Finite Group Databasebeta

← #13252930

Subgroups — #13252930

Order 1792.

624 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
2C7×#1797C211yesmaximal, characteristic
3#11729288C211yesmaximal, characteristic
4C2×#89262C214yesmaximal
5C22×C42×C7C2211yescharacteristic
6C2×#6487C2212yes—
7C2×#6432C411yescharacteristic, complemented
8C2×C7×C4⋊C8—21no—
9C2×C7×C22⋊C8C2212yes—
10#89984—21no—
11#89984—21no—
12C2×C7⋊#95—21no—
13C2×C7⋊#95—21no—
14C2×C7⋊#95C2212yes—
15#89707C411yescharacteristic, complemented
16#89701C412yescomplemented
17#89700—21no—
18#89700—21no—
19C7×#336—21no—
20#89262—28no—
21#9714—71nomaximal, Sylow
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7C2311yescharacteristic
25C23×Dic7—22no—
26C22×Dic14C2×C412yes—
27C22×C7×C8—22no—
28C2×C42×C7—42no—
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C22⋊Dic7—22no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7C2×C412yes—
39#6487—24no—
40#6487—24no—
41C2×Dic7⋊C4—22no—
42#6432—42no—
43C7×C4⋊C8—42no—
44C7×C22⋊C8—24no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C7⋊#95—42no—
49C7⋊#95—42no—
50C7⋊#95D414yes—
51#2857—71no—
52#1797D711yescharacteristic
53C2×#328—74no—
54#1434—71no—
55C24×C7C2×D411yescharacteristic
56C22×C4×C7—22no—
57C22×C4×C7—22no—
58C22×C4×C7—41no—
59C22×C4×C7—41no—
60C22×C4×C7—41no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7SD1612yes—
68C22×C4×C7Q1612yes—
69C22×C4×C7C22×C411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×C4×C7C2×D412yes—
72C22×C4×C7#4112yes—
73C22×Dic7—22no—
74C22×Dic7—22no—
75C22×Dic7—24no—
76C22×Dic7—42no—
77C22×Dic7—42no—
78C22×Dic7—42no—
79C22×Dic7—42no—
80C22×Dic7—42no—
81C22×Dic7—42no—
82C2×Dic14—24no—
83C2×Dic14—42no—
84C2×Dic14—42no—
85C2×C7×C8—42no—
86C2×C7×C8—42no—
87C2×C7×C8—42no—
88C42×C7—22no—
89C42×C7—22no—
90C42×C7—41no—
91C42×C7—41no—
92C22⋊Dic7—44no—
93C4⋊Dic7—24no—
94C4⋊Dic7—42no—
95C4⋊Dic7—42no—
96C4⋊Dic7—42no—
97C4⋊Dic7—42no—
98Dic7⋊C4—42no—
99Dic7⋊C4—42no—
100C2×C4⋊Q8—71no—
101C2×C22⋊Q8—72no—
102C22×C42C2×D711yescharacteristic
103C2×C4⋊C8—21no—
104C2×C22⋊C8C2×D712yes—
105#391—72no—
106#389—141no—
107#389—141no—
108#384—71no—
109#380—141no—
110#380—141no—
111C2×#95—72no—
112C2×#95—141no—
113C2×#95—141no—
114#336—21no—
115#328—148no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7C2×C22⋊C411yescharacteristic
121C23×C7#12112yes—
122C23×C7C2×SD1611yescharacteristic
123C23×C7C2×Q1611yescharacteristic
124C23×C7#13712yes—
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—42no—
141C2×C4×C7—42no—
142C2×C4×C7—44no—
143C2×C4×C7#9912yes—
144C2×C4×C7#10312yes—
145C2×C4×C7#10312yes—
146C2×C4×C7C4×D412yes—
147C2×C4×C7#12411yescharacteristic
148C2×C4×C7#12711yescharacteristic
149C2×Dic7—44no—
150C2×Dic7—44no—
151C2×Dic7—42no—
152C2×Dic7—42no—
153C2×Dic7—42no—
154C2×Dic7—42no—
155C2×Dic7—42no—
156C2×Dic7—42no—
157C2×Dic7—44no—
158C2×Dic7—82no—
159C2×Dic7—82no—
160C2×Dic7—82no—
161C2×Dic7—82no—
162Dic14—84no—
163C7×C8—82no—
164C22×Q8—72no—
165C23×C4—142no—
166C23×C4D2811yescharacteristic
167C23×C4D2811yescharacteristic
168C23×C4C22×D711yescharacteristic
169C22×C8—22no—
170C4⋊Q8—282no—
171C22⋊Q8—144no—
172C22⋊Q8—144no—
173C2×C4⋊C4—72no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4—142no—
179C2×C22⋊C4—142no—
180C2×C42—42no—
181C2×C42C4×D711yescharacteristic
182C2×C42C4×D711yescharacteristic
183C2×C42C22⋊D711yescharacteristic
184C2×C42C22⋊D711yescharacteristic
185C4⋊C8—42no—
186C22⋊C8—24no—
187#95—74no—
188#95—142no—
189#95—142no—
190#95—142no—
