Finite Group Databasebeta

← #13264607

Subgroups — #13264607

Order 1792.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2395C211yesmaximal, characteristic
2#11729371C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725458C212yesmaximal, complemented
5#11725456C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×C7×#117C411yescharacteristic
8C7×#400C2211yescharacteristic
9C7×#399C411yescharacteristic
10C7×#398C2211yescharacteristic
11C7×#397—21no—
12C7×#397C411yescharacteristic
13C7×#394—21no—
14C4×C7×C4⋊C4—21no—
15C4×C7×C22⋊C4—21no—
16C4×C7×C22⋊C4C411yescharacteristic
17C2×#6407—21no—
18#89979—21no—
19#89696—21no—
20#89325C2212yes—
21#89323C2212yes—
22#89320—21no—
23#11830—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C4×C7×D4—41no—
28C4×C7×D4—41no—
29C7×#117—41no—
30C7×#117—41no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2311yescharacteristic
36C2×C7×C22⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4—21no—
40C2×C7×C22⋊C4C2×C411yescharacteristic
41C2×C7×C22⋊C4D411yescharacteristic
42C2×C42×C7—21no—
43C2×C42×C7—21no—
44C2×C42×C7D411yescharacteristic
45C2×#1136—22no—
46C2×#1136—41no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95C2×C411yescharacteristic
52C7×#95C2×C411yescharacteristic
53#6407—42no—
54C22⋊(C7⋊C8)—22no—
55C22⋊(C7⋊C8)—41no—
56C4⋊(C7⋊C8)—41no—
57C4⋊(C7⋊C8)—41no—
58#2395D711yescharacteristic
59#1800—71no—
60#1465—71no—
61#1353—72no—
62#1346—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C22⋊C411yescharacteristic
65C2×C7×D4—21no—
66C2×C7×D4—21no—
67C2×C7×D4—41no—
68C2×C7×D4—41no—
69C22×C4×C7—21no—
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—42no—
78C22×C4×C7—42no—
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22×C411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—42no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C22⋊C4—41no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—42no—
93C7×C22⋊C4—42no—
94C7×C22⋊C4—42no—
95C7×C22⋊C4—42no—
96C42×C7—21no—
97C42×C7—21no—
98C42×C7—42no—
99C42×C7—41no—
100C42×C7—41no—
101#1136—42no—
102#1136—42no—
103#1136—82no—
104C2×C7⋊C8—42no—
105C2×C7⋊C8—42no—
106C2×C4×D4C2×D711yescharacteristic
107C2×#117Dic711yescharacteristic
108#423—141no—
109C2×#100—141no—
110#407—141no—
111#400C2×D711yescharacteristic
112#399Dic711yescharacteristic
113#398C2×D711yescharacteristic
114#397—21no—
115#397Dic711yescharacteristic
116#394—21no—
117C4×C4⋊C4—21no—
118C4×C22⋊C4—21no—
119C4×C22⋊C4Dic711yescharacteristic
120#343—72no—
121#324—72no—
122#323—141no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7C2×C22⋊C411yescharacteristic
134C7×D4—42no—
135C7×D4—42no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—22no—
139C2×C4×C7—22no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—42no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
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—81no—
161C2×C4×C7#9911yescharacteristic
162C2×C4×C7#9911yescharacteristic
163C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C7#13711yescharacteristic
165C7⋊C8—82no—
166C7⋊C8—82no—
167C22×D4C22⋊D711yescharacteristic
168C23×C4C2×Dic711yescharacteristic
169C23×C4C22⋊D711yescharacteristic
170C2×M16—142no—
171C2×M16—281no—
172C4×D4—41no—
173C4×D4—41no—
174#117—41no—
175#117—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×Dic711yescharacteristic
179C2×C4⋊C4C2×Dic711yescharacteristic
180C2×C4⋊C4C22×D711yescharacteristic
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4C2×Dic711yescharacteristic
186C2×C22⋊C4C22⋊D711yescharacteristic
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C22⋊D711yescharacteristic
190C4⋊C8—281no—
191C4⋊C8—281no—
192#100—282no—
193C22⋊C8—142no—
194C22⋊C8—281no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95C2×Dic711yescharacteristic
200#95C2×Dic711yescharacteristic
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—42no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—81no—
211C22×C7—81no—
212C22×C7—81no—
213C22×C7C2×#9911yescharacteristic
214C22×C7#41711yescharacteristic
215C22×C7#42111yescharacteristic
216C4×C7—21no—
217C4×C7—21no—
218C4×C7—21no—
219C4×C7—42no—
220C4×C7—41no—
221C4×C7—41no—
222C4×C7—41no—
223C4×C7—81no—
224C4×C7—81no—
225C4×C7—81no—
226C4×C7#35212yes—
227C24C22⋊Dic711yescharacteristic
228C24C22⋊Dic711yescharacteristic
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—41no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C22⋊Dic711yescharacteristic
244C22×C4C22⋊Dic711yescharacteristic
245C22×C4C22×Dic711yescharacteristic
246C22×C4C2×C22⋊D711yescharacteristic
247C22×C4C2×C22⋊D711yescharacteristic
248M16—282no—
249M16—282no—
250M16—562no—
251C2×C8—282no—
252C2×C8—282no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C42—21no—
266C42—21no—
267C42—42no—
268C42—41no—
269C42—41no—
270C2×C7—21no—
271C2×C7—21no—
272C2×C7—81no—
273C2×C7—81no—
274C2×C7#151311yescharacteristic
275C2×C7C2×#35211yescharacteristic
276C2×C7#213211yescharacteristic
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊Dic711yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4#640811yescharacteristic
316C2×C4#640811yescharacteristic
317C2×C4#651211yescharacteristic
318C2×C4#651411yescharacteristic
319C8—562no—
320C8—562no—
321C7#1183011yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C2×#640811yescharacteristic
335C22#9000411yescharacteristic
336C22#9000811yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4#8933412yes—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—81no—
352C2C2×#8933411yescharacteristic
353C2#1172946311yescharacteristic
354C2#1172957411yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2395C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C4⋊C4C23
hypercenter#2395D7
hypocenterC7#11830
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2395

Complements

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

NH ≅ G/Ntype
4. #11725458C2semidirect
5. #11725456C2semidirect
321. C7#11830semidirect

Maximal subgroups

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

subgroupindex
C7×#23952
#117293712
#117293562
#117254582
#117254562
#118307