Finite Group Databasebeta

← #13247166

Subgroups — #13247166

Order 1792.

496 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739505C211yesmaximal, characteristic
2C4×C7×C22⋊C8C211yesmaximal, characteristic
3#11729284C211yesmaximal, characteristic
4#11725461C212yesmaximal, complemented
5#11725461C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C2×C7×C22⋊C8—21no—
8C2×C4×C7×C8C2212yes—
9#89984C411yescharacteristic
10#89984C411yescharacteristic
11#89983—21no—
12C4×C22⋊Dic7—21no—
13C2×C22⋊(C7⋊C8)—21no—
14#89709—21no—
15#89708C411yescharacteristic
16#89708C411yescharacteristic
17C4×C4⋊Dic7C2211yescharacteristic
18C4×C4⋊Dic7C2211yescharacteristic
19#89704—21no—
20C2×C4⋊(C7⋊C8)C2212yes—
21C7×#336—21no—
22#89319—21no—
23#8711—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×C7×C8—22no—
28C2×C42×C7—24no—
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×C4×Dic7—21no—
40C2×C4×Dic7—21no—
41C22×C7⋊C8—22no—
42C7×C22⋊C8—24no—
43C4×C7×C8—24no—
44C7⋊#95—21no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C22⋊(C7⋊C8)—42no—
53C4⋊(C7⋊C8)—24no—
54#2283—71no—
55#1797—71no—
56C4×C22⋊C8D711yescharacteristic
57#1279—72no—
58#1279—72no—
59C24×C7C22⋊C411yescharacteristic
60C22×C4×C7—22no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—22no—
65C22×C4×C7—22no—
66C22×C4×C7—22no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—41no—
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×Dic7—21no—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C2×C7×C8—24no—
81C2×C7×C8—42no—
82C2×C7×C8—42no—
83C42×C7—22no—
84C42×C7—22no—
85C42×C7—22no—
86C42×C7#4114yes—
87C22⋊Dic7—42no—
88C22⋊Dic7—42no—
89C4⋊Dic7—22no—
90C4⋊Dic7—22no—
91C4⋊Dic7—22no—
92C4⋊Dic7—22no—
93C4×Dic7—42no—
94C4×Dic7—41no—
95C4×Dic7—41no—
96C2×C7⋊C8—42no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C22×C42C2×D711yescharacteristic
100C2×C4⋊C8—72no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—141no—
103C2×C4×C8C2×D712yes—
104#383—141no—
105#382—71no—
106#382—71no—
107#381—141no—
108#380—71no—
109#380—71no—
110C4×C4⋊C4—71no—
111C4×C4⋊C4—71no—
112C4×C22⋊C4—141no—
113#376—141no—
114#336—21no—
115#336—141no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7#10412yes—
123C23×C7C2×C22⋊C411yescharacteristic
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—44no—
136C2×C4×C7—44no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7#11712yes—
140C2×C4×C7#12312yes—
141C2×C4×C7#12312yes—
142C2×C4×C7#13112yes—
143C2×C4×C7#13112yes—
144C2×C4×C7#13512yes—
145C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C7#13711yescharacteristic
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C7×C8—44no—
160C7⋊C8—82no—
161C23×C4C4×D711yescharacteristic
162C23×C4D2811yescharacteristic
163C23×C4C22⋊D711yescharacteristic
164C22×C8—22no—
165C22×C8—142no—
166C2×C4⋊C4—71no—
167C2×C4⋊C4—71no—
168C2×C4⋊C4—71no—
169C2×C4⋊C4—71no—
170C2×C22⋊C4—141no—
171C2×C22⋊C4—141no—
172C2×C42—24no—
173C2×C42—141no—
174C2×C42—141no—
175C2×C42C4×D711yescharacteristic
176C2×C42D2811yescharacteristic
177C2×C42C22⋊D711yescharacteristic
178C2×C42C22×D711yescharacteristic
179C4⋊C8—144no—
180C22⋊C8—24no—
181C22⋊C8—282no—
182C4×C8—24no—
183#95—141no—
184#95—141no—
