Finite Group Databasebeta

← #32980306

Subgroups — #32980306

Order 18688.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618599C211yesmaximal, characteristic
2#22609952C211yesmaximal, characteristic
3#22608706C211yesmaximal, characteristic, complemented
4#22608686C211yesmaximal, characteristic, complemented
5#22608311C211yesmaximal, characteristic
6#22607772C211yesmaximal, characteristic, complemented
7C73×#1303C211yesmaximal, characteristic, complemented
8C4×#11924028C2211yescharacteristic
9#17988647—22no—
10#17988643—21no—
11#17988639—21no—
12#17988611C2211yescharacteristic
13C2×C4⋊#10596831C2211yescharacteristic
14C2×#14556519—21no—
15#17988555—21no—
16#17988545—21no—
17C2×C4×#10596831C2211yescharacteristic
18#17988347—21no—
19#17988340—21no—
20#17988340—21no—
21#17988337—22no—
22#17988317C411yescharacteristic, complemented
23#17988317C411yescharacteristic, complemented
24#17988314C411yescharacteristic, complemented
25#17988314C411yescharacteristic, complemented
26#431×C73C2211yescharacteristic
27#423×C73C2211yescharacteristic
28C4×C4⋊C4×C73C2211yescharacteristic
29C2×#11924028D411yescharacteristic
30C2×#11924012—21no—
31C22×#10596831—21no—
32C22×#10596831—21no—
33C4×Dic146C2×C411yescharacteristic
34C4×Dic146Q811yescharacteristic
35C4×D292C2×C411yescharacteristic
36C4×D292Q811yescharacteristic
37C4×C22⋊D73—21no—
38C4×C22⋊D73—21no—
39#14556550D411yescharacteristic
40#14556548—21no—
41C42×D73—21no—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831D411yescharacteristic
46C4⋊#10596831D411yescharacteristic
47#14556519—42no—
48#14556503—22no—
49#14556503—22no—
50#14556501—22no—
51C4×#10596831—21no—
52C4×#10596831C2×C411yescharacteristic
53C4×#10596831C2×C411yescharacteristic
54C8×Dic73—22no—
55C2×M16×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C42×C73—21no—
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—21no—
60C4⋊C8×C73C2×C411yescharacteristic
61C4⋊C8×C73C2×C411yescharacteristic
62C4⋊C8×C73D412yes—
63C22⋊C8×C73—21no—
64C4×C8×C73—21no—
65#95×C73—21no—
66#11924028—21no—
67#11924028—21no—
68#11924028—21no—
69#11924028—21no—
70C2×Dic146C4⋊C411yescharacteristic
71C2×D292C4⋊C411yescharacteristic
72C2×C22⋊D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76#11924012—41no—
77#11924012—41no—
78C2×#10596831—21no—
79C2×#10596831—21no—
80C2×#10596831—21no—
81C2×#10596831—21no—
82C2×#10596831—42no—
83C2×#10596831—41no—
84C2×#10596831—41no—
85C2×#10596831—41no—
86C4⋊Dic73C4⋊C411yescharacteristic
87C4⋊Dic73C4⋊C411yescharacteristic
88#11924007—21no—
89#11924007—21no—
90C22⋊Dic73—21no—
91#11924005—21no—
92#11924005—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C22×C4×C73—41no—
97C22×C4×C73C2×D411yescharacteristic
98C22×C4×C73#4111yescharacteristic
99C22×C4×C73#4111yescharacteristic
100M16×C73—41no—
101M16×C73—41no—
102C2×C8×C73—21no—
103C2×C8×C73—21no—
104C2×C8×C73—22no—
105C4⋊C4×C73—22no—
106C4⋊C4×C73—41no—
107C42×C73—41no—
108C42×C73—41no—
109C42×C73C22×C411yescharacteristic
110C42×C73C2×D411yescharacteristic
111C42×C73C2×D411yescharacteristic
112C42×C73C2×Q811yescharacteristic
113C23×C73#12311yescharacteristic
114C22×D73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—41no—
118C2×C4×C73—42no—
119C2×C4×C73—81no—
120C2×C4×C73—81no—
121C2×C4×C73C2×C4⋊C411yescharacteristic
122C2×C4×C73C4×D411yescharacteristic
123C2×C4×C73C4×D411yescharacteristic
124C2×C4×C73#12011yescharacteristic
125C2×C4×C73C22⋊Q811yescharacteristic
126C2×C4×C73C22⋊Q811yescharacteristic
127C2×C4×C73#13511yescharacteristic
128C2×C4×C73#13511yescharacteristic
129C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C73#13711yescharacteristic
131C22⋊D73—41no—
132C22⋊D73—41no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136D292—21no—
137D292—21no—
138C4×D73—41no—
139C4×D73—41no—
140C4×D73—41no—
141C4×D73—41no—
142C4×D73—81no—
143Dic146—21no—
144Dic146—21no—
145C8×C73—41no—
146C8×C73—41no—
147C8×C73—42no—
148#10596831—22no—
149#10596831—41no—
150#10596831—41no—
151#10596831—41no—
152#10596831—81no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73#38511yescharacteristic
156C22×C73#48211yescharacteristic
157C22×C73#48511yescharacteristic
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—82no—
165C4×C73#42711yescharacteristic
166C4×C73#42811yescharacteristic
167C4×C73#44311yescharacteristic
168C4×C73#44411yescharacteristic