191#95—282no—
192#95—282no—
193C22×C7—22no—
194C22×C7—22no—
195C22×C7—22no—
196C22×C7—22no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7#39011yescharacteristic
202C22×C7C2×#9911yescharacteristic
203C22×C7#41011yescharacteristic
204C22×C7C2×#10311yescharacteristic
205C22×C7#41911yescharacteristic
206C22×C7#42111yescharacteristic
207C22×C7#42111yescharacteristic
208C22×C7#46112yes—
209C22×C7#46212yes—
210C4×C7—21no—
211C4×C7—22no—
212C4×C7—21no—
213C4×C7—22no—
214C4×C7—22no—
215C4×C7—22no—
216C4×C7—41no—
217Dic7—84no—
218Dic7—82no—
219Dic7—82no—
220C24C2×D2811yescharacteristic
221C2×Q8—144no—
222C2×Q8—282no—
223C2×Q8—282no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—144no—
232C22×C4—142no—
233C22×C4—142no—
234C22×C4—282no—
235C22×C4—282no—
236C22×C4—282no—
237C22×C4—282no—
238C22×C4—282no—
239C22×C4—282no—
240C22×C4#113212yes—
241C22×C4Dic2812yes—
242C22×C4(C2×D7)⋊C411yescharacteristic
243C22×C4(C2×D7)⋊C411yescharacteristic
244C22×C4(C2×D7)⋊C411yescharacteristic
245C22×C4(C2×D7)⋊C411yescharacteristic
246C22×C4C2×C4×D711yescharacteristic
247C22×C4D4×D712yes—
248C22×C4#116112yes—
249C22×C4C2×C22⋊D711yescharacteristic
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C4⋊C4—144no—
254C4⋊C4—282no—
255C4⋊C4—282no—
256C4⋊C4—282no—
257C4⋊C4—282no—
258C4⋊C4—282no—
259C4⋊C4—282no—
260C22⋊C4—284no—
261C42—22no—
262C42—22no—
263C42—41no—
264C42—41no—
265C2×C7—22no—
266C2×C7—22no—
267C2×C7#151111yescharacteristic
268C2×C7#151511yescharacteristic
269C2×C7#151811yescharacteristic
270C2×C7#152011yescharacteristic
271C2×C7#196311yescharacteristic
272C2×C7#196411yescharacteristic
273C2×C7#198111yescharacteristic
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#645812yes—
279C23C2×#113211yescharacteristic
280C23C2×Dic2811yescharacteristic
281C23#647212yes—
282C23C2×(C2×D7)⋊C411yescharacteristic
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—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—284no—
303C2×C4—284no—
304C2×C4—284no—
305C2×C4—282no—
306C2×C4—282no—
307C2×C4—282no—
308C2×C4—282no—
309C2×C4—282no—
310C2×C4—282no—
311C2×C4—562no—
312C2×C4—562no—
313C2×C4—562no—
314C2×C4—562no—
315C2×C4#638012yes—
316C2×C4#639012yes—
317C2×C4#639012yes—
318C2×C4#645612yes—
319C2×C4#650311yescharacteristic
320C2×C4#651011yescharacteristic
321C8—82no—
322C7#971411yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—22no—
326C22—22no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—22no—
331C22#8961312yes—
332C22#8962112yes—
333C22C2×#638011yescharacteristic
334C22#8976011yescharacteristic
335C22#8977811yescharacteristic
336C22C2×#639011yescharacteristic
337C22#8989211yescharacteristic
338C22#8991111yescharacteristic
339C22#8991111yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—41no—
347C4—564no—
348C4—562no—
349C4—562no—
350C2—22no—
351C2—22no—
352C2#1172728211yescharacteristic
353C2#1172770011yescharacteristic
354C2#1172773511yescharacteristic
355C2#1172821011yescharacteristic
356C2#1172826711yescharacteristic
357C2#1172854711yescharacteristic
358C2#1172859111yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1797C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1797D7
hypocenterC7#9714
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
7. C2×#6432C4semidirect
15. #89707C4semidirect
16. #89701C4semidirect
322. C7#9714semidirect

Maximal subgroups

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

subgroupindex
#117395212
C7×#17972
#117292882
C2×#892622
#97147