Finite Group Databasebeta

← #13241906

Subgroups — #13241906

Order 1792.

504 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2#11729285C211yesmaximal, characteristic
3#11729284C211yesmaximal, characteristic
4#11725448C212yesmaximal, complemented
5#11725444C212yesmaximal, complemented
6C2×C7×C22⋊Q8C411yescharacteristic
7C2×C4×C7×Q8C411yescharacteristic
8C22×C42×C7C2211yescharacteristic
9C7×#391C2211yescharacteristic
10C7×#389C2211yescharacteristic
11C7×#387—21no—
12C7×#385—21no—
13C7×#380C411yescharacteristic
14C4×C7×C4⋊C4—21no—
15C4×C7×C4⋊C4C411yescharacteristic
16C4×C7×C22⋊C4—21no—
17C2×C22⋊(C7⋊C8)—21no—
18C2×C22⋊(C7⋊C8)—21no—
19C2×C4⋊(C7⋊C8)—21no—
20#89319—21no—
21#89319C2212yes—
22#89319C2212yes—
23#7600—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C7×C22⋊Q8—22no—
29C7×C22⋊Q8C814yescomplemented
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
46C22×C7⋊C8—22no—
47C22×C7⋊C8—22no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95—21no—
53C22⋊(C7⋊C8)—42no—
54C22⋊(C7⋊C8)—42no—
55C4⋊(C7⋊C8)—42no—
56C4×C22⋊Q8D711yescharacteristic
57#1817—71no—
58#1797—71no—
59#1272—72no—
60#1271—72no—
61C24×C7C22⋊C411yescharacteristic
62C2×C7×Q8—21no—
63C2×C7×Q8—41no—
64C2×C7×Q8—41no—
65C2×C7×Q8C2×C812yes—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—22no—
69C22×C4×C7—21no—
70C22×C4×C7—22no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—41no—
75C22×C4×C7—41no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7—41no—
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C2×C812yes—
83C22×C4×C7M1612yes—
84C22×C4×C7C22×C411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C7×C4⋊C4—24no—
88C7×C4⋊C4—21no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—42no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4C2×C812yes—
95C7×C22⋊C4—24no—
96C7×C22⋊C4—42no—
97C42×C7—22no—
98C42×C7—22no—
99C42×C7—41no—
100C42×C7—41no—
101C42×C7—42no—
102C42×C7—42no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—42no—
105C2×C7⋊C8—42no—
106C2×C7⋊C8—42no—
107C2×C7⋊C8—42no—
108C2×C7⋊C8—42no—
109C2×C22⋊Q8Dic711yescharacteristic
110C2×C4×Q8Dic711yescharacteristic
111C22×C42C2×D711yescharacteristic
112C2×C4⋊C8—141no—
113C2×C22⋊C8—141no—
114C2×C22⋊C8—141no—
115#391C2×D711yescharacteristic
116#389C2×D711yescharacteristic
117#387—21no—
118#385—21no—
119#380Dic711yescharacteristic
120C4×C4⋊C4—21no—
121C4×C4⋊C4Dic711yescharacteristic
122C4×C22⋊C4—21no—
123#336—72no—
124#336—72no—
125#336—141no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7C22⋊C812yes—
133C23×C7C2×C22⋊C411yescharacteristic
134C7×Q8—42no—
135C7×Q8—42no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
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—22no—
147C2×C4×C7—22no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—42no—
152C2×C4×C7—42no—
153C2×C4×C7—44no—
154C2×C4×C7—42no—
155C2×C4×C7—42no—
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×C7C22⋊C812yes—
167C2×C4×C7#9912yes—
168C2×C4×C7C22×C811yescharacteristic
169C2×C4×C7C2×M1611yescharacteristic
170C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C7#13712yes—
172C2×C4×C7#13711yescharacteristic
173C7⋊C8—82no—
174C7⋊C8—82no—
175C22×Q8C2×Dic711yescharacteristic
176C23×C4C2×Dic711yescharacteristic
177C23×C4C22⋊D711yescharacteristic
178C23×C4C22⋊D711yescharacteristic
179C22×C8—142no—
180C22×C8—142no—
181C22⋊Q8—22no—
182C22⋊Q8C7⋊C814yescomplemented
183C4×Q8—42no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×Dic711yescharacteristic