169C4×C73#44911yescharacteristic
170C4×C73#45211yescharacteristic
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174#8905—731nomaximal, Sylow
175C2×C73—21no—
176C2×C73—21no—
177C2×C73#185411yescharacteristic
178C2×C73#186111yescharacteristic
179C2×C73#186611yescharacteristic
180D73—81no—
181#2925—731no—
182#1806—731no—
183#1571—731no—
184#1566—731no—
185#1476—731no—
186#1303D7311yescharacteristic, complemented
187#1279—731no—
188C73#890511yescharacteristic, complemented, Sylow
189C4×#41—731no—
190#433—1462no—
191#432—1461no—
192#431—1461no—
193#431C2×D7311yescharacteristic
194#423—731no—
195#423C2×D7311yescharacteristic
196C2×C4⋊C8—731no—
197C2×#104—1461no—
198#408—1461no—
199#405—1461no—
200C2×C4×C8—731no—
201C4×C4⋊C4C2×D7311yescharacteristic
202#339—1461no—
203#335—1461no—
204#335—1461no—
205#334—1462no—
206Q8⋊C8—731no—
207Q8⋊C8—731no—
208D4⋊C8—731no—
209D4⋊C8—731no—
210C2×#41—731no—
211C2×M16—21no—
212C2×M16—1461no—
213C22×C8—1461no—
214C22×C8—1461no—
215C4×Q8—731no—
216C4×Q8—731no—
217C4×D4—731no—
218C4×D4—731no—
219C4×D4—1461no—
220C4×D4—1461no—
221#117—731no—
222#117—1461no—
223C2×C4⋊C4—21no—
224C2×C42—21no—
225C2×C42—1461no—
226C2×C42C22×D7311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—731no—
229C4⋊C8—731no—
230C4⋊C8—1461no—
231C4⋊C8—1461no—
232C4⋊C8—1461no—
233C4⋊C8C4×D7311yescharacteristic
234C4⋊C8C4×D7311yescharacteristic
235C4⋊C8D29212yes—
236#104—2922no—
237C22⋊C8—21no—
238C22⋊C8—1462no—
239C22⋊C8—1462no—
240#97—1462no—
241C4×C8—21no—
242C4×C8—731no—
243C4×C8—731no—
244C4×C8—1462no—
245C4×C8—1461no—
246#95—21no—
247#41—1461no—
248#41—1461no—
249#41—1461no—
250#41—1461no—
251C2×Q8—731no—
252C2×D4—731no—
253C2×D4—1461no—
254C22×C4—41no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4D4×D7311yescharacteristic
259C22×C4#1192402711yescharacteristic
260C22×C4#1192402811yescharacteristic
261M16—41no—
262M16—41no—
263M16—2921no—
264M16—2921no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—2921no—
269C2×C8—2921no—
270C2×C8—2922no—
271C2×C8—2921no—
272C2×C8—1461no—
273C2×C8—1461no—
274C2×C8—1461no—
275C2×C8—1461no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—731no—
279C4⋊C4—731no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C42—41no—
286C42—41no—
287C42—1461no—
288C42—1461no—
289C42—1461no—
290C42C2×C4×D7311yescharacteristic
291C42D4×D7311yescharacteristic
292C42C2×D29211yescharacteristic
293C42Q8×D7311yescharacteristic
294C23—1461no—
295C23#1455657311yescharacteristic
296Q8—1461no—
297Q8—1461no—
298D4—2921no—
299D4—2921no—
300D4—1461no—
301D4—1461no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—5841no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4C4⋊C4×D7311yescharacteristic
317C2×C4#1455655111yescharacteristic
318C2×C4C4×D29211yescharacteristic
319C2×C4#1455656111yescharacteristic
320C2×C4#1455656911yescharacteristic
321C2×C4#1455657111yescharacteristic
322C2×C4#1455661011yescharacteristic
323C2×C4#1455661411yescharacteristic
324C2×C4#1455661811yescharacteristic
325C2×C4#1455662011yescharacteristic
326C8—41no—
327C8—41no—
328C8—42no—
329C8—2921no—
330C8—2921no—
331C8—2921no—
332C8—5841no—
333C8—1462no—
334C22—21no—
335C22—21no—
336C22—2921no—
337C22—2921no—
338C22—2921no—
339C22#1798846111yescharacteristic
340C22#1798890911yescharacteristic
341C22#1798892711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4#1798862411yescharacteristic
350C4#1798862611yescharacteristic
351C4#1798870111yescharacteristic
352C4#1798870611yescharacteristic
353C4#1798873511yescharacteristic
354C4#1798875011yescharacteristic
355C2—21no—
356C2—21no—
357C2—5841no—
358C2#2261013311yescharacteristic
359C2#2261017411yescharacteristic
360C2#2261020711yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1303C2
socleC22×C73#385
prime radicalC2×#11924028D4
cosocleC2×C42×C73C23
hypercenter#1303D73
hypocenterC73#8905
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #22608706C2semidirect
4. #22608686C2semidirect
6. #22607772C2semidirect
7. C73×#1303C2semidirect
22. #17988317C4semidirect
23. #17988317C4semidirect
24. #17988314C4semidirect
25. #17988314C4semidirect
186. #1303D73semidirect
188. C73#8905semidirect

Maximal subgroups

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

subgroupindex
#226185992
#226099522
#226087062
#226086862
#226083112
#226077722
C73×#13032
#890573