Finite Group Databasebeta

← #13242298

Subgroups — #13242298

Order 1792.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739519C211yesmaximal, characteristic
2C7×#1749C211yesmaximal, characteristic
3C2×#89319C211yesmaximal, characteristic
4#11725284C212yesmaximal, complemented
5#11725283C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C23×C7⋊C8—21no—
8C2×#6433C411yescharacteristic
9C2×C7×C22⋊C8—21no—
10C2×C7×#97—21no—
11#89984C411yescharacteristic
12#89984C411yescharacteristic
13#89982—21no—
14#89982—21no—
15#89708C411yescharacteristic
16#89705—21no—
17#89705—21no—
18#89700C2211yescharacteristic
19#89700C2211yescharacteristic
20C7×#336C2212yes—
21#89319—21no—
22#89319C2212yes—
23#7691—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×C7×C8—22no—
28C2×C42×C7—42no—
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7C2311yescharacteristic
33C2×C22⋊Dic7—21no—
34C2×C22⋊Dic7—21no—
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×C4⋊Dic7C2×C411yescharacteristic
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C22×C7⋊C8—24no—
44C22×C7⋊C8—22no—
45C22×C7⋊C8—42no—
46C22×C7⋊C8—42no—
47#6433—42no—
48C7×C22⋊C8—24no—
49C7×#97—42no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56#2851—71no—
57#1749D711yescharacteristic
58C2×#336—71no—
59#1271—72no—
60#1271—72no—
61C24×C7C22⋊C411yescharacteristic
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—22no—
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7—41no—
71C22×C4×C7—41no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C2×C7×C8—24no—
83C2×C7×C8—42no—
84C2×C7×C8—42no—
85C42×C7—22no—
86C42×C7—22no—
87C42×C7—41no—
88C42×C7—41no—
89C22⋊Dic7—42no—
90C22⋊Dic7—42no—
91C4⋊Dic7—22no—
92C4⋊Dic7—22no—
93C4⋊Dic7—41no—
94C4⋊Dic7—41no—
95Dic7⋊C4—42no—
96Dic7⋊C4—42no—
97Dic7⋊C4—42no—
98Dic7⋊C4—41no—
99Dic7⋊C4—41no—
100C2×C7⋊C8—24no—
101C2×C7⋊C8—48no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C23×C8—141no—
105C2×#125—71no—
106C22×C42C2×D711yescharacteristic
107C2×C22⋊C8—21no—
108C2×#97—21no—
109#389—71no—
110#389—71no—
111#387—141no—
112#387—141no—
113#385—141no—
114#385—141no—
115#382—71no—
116#380—71no—
117#380—71no—
118#336—72no—
119#336—141no—
120#336C2×D712yes—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7#10112yes—
126C23×C7#10412yes—
127C23×C7#10412yes—
128C23×C7C2×C22⋊C411yescharacteristic
129C2×C4×C7—24no—
130C2×C4×C7—24no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—44no—
146C2×C4×C7—44no—
147C2×C4×C7#9912yes—
148C2×C4×C7#13112yes—
149C2×C4×C7#13512yes—
150C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C7#13711yescharacteristic
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C7×C8—44no—
165C7⋊C8—44no—
166C23×C4C4×D711yescharacteristic
167C23×C4D2811yescharacteristic
168C23×C4C22⋊D711yescharacteristic
169C22×C8—22no—
170C22×C8—144no—
171C22×C8—142no—
172C22×C8—282no—
173C22×C8—282no—
174#125—282no—
175C2×C4⋊C4—71no—
176C2×C4⋊C4—71no—
177C2×C4⋊C4—71no—
178C2×C4⋊C4—71no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4—141no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C42—42no—
186C2×C42C4×D711yescharacteristic
187C2×C42D2811yescharacteristic
188C2×C42C22⋊D711yescharacteristic
189C2×C42C22×D711yescharacteristic
190C22⋊C8—24no—
191#97—42no—
192#95—141no—
193#95—141no—
194#95—141no—
195#95—141no—
196#95—141no—
197#95—141no—
198C22×C7—22no—
199C22×C7—22no—
200C22×C7—22no—
201C22×C7—22no—
202C22×C7—22no—
203C22×C7—22no—
204C22×C7#33014yes—
205C22×C7#40811yescharacteristic
206C22×C7C2×#9911yescharacteristic
207C22×C7C2×#10111yescharacteristic
208C22×C7#41611yescharacteristic
209C22×C7#41711yescharacteristic
210C22×C7C2×#10411yescharacteristic
211C22×C7C2×#10411yescharacteristic
212C4×C7—22no—
213C4×C7—22no—
214C4×C7—21no—
215C4×C7—22no—
216C4×C7—21no—
217C4×C7—41no—
218C4×C7—41no—
219Dic7—81no—
220Dic7—81no—
221Dic7—81no—
222Dic7—81no—
223C24(C2×D7)⋊C411yescharacteristic
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4—141no—
237C22×C4—141no—
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4(C2×D7)⋊C411yescharacteristic
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4C2×C4×D711yescharacteristic
242C22×C4C2×D2811yescharacteristic
243C22×C4C2×C22⋊D711yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—144no—
248C2×C8—288no—
249C2×C8—282no—
250C2×C8—282no—
251C4⋊C4—142no—
252C4⋊C4—142no—
253C4⋊C4—281no—
254C4⋊C4—281no—
255C4⋊C4—282no—
256C4⋊C4—281no—
257C4⋊C4—281no—
258C4⋊C4—282no—
259C4⋊C4—282no—
260C22⋊C4—282no—
261C22⋊C4—282no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—41no—
266C2×C7—24no—
267C2×C7#147211yescharacteristic
268C2×C7#148311yescharacteristic
269C2×C7#149411yescharacteristic
270C2×C7#150111yescharacteristic
271C2×C7#150411yescharacteristic
272C2×C7C2×#33011yescharacteristic
273C2×C7#155211yescharacteristic
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#637912yes—
279C23#639812yes—
280C23#639912yes—
281C23C2×(C2×D7)⋊C411yescharacteristic
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4#638012yes—
313C2×C4#647012yes—
314C2×C4#647111yescharacteristic
315C2×C4#647211yescharacteristic
316C2×C4#651312yes—
317C8—44no—
318C8—284no—
319C7#769111yescharacteristic, complemented, Sylow
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#8926014yes—
327C22C2×#637911yescharacteristic
328C22C2×#638011yescharacteristic
329C22#8977411yescharacteristic
330C22#8990111yescharacteristic
331C22#8990511yescharacteristic
332C22C2×#639811yescharacteristic
333C22C2×#639911yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—561no—
342C4—561no—
343C4—561no—
344C4—561no—
345C2—24no—
346C2#1172719711yescharacteristic
347C2C2×#8926011yescharacteristic
348C2#1172760611yescharacteristic
349C2#1172772611yescharacteristic
350C2#1172773011yescharacteristic
351C2#1172855411yescharacteristic
352C2#1172857411yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1749C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1749D7
hypocenterC7#7691
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
4. #11725284C2semidirect
5. #11725283C2semidirect
319. C7#7691semidirect

Maximal subgroups

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

subgroupindex
#117395192
C7×#17492
C2×#893192
#117252842
#117252832
#76917