185#95—141no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190#95—141no—
191C22×C7—22no—
192C22×C7—22no—
193C22×C7—22no—
194C22×C7—41no—
195C22×C7—41no—
196C22×C7—41no—
197C22×C7—41no—
198C22×C7#38111yescharacteristic
199C22×C7#40811yescharacteristic
200C22×C7#40811yescharacteristic
201C22×C7#41611yescharacteristic
202C22×C7#41711yescharacteristic
203C22×C7C2×#10411yescharacteristic
204C22×C7#42111yescharacteristic
205C4×C7—22no—
206C4×C7—41no—
207C4×C7—41no—
208C4×C7—41no—
209C4×C7#43314yes—
210C4×C7#48212yes—
211C4×C7#48512yes—
212Dic7—81no—
213Dic7—81no—
214Dic7—81no—
215Dic7—81no—
216C24(C2×D7)⋊C411yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—141no—
228C22×C4—141no—
229C22×C4—141no—
230C22×C4—141no—
231C22×C4(C2×D7)⋊C411yescharacteristic
232C22×C4(C2×D7)⋊C411yescharacteristic
233C22×C4(C2×D7)⋊C411yescharacteristic
234C22×C4C2×C4×D711yescharacteristic
235C22×C4C2×D2811yescharacteristic
236C22×C4C2×C22⋊D711yescharacteristic
237C2×C8—24no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—282no—
241C2×C8—282no—
242C2×C8—282no—
243C4⋊C4—142no—
244C4⋊C4—142no—
245C4⋊C4—142no—
246C4⋊C4—142no—
247C22⋊C4—282no—
248C22⋊C4—282no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—282no—
253C42—281no—
254C42—281no—
255C42#115914yes—
256C2×C7—42no—
257C2×C7#148211yescharacteristic
258C2×C7#148311yescharacteristic
259C2×C7#149411yescharacteristic
260C2×C7#149511yescharacteristic
261C2×C7#181811yescharacteristic
262C2×C7#182511yescharacteristic
263C2×C7#182611yescharacteristic
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23#637912yes—
271C23C2×(C2×D7)⋊C411yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—281no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4—281no—
291C2×C4—281no—
292C2×C4—281no—
293C2×C4—281no—
294C2×C4—281no—
295C2×C4—281no—
296C2×C4—281no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4#644012yes—
300C2×C4#644912yes—
301C2×C4#646412yes—
302C2×C4#646712yes—
303C2×C4#647012yes—
304C2×C4#647111yescharacteristic
305C2×C4#647211yescharacteristic
306C2×C4#649812yes—
307C8—44no—
308C8—562no—
309C7#871111yescharacteristic, complemented, Sylow
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×#637911yescharacteristic
318C22#8971511yescharacteristic
319C22#8977711yescharacteristic
320C22#8988211yescharacteristic
321C22#8988511yescharacteristic
322C22#8990111yescharacteristic
323C22#8990511yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—561no—
329C4—561no—
330C4—561no—
331C4—561no—
332C4#8949214yes—
333C4#8949512yes—
334C4#8950912yes—
335C2—42no—
336C2#1172719611yescharacteristic
337C2#1172749011yescharacteristic
338C2#1172760611yescharacteristic
339C2#1172766511yescharacteristic
340C2#1172768011yescharacteristic
341C2#1172851411yescharacteristic
342C2#1172851811yescharacteristic
subgroupG/H
centerC22×C4C2×D28
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC4×C7×C22⋊C8C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC4×C22⋊C8D7
hypocenterC7#8711
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #11725461C2semidirect
5. #11725461C2semidirect
309. C7#8711semidirect

Maximal subgroups

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

subgroupindex
#117395052
C4×C7×C22⋊C82
#117292842
#117254612
#87117