Finite Group Databasebeta

← #13253975

Subgroups — #13253975

Order 1792.

640 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2851C211yesmaximal, characteristic
2C4×C7⋊#95C211yesmaximal, characteristic
3#11729284C211yesmaximal, characteristic
4#11725430C212yesmaximal
5#11725430C212yesmaximal
6C2×C7×#125C411yescharacteristic, complemented
7C22×C42×C7C2211yescharacteristic
8C22×C4×Dic7—21no—
9C7×#389C411yescharacteristic, complemented
10C7×#389C411yescharacteristic, complemented
11C7×#387—21no—
12C7×#387—21no—
13C7×#385—21no—
14C7×#385—21no—
15C7×#382C411yescharacteristic, complemented
16C7×#380C2211yescharacteristic
17C7×#380C2211yescharacteristic
18C2×C7⋊#95—21no—
19C2×C7⋊#95C2212yes—
20C2×C22⋊(C7⋊C8)C2212yes—
21C2×C4⋊(C7⋊C8)—21no—
22#89319—21no—
23#9910—71nomaximal, Sylow
24C23×C4×C7D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C23×Dic7—22no—
28C7×#125—42no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C42×C7—42no—
40C2×C42×C7C2×C411yescharacteristic
41C2×C42×C7C2×C411yescharacteristic
42C2×C42×C7D411yescharacteristic
43C2×C42×C7D411yescharacteristic
44C2×C4×Dic7—24no—
45C2×C4×Dic7—42no—
46C2×C4×Dic7—42no—
47C22×C7⋊C8—22no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7⋊#95—24no—
55C7⋊#95—22no—
56C7⋊#95Q814yes—
57C22⋊(C7⋊C8)—24no—
58C4⋊(C7⋊C8)—42no—
59#2851D711yescharacteristic
60#1797—71no—
61C4×#95—71no—
62#1294—72no—
63#1294—72no—
64C24×C7C2×D411yescharacteristic
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7—22no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—41no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22×C411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C22×C4×C7C2×Q812yes—
85C22×C4×C7#4112yes—
86C22×Dic7—24no—
87C22×Dic7—24no—
88C22×Dic7—24no—
89C22×Dic7—42no—
90C22×Dic7—42no—
91C22×Dic7—42no—
92C22×Dic7—42no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4—41no—
95C7×C4⋊C4—41no—
96C7×C4⋊C4—41no—
97C7×C4⋊C4—42no—
98C7×C4⋊C4—42no—
99C7×C4⋊C4—42no—
100C7×C4⋊C4—42no—
101C7×C22⋊C4—42no—
102C7×C22⋊C4—41no—
103C7×C22⋊C4—41no—
104C42×C7—22no—
105C42×C7—22no—
106C42×C7—41no—
107C42×C7—41no—
108C4×Dic7—48no—
109C2×C7⋊C8—42no—
110C2×C7⋊C8—42no—
111C2×C7⋊C8—42no—
112C2×#125Dic711yescharacteristic, complemented
113C22×C42—141no—
114C22×C42C2×D711yescharacteristic
115C2×C4⋊C8—141no—
116C2×C22⋊C8—72no—
117#389Dic711yescharacteristic, complemented
118#389Dic711yescharacteristic, complemented
119#387—21no—
120#387—21no—
121#385—21no—
122#385—21no—
123#382Dic711yescharacteristic, complemented
124#380C2×D711yescharacteristic
125#380C2×D711yescharacteristic
126C2×#95—72no—
127C2×#95—141no—
128#336—141no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7C2×C22⋊C411yescharacteristic
134C23×C7C22⋊Q812yes—
135C23×C7#13512yes—
136C23×C7AGL(1,ℤ/8)11yescharacteristic
137C23×C7#13711yescharacteristic
138C2×C4×C7—24no—
139C2×C4×C7—24no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—42no—
154C2×C4×C7—42no—
155C2×C4×C7—44no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7#9912yes—
169C2×C4×C7#10412yes—
170C2×C4×C7#10412yes—
171C2×C4×C7C4×Q812yes—
172C2×C4×C7#12411yescharacteristic
173C2×C4×C7C4⋊Q811yescharacteristic
174C2×Dic7—28no—
175C2×Dic7—44no—
176C2×Dic7—44no—
177C2×Dic7—44no—
178C2×Dic7—44no—
179C2×Dic7—44no—
180C2×Dic7—44no—
181C7⋊C8—82no—
182C23×C4—142no—
183C23×C4C22⋊D711yescharacteristic
184C23×C4C22⋊D711yescharacteristic
185C23×C4C22×D711yescharacteristic
186C22×C8—142no—
187#125—42no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×Dic711yescharacteristic
193C2×C4⋊C4C2×Dic711yescharacteristic
194C2×C4⋊C4C2×Dic711yescharacteristic
