Finite Group Databasebeta

← #32985739

Subgroups — #32985739

Order 18688.

578 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988933C211yesmaximal, characteristic
2#22610891C211yesmaximal, characteristic, complemented
3#22610738C211yesmaximal, characteristic
4#22610733C211yesmaximal, characteristic, complemented
5#22610058C211yesmaximal, characteristic, complemented
6C2×C8×#10596831C211yesmaximal, characteristic, complemented
7C73×#1957C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9#17988933—22no—
10#17988933C414yescomplemented
11C2×#14556516—22no—
12C2×#14556512—22no—
13C2×#14556512—22no—
14C2×C4×#10596831C2211yescharacteristic
15C2×C4×#10596831C2211yescharacteristic
16#17988457C2211yescharacteristic
17#17988349—22no—
18#17988349—22no—
19C8×#10596831—22no—
20C2×#127×C73C2211yescharacteristic
21C2×#102×C73—22no—
22C2×C4×C8×C73C2211yescharacteristic
23#384×C73C2211yescharacteristic
24C22×Dic146—21no—
25C22×#10596831D412yes—
26C22×#10596831D412yes—
27#14556591—21no—
28#14556591—21no—
29#14556591—21no—
30#14556591C2×C412yes—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73—21no—
36#14556516—44no—
37#14556512—28no—
38#14556512—44no—
39C4×#10596831—21no—
40C4×#10596831—21no—
41C4×#10596831C2×C412yes—
42C4×#10596831D412yes—
43C22×D4×C73—21no—
44C22×D4×C73—21no—
45C22×D4×C73—21no—
46C22×C8×C73D412yes—
47#127×C73—21no—
48#127×C73—21no—
49#127×C73—21no—
50#127×C73C2×C412yes—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73—21no—
54C2×C42×C73C2311yescharacteristic
55#102×C73—44no—
56C4×C8×C73—21no—
57C4×C8×C73—21no—
58C2×Dic146—22no—
59C2×Dic146—42no—
60C2×Dic146—42no—
61C2×Dic146—41no—
62C22×Dic73—41no—
63C22×Dic73—41no—
64C2×#10596831—22no—
65C2×#10596831—22no—
66C2×#10596831—22no—
67C2×#10596831—22no—
68C2×#10596831C22⋊C414yes—
69C2×#10596831SD1614yes—
70C4⋊Dic73—22no—
71C4⋊Dic73—22no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—42no—
75C4⋊Dic73—42no—
76C4⋊Dic73—42no—
77C24×C73—41no—
78C2×D4×C73—22no—
79C2×D4×C73—22no—
80C2×D4×C73—22no—
81C2×D4×C73—41no—
82C2×D4×C73—41no—
83C2×D4×C73—41no—
84C2×D4×C73—42no—
85C2×D4×C73—42no—
86C2×D4×C73—42no—
87C2×D4×C73—42no—
88C2×D4×C73—42no—
89C2×D4×C73—42no—
90C22×C4×C73—41no—
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C2×C8×C73—22no—
95C2×C8×C73—22no—
96C2×C8×C73D814yes—
97C4⋊C4×C73—42no—
98C4⋊C4×C73—42no—
99C4⋊C4×C73—42no—
100C42×C73C22×C411yescharacteristic
101C42×C73C2×D411yescharacteristic
102C42×C73#4111yescharacteristic
103C42×C73#4111yescharacteristic
104C23×C73—42no—
105C23×C73—81no—
106C23×C73—81no—
107C23×C73—81no—
108C23×C73—81no—
109C23×C73—81no—
110C23×C73—81no—
111C23×C73#12711yescharacteristic
112D4×C73—44no—
113D4×C73—44no—
114D4×C73—44no—
115D4×C73—82no—
116D4×C73—82no—
117D4×C73—82no—
118C2×C4×C73—81no—
119C2×C4×C73—81no—
120C2×C4×C73—81no—
121C2×C4×C73C2×C22⋊C411yescharacteristic
122C2×C4×C73C4×D411yescharacteristic
123C2×C4×C73C4×D411yescharacteristic
124C2×C4×C73#12111yescharacteristic
125C2×C4×C73#12111yescharacteristic
126C2×C4×C73#12411yescharacteristic
127C2×C4×C73C2×D812yes—
128C2×C4×C73C2×SD1612yes—
129C2×C4×C73#13512yes—
130C2×C4×C73#13512yes—
131C2×C4×C73#13512yes—
132C2×C4×C73#13512yes—
133C2×Dic73—42no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136C2×Dic73—81no—
137C2×Dic73—81no—
138C2×Dic73—81no—
139Dic146—44no—
140Dic146—82no—
141C8×C73—24no—
142#10596831—24no—
143#10596831—24no—
144C22×C73—82no—
145C22×C73—82no—
146C22×C73—82no—
147C22×C73—161no—
148C22×C73—161no—
149C22×C73—161no—
150C22×C73—161no—
151C22×C73#39011yescharacteristic
152C22×C73#49211yescharacteristic
153C22×C73#49311yescharacteristic
154C22×C73#49511yescharacteristic
155C22×C73#49511yescharacteristic
156C22×C73#49511yescharacteristic
157C22×C73#49511yescharacteristic
158C4×C73—161no—
159C4×C73#41612yes—
160C4×C73C4×D812yes—
161C4×C73C4×SD1612yes—
162C4×C73#46512yes—
163C4×C73#46612yes—
164C4×C73#48812yes—
165Dic73—82no—
166Dic73—161no—
167#9822—731nomaximal, Sylow
168C2×C73—162no—
169C2×C73#170611yescharacteristic
170C2×C73#170811yescharacteristic
171C2×C73#170911yescharacteristic
172C2×C73#171111yescharacteristic
