Finite Group Databasebeta

← #13242052

Subgroups — #13242052

Order 1792.

556 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2#11729283C211yesmaximal, characteristic
3#11729281C211yesmaximal, characteristic
4#11725448C212yesmaximal, complemented
5#11725444C212yesmaximal, complemented
6C2×C7×C22⋊Q8C411yescharacteristic
7C2×C4×C7×Q8C411yescharacteristic
8C22×C42×C7C2211yescharacteristic
9C22×#1136—21no—
10C7×#391C2211yescharacteristic
11C7×#389C2211yescharacteristic
12C7×#387—21no—
13C7×#385—21no—
14C7×#380C411yescharacteristic
15C4×C7×C4⋊C4—21no—
16C4×C7×C4⋊C4C411yescharacteristic
17C4×C7×C22⋊C4—21no—
18C2×C22⋊(C7⋊C8)—21no—
19C2×#6377—21no—
20#89319—21no—
21#89319C2212yes—
22#89319C2212yes—
23#7634—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C7×C22⋊Q8—22no—
29C7×C22⋊Q8—22no—
30C4×C7×Q8—42no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
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—21no—
40C2×C42×C7—21no—
41C2×C42×C7—42no—
42C2×C42×C7C2×C411yescharacteristic
43C2×C42×C7D411yescharacteristic
44C2×C42×C7D411yescharacteristic
45C2×C42×C7C2311yescharacteristic
46C2×#1136—24no—
47C2×#1136—42no—
48C2×#1136—42no—
49C22×C7⋊C8—22no—
50C22×C7⋊C8—22no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95—21no—
55C7×#95—21no—
56C22⋊(C7⋊C8)—24no—
57#6377—42no—
58C4×C22⋊Q8D711yescharacteristic
59#1749—71no—
60#1728—71no—
61#1272—72no—
62#1271—72no—
63C24×C7C22⋊C411yescharacteristic
64C2×C7×Q8—21no—
65C2×C7×Q8—41no—
66C2×C7×Q8—41no—
67C2×C7×Q8M1612yescomplemented
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—22no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—22no—
78C22×C4×C7—21no—
79C22×C4×C7—21no—
80C22×C4×C7—41no—
81C22×C4×C7—41no—
82C22×C4×C7—41no—
83C22×C4×C7C22⋊C411yescharacteristic
84C22×C4×C7C22⋊C411yescharacteristic
85C22×C4×C7C22⋊C411yescharacteristic
86C22×C4×C7C22×C411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C7×C4⋊C4—24no—
90C7×C4⋊C4—21no—
91C7×C4⋊C4—41no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—42no—
94C7×C4⋊C4—41no—
95C7×C4⋊C4—41no—
96C7×C4⋊C4M1612yescomplemented
97C7×C22⋊C4—24no—
98C7×C22⋊C4—42no—
99C42×C7—22no—
100C42×C7—22no—
101C42×C7—41no—
102C42×C7—41no—
103C42×C7—42no—
104C42×C7—42no—
105#1136—48no—
106C2×C7⋊C8—24no—
107C2×C7⋊C8—24no—
108C2×C7⋊C8—42no—
109C2×C7⋊C8—42no—
110C2×C7⋊C8—42no—
111C2×C7⋊C8—42no—
112C22×M16—141no—
113C2×C22⋊Q8Dic711yescharacteristic
114C2×C4×Q8Dic711yescharacteristic
115C22×C42C2×D711yescharacteristic
116C2×C22⋊C8—141no—
117C2×#97—141no—
118#391C2×D711yescharacteristic
119#389C2×D711yescharacteristic
120#387—21no—
121#385—21no—
122#380Dic711yescharacteristic
123C4×C4⋊C4—21no—
124C4×C4⋊C4Dic711yescharacteristic
125C4×C22⋊C4—21no—
126#336—72no—
127#336—72no—
128#336—141no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7#10412yes—
136C23×C7C2×C22⋊C411yescharacteristic
137C7×Q8—42no—
138C7×Q8—42no—
139C2×C4×C7—24no—
140C2×C4×C7—24no—
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—22no—
152C2×C4×C7—22no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—44no—
157C2×C4×C7—42no—
158C2×C4×C7—42no—
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—41no—
169C2×C4×C7#9912yes—
170C2×C4×C7#10412yes—
171C2×C4×C7C2×M1611yescharacteristic
172C2×C4×C7C2×M1611yescharacteristic
173C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C7#13712yes—
175C2×C4×C7#13711yescharacteristic
176C7⋊C8—44no—
177C7⋊C8—44no—
178C22×Q8C2×Dic711yescharacteristic
179C23×C4C2×Dic711yescharacteristic
180C23×C4C22⋊D711yescharacteristic
181C23×C4C22⋊D711yescharacteristic
182C2×M16—144no—
183C2×M16—282no—
184C2×M16—282no—
185C22×C8—142no—