195C2×C4⋊C4C2×Dic711yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42—42no—
199C2×C42—144no—
200C2×C42—282no—
201C2×C42—282no—
202C2×C42C2×Dic711yescharacteristic
203C2×C42C2×Dic711yescharacteristic
204C2×C42C22⋊D711yescharacteristic
205C2×C42C22⋊D711yescharacteristic
206C4⋊C8—282no—
207C22⋊C8—144no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—74no—
215#95—144no—
216#95—142no—
217C22×C7—22no—
218C22×C7—22no—
219C22×C7—22no—
220C22×C7—22no—
221C22×C7—21no—
222C22×C7—21no—
223C22×C7—21no—
224C22×C7—21no—
225C22×C7#39111yescharacteristic
226C22×C7C2×#9911yescharacteristic
227C22×C7#41011yescharacteristic
228C22×C7#41611yescharacteristic
229C22×C7#41711yescharacteristic
230C22×C7C2×#10411yescharacteristic
231C22×C7C2×#10411yescharacteristic
232C22×C7#47812yes—
233C22×C7#47912yes—
234C4×C7—21no—
235C4×C7—22no—
236C4×C7—21no—
237C4×C7—22no—
238C4×C7—22no—
239C4×C7—22no—
240C4×C7—41no—
241C4×C7—81no—
242C4×C7—81no—
243C4×C7—81no—
244C4×C7—81no—
245Dic7—48no—
246C24C2×C22⋊D711yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—144no—
261C22×C4—144no—
262C22×C4—144no—
263C22×C4—282no—
264C22×C4—282no—
265C22×C4—282no—
266C22×C4—282no—
267C22×C4C22⋊Dic711yescharacteristic
268C22×C4C22⋊Dic711yescharacteristic
269C22×C4C22⋊Dic711yescharacteristic
270C22×C4C22⋊Dic711yescharacteristic
271C22×C4Q8×D712yes—
272C22×C4#116112yes—
273C22×C4C22×Dic711yescharacteristic
274C22×C4C2×C22⋊D711yescharacteristic
275C2×C8—282no—
276C2×C8—282no—
277C2×C8—282no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C42—288no—
294C2×C7—22no—
295C2×C7—22no—
296C2×C7#150011yescharacteristic
297C2×C7#150111yescharacteristic
298C2×C7#150411yescharacteristic
299C2×C7#150911yescharacteristic
300C2×C7#198911yescharacteristic
301C2×C7#199411yescharacteristic
302C2×C7#199611yescharacteristic
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23#650912yes—
308C23#651211yescharacteristic
309C23#651312yes—
310C23#651411yescharacteristic
311C23C2×C22⋊Dic711yescharacteristic
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—148no—
343C2×C4—284no—
344C2×C4—284no—
345C2×C4—284no—
346C2×C4—284no—
347C2×C4—284no—
348C2×C4—284no—
349C2×C4#640812yes—
350C2×C4#641112yes—
351C2×C4#641112yes—
352C2×C4#650711yescharacteristic
353C2×C4Q8×Dic712yes—
354C2×C4#651011yescharacteristic
355C8—562no—
356C7#991011yescharacteristic, complemented, Sylow
357C22—22no—
358C22—22no—
359C22—21no—
360C22—21no—
361C22—22no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22#8983512yes—
366C22#8983812yes—
367C22C2×#640811yescharacteristic
368C22#9000211yescharacteristic
369C22#9000411yescharacteristic
370C22#9000511yescharacteristic
371C22C2×#641111yescharacteristic
372C22C2×#641111yescharacteristic
373C22#9001211yescharacteristic
374C4—21no—
375C4—21no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—288no—
386C2—22no—
387C2—22no—
388C2#1172945511yescharacteristic
389C2#1172946111yescharacteristic
390C2#1172946211yescharacteristic
391C2#1172949211yescharacteristic
392C2#1172950811yescharacteristic
393C2#1172950911yescharacteristic
394C2#1172959311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#2851C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#2851D7
hypocenterC7#9910
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
6. C2×C7×#125C4semidirect
9. C7×#389C4semidirect
10. C7×#389C4semidirect
15. C7×#382C4semidirect
112. C2×#125Dic7semidirect
117. #389Dic7semidirect
118. #389Dic7semidirect
123. #382Dic7semidirect
356. C7#9910semidirect

Maximal subgroups

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

subgroupindex
C7×#28512
C4×C7⋊#952
#117292842
#117254302
#99107