Finite Group Databasebeta

← #13263427

Subgroups — #13263427

Order 1792.

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

normal subgroups only

This group has 412 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#11739919C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic, complemented
3#11729378C211yesmaximal, characteristic, complemented
4#11725261C212yesmaximal, complemented
5#11725260C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6510C411yescharacteristic
8C2×#6507C411yescharacteristic
9C2×#6438C411yescharacteristic
10C7×#432—21no—
11#89766—21no—
12#89766—21no—
13#89760C2211yescharacteristic
14#89746C2211yescharacteristic
15#89712—21no—
16#89712—21no—
17C4×C4⋊Dic7C411yescharacteristic
18#89697—21no—
19C7×#324—21no—
20C7×#324C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11565—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C22×D28C2×C411yescharacteristic
26C22×Dic14C2×C411yescharacteristic
27C4×C7×Q8—41no—
28C4×C7×Q8—41no—
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C4⋊C4C2311yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35#6510—42no—
36#6507—42no—
37C2×(C2×D7)⋊C4—21no—
38C2×(C2×D7)⋊C4—21no—
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×C4⋊Dic7—21no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×C4×Dic7C2×C411yescharacteristic
47C2×C4×Dic7C2×C411yescharacteristic
48#6438—41no—
49#6438—41no—
50C7×C4⋊C8—41no—
51C7×C22⋊C8—22no—
52C7×#97—41no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C22⋊(C7⋊C8)—22no—
57C4⋊(C7⋊C8)—41no—
58C4×C7⋊C8—41no—
59#2545—71no—
60#1467D711yescharacteristic, complemented
61#1461—71no—
62#1319—72no—
63#1318—72no—
64C23×D7—21no—
65C2×C7×Q8—22no—
66C2×C7×Q8—22no—
67C2×C7×Q8—41no—
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22×C411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—21no—
78C2×D28—22no—
79C2×D28—41no—
80C2×D28—41no—
81C2×Dic14—22no—
82C2×Dic14—41no—
83C2×Dic14—41no—
84C2×C7×C8—42no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7—21no—
94(C2×D7)⋊C4—42no—
95(C2×D7)⋊C4—42no—
96(C2×D7)⋊C4—42no—
97(C2×D7)⋊C4—42no—
98(C2×D7)⋊C4—41no—
99(C2×D7)⋊C4—41no—
100(C2×D7)⋊C4—42no—
101C4⋊Dic7—42no—
102Dic7⋊C4—42no—
103Dic7⋊C4—42no—
104C4×Dic7—41no—
105C4×Dic7—41no—
106C2×C7⋊C8—42no—
107C2×C4⋊Q8—71no—
108C2×#124—71no—
109C2×#124—71no—
110C2×C4×Q8C2×D711yescharacteristic
111#432—21no—
112#431—141no—
113#396—141no—
114#396—141no—
115#391—71no—
116#390—71no—
117#388—141no—
118#388—141no—
119C4×C4⋊C4—71no—
120#324—21no—
121#324—72no—
122#324—141no—
123#324C2×D712yes—
124C23×C7C2×C22⋊C411yescharacteristic
125C22×D7—41no—
126C22×D7—41no—
127C22×D7—41no—
128C22×D7—41no—
129C22×D7—41no—
130C22×D7—41no—
131C22×D7—41no—
132C7×Q8—44no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
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—21no—
142C2×C4×C7—21no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#9911yescharacteristic
149C2×C4×C7#10012yes—
150C2×C4×C7#13112yes—
151C2×Dic7—22no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160D28—82no—
161Dic14—82no—
162C7×C8—82no—
163C7⋊C8—82no—
164C22×Q8—71no—
165C22×Q8C4×D711yescharacteristic
166C22×D4—71no—
167C4⋊Q8—282no—
168#124—281no—
169#124—281no—
170#124—282no—
171C4×Q8—41no—