186C22×C8—142no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C4×Q8—42no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×Dic711yescharacteristic
194C2×C4⋊C4C2×Dic711yescharacteristic
195C2×C4⋊C4C2×Dic711yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—42no—
201C2×C42C2×Dic711yescharacteristic
202C2×C42C22⋊D711yescharacteristic
203C2×C42C22⋊D711yescharacteristic
204C2×C42C22×D711yescharacteristic
205C22⋊C8—144no—
206#97—282no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212C22×C7—22no—
213C22×C7—22no—
214C22×C7—22no—
215C22×C7—41no—
216C22×C7—41no—
217C22×C7—41no—
218C22×C7—41no—
219C22×C7#40711yescharacteristic
220C22×C7C2×#9911yescharacteristic
221C22×C7#41311yescharacteristic
222C22×C7#41711yescharacteristic
223C22×C7#41911yescharacteristic
224C22×C7C2×#10411yescharacteristic
225C22×C7C2×#10411yescharacteristic
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—21no—
229C4×C7—22no—
230C4×C7—21no—
231C4×C7—22no—
232C4×C7—22no—
233C4×C7—41no—
234C4×C7—42no—
235C4×C7—42no—
236C4×C7—81no—
237C4×C7—81no—
238C24C22⋊Dic711yescharacteristic
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8#113612yescomplemented
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C22⋊Dic711yescharacteristic
259C22×C4C22⋊Dic711yescharacteristic
260C22×C4C22⋊Dic711yescharacteristic
261C22×C4C22×Dic711yescharacteristic
262C22×C4C2×C22⋊D711yescharacteristic
263C22×C4C2×C22⋊D711yescharacteristic
264M16—288no—
265C2×C8—144no—
266C2×C8—144no—
267C2×C8—282no—
268C2×C8—282no—
269C2×C8—282no—
270C2×C8—282no—
271C4⋊C4—24no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4#113612yescomplemented
279C22⋊C4—24no—
280C22⋊C4—42no—
281C42—22no—
282C42—22no—
283C42—41no—
284C42—41no—
285C42—42no—
286C42—42no—
287C2×C7—42no—
288C2×C7#146511yescharacteristic
289C2×C7#148911yescharacteristic
290C2×C7#149111yescharacteristic
291C2×C7#150411yescharacteristic
292C2×C7#150811yescharacteristic
293C2×C7#152411yescharacteristic
294C2×C7#155911yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23#641112yes—
302C23C2×C22⋊Dic711yescharacteristic
303Q8—42no—
304Q8—42no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—44no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4#640812yes—
336C2×C4#641112yes—
337C2×C4C2×#113611yescharacteristic
338C2×C4C2×#113611yescharacteristic
339C2×C4#650512yes—
340C2×C4#651211yescharacteristic
341C2×C4#651411yescharacteristic
342C8—284no—
343C8—284no—
344C7#763411yescharacteristic, complemented, Sylow
345C22—22no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22#8997911yescharacteristic
353C22C2×#640811yescharacteristic
354C22#8999711yescharacteristic
355C22#9000411yescharacteristic
356C22C2×#641111yescharacteristic
357C22C2×#641111yescharacteristic
358C22#9000911yescharacteristic
359C4—22no—
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—42no—
368C4—42no—
369C4—81no—
370C4—81no—
371C2—42no—
372C2#1172935611yescharacteristic
373C2#1172937711yescharacteristic
374C2#1172939511yescharacteristic
375C2#1172944211yescharacteristic
376C2#1172946211yescharacteristic
377C2#1172950011yescharacteristic
378C2#1172958711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC4×C7×C22⋊Q8C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC4×C22⋊Q8D7
hypocenterC7#7634
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11725448C2semidirect
5. #11725444C2semidirect
67. C2×C7×Q8M16semidirect
96. C7×C4⋊C4M16semidirect
242. C2×Q8#1136semidirect
278. C4⋊C4#1136semidirect
344. C7#7634semidirect

Maximal subgroups

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

subgroupindex
C4×C7×C22⋊Q82
#117292832
#117292812
#117254482
#117254442
#76347