Finite Group Databasebeta

← #13252791

Subgroups — #13252791

Order 1792.

630 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739521C211yesmaximal, characteristic
2C7×#1434C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4C2×#89247C214yesmaximal
5C22×C42×C7C2211yescharacteristic
6C2×#6487C2212yes—
7C2×#6432C411yescharacteristic, complemented
8C2×C7×#95—21no—
9C2×C7×#95—21no—
10C2×C7×#95C2212yes—
11#89984—21no—
12#89984—21no—
13C2×C22⋊(C7⋊C8)C2212yes—
14#89707C411yescharacteristic, complemented
15#89701C412yescomplemented
16#89700—21no—
17#89700—21no—
18C2×#6377—21no—
19#89319—21no—
20#89247—28no—
21#9683—71nomaximal, Sylow
22C23×C4×C7—22no—
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7C2311yescharacteristic
26C22×Dic14C2×C412yes—
27C2×C42×C7—42no—
28C2×C42×C7C2×C411yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C22⋊Dic7—22no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7C2×C412yes—
38#6487—24no—
39#6487—24no—
40C2×Dic7⋊C4—22no—
41C22×C7⋊C8—22no—
42#6432—42no—
43C7×#95—24no—
44C7×#95—24no—
45C7×#95—42no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C22⋊(C7⋊C8)—22no—
49C22⋊(C7⋊C8)D414yes—
50#6377—42no—
51#2857—71no—
52#1749—71no—
53C2×#328—74no—
54#1434D711yescharacteristic
55C24×C7C2×D411yescharacteristic
56C22×C4×C7—22no—
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—24no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7—41no—
64C22×C4×C7—41no—
65C22×C4×C7—42no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7—42no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D412yes—
78C22×C4×C7#4112yes—
79C22×Dic7—22no—
80C22×Dic7—22no—
81C2×Dic14—24no—
82C2×Dic14—42no—
83C2×Dic14—42no—
84C42×C7—22no—
85C42×C7—22no—
86C42×C7—41no—
87C42×C7—41no—
88C22⋊Dic7—42no—
89C22⋊Dic7—42no—
90C4⋊Dic7—24no—
91C4⋊Dic7—42no—
92C4⋊Dic7—42no—
93C4⋊Dic7—42no—
94C4⋊Dic7—42no—
95Dic7⋊C4—44no—
96C2×C7⋊C8—24no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C2×C4⋊Q8—71no—
100C2×C22⋊Q8—72no—
101C22×C42C2×D711yescharacteristic
102C2×C22⋊C8—72no—
103C2×#97—141no—
104#391—72no—
105#389—141no—
106#389—141no—
107#384—71no—
108#380—141no—
109#380—141no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95C2×D712yes—
113#336—141no—
114#328—148no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7C2×C22⋊C411yescharacteristic
120C23×C7#12411yescharacteristic
121C23×C7#12711yescharacteristic
122C23×C7#13712yes—
123C23×C7#13712yes—
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—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
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—82no—
146C2×C4×C7—82no—
147C2×C4×C7—82no—
148C2×C4×C7—82no—
149C2×C4×C7#9912yes—
150C2×C4×C7#10412yes—
151C2×C4×C7C4×D412yes—
152C2×C4×C7#12112yes—
153C2×Dic7—42no—
154C2×Dic7—42no—
155C2×Dic7—42no—
156C2×Dic7—42no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159Dic14—84no—
160C7⋊C8—44no—
161C22×Q8—72no—
162C23×C4—22no—
163C23×C4C22⋊D711yescharacteristic
164C23×C4C22⋊D711yescharacteristic
165C23×C4C22×D711yescharacteristic
166C22×C8—142no—
167C4⋊Q8—282no—
168C22⋊Q8—144no—
169C22⋊Q8—144no—
170C2×C4⋊C4—72no—
171C2×C4⋊C4—141no—
172C2×C4⋊C4—141no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—142no—
176C2×C22⋊C4—142no—
177C2×C42—42no—
178C2×C42C4×D711yescharacteristic
179C2×C42C4×D711yescharacteristic
180C2×C42D2811yescharacteristic
