Finite Group Databasebeta

← #13264402

Subgroups — #13264402

Order 1792.

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

normal subgroups only

This group has 460 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#11739833C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3C4×#6408C211yesmaximal, characteristic
4#11725257C212yesmaximal, complemented
5#11725255C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×C4×Dic14C411yescharacteristic, complemented
8C7×#407—21no—
9#89993—21no—
10C2×#6408—21no—
11#89982—21no—
12#89982—21no—
13C4×C22⋊Dic7—21no—
14#89745—21no—
15#89721C411yescharacteristic, complemented
16#89721C2211yescharacteristic
17#89719C411yescharacteristic, complemented
18#89719C2211yescharacteristic
19#89708C411yescharacteristic, complemented
20C7×#324—21no—
21C7×#323C2212yes—
22#89321C2212yes—
23#11784—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C2×C7×M16—41no—
29C4×C7×D4—41no—
30C4×C7×D4—41no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C22⋊C4C2×C411yescharacteristic
33C2×C7×C22⋊C4C2311yescharacteristic
34C2×C42×C7C2×C411yescharacteristic
35C2×C22⋊Dic7—22no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C22⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×C4×Dic7—21no—
46C2×C4×Dic7—41no—
47C4×Dic14—41no—
48C4×Dic14—41no—
49C7×C22⋊C8—22no—
50C7×C22⋊C8—41no—
51#6408—24no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—41no—
56C7⋊#95C2×C411yescharacteristic
57C7⋊#95C2×C411yescharacteristic
58#2580—71no—
59C4×#99—71no—
60#1465D711yescharacteristic
61#1352—72no—
62#1351—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C2×C7×D4—22no—
66C2×C7×D4—22no—
67C2×C7×D4—41no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—81no—
73C22×C4×C7—81no—
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—42no—
84C2×Dic14—41no—
85C2×Dic14—42no—
86C7×M16—82no—
87C2×C7×C8—42no—
88C7×C4⋊C4—41no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—41no—
91C42×C7—21no—
92C42×C7—21no—
93C22⋊Dic7—24no—
94C22⋊Dic7—42no—
95C22⋊Dic7—42no—
96C22⋊Dic7—42no—
97C22⋊Dic7—81no—
98C22⋊Dic7—81no—
99C4⋊Dic7—42no—
100C4⋊Dic7—41no—
101Dic7⋊C4—41no—
102Dic7⋊C4—41no—
103Dic7⋊C4—81no—
104Dic7⋊C4—81no—
105C4×Dic7—42no—
106C4×Dic7—82no—
107C2×C4×Q8—71no—
108C2×C4×D4C2×D711yescharacteristic
109C2×#99—141no—
110#407—21no—
111#399—71no—
112#399—71no—
113#393—71no—
114#393—71no—
115#390—141no—
116#389—141no—
117#385—141no—
118#385—141no—
119#382—71no—
120C4×C22⋊C4—141no—
121#342—72no—
122#324—21no—
123#323C2×D712yes—
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
134C23×C7#13712yes—
135C7×D4—44no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—41no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—81no—
148C2×C4×C7—81no—
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7#10412yes—
152C2×Dic7—22no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—44no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—82no—
166C2×Dic7—82no—
167Dic14—42no—
168Dic14—42no—
169C7×C8—82no—
170C22×Q8—71no—
171C22×D4D2811yescharacteristic
172C23×C4D2811yescharacteristic
173C23×C4C22⋊D711yescharacteristic
174C2×M16—41no—
175C4×Q8—281no—
176C4×Q8—281no—
177C4×D4—41no—
178C4×D4—41no—
179C2×C4⋊C4—71no—
180C2×C4⋊C4—141no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4C22⋊D711yescharacteristic
185C2×C22⋊C4—142no—
186C2×C22⋊C4—141no—
187C2×C22⋊C4—141no—
188C2×C22⋊C4—141no—
189C2×C22⋊C4—141no—
190C2×C22⋊C4C4×D711yescharacteristic
191C2×C22⋊C4C22×D711yescharacteristic
192C2×C42—141no—
193C2×C42—281no—
194C2×C42C4×D711yescharacteristic
195#99—144no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198#95—71no—
199#95—71no—
200#95—141no—
201#95—141no—
202#95—141no—
203#95—281no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—22no—
207C22×C7—42no—
208C22×C7—42no—
209C22×C7—41no—
210C22×C7—41no—
211C22×C7—41no—
212C22×C7—41no—
213C22×C7—41no—
214C22×C7—81no—
215C22×C7—81no—
216C22×C7C2×#9911yescharacteristic
217C22×C7#41911yescharacteristic
218C22×C7C2×#10411yescharacteristic
219C4×C7—21no—
220C4×C7—21no—
221C4×C7—22no—
222C4×C7—41no—
223C4×C7—41no—
224C4×C7—41no—
225Dic7—42no—
226Dic7—81no—
227Dic7—81no—
228Dic7—84no—
229Dic7—81no—
230C24(C2×D7)⋊C411yescharacteristic
231C24C2×D2811yescharacteristic
232C2×Q8—281no—
233C2×Q8—282no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4—141no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4—282no—
248C22×C4(C2×D7)⋊C411yescharacteristic
249C22×C4(C2×D7)⋊C411yescharacteristic
250C22×C4(C2×D7)⋊C411yescharacteristic
251C22×C4C2×C4×D711yescharacteristic
252C22×C4C2×C22⋊D711yescharacteristic
253M16—82no—
254C2×C8—42no—
255C4⋊C4—41no—
256C4⋊C4—281no—
257C4⋊C4—281no—
258C4⋊C4—281no—
259C4⋊C4—282no—
260C4⋊C4—561no—
261C4⋊C4—561no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—144no—
265C22⋊C4—282no—
266C22⋊C4—282no—
267C22⋊C4—282no—
268C22⋊C4—561no—
269C22⋊C4—561no—
270C42—21no—
271C42—21no—
272C42—282no—
273C42—562no—
274C2×C7—21no—
275C2×C7—21no—
276C2×C7—42no—
277C2×C7—81no—
278C2×C7#150811yescharacteristic
279C2×C7#212011yescharacteristic
280C2×C7#212711yescharacteristic
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#647212yes—
291C23C2×(C2×D7)⋊C411yescharacteristic
292Q8—282no—
293Q8—282no—
294D4—44no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—142no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—284no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4—562no—
322C2×C4—562no—
323C2×C4#638011yescharacteristic
324C2×C4#638011yescharacteristic
325C2×C4#639912yes—
326C8—82no—
327C7#1178411yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#638011yescharacteristic
341C22#8989211yescharacteristic
342C22C2×#639911yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—282no—
350C4—561no—
351C4—561no—
352C4—564no—
353C4—561no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#1172773411yescharacteristic
359C2#1172777311yescharacteristic
360C2#1172789911yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1465C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1465D7
hypocenterC7#11784
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725257C2semidirect
5. #11725255C2semidirect
7. C2×C4×Dic14C4semidirect
15. #89721C4semidirect
17. #89719C4semidirect
19. #89708C4semidirect
327. C7#11784semidirect

Maximal subgroups

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

subgroupindex
#117398332
C7×#14652
C4×#64082
#117252572
#117252552
#117847