Finite Group Databasebeta

← #13249474

Subgroups — #13249474

Order 1792.

568 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739521C211yesmaximal, characteristic
2C2×#89698C211yesmaximal, characteristic
3C7×#1797C211yesmaximal, characteristic
4C2×#89276C212yesmaximal, complemented
5#11725508C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C2×#6487C412yes—
8C2×#6432C2211yescharacteristic
9C2×C7×C4⋊C8C2212yes—
10C2×C7×C22⋊C8—21no—
11#89984—21no—
12#89984—21no—
13C2×C22⋊(C7⋊C8)—21no—
14#89707C2211yescharacteristic
15#89701C412yes—
16#89700—21no—
17#89700—21no—
18#89698—24no—
19C2×C4⋊(C7⋊C8)C2212yes—
20C2×#6377—21no—
21C7×#336—21no—
22#89276—24no—
23#9136—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C412yes—
28C22×C7×C8—22no—
29C2×C42×C7—22no—
30C2×C42×C7—22no—
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7C2311yescharacteristic
35C2×C22⋊Dic7—22no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7C2×C412yes—
41#6487—44no—
42C2×Dic7⋊C4—22no—
43C22×C7⋊C8—22no—
44#6432—22no—
45#6432—22no—
46C7×C4⋊C8—22no—
47C7×C4⋊C8—22no—
48C7×C22⋊C8—42no—
49C7⋊#95—22no—
50C7⋊#95—22no—
51C22⋊(C7⋊C8)—24no—
52C4⋊(C7⋊C8)—22no—
53C4⋊(C7⋊C8)D414yes—
54#6377—24no—
55C2×#432—71no—
56#2857—71no—
57#1797D711yescharacteristic
58C2×#333—72no—
59#1296—72no—
60C24×C7C22⋊C411yescharacteristic
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—21no—
64C22×C4×C7—22no—
65C22×C4×C7—21no—
66C22×C4×C7—22no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—22no—
70C22×C4×C7—22no—
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—22no—
79C22×Dic7—22no—
80C2×Dic14—24no—
81C2×Dic14—42no—
82C2×Dic14—42no—
83C2×C7×C8—42no—
84C2×C7×C8—42no—
85C2×C7×C8—42no—
86C42×C7—22no—
87C42×C7—21no—
88C42×C7—22no—
89C42×C7—21no—
90C42×C7C2×D412yes—
91C42×C7#4112yes—
92C22⋊Dic7—44no—
93C4⋊Dic7—41no—
94C4⋊Dic7—42no—
95C4⋊Dic7—41no—
96C4⋊Dic7—42no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C4⋊Dic7—42no—
100Dic7⋊C4—44no—
101C2×C7⋊C8—24no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C2×C4⋊Q8—71no—
105C2×C22⋊Q8—72no—
106C22×C42C2×D711yescharacteristic
107#432—144no—
108C2×C4⋊C8—72no—
109C2×C4⋊C8C2×D712yes—
110C2×C22⋊C8—21no—
111C2×C22⋊C8—141no—
112C2×#97—141no—
113#391—72no—
114#389—141no—
115#389—141no—
116#384—71no—
117#380—141no—
118#380—141no—
119#336—21no—
120#333—144no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7#10012yes—
128C23×C7C2×C22⋊C411yescharacteristic
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—21no—
139C2×C4×C7—21no—
140C2×C4×C7—44no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7C4×D412yes—
146C2×C4×C7#12011yescharacteristic
147C2×C4×C7#12112yes—
148C2×C4×C7#12311yescharacteristic
149C2×C4×C7#13512yes—
150C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C7#13712yes—
152C2×C4×C7#13711yescharacteristic
153C2×C4×C7#13712yes—
154C2×Dic7—42no—
155C2×Dic7—42no—
156C2×Dic7—42no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159C2×Dic7—42no—
160Dic14—84no—
161C7×C8—82no—
162C7⋊C8—44no—
163C22×Q8—72no—
164C23×C4C4×D711yescharacteristic
165C23×C4D2811yescharacteristic
166C23×C4C22⋊D711yescharacteristic
167C22×C8—22no—
168C22×C8—142no—
169C4⋊Q8—142no—
170C4⋊Q8—142no—
171C22⋊Q8—284no—
172C2×C4⋊C4—72no—
173C2×C4⋊C4—142no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C22⋊C4—142no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42C4×D711yescharacteristic
