Finite Group Databasebeta

← #13263383

Subgroups — #13263383

Order 1792.

414 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739623C211yesmaximal, characteristic
2C7×#1463C211yesmaximal, characteristic
3C2×#89323C211yesmaximal, characteristic
4#11725261C212yesmaximal, complemented
5#11725259C212yesmaximal, complemented
6C22×C7×C4⋊C4C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C7×#407—21no—
9#89982—21no—
10#89982—21no—
11C4×C22⋊Dic7C411yescharacteristic
12C2×C22⋊(C7⋊C8)—21no—
13#89752—21no—
14#89752—21no—
15#89748C411yescharacteristic
16#89748C2211yescharacteristic
17#89746C411yescharacteristic
18#89746C2211yescharacteristic
19C7×#324—21no—
20C7×#324C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11555—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C2×C7×M16—41no—
29C2×C7×C4⋊C4—41no—
30C2×C7×C4⋊C4—41no—
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C7×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C4⋊Dic7C2×C411yescharacteristic
38#6487—41no—
39#6487—41no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×C4×Dic7C2×C411yescharacteristic
46C2×C4×Dic7C2×C411yescharacteristic
47C22×C7⋊C8—41no—
48C7×C22⋊C8—22no—
49C7×C22⋊C8—41no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C22⋊(C7⋊C8)—22no—
56C22⋊(C7⋊C8)—41no—
57#2502—71no—
58#1463D711yescharacteristic
59C2×#324—71no—
60#1325—72no—
61#1319—72no—
62C24×C7C22⋊C411yescharacteristic
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—22no—
70C22×C4×C7—41no—
71C22×C4×C7—81no—
72C22×C4×C7—81no—
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C2×Dic14—22no—
84C2×Dic14—41no—
85C2×Dic14—41no—
86C7×M16—82no—
87C2×C7×C8—42no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—41no—
92C22⋊Dic7—24no—
93C22⋊Dic7—41no—
94C22⋊Dic7—41no—
95C4⋊Dic7—41no—
96Dic7⋊C4—42no—
97Dic7⋊C4—81no—
98Dic7⋊C4—81no—
99Dic7⋊C4—81no—
100Dic7⋊C4—81no—
101C4×Dic7—22no—
102C4×Dic7—41no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—82no—
105C2×C22⋊Q8—71no—
106C22×C4⋊C4C2×D711yescharacteristic
107#407—21no—
108C2×C22⋊C8—141no—
109#398—141no—
110#398—141no—
111#391—71no—
112#391—71no—
113#385—141no—
114#385—141no—
115#384—71no—
116#384—71no—
117C4×C22⋊C4—71no—
118#324—21no—
119#324—72no—
120#324—141no—
121#324C2×D712yes—
122C23×C7—22no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—41no—
126C23×C7#9911yescharacteristic
127C23×C7#9911yescharacteristic
128C23×C7C2×C22⋊C411yescharacteristic
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—42no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—81no—
147C2×C4×C7—81no—
148C2×C4×C7#13112yes—
149C2×Dic7—22no—
150C2×Dic7—22no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161Dic14—82no—
162C7×C8—82no—
163C7⋊C8—82no—
164C22×Q8—71no—
165C23×C4C4×D711yescharacteristic
166C23×C4D2811yescharacteristic
167C23×C4C22⋊D711yescharacteristic
168C2×M16—41no—
169C22×C8—281no—
170C22⋊Q8—281no—
171C22⋊Q8—281no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—71no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4C4×D711yescharacteristic
181C2×C4⋊C4D2811yescharacteristic
182C2×C4⋊C4C22⋊D711yescharacteristic
183C2×C4⋊C4C22×D711yescharacteristic
184C2×C22⋊C4—141no—
185C2×C22⋊C4—141no—
186C2×C42—71no—
187C2×C42—71no—
188C22⋊C8—22no—
189C22⋊C8—41no—
190C22⋊C8—142no—
191C22⋊C8—281no—
192#95—141no—
193#95—141no—
194#95—141no—
195#95—141no—
196#95—141no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—42no—
205C22×C7—42no—
206C22×C7#35612yes—
207C22×C7#40811yescharacteristic
208C22×C7C2×#9911yescharacteristic
209C22×C7#41311yescharacteristic
210C4×C7—22no—
211C4×C7—41no—
212C4×C7—41no—
213C4×C7—41no—
214C4×C7—41no—
215C4×C7—41no—
216Dic7—42no—
217Dic7—42no—
218Dic7—81no—
219Dic7—81no—
220C24(C2×D7)⋊C411yescharacteristic
221C2×Q8—142no—
222C2×Q8—281no—
223C2×Q8—281no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—41no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4—141no—
237C22×C4—141no—
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4(C2×D7)⋊C411yescharacteristic
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4C2×C4×D711yescharacteristic
242C22×C4C2×D2811yescharacteristic
243C22×C4C2×C22⋊D711yescharacteristic
244M16—82no—
245C2×C8—42no—
246C2×C8—282no—
247C2×C8—562no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—281no—
253C4⋊C4—282no—
254C4⋊C4—561no—
255C4⋊C4—561no—
256C4⋊C4—561no—
257C4⋊C4—561no—
258C22⋊C4—144no—
259C22⋊C4—281no—
260C22⋊C4—281no—
261C42—142no—
262C42—281no—
263C2×C7—21no—
264C2×C7—21no—
265C2×C7—22no—
266C2×C7—41no—
267C2×C7#146811yescharacteristic
268C2×C7#212711yescharacteristic
269C2×C7C2×#35611yescharacteristic
270C23—21no—
271C23—21no—
272C23—22no—
273C23—41no—
274C23#638011yescharacteristic
275C23#638011yescharacteristic
276C23C2×(C2×D7)⋊C411yescharacteristic
277Q8—562no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—142no—
298C2×C4—142no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4#647012yes—
310C8—82no—
311C8—562no—
312C7#1155511yescharacteristic, complemented, Sylow
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22#8927312yes—
323C22C2×#638011yescharacteristic
324C22#8990111yescharacteristic
325C22#8990411yescharacteristic
326C4—22no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—282no—
333C4—282no—
334C4—561no—
335C4—561no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2#1172772311yescharacteristic
341C2#1172777311yescharacteristic
342C2C2×#8927311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1463C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1463D7
hypocenterC7#11555
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #11725261C2semidirect
5. #11725259C2semidirect
312. C7#11555semidirect

Maximal subgroups

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

subgroupindex
#117396232
C7×#14632
C2×#893232
#117252612
#117252592
#115557