Finite Group Databasebeta

← #13264327

Subgroups — #13264327

Order 1792.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2583C211yesmaximal, characteristic
2C2×#89325C211yesmaximal, characteristic
3#11729306C211yesmaximal, characteristic
4#11725456C212yesmaximal, complemented
5#11725454C212yesmaximal, complemented
6C2×C7×C22⋊Q8C411yescharacteristic
7C22×C7×C4⋊C4C2211yescharacteristic
8C22×#1136—21no—
9C7×#398C411yescharacteristic
10C7×#398C2211yescharacteristic
11C7×#395C411yescharacteristic
12C7×#395C2211yescharacteristic
13C7×#389—21no—
14C7×#389—21no—
15C7×#385—21no—
16C7×#385—21no—
17C4×C7×C22⋊C4C411yescharacteristic
18#89979—21no—
19#89325—21no—
20#89325C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11768—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C7×C22⋊Q8—41no—
29C7×C22⋊Q8—41no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—41no—
36C2×C7×C4⋊C4—41no—
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C7×C4⋊C4D411yescharacteristic
41C2×C7×C4⋊C4C2311yescharacteristic
42C2×C7×C22⋊C4—21no—
43C2×C7×C22⋊C4—21no—
44C2×C42×C7—21no—
45C2×#1136—24no—
46C2×#1136—22no—
47C2×#1136—41no—
48C2×#1136—42no—
49C2×#1136—41no—
50C22×C7⋊C8—41no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95—21no—
55C7×#95C2×C411yescharacteristic
56C7×#95C2×C411yescharacteristic
57C22⋊(C7⋊C8)—22no—
58C22⋊(C7⋊C8)—41no—
59#2583D711yescharacteristic
60C2×#343—71no—
61#1463—71no—
62#1354—72no—
63#1346—72no—
64C24×C7C22⋊C411yescharacteristic
65C2×C7×Q8—41no—
66C2×C7×Q8—81no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—22no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—21no—
80C22×C4×C7—81no—
81C22×C4×C7—81no—
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22⋊C411yescharacteristic
84C22×C4×C7C22⋊C411yescharacteristic
85C22×C4×C7C22×C411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—41no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—42no—
94C7×C4⋊C4—42no—
95C7×C4⋊C4—41no—
96C7×C4⋊C4—41no—
97C7×C4⋊C4—81no—
98C7×C4⋊C4—81no—
99C7×C22⋊C4—24no—
100C7×C22⋊C4—41no—
101C7×C22⋊C4—41no—
102C42×C7—81no—
103#1136—24no—
104#1136—44no—
105#1136—42no—
106#1136—82no—
107C2×C7⋊C8—44no—
108C2×C7⋊C8—42no—
109C2×C7⋊C8—42no—
110C22×M16—141no—
111C2×C22⋊Q8Dic711yescharacteristic
112C22×C4⋊C4C2×D711yescharacteristic
113#407—141no—
114#398Dic711yescharacteristic
115#398C2×D711yescharacteristic
116#395Dic711yescharacteristic
117#395C2×D711yescharacteristic
118#389—21no—
119#389—21no—
120#385—21no—
121#385—21no—
122C4×C22⋊C4Dic711yescharacteristic
123#343—72no—
124#343—141no—
125#324—72no—
126#324—141no—
127C23×C7—22no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—41no—
131C23×C7#9911yescharacteristic
132C23×C7#9911yescharacteristic
133C23×C7C2×C22⋊C411yescharacteristic
134C7×Q8—82no—
135C2×C4×C7—22no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
138C2×C4×C7—22no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—22no—
144C2×C4×C7—22no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—42no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
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×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—81no—
165C2×C4×C7—81no—
166C2×C4×C7—81no—
167C2×C4×C7#10412yes—
168C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C7#13711yescharacteristic
170C7⋊C8—44no—
171C7⋊C8—82no—
172C22×Q8C2×Dic711yescharacteristic
173C23×C4C2×Dic711yescharacteristic
174C23×C4C22⋊D711yescharacteristic
175C23×C4C22⋊D711yescharacteristic
176C2×M16—144no—
177C2×M16—142no—
178C2×M16—281no—
179C2×M16—282no—
180C2×M16—281no—
181C22×C8—281no—
182C22⋊Q8—41no—
183C22⋊Q8—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×Dic711yescharacteristic
192C2×C4⋊C4C2×Dic711yescharacteristic
193C2×C4⋊C4C22⋊D711yescharacteristic
194C2×C4⋊C4C22⋊D711yescharacteristic
195C2×C4⋊C4C22×D711yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42—21no—
199C22⋊C8—142no—
200C22⋊C8—281no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95C2×Dic711yescharacteristic
206#95C2×Dic711yescharacteristic
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—21no—
213C22×C7—21no—
214C22×C7—42no—
215C22×C7—42no—
216C22×C7#35612yes—
217C22×C7C2×#9911yescharacteristic
218C22×C7#41711yescharacteristic
219C22×C7C2×#10411yescharacteristic
220C4×C7—21no—
221C4×C7—22no—
222C4×C7—21no—
223C4×C7—42no—
224C4×C7—42no—
225C4×C7—41no—
226C4×C7—41no—
227C4×C7—41no—
228C4×C7—41no—
229C4×C7—81no—
230C4×C7—81no—
231C24C22⋊Dic711yescharacteristic
232C2×Q8—41no—
233C2×Q8—81no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4C22⋊Dic711yescharacteristic
250C22×C4C22⋊Dic711yescharacteristic
251C22×C4C22⋊Dic711yescharacteristic
252C22×C4C22×Dic711yescharacteristic
253C22×C4C2×C22⋊D711yescharacteristic
254C22×C4C2×C22⋊D711yescharacteristic
255M16—144no—
256M16—284no—
257M16—282no—
258M16—562no—
259C2×C8—284no—
260C2×C8—282no—
261C2×C8—282no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C22⋊C4—24no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—81no—
277C2×C7—21no—
278C2×C7—21no—
279C2×C7—22no—
280C2×C7—41no—
281C2×C7#150411yescharacteristic
282C2×C7#212111yescharacteristic
283C2×C7C2×#35611yescharacteristic
284C23—21no—
285C23—21no—
286C23—22no—
287C23—41no—
288C23#640811yescharacteristic
289C23#640811yescharacteristic
290C23C2×C22⋊Dic711yescharacteristic
291Q8—82no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
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×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4#641112yes—
325C2×C4#651211yescharacteristic
326C2×C4#651411yescharacteristic
327C8—284no—
328C8—562no—
329C7#1176811yescharacteristic, complemented, Sylow
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#8934312yes—
340C22C2×#640811yescharacteristic
341C22#9000411yescharacteristic
342C22C2×#641111yescharacteristic
343C4—21no—
344C4—22no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—41no—
358C2#1172946211yescharacteristic
359C2C2×#8934311yescharacteristic
360C2#1172960111yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2583C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2583D7
hypocenterC7#11768
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
4. #11725456C2semidirect
5. #11725454C2semidirect
329. C7#11768semidirect

Maximal subgroups

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

subgroupindex
C7×#25832
C2×#893252
#117293062
#117254562
#117254542
#117687