182C2×C42D2811yescharacteristic
183C2×C42C22⋊D711yescharacteristic
184C2×C42C22×D711yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—74no—
188C4⋊C8—142no—
189C22⋊C8—42no—
190C22⋊C8—144no—
191#97—144no—
192#95—142no—
193#95—142no—
194C22×C7—22no—
195C22×C7—22no—
196C22×C7—22no—
197C22×C7—41no—
198C22×C7—41no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7#38611yescharacteristic
202C22×C7C2×#10011yescharacteristic
203C22×C7#41311yescharacteristic
204C22×C7#41611yescharacteristic
205C22×C7#41711yescharacteristic
206C22×C7#41911yescharacteristic
207C22×C7#41911yescharacteristic
208C4×C7—22no—
209C4×C7—41no—
210C4×C7—41no—
211C4×C7—41no—
212C4×C7#45212yes—
213C4×C7#46812yes—
214C4×C7#47012yes—
215C4×C7#48512yes—
216Dic7—82no—
217Dic7—82no—
218C24(C2×D7)⋊C411yescharacteristic
219C2×Q8—144no—
220C2×Q8—282no—
221C2×Q8—282no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—142no—
234C22×C4—142no—
235C22×C4(C2×D7)⋊C411yescharacteristic
236C22×C4(C2×D7)⋊C411yescharacteristic
237C22×C4(C2×D7)⋊C411yescharacteristic
238C22×C4C2×C4×D711yescharacteristic
239C22×C4C2×D2811yescharacteristic
240C22×C4C2×C22⋊D711yescharacteristic
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—144no—
245C2×C8—282no—
246C2×C8—282no—
247C4⋊C4—282no—
248C4⋊C4—284no—
249C4⋊C4—281no—
250C4⋊C4—281no—
251C4⋊C4—282no—
252C4⋊C4—281no—
253C4⋊C4—282no—
254C4⋊C4—281no—
255C22⋊C4—284no—
256C42—22no—
257C42—21no—
258C42—21no—
259C42—22no—
260C42D4×D712yes—
261C42#115912yes—
262C2×C7—42no—
263C2×C7#155111yescharacteristic
264C2×C7#155411yescharacteristic
265C2×C7#155811yescharacteristic
266C2×C7#155911yescharacteristic
267C2×C7#187311yescharacteristic
268C2×C7#189411yescharacteristic
269C2×C7#190011yescharacteristic
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#639712yes—
277C23C2×(C2×D7)⋊C411yescharacteristic
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—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—282no—
296C2×C4—282no—
297C2×C4—282no—
298C2×C4—282no—
299C2×C4—282no—
300C2×C4—282no—
301C2×C4(C22⋊D7)⋊C412yes—
302C2×C4#644511yescharacteristic
303C2×C4#644911yescharacteristic
304C2×C4#646712yes—
305C2×C4#647212yes—
306C2×C4#649511yescharacteristic
307C2×C4#650212yes—
308C2×C4#650511yescharacteristic
309C2×C4#651412yes—
310C8—82no—
311C8—284no—
312C7#913611yescharacteristic, complemented, Sylow
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#8973011yescharacteristic
321C22#8973811yescharacteristic
322C22#8977611yescharacteristic
323C22#8988511yescharacteristic
324C22#8989211yescharacteristic
325C22C2×#639711yescharacteristic
326C22#8990411yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—562no—
332C4—562no—
333C4#8949512yes—
334C4#8950512yes—
335C4#8981412yes—
336C4#8982412yes—
337C2—42no—
338C2#1172727011yescharacteristic
339C2#1172768511yescharacteristic
340C2#1172773911yescharacteristic
341C2#1172818711yescharacteristic
342C2#1172826411yescharacteristic
343C2#1172853511yescharacteristic
344C2#1172857811yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1797C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1797D7
hypocenterC7#9136
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
4. C2×#89276C2semidirect
5. #11725508C2semidirect
312. C7#9136semidirect

Maximal subgroups

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

subgroupindex
#117395212
C2×#896982
C7×#17972
C2×#892762
#117255082
#91367