Finite Group Databasebeta

← #13247358

Subgroups — #13247358

Order 1792.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#11739781C211yesmaximal, characteristic
2C7×#1459C211yesmaximal, characteristic
3#11729373C211yesmaximal, characteristic
4#11725482C212yesmaximal, complemented
5#11725481C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×C7×C22⋊C8C2212yes—
8#89992—21no—
9C2×#6408—21no—
10#89984C2212yes—
11#89984C2211yescharacteristic
12#89983C411yescharacteristic, complemented
13C4×C22⋊Dic7C411yescharacteristic, complemented
14C2×C7⋊#95C2211yescharacteristic
15#89753—21no—
16#89723—21no—
17C22⋊C4×Dic7—21no—
18#89709C411yescharacteristic, complemented
19#89704C411yescharacteristic, complemented
20C7×#324—21no—
21C7×#323—21no—
22#89321—21no—
23#8763—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C23×Dic7—21no—
28C22×C7×C8—22no—
29C4×C7×D4—22no—
30C4×C7×D4—22no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C42×C7C2×C411yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—22no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7—22no—
41C2×C4×Dic7—21no—
42C2×C4×Dic7—21no—
43C7×C22⋊C8—22no—
44C7×C22⋊C8—22no—
45#6408—42no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—22no—
52C7⋊#95C2×C411yescharacteristic
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56#2353—71no—
57#1799—71no—
58#1459D711yescharacteristic
59#1294—72no—
60#1289—72no—
61C24×C7C22⋊C411yescharacteristic
62C24×C7C2×D411yescharacteristic
63C2×C7×D4—22no—
64C2×C7×D4—22no—
65C2×C7×D4—21no—
66C2×C7×D4—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—81no—
70C22×C4×C7—81no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22×C411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7#4112yes—
77C22×C4×C7#4112yes—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—42no—
83C22×Dic7—42no—
84C22×Dic7—42no—
85C22×Dic7—81no—
86C2×C7×C8—42no—
87C2×C7×C8—82no—
88C7×C4⋊C4—22no—
89C7×C22⋊C4—22no—
90C7×C22⋊C4—22no—
91C42×C7—21no—
92C42×C7—21no—
93C22⋊Dic7—42no—
94C22⋊Dic7—41no—
95C22⋊Dic7—41no—
96C22⋊Dic7—42no—
97C22⋊Dic7—42no—
98C22⋊Dic7—81no—
99C4⋊Dic7—81no—
100C4⋊Dic7—82no—
101C4×Dic7—42no—
102C4×Dic7—81no—
103C2×C4×D4C2×D711yescharacteristic
104C2×#99—141no—
105C2×C22⋊C8C2×D712yes—
106#388—141no—
107#387—141no—
108#386—141no—
109#383—71no—
110#381—71no—
111#380—71no—
112#380—72no—
113C4×C22⋊C4—71no—
114C4×C22⋊C4—141no—
115#376—71no—
116C2×#95—71no—
117#342—141no—
118#324—21no—
119#323—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—41no—
124C23×C7—41no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7C2×C22⋊C411yescharacteristic
128C23×C7#12312yes—
129C23×C7#13512yes—
130C23×C7AGL(1,ℤ/8)11yescharacteristic
131C23×C7#13711yescharacteristic
132C7×D4—42no—
133C7×D4—42no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—41no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—81no—
146C2×C4×C7—81no—
147C2×C4×C7#11711yescharacteristic
148C2×C4×C7#11711yescharacteristic
149C2×C4×C7#12312yes—
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—
161C2×Dic7—41no—
162C2×Dic7—84no—
163C2×Dic7—82no—
164C2×Dic7—82no—
165C2×Dic7—82no—
166C7×C8—82no—
167C22×D4D2811yescharacteristic
168C23×C4—141no—
169C23×C4C4×D711yescharacteristic
170C23×C4C22×D711yescharacteristic
171C22×C8—22no—
172C4×D4—22no—
173C4×D4—22no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—142no—
176C2×C4⋊C4C22⋊D711yescharacteristic
177C2×C22⋊C4—141no—
178C2×C22⋊C4—141no—
