Finite Group Databasebeta

← #13241833

Subgroups — #13241833

Order 1792.

522 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2#11729285C211yesmaximal, characteristic
3C4×C22⋊(C7⋊C8)C211yesmaximal, 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#7583—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)—24no—
54C22⋊(C7⋊C8)—42no—
55C4×C7⋊C8—42no—
56C4×C22⋊Q8D711yescharacteristic
57#1817—71no—
58C4×C22⋊C8—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—22no—
70C22×C4×C7—22no—
71C22×C4×C7—22no—
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×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C2×C812yes—
82C22×C4×C7M1612yes—
83C22×C4×C7C22×C411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C7×C4⋊C4—24no—
87C7×C4⋊C4—21no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—42no—
91C7×C4⋊C4—42no—
92C7×C4⋊C4C2×C812yes—
93C7×C22⋊C4—24no—
94C7×C22⋊C4—42no—
95C42×C7—22no—
96C42×C7—22no—
97C42×C7—41no—
98C42×C7—41no—
99C42×C7—42no—
100C42×C7—42no—
101C2×C7⋊C8—24no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—42no—
105C2×C7⋊C8—42no—
106C2×C7⋊C8—42no—
107C2×C22⋊Q8Dic711yescharacteristic
108C2×C4×Q8Dic711yescharacteristic
109C22×C42C2×D711yescharacteristic
110C2×C22⋊C8—141no—
111C2×C22⋊C8—141no—
112C2×C4×C8—141no—
113#391C2×D711yescharacteristic
114#389C2×D711yescharacteristic
115#387—21no—
116#385—21no—
117#380Dic711yescharacteristic
118C4×C4⋊C4—21no—
119C4×C4⋊C4Dic711yescharacteristic
120C4×C22⋊C4—21no—
121#336—72no—
122#336—72no—
123#336—141no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7C22⋊C812yes—
131C23×C7C2×C22⋊C411yescharacteristic
132C7×Q8—42no—
133C7×Q8—42no—
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—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—42no—
149C2×C4×C7—42no—
150C2×C4×C7—44no—
151C2×C4×C7—44no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
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×C7C22⋊C812yes—
163C2×C4×C7#9912yes—
164C2×C4×C7#10412yes—
165C2×C4×C7C22×C811yescharacteristic
166C2×C4×C7C2×M1611yescharacteristic
167C2×C4×C7#13512yes—
168C2×C4×C7#13712yes—
169C7⋊C8—44no—
170C7⋊C8—82no—
171C22×Q8C2×Dic711yescharacteristic
172C23×C4C2×Dic711yescharacteristic
173C23×C4C22⋊D711yescharacteristic
174C23×C4C22⋊D711yescharacteristic
175C22×C8—142no—
176C22×C8—142no—
177C22⋊Q8—22no—
178C22⋊Q8C7⋊C814yescomplemented
179C4×Q8—42no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic711yescharacteristic
184C2×C4⋊C4C2×Dic711yescharacteristic
185C2×C4⋊C4C2×Dic711yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—42no—
191C2×C42C2×Dic711yescharacteristic
192C2×C42C22⋊D711yescharacteristic
193C2×C42C22⋊D711yescharacteristic
194C2×C42C22×D711yescharacteristic
195C22⋊C8—144no—
196C22⋊C8—282no—
197C4×C8—282no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203C22×C7—22no—
204C22×C7—22no—
205C22×C7—22no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7C2×C22⋊C811yescharacteristic
211C22×C7C2×#9911yescharacteristic
212C22×C7#41311yescharacteristic
213C22×C7#41611yescharacteristic
214C22×C7#41911yescharacteristic
215C22×C7C2×#10411yescharacteristic
216C22×C7#42111yescharacteristic
217C4×C7—22no—
218C4×C7—21no—
219C4×C7—21no—
220C4×C7—22no—
221C4×C7—22no—
222C4×C7—22no—
223C4×C7—22no—
224C4×C7—42no—
225C4×C7—42no—
226C4×C7—81no—
227C4×C7—81no—
228C24C22⋊Dic711yescharacteristic
229C2×Q8—21no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8C2×C7⋊C812yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C2×C7⋊C812yes—
246C22×C4#113612yes—
247C22×C4C22⋊Dic711yescharacteristic
248C22×C4C22⋊Dic711yescharacteristic
249C22×C4C22⋊Dic711yescharacteristic
250C22×C4C22×Dic711yescharacteristic
251C22×C4C2×C22⋊D711yescharacteristic
252C22×C4C2×C22⋊D711yescharacteristic
253C2×C8—144no—
254C2×C8—282no—
255C2×C8—282no—
256C2×C8—282no—
257C2×C8—282no—
258C2×C8—282no—
259C4⋊C4—24no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4C2×C7⋊C812yes—
266C22⋊C4—24no—
267C22⋊C4—42no—
268C42—22no—
269C42—22no—
270C42—41no—
271C42—41no—
272C42—42no—
273C42—42no—
274C2×C7—42no—
275C2×C7#145911yescharacteristic
276C2×C7#147611yescharacteristic
277C2×C7#147911yescharacteristic
278C2×C7#150811yescharacteristic
279C2×C7#151611yescharacteristic
280C2×C7#152911yescharacteristic
281C2×C7#155411yescharacteristic
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23C22⋊(C7⋊C8)12yes—
289C23C2×C22⋊Dic711yescharacteristic
290Q8—42no—
291Q8—42no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4C22⋊(C7⋊C8)12yes—
321C2×C4#640812yes—
322C2×C4#641112yes—
323C2×C4C22×C7⋊C811yescharacteristic
324C2×C4C2×#113611yescharacteristic
325C2×C4#650512yes—
326C2×C4#651312yes—
327C8—284no—
328C8—562no—
329C7#758311yescharacteristic, complemented, Sylow
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×C22⋊(C7⋊C8)11yescharacteristic
338C22C2×#640811yescharacteristic
339C22#8999711yescharacteristic
340C22#9000511yescharacteristic
341C22C2×#641111yescharacteristic
342C22#9000811yescharacteristic
343C22#9000911yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—42no—
353C4—81no—
354C4—81no—
355C2—42no—
356C2#1172935411yescharacteristic
357C2#1172937511yescharacteristic
358C2#1172939211yescharacteristic
359C2#1172944211yescharacteristic
360C2#1172946411yescharacteristic
361C2#1172950111yescharacteristic
362C2#1172958611yescharacteristic
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#7583
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
178. C22⋊Q8C7⋊C8semidirect
329. C7#7583semidirect

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
C4×C22⋊(C7⋊C8)2
#117254482
#117254442
#75837