188C2×C4⋊C4C2×Dic711yescharacteristic
189C2×C4⋊C4C2×Dic711yescharacteristic
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—42no—
195C2×C42C2×Dic711yescharacteristic
196C2×C42C22⋊D711yescharacteristic
197C2×C42C22⋊D711yescharacteristic
198C2×C42C22×D711yescharacteristic
199C4⋊C8—282no—
200C22⋊C8—282no—
201C22⋊C8—282no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207C22×C7—22no—
208C22×C7—22no—
209C22×C7—22no—
210C22×C7—41no—
211C22×C7—41no—
212C22×C7—41no—
213C22×C7—41no—
214C22×C7C2×C22⋊C811yescharacteristic
215C22×C7C2×#9911yescharacteristic
216C22×C7#41311yescharacteristic
217C22×C7#41711yescharacteristic
218C22×C7#41911yescharacteristic
219C22×C7#42111yescharacteristic
220C22×C7#42111yescharacteristic
221C4×C7—22no—
222C4×C7—21no—
223C4×C7—21no—
224C4×C7—22no—
225C4×C7—22no—
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—42no—
229C4×C7—42no—
230C4×C7—41no—
231C4×C7—81no—
232C4×C7—81no—
233C24C22⋊Dic711yescharacteristic
234C2×Q8—21no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8C2×C7⋊C812yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×C7⋊C812yes—
252C22×C4#113612yes—
253C22×C4C22⋊Dic711yescharacteristic
254C22×C4C22⋊Dic711yescharacteristic
255C22×C4C22⋊Dic711yescharacteristic
256C22×C4C22×Dic711yescharacteristic
257C22×C4C2×C22⋊D711yescharacteristic
258C22×C4C2×C22⋊D711yescharacteristic
259C2×C8—282no—
260C2×C8—282no—
261C2×C8—282no—
262C2×C8—282no—
263C2×C8—282no—
264C2×C8—282no—
265C4⋊C4—24no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4C2×C7⋊C812yes—
273C22⋊C4—24no—
274C22⋊C4—42no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—42no—
280C42—42no—
281C2×C7—42no—
282C2×C7#145911yescharacteristic
283C2×C7#147711yescharacteristic
284C2×C7#147911yescharacteristic
285C2×C7#151111yescharacteristic
286C2×C7#151311yescharacteristic
287C2×C7#153511yescharacteristic
288C2×C7#155911yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C22⋊(C7⋊C8)12yes—
296C23C2×C22⋊Dic711yescharacteristic
297Q8—42no—
298Q8—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4C22⋊(C7⋊C8)12yes—
330C2×C4#640812yes—
331C2×C4C22×C7⋊C811yescharacteristic
332C2×C4C2×#113611yescharacteristic
333C2×C4#650512yes—
334C2×C4#651211yescharacteristic
335C2×C4#651411yescharacteristic
336C8—562no—
337C8—562no—
338C7#760011yescharacteristic, complemented, Sylow
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×C22⋊(C7⋊C8)11yescharacteristic
347C22C2×#640811yescharacteristic
348C22#8999711yescharacteristic
349C22#9000411yescharacteristic
350C22#9000811yescharacteristic
351C22#9000811yescharacteristic
352C22#9000911yescharacteristic
353C4—22no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—42no—
362C4—42no—
363C4—81no—
364C4—81no—
365C2—42no—
366C2#1172935411yescharacteristic
367C2#1172937511yescharacteristic
368C2#1172939311yescharacteristic
369C2#1172944311yescharacteristic
370C2#1172946311yescharacteristic
371C2#1172950311yescharacteristic
372C2#1172958711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC2×C4×C7C22×C8
FrattiniC2×C42C22×D7
FittingC4×C7×C22⋊Q8C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC4×C22⋊Q8D7
hypocenterC7#7600
LCSG ▷ C2×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
29. C7×C22⋊Q8C8semidirect
182. C22⋊Q8C7⋊C8semidirect
338. C7#7600semidirect

Maximal subgroups

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

subgroupindex
C4×C7×C22⋊Q82
#117292852
#117292842
#117254482
#117254442
#76007