Finite Group Databasebeta

← #13252137

Subgroups — #13252137

Order 1792.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C8×C4⋊C4C211yesmaximal, characteristic
2C2×#89281C211yesmaximal, characteristic
3#11727531C211yesmaximal, characteristic
4#11727240C211yesmaximal, characteristic
5#11727221C211yesmaximal, characteristic
6#11725508C211yesmaximal, characteristic
7#11725460C211yesmaximal, characteristic
8C2×#6432C2211yescharacteristic
9C2×C7×C4⋊C8C2211yescharacteristic
10C2×C4×C7×C8—21no—
11C2×C4×C7×C8C2211yescharacteristic
12C4×C7×C4⋊C4C2211yescharacteristic
13C2×#6384—21no—
14C2×#6384—21no—
15C2×#6382—21no—
16#89707C2211yescharacteristic
17C2×C4⋊(C7⋊C8)C2211yescharacteristic
18C2×C4⋊(C7⋊C8)C2211yescharacteristic
19C7×#336—21no—
20#89346—21no—
21#89346—21no—
22#89324—21no—
23#89281C414yescomplemented
24#9565—71nomaximal, Sylow
25C22×Dic14—21no—
26C22×C7×C8—21no—
27C22×C7×C8D411yescharacteristic
28C22×C7×C8D411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C42×C7—21no—
32C2×C42×C7C2311yescharacteristic
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C22×C7⋊C8—21no—
39C22×C7⋊C8—21no—
40#6432—21no—
41#6432—21no—
42#6432—21no—
43#6432C2×C412yes—
44C7×C4⋊C8—21no—
45C7×C4⋊C8C2×C412yes—
46C4×C7×C8—21no—
47C4×C7×C8—21no—
48C4×C7×C8—42no—
49C7×#95—21no—
50#6384—42no—
51#6384—42no—
52#6382—42no—
53C4⋊(C7⋊C8)—21no—
54C4⋊(C7⋊C8)—21no—
55C4⋊(C7⋊C8)—21no—
56C4⋊(C7⋊C8)C2×C412yes—
57#1990—71no—
58#1981—71no—
59#1948—71no—
60C8×C4⋊C4D711yescharacteristic
61C2×#332—71no—
62#1296—71no—
63#1277—71no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7#4111yescharacteristic
69C22×Dic7—41no—
70C22×Dic7—41no—
71C2×Dic14—22no—
72C2×Dic14—41no—
73C2×Dic14—41no—
74C2×Dic14—41no—
75C2×Dic14—41no—
76C2×Dic14—41no—
77C2×C7×C8—21no—
78C2×C7×C8—21no—
79C2×C7×C8—22no—
80C2×C7×C8—21no—
81C2×C7×C8—21no—
82C2×C7×C8—21no—
83C2×C7×C8—41no—
84C2×C7×C8—41no—
85C2×C7×C8SD1612yes—
86C7×C4⋊C4—21no—
87C7×C4⋊C4—21no—
88C7×C4⋊C4D812yes—
89C7×C4⋊C4SD1612yes—
90C42×C7—41no—
91C42×C7—41no—
92C42×C7C22×C411yescharacteristic
93C42×C7#4111yescharacteristic
94C42×C7#4111yescharacteristic
95C42×C7#4111yescharacteristic
96C4⋊Dic7—22no—
97C4⋊Dic7—22no—
98C4⋊Dic7—41no—
99C4⋊Dic7—41no—
100C4⋊Dic7—41no—
101C4⋊Dic7—41no—
102C4⋊Dic7—41no—
103C4⋊Dic7—41no—
104C4⋊Dic7—81no—
105C2×C7⋊C8—22no—
106C2×C7⋊C8—41no—
107C2×C7⋊C8—41no—
108C2×C7⋊C8—41no—
109C2×C7⋊C8—41no—
110C2×C7⋊C8—41no—
111C2×C4⋊Q8—71no—
112C2×#106—141no—
113C2×C4⋊C8—71no—
114C2×C4⋊C8—71no—
115C2×C4⋊C8C2×D711yescharacteristic
116C2×#103—141no—
117C2×#103—141no—
118C2×C4×C8—21no—
119C2×C4×C8C2×D711yescharacteristic
120#384—71no—
121C4×C4⋊C4C2×D711yescharacteristic
122#340—141no—
123#340—141no—
124#340—141no—
125#336—21no—
126#332—74no—
127C23×C7#12111yescharacteristic
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—22no—
131C2×C4×C7—22no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7#11711yescharacteristic
137C2×C4×C7C4×D411yescharacteristic
138C2×C4×C7C4×D411yescharacteristic
139C2×C4×C7#12311yescharacteristic
140C2×C4×C7#12411yescharacteristic
141C2×C4×C7#12611yescharacteristic
142C2×C4×C7C2×D811yescharacteristic
143C2×C4×C7C2×SD1611yescharacteristic
144C2×C4×C7C2×SD1611yescharacteristic
145C2×C4×C7#13511yescharacteristic
146C2×C4×C7#13511yescharacteristic
147C2×C4×C7#13511yescharacteristic
148C2×C4×C7#13711yescharacteristic
149C2×C4×C7#13711yescharacteristic
150C2×Dic7—42no—
151C2×Dic7—81no—
152C2×Dic7—81no—
153C2×Dic7—81no—
154C2×Dic7—81no—
155C2×Dic7—81no—
156Dic14—42no—
157Dic14—42no—
158Dic14—81no—
159Dic14—81no—
160C7×C8—22no—
161C7×C8—42no—
162C7×C8—41no—
163C7⋊C8—42no—
164C7⋊C8—81no—
165C22×Q8—141no—
166C22×C8—21no—
167C22×C8—141no—
168C22×C8—141no—
169C22×C8C22⋊D711yescharacteristic
170C22×C8C22⋊D711yescharacteristic
171C4⋊Q8—72no—
172C4⋊Q8—141no—
173C4⋊Q8—141no—
174C4⋊Q8—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4D2811yescharacteristic
181C2×C4⋊C4D2811yescharacteristic
182C2×C42—21no—
