dic7⋊C4—21no—
148C4×Dic7—21no—
149C4×Dic7—21no—
150C4×Dic7—21no—
151#1136—42no—
152#1136—42no—
153C2×C7⋊C8—22no—
154C2×C7⋊C8—22no—
155C2×C7⋊C8—22no—
156C8×D7—44no—
157C2×#137—141no—
158C2×C4⋊Q8C2×D711yescharacteristic
159C2×C4⋊Q8C2×D711yescharacteristic
160C4×#41—71no—
161#487—21no—
162#487—21no—
163#487C2×D714yes—
164#477—141no—
165#476—141no—
166#475—72no—
167#474—72no—
168#462—72no—
169#462—141no—
170#461—72no—
171#461—141no—
172C8×Q8—72no—
173C8×D4—72no—
174C8×D4—142no—
175#431—71no—
176#431—141no—
177#428—141no—
178#423—71no—
179#423—71no—
180#419—141no—
181#417—141no—
182C2×#103—22no—
183C2×C4×C8—141no—
184C2×C4×C8C2×D711yescharacteristic
185#334—74no—
186#332—74no—
187#332—74no—
188C23×C7#12111yescharacteristic
189C22×D7—21no—
190C7×Q8—42no—
191C7×Q8—42no—
192C7×Q8—44no—
193C7×Q8—82no—
194C7×Q8—82no—
195C2×C4×C7—22no—
196C2×C4×C7—22no—
197C2×C4×C7—42no—
198C2×C4×C7—42no—
199C2×C4×C7—82no—
200C2×C4×C7—82no—
201C2×C4×C7#12111yescharacteristic
202C2×C4×C7#12111yescharacteristic
203C2×C4×C7#12111yescharacteristic
204C2×C4×C7C2×SD1612yes—
205C2×C4×C7#13512yes—
206C2×C4×C7C22×D411yescharacteristic
207C2×C4×C7C22×D411yescharacteristic
208C2×C4×C7C2×#4111yescharacteristic
209C22⋊D7—24no—
210C2×Dic7—21no—
211C2×Dic7—21no—
212C2×Dic7—21no—
213D28—21no—
214D28C2×SD1612yes—
215C4×D7—24no—
216C4×D7—42no—
217C4×D7—42no—
218Dic14—21no—
219Dic14C2×SD1612yes—
220C7×C8—22no—
221C7×C8—22no—
222C7⋊C8—42no—
223C7⋊C8—42no—
224C7⋊C8—42no—
225C2×#41—71no—
226C22×Q8—21no—
227C22×Q8—21no—
228#137—284no—
229C2×Q16—142no—
230C2×SD16—142no—
231C2×M16—141no—
232C2×M16—141no—
233C22×C8—142no—
234C22×C8C22⋊D712yes—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8C22×D712yes—
242C4⋊Q8C22×D712yes—
243C4×Q8—71no—
244C4×Q8—71no—
245C4×D4—71no—
246C4×D4—71no—
247C4×D4—141no—
248C4×D4—141no—
249#117—71no—
250#117—141no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C42—141no—
256C2×C42C22×D711yescharacteristic
257#107—142no—
258#106—142no—
259C4⋊C8—72no—
260C4⋊C8—72no—
261C4⋊C8—72no—
262C4⋊C8—142no—
263C4⋊C8—141no—
264C4⋊C8—141no—
265#103—24no—
266#103—24no—
267#103—142no—
268#103—142no—
269#103—142no—
270#102—142no—
271C22⋊C8—141no—
272C22⋊C8—142no—
273C4×C8—142no—
274C4×C8—141no—
275C4×C8C22⋊D711yescharacteristic
276C4×C8C22⋊D711yescharacteristic
277C4×C8C22×D712yes—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7#46512yes—
281C22×C7C2×#12111yescharacteristic
282C2×D7—22no—
283C2×D7—41no—
284C2×D7—41no—
285C4×C7—21no—
286C4×C7—21no—
287C4×C7—82no—
288C4×C7—82no—
289C4×C7#46512yes—
290C4×C7#47312yes—
291C4×C7C22×SD1611yescharacteristic
292C4×C7C2×#13511yescharacteristic
293C4×C7#57512yes—
294Dic7—22no—
295Dic7—41no—
296Dic7—41no—
297#41—74no—
298#41—142no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—42no—
305C2×Q8—42no—
306C2×Q8—71no—
307C2×D4—71no—
308C2×D4—141no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—141no—
312C22×C4—141no—
313C22×C4—141no—
314C22×C4D4×D711yescharacteristic
315C22×C4#115911yescharacteristic
316C22×C4C2×C22⋊D711yescharacteristic
317Q16—284no—
318SD16—284no—
319M16—282no—
320M16—282no—
321C2×C8—42no—
322C2×C8—142no—
323C2×C8—142no—
324C2×C8—142no—
325C2×C8—284no—
326C2×C8C2×C22⋊D712yes—
327C2×C8C2×C22⋊D712yes—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—71no—
337C4⋊C4—71no—
338C4⋊C4—141no—
339C4⋊C4—141no—
340C22⋊C4—141no—
341C22⋊C4—141no—
342C22⋊C4—141no—
343C42—141no—
344C42—141no—
345C42—141no—
346C42D4×D711yescharacteristic
347C42#115911yescharacteristic
348C42C2×C22⋊D711yescharacteristic
349C42C23×D711yescharacteristic
350C2×C7—22no—
351C2×C7#304011yescharacteristic
352C2×C7C2×#46511yescharacteristic
353C2×C7C2×#47311yescharacteristic
354D7—42no—
355C23—141no—
356C23#650111yescharacteristic
357Q8—42no—
358Q8—42no—
359Q8—44no—
360Q8—72no—
361Q8—82no—
362Q8—82no—
363Q8—141no—
364D4—72no—
365D4—144no—
366D4—141no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—141no—
374C2×C4—144no—
375C2×C4—141no—
376C2×C4—141no—
377C2×C4—282no—
378C2×C4—282no—
379C2×C4D7×SD1612yes—
380C2×C4#647912yes—
381C2×C4#650111yescharacteristic
382C2×C4#650111yescharacteristic
383C2×C4#650111yescharacteristic
384C2×C4C2×D4×D711yescharacteristic
385C2×C4C2×#115911yescharacteristic
386C2×C4C22×C22⋊D711yescharacteristic
387C8—22no—
388C8—22no—
389C8—282no—
390C8—282no—
391C8—282no—
392C7#1927511yescharacteristic, complemented, Sylow
393C22—21no—
394C22—21no—
395C22—142no—
396C22—281no—
397C22—281no—
398C22#8994312yes—
399C22C2×#650111yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—142no—
405C4—281no—
406C4—281no—
407C4#8994312yes—
408C4#8996412yes—
409C4C2×D7×SD1611yescharacteristic
410C4C2×#647911yescharacteristic
411C4#9051312yes—
412C2—22no—
413C2—282no—
414C2#1174039011yescharacteristic
415C2C2×#8994311yescharacteristic
416C2C2×#8996411yescharacteristic
subgroupG/H
centerC22C2×#6501
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#487C2
socleC22×C7C2×#121
prime radicalC2×#1157D4
hypercenterC2×#487D7
hypocenterC7#19275
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. C2×C7×#487C2semidirect
5. #11729529C2semidirect
6. #11729527C2semidirect
7. #11728994C2semidirect
8. #11728986C2semidirect
9. #11727484C2semidirect
95. C2×#487D7semidirect
392. C7#19275semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4872
#117406572
#117406542
C8×#11572
#117295292
#117295272
#117289942
#117289862
#117274842
#192757