181C2×C42D2811yescharacteristic
182C22⋊C8—74no—
183C22⋊C8—142no—
184#97—282no—
185#95—24no—
186#95—24no—
187#95—42no—
188#95—142no—
189#95—142no—
190C22×C7—21no—
191C22×C7—21no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7—22no—
195C22×C7—22no—
196C22×C7—22no—
197C22×C7—22no—
198C22×C7#39011yescharacteristic
199C22×C7C2×#9911yescharacteristic
200C22×C7#41011yescharacteristic
201C22×C7#41911yescharacteristic
202C22×C7#41911yescharacteristic
203C22×C7C2×#10411yescharacteristic
204C22×C7#42111yescharacteristic
205C22×C7#49112yes—
206C22×C7#49712yes—
207C4×C7—22no—
208C4×C7—22no—
209C4×C7—22no—
210C4×C7—22no—
211C4×C7—41no—
212C4×C7—41no—
213C4×C7—84no—
214Dic7—82no—
215Dic7—82no—
216C24C2×C22⋊D711yescharacteristic
217C2×Q8—144no—
218C2×Q8—282no—
219C2×Q8—282no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—142no—
236C22×C4—142no—
237C22×C4(C2×D7)⋊C411yescharacteristic
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4(C2×D7)⋊C411yescharacteristic
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4C2×C4×D711yescharacteristic
242C22×C4C2×D2811yescharacteristic
243C22×C4D4×D712yes—
244C22×C4#116112yes—
245C2×C8—144no—
246C2×C8—282no—
247C2×C8—282no—
248C4⋊C4—144no—
249C4⋊C4—282no—
250C4⋊C4—282no—
251C4⋊C4—284no—
252C4⋊C4—282no—
253C4⋊C4—282no—
254C22⋊C4—282no—
255C22⋊C4—282no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C2×C7—22no—
261C2×C7—22no—
262C2×C7#150611yescharacteristic
263C2×C7#150811yescharacteristic
264C2×C7#151111yescharacteristic
265C2×C7#151511yescharacteristic
266C2×C7#196011yescharacteristic
267C2×C7#196411yescharacteristic
268C2×C7#198011yescharacteristic
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23C2×(C2×D7)⋊C411yescharacteristic
274C23#650311yescharacteristic
275C23#651011yescharacteristic
276C23#651412yes—
277C23#651412yes—
278Q8—564no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
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—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—282no—
305C2×C4—282no—
306C2×C4—282no—
307C2×C4—282no—
308C2×C4—282no—
309C2×C4—282no—
310C2×C4#637912yes—
311C2×C4#638012yes—
312C2×C4#645612yes—
313C2×C4#645812yes—
314C8—284no—
315C7#968311yescharacteristic, complemented, Sylow
316C22—22no—
317C22—22no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22C2×#637911yescharacteristic
325C22C2×#638011yescharacteristic
326C22#8976011yescharacteristic
327C22#8977611yescharacteristic
328C22#8977611yescharacteristic
329C22#8977711yescharacteristic
330C22#8977811yescharacteristic
331C22#8983212yes—
332C22#8984112yes—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—84no—
340C4—562no—
341C4—562no—
342C2—22no—
343C2—22no—
344C2#1172718711yescharacteristic
345C2#1172719911yescharacteristic
346C2#1172724611yescharacteristic
347C2#1172728211yescharacteristic
348C2#1172728711yescharacteristic
349C2#1172730611yescharacteristic
350C2#1172732011yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1434C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1434D7
hypocenterC7#9683
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
7. C2×#6432C4semidirect
14. #89707C4semidirect
15. #89701C4semidirect
315. C7#9683semidirect

Maximal subgroups

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

subgroupindex
#117395212
C7×#14342
#117292832
C2×#892472
#96837