Finite Group Databasebeta

← #13264151

Subgroups — #13264151

Order 1792.

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

normal subgroups only

This group has 436 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#11739837C211yesmaximal, characteristic
2C7×#1460C211yesmaximal, characteristic
3C4×#6408C211yesmaximal, characteristic
4#11725256C212yesmaximal, complemented
5#11725255C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6487C411yescharacteristic, complemented
8C7×#431—21no—
9#89994—21no—
10C2×#6408—21no—
11#89983C411yescharacteristic, complemented
12#89982—21no—
13C4×C22⋊Dic7—21no—
14#89755C411yescharacteristic, complemented
15#89751C411yescharacteristic, complemented
16#89725C2211yescharacteristic
17#89724—21no—
18#89719C2211yescharacteristic
19#89705—21no—
20C7×#323—21no—
21C7×#323C2212yes—
22#89321C2212yes—
23#11731—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C4×C7×D4—41no—
29C4×C7×D4—41no—
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C7×C22⋊C4C2311yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—22no—
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40#6487—41no—
41#6487—41no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×C4×Dic7—41no—
46C7×C4⋊C8—41no—
47C7×C22⋊C8—22no—
48C4×C7×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#2638—71no—
59C4×#99—71no—
60#1460D711yescharacteristic
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—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—81no—
86C2×C7×C8—42no—
87C7×C4⋊C4—41no—
88C7×C22⋊C4—41no—
89C7×C22⋊C4—41no—
90C42×C7—21no—
91C42×C7—21no—
92C22⋊Dic7—24no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C22⋊Dic7—42no—
96C22⋊Dic7—81no—
97C22⋊Dic7—81no—
98C4⋊Dic7—41no—
99Dic7⋊C4—41no—
100Dic7⋊C4—41no—
101Dic7⋊C4—42no—
102Dic7⋊C4—81no—
103C4×Dic7—82no—
104C2×C22⋊Q8—71no—
105C2×C4×D4C2×D711yescharacteristic
106#431—21no—
107C2×#99—141no—
108#398—71no—
109#397—71no—
110#397—141no—
111#395—71no—
112#394—141no—
113#393—71no—
114#387—141no—
115#385—141no—
116#381—71no—
117C4×C22⋊C4—141no—
118#342—72no—
119#323—21no—
120#323C2×D712yes—
121C23×C7—21no—
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×C7C2×C22⋊C411yescharacteristic
131C23×C7#13512yes—
132C7×D4—44no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—41no—
139C2×C4×C7—42no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7—81no—
144C2×C4×C7—81no—
145C2×C4×C7—81no—
146C2×C4×C7#9911yescharacteristic
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#10412yes—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—44no—
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—82no—
163C2×Dic7—82no—
164Dic14—82no—
165C7×C8—82no—
166C22×Q8—71no—
167C22×D4D2811yescharacteristic
168C23×C4C4×D711yescharacteristic
169C23×C4D2811yescharacteristic
170C22⋊Q8—281no—
171C22⋊Q8—281no—
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—71no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4C4×D711yescharacteristic
179C2×C22⋊C4—142no—
180C2×C22⋊C4—141no—
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4C22⋊D711yescharacteristic
185C2×C22⋊C4C22×D711yescharacteristic
186C2×C42—281no—
187C2×C42C22⋊D711yescharacteristic
188C4⋊C8—41no—
189#99—144no—
190C22⋊C8—22no—
191C4×C8—41no—
192#95—71no—
193#95—71no—
194#95—141no—
195#95—141no—
196#95—141no—
197#95—141no—
198#95—141no—
199#95—281no—
200C22×C7—21no—
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—81no—
212C22×C7C2×#9911yescharacteristic
213C22×C7#41611yescharacteristic
214C22×C7C2×#10411yescharacteristic
215C4×C7—21no—
216C4×C7—21no—
217C4×C7—22no—
218C4×C7—41no—
219C4×C7—41no—
220C4×C7—41no—
221Dic7—81no—
222Dic7—81no—
223Dic7—84no—
224Dic7—81no—
225Dic7—81no—
226C24(C2×D7)⋊C411yescharacteristic
227C24C2×D2811yescharacteristic
228C2×Q8—281no—
229C2×Q8—561no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4—141no—
242C22×C4—141no—
243C22×C4—282no—
244C22×C4(C2×D7)⋊C411yescharacteristic
245C22×C4(C2×D7)⋊C411yescharacteristic
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4C2×C4×D711yescharacteristic
248C22×C4C2×C22⋊D711yescharacteristic
249C2×C8—42no—
250C4⋊C4—41no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C4⋊C4—281no—
254C4⋊C4—282no—
255C4⋊C4—561no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—144no—
259C22⋊C4—282no—
260C22⋊C4—282no—
261C22⋊C4—282no—
262C22⋊C4—561no—
263C22⋊C4—561no—
264C42—21no—
265C42—21no—
266C42—562no—
267C2×C7—21no—
268C2×C7—21no—
269C2×C7—42no—
270C2×C7—81no—
271C2×C7#150111yescharacteristic
272C2×C7#212111yescharacteristic
273C2×C7#212911yescharacteristic
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#646712yes—
284C23C2×(C2×D7)⋊C411yescharacteristic
285Q8—562no—
286D4—44no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—284no—
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—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4—562no—
314C2×C4—562no—
315C2×C4#638011yescharacteristic
316C2×C4#638011yescharacteristic
317C2×C4#639912yes—
318C8—82no—
319C7#1173111yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22C2×#638011yescharacteristic
333C22#8988511yescharacteristic
334C22C2×#639911yescharacteristic
335C4—22no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—561no—
342C4—561no—
343C4—564no—
344C4—561no—
345C4—561no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1172769611yescharacteristic
351C2#1172781311yescharacteristic
352C2#1172784811yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1460C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1460D7
hypocenterC7#11731
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
4. #11725256C2semidirect
5. #11725255C2semidirect
7. C2×#6487C4semidirect
11. #89983C4semidirect
14. #89755C4semidirect
15. #89751C4semidirect
319. C7#11731semidirect

Maximal subgroups

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

subgroupindex
#117398372
C7×#14602
C4×#64082
#117252562
#117252552
#117317