173C2×C73#195811yescharacteristic
174C2×C73#196811yescharacteristic
175C2×C73#197011yescharacteristic
176C2×#486—731no—
177#1990—731no—
178#1957—731no—
179#1957D7311yescharacteristic
180#1956—731no—
181#1834—731no—
182C2×C82—731no—
183C73#982211yescharacteristic, complemented, Sylow
184C2×C4⋊Q8—731no—
185C2×#127C2×D7311yescharacteristic
186#486—734no—
187#486—1462no—
188C2×#103—1462no—
189C2×#102—22no—
190C2×#102—1462no—
191C2×#102—1462no—
192C2×C4×C8—731no—
193C2×C4×C8—731no—
194C2×C4×C8C2×D7311yescharacteristic
195#384—731no—
196#384C2×D7311yescharacteristic
197#340—1462no—
198#340—1462no—
199C82—1462no—
200C22×Q8—1461no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×C8—732no—
205C22×C8—732no—
206C22×C8C22⋊D7312yes—
207C4⋊Q8—732no—
208C4⋊Q8—1461no—
209C4⋊Q8—1461no—
210C4⋊Q8—1461no—
211#127—21no—
212#127—21no—
213#127—21no—
214#127C4×D7312yes—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4—1461no—
220C2×C4⋊C4—1461no—
221C2×C4⋊C4—1461no—
222C2×C4⋊C4—1461no—
223C2×C42C22×D7311yescharacteristic
224#103—2924no—
225#102—44no—
226#102—2924no—
227#102—1468no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—732no—
231C4×C8—732no—
232C4×C8—1461no—
233C4×C8—1461no—
234C24—41no—
235C2×Q8—2921no—
236C2×Q8—2922no—
237C2×Q8—2922no—
238C2×Q8—1462no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—42no—
251C22×C4—41no—
252C22×C4—2921no—
253C22×C4—2921no—
254C22×C4D4×D7311yescharacteristic
255C22×C4D4×D7311yescharacteristic
256C22×C4C2×C22⋊D7311yescharacteristic
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—734no—
260C2×C8—734no—
261C2×C8—1462no—
262C2×C8—1462no—
263C2×C8—1462no—
264C2×C8—1462no—
265C2×C8#1192401314yes—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—2921no—
270C4⋊C4—2921no—
271C4⋊C4—2922no—
272C4⋊C4—2922no—
273C4⋊C4—2922no—
274C4⋊C4—1462no—
275C4⋊C4—1462no—
276C42C2×C4×D7311yescharacteristic
277C42D4×D7311yescharacteristic
278C42#1192402711yescharacteristic
279C42#1192402811yescharacteristic
280C23—42no—
281C23—81no—
282C23—81no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23—81no—
287C23#1455658711yescharacteristic
288Q8—2924no—
289Q8—5842no—
290D4—44no—
291D4—44no—
292D4—44no—
293D4—82no—
294D4—82no—
295D4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—2922no—
300C2×C4—5841no—
301C2×C4—5841no—
302C2×C4—5841no—
303C2×C4—5841no—
304C2×C4—5841no—
305C2×C4C22⋊C4×D7311yescharacteristic
306C2×C4#1455655111yescharacteristic
307C2×C4C4×C22⋊D7311yescharacteristic
308C2×C4#1455656311yescharacteristic
309C2×C4#1455656411yescharacteristic
310C2×C4#1455657711yescharacteristic
311C2×C4C2×#1192401312yes—
312C2×C4SD16×D7312yes—
313C2×C4#1455661012yes—
314C2×C4#1455661012yes—
315C2×C4#1455661112yes—
316C2×C4#1455661212yes—
317C8—24no—
318C8—1464no—
319C8—1464no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—161no—
324C22—161no—
325C22—161no—
326C22—161no—
327C22#1798848711yescharacteristic
328C22#1798895811yescharacteristic
329C22#1798896311yescharacteristic
330C22#1798896811yescharacteristic
331C22#1798896911yescharacteristic
332C22#1798897011yescharacteristic
333C22#1798897011yescharacteristic
334C4—161no—
335C4—5842no—
336C4—11681no—
337C4#1798858012yes—
338C4C4×#1192401312yes—
339C4#1798867812yes—
340C4#1798881512yes—
341C4#1798882112yes—
342C4#1798894012yes—
343C2—162no—
344C2#2260952111yescharacteristic
345C2#2260953111yescharacteristic
346C2#2260953611yescharacteristic
347C2#2260954211yescharacteristic
348C2#2261074111yescharacteristic
349C2#2261078611yescharacteristic
350C2#2261079611yescharacteristic
subgroupG/H
centerC23#14556587
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1957C2
socleC23×C73#127
prime radicalC2×#127×C73C22
cosocleC2×C42×C73C23
hypercenter#1957D73
hypocenterC73#9822
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #22610891C2semidirect
4. #22610733C2semidirect
5. #22610058C2semidirect
6. C2×C8×#10596831C2semidirect
10. #17988933C4semidirect
183. C73#9822semidirect

Maximal subgroups

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

subgroupindex
C2×#179889332
#226108912
#226107382
#226107332
#226100582
C2×C8×#105968312
C73×#19572
#982273