183C2×C42C22×D711yescharacteristic
184#106—282no—
185C4⋊C8—21no—
186C4⋊C8—72no—
187C4⋊C8—141no—
188C4⋊C8—141no—
189C4⋊C8—141no—
190C4⋊C8C4×D712yes—
191#103—282no—
192#103—282no—
193C4×C8—21no—
194C4×C8—21no—
195C4×C8—42no—
196#95—21no—
197C22×C7#38811yescharacteristic
198C22×C7#46111yescharacteristic
199C22×C7#46411yescharacteristic
200C22×C7#46511yescharacteristic
201C22×C7#46611yescharacteristic
202C22×C7#47111yescharacteristic
203C22×C7#47311yescharacteristic
204C4×C7—21no—
205C4×C7—21no—
206C4×C7—42no—
207C4×C7—42no—
208C4×C7C4×D811yescharacteristic
209C4×C7C4×SD1611yescharacteristic
210C4×C7C4×SD1611yescharacteristic
211C4×C7#44111yescharacteristic
212C4×C7#48311yescharacteristic
213C4×C7#48511yescharacteristic
214C4×C7#48611yescharacteristic
215C4×C7#48811yescharacteristic
216Dic7—82no—
217Dic7—161no—
218C2×Q8—142no—
219C2×Q8—281no—
220C2×Q8—281no—
221C2×Q8—281no—
222C2×Q8—281no—
223C2×Q8—281no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—281no—
227C22×C4—281no—
228C22×C4C2×D2811yescharacteristic
229C22×C4#115711yescharacteristic
230C22×C4C2×C22⋊D711yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—142no—
240C2×C8—281no—
241C2×C8—281no—
242C2×C8—281no—
243C2×C8—281no—
244C2×C8—281no—
245C2×C8#114212yes—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—142no—
249C4⋊C4—142no—
250C4⋊C4—281no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C4⋊C4—281no—
254C4⋊C4—281no—
255C4⋊C4—281no—
256C4⋊C4—561no—
257C4⋊C4#113212yes—
258C4⋊C4D5612yes—
259C42—41no—
260C42—41no—
261C42C2×C4×D711yescharacteristic
262C42#115711yescharacteristic
263C42#115711yescharacteristic
264C42#115711yescharacteristic
265C2×C7#167111yescharacteristic
266C2×C7#167311yescharacteristic
267C2×C7#168011yescharacteristic
268C2×C7#168211yescharacteristic
269C2×C7#192711yescharacteristic
270C2×C7#193011yescharacteristic
271C2×C7#193411yescharacteristic
272C23#649311yescharacteristic
273Q8—282no—
274Q8—282no—
275Q8—561no—
276Q8—561no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—282no—
286C2×C4—561no—
287C2×C4—561no—
288C2×C4—561no—
289C2×C4—561no—
290C2×C4—561no—
291C2×C4#643511yescharacteristic
292C2×C4C4×D2811yescharacteristic
293C2×C4#643811yescharacteristic
294C2×C4#643911yescharacteristic
295C2×C4C2×#113211yescharacteristic
296C2×C4C2×D5611yescharacteristic
297C2×C4#646711yescharacteristic
298C2×C4#646711yescharacteristic
299C2×C4C4×C22⋊D711yescharacteristic
300C2×C4#649211yescharacteristic
301C2×C4C2×#114211yescharacteristic
302C2×C4#650511yescharacteristic
303C2×C4#651311yescharacteristic
304C2×C4#651411yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—282no—
309C8—561no—
310C7#956511yescharacteristic, complemented, Sylow
311C22#8971211yescharacteristic
312C22#8979111yescharacteristic
313C22#8980011yescharacteristic
314C22#8988611yescharacteristic
315C22#8988711yescharacteristic
316C22#8991311yescharacteristic
317C22#8991511yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—562no—
323C4—1121no—
324C4C4×#113211yescharacteristic
325C4C4×D5611yescharacteristic
326C4#8946611yescharacteristic
327C4#8946911yescharacteristic
328C4#8974311yescharacteristic
329C4#8976811yescharacteristic
330C4C4×#114211yescharacteristic
331C4#8980211yescharacteristic
332C2#1172721811yescharacteristic
333C2#1172752211yescharacteristic
334C2#1172764511yescharacteristic
335C2#1172860511yescharacteristic
336C2#1172860611yescharacteristic
337C2#1172869511yescharacteristic
338C2#1172870011yescharacteristic
subgroupG/H
centerC23#6493
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×C8×C4⋊C4C2
socle, prime radicalC23×C7#121
cosocleC2×C42×C7C23
hypercenterC8×C4⋊C4D7
hypocenterC7#9565
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
23. #89281C4semidirect
310. C7#9565semidirect

Maximal subgroups

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

subgroupindex
C7×C8×C4⋊C42
C2×#892812
#117275312
#117272402
#117272212
#117255082
#117254602
#95657