Finite Group Databasebeta

← #13253965

Subgroups — #13253965

Order 1792.

684 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739521C211yesmaximal, characteristic
2C4×C7×#95C211yesmaximal, characteristic
3#11729284C211yesmaximal, characteristic
4#11725418C214yesmaximal
5C22×C42×C7—21no—
6C22×C42×C7C2211yescharacteristic
7C2×#6487—21no—
8C2×#6432C411yescharacteristic, complemented
9C2×C7×#95—21no—
10C2×C7×#95C2212yes—
11#89984—21no—
12#89984C2212yes—
13C2×C22⋊(C7⋊C8)C2212yes—
14#89707C411yescharacteristic, complemented
15#89701—21no—
16#89700—21no—
17#89700C412yescomplemented
18C2×C4⋊(C7⋊C8)—21no—
19#89319—21no—
20#9908—71nomaximal, Sylow
21C23×C4×C7—22no—
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7C2311yescharacteristic
25C22×Dic14—21no—
26C2×C42×C7—24no—
27C2×C42×C7—42no—
28C2×C42×C7—42no—
29C2×C42×C7—42no—
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—22no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7C2×C412yes—
39C2×C4⋊Dic7C2×C412yes—
40#6487—44no—
41C2×Dic7⋊C4—22no—
42C22×C7⋊C8—22no—
43#6432—42no—
44C7×#95—24no—
45C7×#95—22no—
46C7×#95Q814yescomplemented
47C7⋊#95—22no—
48C7⋊#95—22no—
49C22⋊(C7⋊C8)—24no—
50C4⋊(C7⋊C8)—42no—
51#2857—71no—
52#1797—71no—
53C4×#95D711yescharacteristic
54#1294—74no—
55C24×C7C2×D411yescharacteristic
56C22×C4×C7—22no—
57C22×C4×C7—22no—
58C22×C4×C7—24no—
59C22×C4×C7—24no—
60C22×C4×C7—24no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—41no—
64C22×C4×C7—41no—
65C22×C4×C7—41no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7SD1612yes—
75C22×C4×C7Q1612yes—
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×Q812yes—
79C22×C4×C7#4112yes—
80C22×Dic7—22no—
81C22×Dic7—22no—
82C2×Dic14—42no—
83C2×Dic14—42no—
84C2×Dic14—42no—
85C42×C7—22no—
86C42×C7—22no—
87C42×C7—41no—
88C42×C7—41no—
89C42×C7—48no—
90C22⋊Dic7—44no—
91C4⋊Dic7—42no—
92C4⋊Dic7—42no—
93C4⋊Dic7—42no—
94C4⋊Dic7—42no—
95C4⋊Dic7—42no—
96Dic7⋊C4—44no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C2×C7⋊C8—42no—
100C2×C4⋊Q8—71no—
101C2×C22⋊Q8—141no—
102C22×C42—21no—
103C22×C42C2×D711yescharacteristic
104C2×C4⋊C8—141no—
105C2×C22⋊C8—72no—
106#391—141no—
107#389—72no—
108#389—141no—
109#384—71no—
110#380—72no—
111#380—141no—
112C2×#95—21no—
113C2×#95C2×D712yes—
114#336—141no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7C2×C22⋊C411yescharacteristic
120C23×C7C22⋊Q812yes—
121C23×C7C2×SD1611yescharacteristic
122C23×C7C2×Q1611yescharacteristic
123C23×C7AGL(1,ℤ/8)12yes—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—24no—
133C2×C4×C7—24no—
134C2×C4×C7—28no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—42no—
139C2×C4×C7—42no—
140C2×C4×C7—44no—
141C2×C4×C7—44no—
142C2×C4×C7—44no—
143C2×C4×C7—44no—
144C2×C4×C7—44no—
145C2×C4×C7—44no—
146C2×C4×C7—44no—
147C2×C4×C7#9912yes—
148C2×C4×C7#10312yes—
149C2×C4×C7#10312yes—
150C2×C4×C7#10412yes—
151C2×C4×C7#10412yes—
152C2×C4×C7C4×Q812yes—
153C2×C4×C7#12411yescharacteristic
154C2×C4×C7C4⋊Q811yescharacteristic
155C2×Dic7—42no—
156C2×Dic7—42no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159C2×Dic7—42no—
160C2×Dic7—42no—
161Dic14—84no—
162C7⋊C8—82no—
163C22×Q8—141no—
164C23×C4—22no—
165C23×C4C22⋊D711yescharacteristic
166C23×C4C22⋊D711yescharacteristic
167C23×C4C22×D711yescharacteristic
168C22×C8—142no—
169C4⋊Q8—282no—
170C22⋊Q8—284no—
171C2×C4⋊C4—72no—
172C2×C4⋊C4—72no—
173C2×C4⋊C4—142no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C22⋊C4—142no—
178C2×C42—24no—
179C2×C42—42no—
180C2×C42—42no—
181C2×C42—42no—
182C2×C42C4×D711yescharacteristic
183C2×C42C4×D711yescharacteristic
184C2×C42D2811yescharacteristic
