Finite Group Databasebeta

← #34001362

Subgroups — #34001362

Order 18688.

444 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625846C211yesmaximal, characteristic
2C4×C4⋊#10596833C211yesmaximal, characteristic
3#22624752C212yesmaximal
4#22624750C212yesmaximal
5#22612405C211yesmaximal, characteristic
6C2×C4⋊#10596833—21no—
7C2×C4⋊#10596833—21no—
8C2×C4×#10596833—21no—
9#17989453—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×C4×Dic146C411yescharacteristic
13#17988492C411yescharacteristic
14#17988492C2211yescharacteristic
15#17988483C411yescharacteristic
16#17988483C2211yescharacteristic
17#17988469—21no—
18#17988469—21no—
19C4×#11924007—21no—
20#17988433—21no—
21C42×Dic73C2211yescharacteristic
22C4×C4⋊C4×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25C4⋊#10596833—24no—
26C4⋊#10596833—42no—
27C4×#10596833—42no—
28C22×Dic146C2×C411yescharacteristic
29C4×Dic146—22no—
30C4×Dic146C814yescomplemented
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×C4×Dic73—21no—
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73C2311yescharacteristic
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48C2×C4⋊C4×C73C2×C411yescharacteristic
49C2×C4⋊C4×C73C2×C411yescharacteristic
50C2×C42×C73—21no—
51C2×C42×C73C2×C411yescharacteristic
52#95×C73—21no—
53C2×#10596833—24no—
54C2×#10596833—42no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C2×Dic146—21no—
60C2×Dic146—41no—
61C2×Dic146—41no—
62C2×Dic146C2×C812yes—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73C22⋊C411yescharacteristic
66C22×Dic73C22⋊C411yescharacteristic
67C22×Dic73C2×D411yescharacteristic
68C22×Dic73C2×D411yescharacteristic
69C4⋊Dic73—21no—
70C4⋊Dic73C2×C812yes—
71#11924007—24no—
72#11924007—42no—
73#11924007—41no—
74#11924007—41no—
75C4×Dic73—24no—
76C4×Dic73—22no—
77C4×Dic73—21no—
78C4×Dic73—21no—
79C4×Dic73—41no—
80C4×Dic73—41no—
81C4×Dic73—41no—
82C4×Dic73SD1612yes—
83C4×Dic73Q1612yes—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22×C411yescharacteristic
89C4⋊C4×C73—41no—
90C4⋊C4×C73—41no—
91C42×C73—42no—
92C42×C73C2×C812yes—
93C42×C73M1612yes—
94C23×C73C2×C22⋊C411yescharacteristic
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—41no—
102C2×C4×C73—41no—
103C2×C4×C73—41no—
104C2×C4×C73—41no—
105C2×C4×C73C22⋊C812yes—
106C2×C4×C73C22⋊C812yes—
107C2×C4×C73#10312yes—
108C2×C4×C73#10412yes—
109C2×C4×C73C22×C811yescharacteristic
110C2×C4×C73C2×M1611yescharacteristic
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—22no—
118C2×Dic73—22no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73#10312yes—
127C2×Dic73C2×SD1611yescharacteristic
128C2×Dic73C2×Q1611yescharacteristic
129C2×Dic73AGL(1,ℤ/8)11yescharacteristic
130C2×Dic73#13711yescharacteristic
131Dic146—42no—
132Dic146—42no—
133#10596833—44no—
134#10596833—82no—
135C22×C73C2×C22⋊C811yescharacteristic
136C22×C73#41011yescharacteristic
137C22×C73#41311yescharacteristic
138C22×C73C2×#10311yescharacteristic
139C22×C73#41711yescharacteristic
140C22×C73C2×#10411yescharacteristic
141C22×C73#42111yescharacteristic
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—22no—
145C4×C73—81no—
146C4×C73—81no—
147C4×C73Q8⋊C814yes—
148Dic73—22no—
149Dic73—21no—
150Dic73—21no—
151Dic73—21no—
152Dic73—21no—
153Dic73—42no—
154Dic73—42no—
155Dic73—41no—
156#7577—731nomaximal, Sylow
157C2×C73#145811yescharacteristic
158C2×C73C2×Q8⋊C811yescharacteristic
159C2×C73#147711yescharacteristic
160C2×C73#150911yescharacteristic
161C2×C73#151811yescharacteristic
