Finite Group Databasebeta

← #13264136

Subgroups — #13264136

Order 1792.

470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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#11739793C211yesmaximal, characteristic
2C7×#1459C211yesmaximal, characteristic
3C4×#6408C211yesmaximal, characteristic
4#11725256C212yesmaximal, complemented
5#11725255C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×C4×Dic14C411yescharacteristic, complemented
8C2×C7×C22⋊C8—21no—
9#89994—21no—
10C2×#6408—21no—
11C4×C22⋊Dic7—21no—
12C4×C22⋊Dic7—21no—
13C4×C22⋊Dic7—21no—
14#89754—21no—
15#89725C411yescharacteristic, complemented
16#89725C2211yescharacteristic
17#89719C411yescharacteristic, complemented
18#89719C2211yescharacteristic
19#89704C411yescharacteristic, complemented
20C7×#324—21no—
21C7×#323C2212yes—
22#89321C2212yes—
23#11728—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C22×C7×C8—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⋊Dic7C2×C411yescharacteristic
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7—21no—
43C2×C4×Dic7—21no—
44C2×C4×Dic7—41no—
45C4×Dic14—41no—
46C4×Dic14—41no—
47C7×C22⋊C8—22no—
48C7×C22⋊C8—41no—
49#6408—24no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—41no—
56C7⋊#95C2×C411yescharacteristic
57C7⋊#95C2×C411yescharacteristic
58#2398—71no—
59C4×#99—71no—
60#1459D711yescharacteristic
61#1351—72no—
62#1344—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—42no—
73C22×C4×C7—42no—
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—
86C2×C7×C8—42no—
87C2×C7×C8—82no—
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—42no—
98C22⋊Dic7—42no—
99C4⋊Dic7—41no—
100Dic7⋊C4—42no—
101C4×Dic7—42no—
102C4×Dic7—41no—
103C4×Dic7—41no—
104C4×Dic7—82no—
105C2×C4×Q8—71no—
106C2×C4×D4C2×D711yescharacteristic
107C2×#99—141no—
108C2×C22⋊C8—21no—
109#400—141no—
110#397—71no—
111#397—71no—
112#394—141no—
113#393—71no—
114#393—71no—
115C4×C22⋊C4—141no—
116C4×C22⋊C4—141no—
117C4×C22⋊C4—141no—
118#376—71no—
119#342—72no—
120#324—21no—
121#323C2×D712yes—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—41no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7#10412yes—
131C23×C7C2×C22⋊C411yescharacteristic
132C23×C7#13512yes—
133C7×D4—44no—
134C2×C4×C7—22no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—81no—
147C2×C4×C7—81no—
148C2×C4×C7#9911yescharacteristic
149C2×C4×C7#9911yescharacteristic
150C2×Dic7—22no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—44no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—82no—
164C2×Dic7—82no—
165Dic14—42no—
166Dic14—42no—
167C7×C8—82no—
168C22×Q8—71no—
169C22×D4D2811yescharacteristic
170C23×C4D2811yescharacteristic
171C23×C4C22⋊D711yescharacteristic
172C22×C8—41no—
173C4×Q8—281no—
174C4×Q8—281no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—71no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4C22⋊D711yescharacteristic
180C2×C22⋊C4—142no—
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4C4×D711yescharacteristic
186C2×C22⋊C4C22×D711yescharacteristic
187C2×C42—141no—
188C2×C42—141no—
189C2×C42—281no—
190C2×C42C4×D711yescharacteristic
191#99—144no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194#95—71no—
195#95—71no—
196#95—141no—
197#95—141no—
198#95—141no—
199#95—141no—
200#95—141no—
201#95—281no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—22no—
205C22×C7—22no—
206C22×C7—42no—
207C22×C7—42no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—41no—
211C22×C7—41no—
212C22×C7—81no—
213C22×C7—81no—
214C22×C7C2×#9911yescharacteristic
215C22×C7#41611yescharacteristic
216C22×C7C2×#10411yescharacteristic
217C4×C7—21no—
218C4×C7—41no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—41no—
222C4×C7#35412yes—
223Dic7—42no—
224Dic7—81no—
225Dic7—81no—
226Dic7—84no—
227Dic7—81no—
228C24(C2×D7)⋊C411yescharacteristic
229C24C2×D2811yescharacteristic
230C2×Q8—281no—
231C2×Q8—282no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—141no—
242C22×C4—141no—
243C22×C4—141no—
244C22×C4—141no—
245C22×C4—282no—
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4(C2×D7)⋊C411yescharacteristic
249C22×C4C2×C4×D711yescharacteristic
250C22×C4C2×C22⋊D711yescharacteristic
251C2×C8—42no—
252C2×C8—82no—
253C4⋊C4—41no—
254C4⋊C4—281no—
255C4⋊C4—282no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—144no—
259C22⋊C4—282no—
260C22⋊C4—282no—
261C22⋊C4—282no—
262C22⋊C4—282no—
263C22⋊C4—282no—
264C42—21no—
265C42—21no—
266C42—282no—
267C42—281no—
268C42—281no—
269C42—562no—
270C2×C7—21no—
271C2×C7—21no—
272C2×C7—42no—
273C2×C7—42no—
274C2×C7#150111yescharacteristic
275C2×C7#212011yescharacteristic
276C2×C7C2×#35411yescharacteristic
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#639912yes—
286C23#646712yes—
287C23C2×(C2×D7)⋊C411yescharacteristic
288Q8—282no—
289Q8—282no—
290D4—44no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—142no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—284no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—562no—
319C2×C4—562no—
320C2×C4#638011yescharacteristic
321C2×C4#638011yescharacteristic
322C8—82no—
323C7#1172811yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×#638011yescharacteristic
337C22#8988511yescharacteristic
338C22C2×#639911yescharacteristic
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—282no—
345C4—561no—
346C4—561no—
347C4—564no—
348C4—561no—
349C4#8926812yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2#1172769611yescharacteristic
355C2C2×#8926811yescharacteristic
356C2#1172789911yescharacteristic
subgroupG/H
centerC2×C4#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1459C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1459D7
hypocenterC7#11728
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #11725256C2semidirect
5. #11725255C2semidirect
7. C2×C4×Dic14C4semidirect
15. #89725C4semidirect
17. #89719C4semidirect
19. #89704C4semidirect
323. C7#11728semidirect

Maximal subgroups

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

subgroupindex
#117397932
C7×#14592
C4×#64082
#117252562
#117252552
#117287