Finite Group Databasebeta

← #13264927

Subgroups — #13264927

Order 1792.

452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#11739829C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725296C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6432C411yescharacteristic, complemented
7C2×C7×#99—21no—
8C7×#380—21no—
9#89993—21no—
10#89984—21no—
11#89984—21no—
12C2×C22⋊(C7⋊C8)—21no—
13#89749—21no—
14#89719C412yescomplemented
15#89719C2212yes—
16C4×C4⋊Dic7C411yescharacteristic, complemented
17C7×#342C2212yes—
18#89323—21no—
19#89320C2212yes—
20#11900—71nomaximal, Sylow
21C22×C7×D4D411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C22×Dic14C2×C412yes—
25C4×C7×D4—41no—
26C4×C7×D4—41no—
27C2×C7×C4⋊C4—41no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C22⋊C4—22no—
30C2×C7×C22⋊C4C2×C411yescharacteristic
31C2×C7×C22⋊C4C2311yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C22⋊Dic7—22no—
34C2×C22⋊Dic7—22no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4×Dic7—21no—
39C22×C7⋊C8—41no—
40#6432—41no—
41#6432—41no—
42C7×#99—42no—
43C7×#95—41no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C7⋊#95C2×C412yes—
47C22⋊(C7⋊C8)—22no—
48C22⋊(C7⋊C8)—41no—
49#2563—71no—
50#1799D711yescharacteristic
51#1459—71no—
52#1351—74no—
53C24×C7C22⋊C411yescharacteristic
54C24×C7C2×D411yescharacteristic
55C2×C7×D4—41no—
56C2×C7×D4—41no—
57C2×C7×D4SD1612yes—
58C2×C7×D4Q1612yes—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7—42no—
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22×C411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×Dic7—22no—
72C22×Dic7—22no—
73C2×Dic14—42no—
74C2×Dic14—82no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—82no—
77C7×C22⋊C4—41no—
78C7×C22⋊C4—41no—
79C7×C22⋊C4—42no—
80C7×C22⋊C4—42no—
81C42×C7—21no—
82C42×C7—21no—
83C22⋊Dic7—82no—
84C22⋊Dic7—82no—
85C4⋊Dic7—42no—
86C4⋊Dic7—42no—
87C4⋊Dic7—41no—
88C4⋊Dic7—41no—
89C4×Dic7—42no—
90C2×C7⋊C8—42no—
91C2×C7⋊C8—82no—
92C2×C4⋊Q8—71no—
93C2×C4×D4C2×D711yescharacteristic
94C2×#99—21no—
95C2×C22⋊C8—141no—
96#393—72no—
97#393—72no—
98#390—141no—
99#382—141no—
100#380—21no—
101#380—141no—
102#380—141no—
103C4×C4⋊C4—71no—
104#342C2×D712yes—
105#324—141no—
106#323—72no—
107C23×C7—21no—
108C23×C7—21no—
109C23×C7—21no—
110C23×C7—21no—
111C23×C7—41no—
112C23×C7—41no—
113C23×C7—41no—
114C23×C7—41no—
115C23×C7#10312yes—
116C23×C7C2×C22⋊C411yescharacteristic
117C23×C7C2×SD1611yescharacteristic
118C23×C7C2×Q1611yescharacteristic
119C7×D4—42no—
120C7×D4—42no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—22no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—42no—
128C2×C4×C7—42no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—81no—
133C2×C4×C7—81no—
134C2×C4×C7—82no—
135C2×C4×C7—82no—
136C2×C4×C7—82no—
137C2×C4×C7#9911yescharacteristic
138C2×C4×C7#9911yescharacteristic
139C2×C4×C7#10312yes—
140C2×Dic7—42no—
141C2×Dic7—42no—
142C2×Dic7—42no—
143C2×Dic7—42no—
144C2×Dic7—42no—
145C2×Dic7—42no—
146Dic14—84no—
147C7⋊C8—82no—
148C22×Q8—72no—
149C22×D4C22⋊D711yescharacteristic
150C23×C4D2811yescharacteristic
151C23×C4C22⋊D711yescharacteristic
152C22×C8—281no—
153C4⋊Q8—281no—
154C4⋊Q8—281no—
155C4×D4—41no—