162C2×C73#152911yescharacteristic
163C2×C73#155011yescharacteristic
164#2295—731no—
165#1831—731no—
166C4×C4⋊C8—731no—
167#1272—732no—
168#1271—732no—
169C73#757711yescharacteristic, complemented, Sylow
170C2×C4×Q8—731no—
171C2×C4⋊C8—1461no—
172C2×C4⋊C8—1461no—
173C2×C4×C8—1461no—
174#391—731no—
175#391—731no—
176#389—731no—
177#389—731no—
178#387—1461no—
179#387—1461no—
180C4×C4⋊C4—1461no—
181C4×C4⋊C4#6440811yescharacteristic
182#376—1461no—
183C43—731no—
184#336—732no—
185#336—732no—
186#336—1461no—
187C22×Q8—731no—
188C22×C8—1462no—
189C22×C8—1462no—
190C4×Q8—734no—
191C4×Q8—1462no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—1461no—
194C2×C4⋊C4—1461no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4C2×#6440811yescharacteristic
197C2×C4⋊C4C2×#6440811yescharacteristic
198C2×C42—21no—
199C2×C42—731no—
200C2×C42—731no—
201C2×C42—731no—
202C2×C42—731no—
203C2×C42—731no—
204C2×C42—731no—
205C2×C42—1461no—
206C2×C42C2×#6440811yescharacteristic
207C4⋊C8—2922no—
208C4⋊C8—1464no—
209C4×C8—2922no—
210#95—21no—
211#95—1461no—
212#95—1461no—
213#95—1461no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217C2×Q8—2921no—
218C2×Q8—2921no—
219C2×Q8—732no—
220C2×Q8—1461no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—731no—
224C22×C4—731no—
225C22×C4—731no—
226C22×C4—731no—
227C22×C4—1461no—
228C22×C4—1461no—
229C22×C4C22⋊#6440811yescharacteristic
230C22×C4C22⋊#6440811yescharacteristic
231C22×C4C22×#6440811yescharacteristic
232C2×C8—2922no—
233C2×C8—2922no—
234C2×C8—2922no—
235C2×C8—2922no—
236C2×C8—2922no—
237C2×C8—1464no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—2921no—
241C4⋊C4—2921no—
242C4⋊C4—2922no—
243C4⋊C4—732no—
244C4⋊C4—1461no—
245C4⋊C4—1464no—
246C42—42no—
247C42—2921no—
248C42—2921no—
249C42—2921no—
250C42—732no—
251C42—732no—
252C42—1461no—
253C42—1461no—
254C42—1464no—
255C42—1462no—
256C42#1192403612yes—
257C42#1192403812yes—
258C23C2×C22⋊#6440811yescharacteristic
259Q8—2922no—
260Q8—2922no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—2921no—
272C2×C4—2921no—
273C2×C4—2921no—
274C2×C4—2921no—
275C2×C4—731no—
276C2×C4—732no—
277C2×C4—731no—
278C2×C4—731no—
279C2×C4—731no—
280C2×C4—1462no—
281C2×C4—1462no—
282C2×C4—1461no—
283C2×C4—1461no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4#1455664812yes—
292C2×C4#1455664812yes—
293C2×C4#1455665412yes—
294C2×C4#1455665512yes—
295C2×C4C2×#1192403611yescharacteristic
296C2×C4C2×#1192403811yescharacteristic
297C8—2924no—
298C8—5842no—
299C22C2×#1455664811yescharacteristic
300C22#1798956611yescharacteristic
301C22#1798957311yescharacteristic
302C22C2×#1455665411yescharacteristic
303C22#1798957811yescharacteristic
304C22C2×#1455665511yescharacteristic
305C22#1798958411yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—81no—
310C4—81no—
311C4—2921no—
312C4—2922no—
313C4—2922no—
314C4—1461no—
315C4—1461no—
316C4—1461no—
317C4—1461no—
318C4—1462no—
319C4#1798943714yes—
320C2#2262516411yescharacteristic
321C2C2×#1798943711yescharacteristic
322C2#2262522811yescharacteristic
323C2#2262533311yescharacteristic
324C2#2262536411yescharacteristic
325C2#2262539611yescharacteristic
326C2#2262544811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#7577
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
30. C4×Dic146C8semidirect
169. C73#7577semidirect

Maximal subgroups

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

subgroupindex
#226258462
C4×C4⋊#105968332
#226247522
#226247502
#226124052
#757773