185C2×C42D2811yescharacteristic
186C4⋊C8—282no—
187C22⋊C8—144no—
188#95—24no—
189#95—22no—
190#95—142no—
191#95—142no—
192#95Dic1414yescomplemented
193C22×C7—22no—
194C22×C7—22no—
195C22×C7—21no—
196C22×C7—21no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—22no—
200C22×C7—22no—
201C22×C7#39111yescharacteristic
202C22×C7C2×#9911yescharacteristic
203C22×C7#41011yescharacteristic
204C22×C7C2×#10311yescharacteristic
205C22×C7#41811yescharacteristic
206C22×C7C2×#10411yescharacteristic
207C22×C7C2×#10411yescharacteristic
208C22×C7#47612yes—
209C22×C7#47712yes—
210C4×C7—21no—
211C4×C7—22no—
212C4×C7—21no—
213C4×C7—22no—
214C4×C7—22no—
215C4×C7—48no—
216C4×C7—41no—
217C4×C7#32814yes—
218Dic7—82no—
219Dic7—82no—
220C24C2×C22⋊D711yescharacteristic
221C2×Q8—282no—
222C2×Q8—282no—
223C2×Q8—282no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—142no—
239C22×C4—142no—
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4(C2×D7)⋊C411yescharacteristic
242C22×C4(C2×D7)⋊C411yescharacteristic
243C22×C4(C2×D7)⋊C411yescharacteristic
244C22×C4#114212yes—
245C22×C4#114412yes—
246C22×C4C2×Dic1412yes—
247C22×C4C2×C4×D711yescharacteristic
248C22×C4C2×D2811yescharacteristic
249C22×C4#115712yes—
250C2×C8—282no—
251C2×C8—282no—
252C2×C8—282no—
253C4⋊C4—282no—
254C4⋊C4—282no—
255C4⋊C4—284no—
256C4⋊C4—282no—
257C4⋊C4—282no—
258C4⋊C4—282no—
259C22⋊C4—284no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C42—48no—
265C2×C7—22no—
266C2×C7—22no—
267C2×C7C2×#32811yescharacteristic
268C2×C7#150311yescharacteristic
269C2×C7#150511yescharacteristic
270C2×C7#150711yescharacteristic
271C2×C7#198711yescharacteristic
272C2×C7#199411yescharacteristic
273C2×C7#199611yescharacteristic
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#648712yes—
279C23C2×(C2×D7)⋊C411yescharacteristic
280C23C2×#114211yescharacteristic
281C23C2×#114411yescharacteristic
282C23#651212yes—
283Q8—564no—
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—24no—
293C2×C4—24no—
294C2×C4—28no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—282no—
308C2×C4—282no—
309C2×C4—282no—
310C2×C4—282no—
311C2×C4—282no—
312C2×C4—282no—
313C2×C4#637912yes—
314C2×C4#637912yes—
315C2×C4#638012yes—
316C2×C4#638412yes—
317C2×C4#638412yes—
318C2×C4C4×Dic1412yes—
319C2×C4#643211yescharacteristic
320C2×C4#643811yescharacteristic
321C8—562no—
322C7#990811yescharacteristic, complemented, Sylow
323C22—22no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22C2×#637911yescharacteristic
332C22C2×#637911yescharacteristic
333C22#8970111yescharacteristic
334C22C2×#638011yescharacteristic
335C22C2×#638411yescharacteristic
336C22#8977311yescharacteristic
337C22#8977811yescharacteristic
338C22#8978012yes—
339C22#8979312yes—
340C4—22no—
341C4—22no—
342C4—21no—
343C4—22no—
344C4—21no—
345C4—48no—
346C4—41no—
347C4—562no—
348C4—562no—
349C4#8924714yes—
350C2—22no—
351C2—22no—
352C2#1172715011yescharacteristic
353C2C2×#8924711yescharacteristic
354C2#1172718611yescharacteristic
355C2#1172719811yescharacteristic
356C2#1172721111yescharacteristic
357C2#1172722511yescharacteristic
358C2#1172724311yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC4×C7×#95C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC4×#95D7
hypocenterC7#9908
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
8. C2×#6432C4semidirect
14. #89707C4semidirect
17. #89700C4semidirect
46. C7×#95Q8semidirect
192. #95Dic14semidirect
322. C7#9908semidirect

Maximal subgroups

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

subgroupindex
#117395212
C4×C7×#952
#117292842
#117254182
#99087