179C2×C22⋊C4—142no—
180C2×C22⋊C4—141no—
181C2×C22⋊C4D2811yescharacteristic
182C2×C22⋊C4C22⋊D711yescharacteristic
183C2×C42—141no—
184C2×C42—141no—
185C2×C42C4×D711yescharacteristic
186#99—282no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189#95—71no—
190#95—71no—
191#95—71no—
192#95—71no—
193#95—141no—
194#95—141no—
195#95—141no—
196#95—141no—
197#95—141no—
198#95—142no—
199C22×C7—21no—
200C22×C7—22no—
201C22×C7—21no—
202C22×C7—22no—
203C22×C7—42no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—81no—
210C22×C7—81no—
211C22×C7#38111yescharacteristic
212C22×C7#41611yescharacteristic
213C22×C7#41711yescharacteristic
214C22×C7#48212yes—
215C22×C7#48512yes—
216C4×C7—22no—
217C4×C7—21no—
218C4×C7—21no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—41no—
222Dic7—42no—
223Dic7—81no—
224Dic7—81no—
225Dic7—81no—
226Dic7—162no—
227C24(C2×D7)⋊C411yescharacteristic
228C24C2×D2811yescharacteristic
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—21no—
232C2×D4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—81no—
236C22×C4—81no—
237C22×C4—141no—
238C22×C4—141no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4—282no—
242C22×C4—282no—
243C22×C4—282no—
244C22×C4—561no—
245C22×C4(C2×D7)⋊C411yescharacteristic
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4C2×C4×D711yescharacteristic
249C22×C4#115912yes—
250C22×C4#115912yes—
251C22×C4C2×C22⋊D711yescharacteristic
252C2×C8—42no—
253C2×C8—82no—
254C4⋊C4—22no—
255C4⋊C4—561no—
256C4⋊C4—562no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—282no—
260C22⋊C4—281no—
261C22⋊C4—281no—
262C22⋊C4—282no—
263C22⋊C4—282no—
264C22⋊C4—561no—
265C42—21no—
266C42—21no—
267C42—282no—
268C42—561no—
269C2×C7—21no—
270C2×C7—21no—
271C2×C7—22no—
272C2×C7—22no—
273C2×C7—81no—
274C2×C7#182511yescharacteristic
275C2×C7#182711yescharacteristic
276C2×C7#182811yescharacteristic
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#644912yes—
285C23#646712yes—
286C23#647111yescharacteristic
287C23#647211yescharacteristic
288C23C2×(C2×D7)⋊C411yescharacteristic
289D4—42no—
290D4—42no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—142no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—564no—
317C2×C4—562no—
318C2×C4—562no—
319C2×C4—562no—
320C2×C4#644011yescharacteristic
321C2×C4#644011yescharacteristic
322C2×C4#649812yes—
323C8—82no—
324C7#876311yescharacteristic, complemented, Sylow
325C22—21no—
326C22—22no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22—81no—
337C22#8949512yes—
338C22#8950912yes—
339C22#8971511yescharacteristic
340C22#8988511yescharacteristic
341C22#8990511yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—282no—
349C4—561no—
350C4—561no—
351C4—561no—
352C4—1122no—
353C2—21no—
354C2—21no—
355C2—22no—
356C2—22no—
357C2—81no—
358C2#1172768011yescharacteristic
359C2#1172777411yescharacteristic
360C2#1172788511yescharacteristic
subgroupG/H
centerC22#89715
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1459C2
socleC22×C7#381
prime radicalC22×C7×D4D4
cosocleC23×C4×C7C23
hypercenter#1459D7
hypocenterC7#8763
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #11725482C2semidirect
5. #11725481C2semidirect
12. #89983C4semidirect
13. C4×C22⋊Dic7C4semidirect
18. #89709C4semidirect
19. #89704C4semidirect
324. C7#8763semidirect

Maximal subgroups

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

subgroupindex
#117397812
C7×#14592
#117293732
#117254822
#117254812
#87637