156C4×D4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—141no—
159C2×C4⋊C4—141no—
160C2×C4⋊C4—141no—
161C2×C4⋊C4D2811yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4—142no—
164C2×C22⋊C4—142no—
165C2×C22⋊C4C4×D711yescharacteristic
166C2×C22⋊C4C22×D711yescharacteristic
167C2×C42—141no—
168C2×C42C4×D711yescharacteristic
169#99—42no—
170C22⋊C8—142no—
171C22⋊C8—281no—
172#95—41no—
173#95—72no—
174#95—142no—
175#95—142no—
176C22×C7—21no—
177C22×C7—21no—
178C22×C7—21no—
179C22×C7—22no—
180C22×C7—21no—
181C22×C7—42no—
182C22×C7—41no—
183C22×C7—41no—
184C22×C7—41no—
185C22×C7—41no—
186C22×C7—41no—
187C22×C7—41no—
188C22×C7—81no—
189C22×C7—81no—
190C22×C7C2×#9911yescharacteristic
191C22×C7C2×#10311yescharacteristic
192C22×C7#42111yescharacteristic
193C4×C7—21no—
194C4×C7—22no—
195C4×C7—41no—
196C4×C7—41no—
197C4×C7—41no—
198C4×C7—162no—
199C4×C7#35412yes—
200Dic7—82no—
201Dic7—82no—
202C24(C2×D7)⋊C411yescharacteristic
203C24C2×C22⋊D711yescharacteristic
204C2×Q8—282no—
205C2×Q8—562no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4#114212yes—
209C2×D4#114412yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—142no—
218C22×C4—142no—
219C22×C4(C2×D7)⋊C411yescharacteristic
220C22×C4(C2×D7)⋊C411yescharacteristic
221C22×C4(C2×D7)⋊C411yescharacteristic
222C22×C4C2×C4×D711yescharacteristic
223C22×C4C2×D2811yescharacteristic
224C2×C8—282no—
225C2×C8—562no—
226C4⋊C4—41no—
227C4⋊C4—82no—
228C4⋊C4—282no—
229C4⋊C4—282no—
230C4⋊C4—281no—
231C4⋊C4—281no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C22⋊C4—562no—
237C22⋊C4—562no—
238C42—21no—
239C42—21no—
240C42—282no—
241C2×C7—21no—
242C2×C7—21no—
243C2×C7—41no—
244C2×C7—42no—
245C2×C7—41no—
246C2×C7#152011yescharacteristic
247C2×C7#212211yescharacteristic
248C2×C7C2×#35411yescharacteristic
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#638412yes—
258C23C2×(C2×D7)⋊C411yescharacteristic
259C23C2×#114211yescharacteristic
260C23C2×#114411yescharacteristic
261Q8—564no—
262D4—42no—
263D4—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—282no—
281C2×C4—282no—
282C2×C4—282no—
283C2×C4—282no—
284C2×C4—282no—
285C2×C4—282no—
286C2×C4#638011yescharacteristic
287C2×C4#638011yescharacteristic
288C2×C4#638412yes—
289C8—562no—
290C7#1190011yescharacteristic, complemented, Sylow
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—41no—
297C22—41no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22—81no—
305C22C2×#638011yescharacteristic
306C22C2×#638411yescharacteristic
307C22#8977711yescharacteristic
308C4—21no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—162no—
314C4—562no—
315C4—562no—
316C4#8926812yes—
317C2—21no—
318C2—21no—
319C2—41no—
320C2—41no—
321C2—42no—
322C2#1172726411yescharacteristic
323C2C2×#8926811yescharacteristic
324C2#1172781111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1799C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1799D7
hypocenterC7#11900
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
4. #11725296C2semidirect
6. C2×#6432C4semidirect
14. #89719C4semidirect
16. C4×C4⋊Dic7C4semidirect
290. C7#11900semidirect

Maximal subgroups

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

subgroupindex
#117398292
C7×#17992
#117293542
#117252962
#119007