172C4×Q8—41no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4D2811yescharacteristic
177C2×C4⋊C4C22⋊D711yescharacteristic
178C2×C4⋊C4C22×D711yescharacteristic
179C2×C22⋊C4—141no—
180C2×C22⋊C4—141no—
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C42—71no—
186C2×C42—71no—
187C2×C42C4×D711yescharacteristic
188C2×C42D2811yescharacteristic
189C2×C42C22⋊D711yescharacteristic
190C4⋊C8—41no—
191C4⋊C8—281no—
192C22⋊C8—22no—
193C22⋊C8—142no—
194#97—41no—
195C4×C8—281no—
196#95—141no—
197#95—141no—
198#95—141no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7#40811yescharacteristic
202C22×C7C2×#9911yescharacteristic
203C22×C7C2×#10011yescharacteristic
204C2×D7—81no—
205C2×D7—81no—
206C2×D7—81no—
207C2×D7—81no—
208C2×D7—81no—
209C2×D7—81no—
210C2×D7—81no—
211C4×C7—21no—
212C4×C7—21no—
213C4×C7—22no—
214C4×C7—22no—
215C4×C7—41no—
216C4×C7—41no—
217C4×C7—41no—
218C4×C7—41no—
219Dic7—42no—
220Dic7—81no—
221Dic7—81no—
222C24—141no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—142no—
227C2×Q8—281no—
228C2×Q8—281no—
229C2×D4—142no—
230C2×D4—281no—
231C2×D4—281no—
232C22×C4—141no—
233C22×C4—141no—
234C22×C4—141no—
235C22×C4(C2×D7)⋊C411yescharacteristic
236C22×C4(C2×D7)⋊C411yescharacteristic
237C22×C4(C2×D7)⋊C411yescharacteristic
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4C2×C4×D711yescharacteristic
240C22×C4C2×D2811yescharacteristic
241C22×C4C2×C22⋊D711yescharacteristic
242C2×C8—42no—
243C2×C8—282no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—282no—
248C4⋊C4—282no—
249C4⋊C4—282no—
250C22⋊C4—282no—
251C22⋊C4—282no—
252C22⋊C4—282no—
253C22⋊C4—282no—
254C22⋊C4—281no—
255C22⋊C4—281no—
256C22⋊C4—282no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—281no—
264C42—281no—
265C2×C7—21no—
266C2×C7—21no—
267C2×C7#147111yescharacteristic
268C2×C7#212611yescharacteristic
269C2×C7#213311yescharacteristic
270D7—161no—
271C23—281no—
272C23—281no—
273C23—281no—
274C23—281no—
275C23—281no—
276C23—281no—
277C23—281no—
278C23C2×(C2×D7)⋊C411yescharacteristic
279Q8—44no—
280Q8—562no—
281D4—562no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—142no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4#638011yescharacteristic
306C2×C4#638011yescharacteristic
307C2×C4#639712yes—
308C2×C4#647012yes—
309C8—82no—
310C8—562no—
311C7#1156511yescharacteristic, complemented, Sylow
312C22—21no—
313C22—21no—
314C22—561no—
315C22—561no—
316C22—561no—
317C22—561no—
318C22—561no—
319C22—561no—
320C22—561no—
321C22C2×#638011yescharacteristic
322C22#8990111yescharacteristic
323C22C2×#639711yescharacteristic
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—282no—
333C4—561no—
334C4—561no—
335C2—21no—
336C2—21no—
337C2—1121no—
338C2#1172772411yescharacteristic
339C2#1172781411yescharacteristic
340C2#1172788211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1467C2
socleC22×C7C2×#99
prime radicalC22×D28C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1467D7
hypocenterC7#11565
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C7×#1467C2semidirect
3. #11729378C2semidirect
4. #11725261C2semidirect
60. #1467D7semidirect
311. C7#11565semidirect

Maximal subgroups

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

subgroupindex
#117399192
C7×#14672
#117293782
#117252612
#117252602
#115657