Finite Group Databasebeta

← #32990539

Subgroups — #32990539

Order 18688.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610893C211yesmaximal, characteristic
2#22610880C211yesmaximal, characteristic
3#22610690C211yesmaximal, characteristic
4#22610647C211yesmaximal, characteristic
5C2×#17988339C211yesmaximal, characteristic
6#22607815C211yesmaximal, characteristic
7C2×#333×C73C211yesmaximal, characteristic
8C2×#14556525—21no—
9C2×C4⋊#10596831C2211yescharacteristic
10C2×#14556520—21no—
11C2×C4×#10596831C2211yescharacteristic
12#17988457C2211yescharacteristic
13C4×C4⋊Dic73C2211yescharacteristic
14#17988350—21no—
15#17988349—21no—
16#17988349—21no—
17#17988349—21no—
18#17988349—21no—
19#17988341—21no—
20#17988339—22no—
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24#333×C73—22no—
25C22×#10596831—21no—
26C22×#10596831D411yescharacteristic
27C22×#10596831D411yescharacteristic
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73D411yescharacteristic
32C2×C4⋊Dic73D411yescharacteristic
33C2×C4×Dic73—21no—
34#14556525—42no—
35C4⋊#10596831—21no—
36C4⋊#10596831—21no—
37#14556520—42no—
38C4×#10596831—21no—
39C4×#10596831—21no—
40#14556498—21no—
41C22×Q8×C73—21no—
42C22×C8×C73—21no—
43C22×C8×C73—21no—
44C4⋊Q8×C73—21no—
45C4⋊Q8×C73—21no—
46C4⋊Q8×C73—21no—
47C4⋊Q8×C73Q812yes—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C42×C73C2311yescharacteristic
51C4⋊C8×C73—21no—
52C4⋊C8×C73—21no—
53C4⋊C8×C73—21no—
54C4⋊C8×C73D412yes—
55C22×Dic73—21no—
56C22×Dic73—21no—
57C22×Dic73—41no—
58C2×#10596831—21no—
59C2×#10596831—21no—
60C2×#10596831—21no—
61C2×#10596831—21no—
62C2×#10596831—21no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831Q1612yes—
67C4⋊Dic73—21no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—81no—
75C4⋊Dic73Q1612yes—
76C4×Dic73—41no—
77C4×Dic73—41no—
78C2×Q8×C73—22no—
79C2×Q8×C73—41no—
80C2×Q8×C73—81no—
81C2×Q8×C73—81no—
82C22×C4×C73—41no—
83C22×C4×C73C2×D411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73#4111yescharacteristic
86C2×C8×C73—22no—
87C2×C8×C73—41no—
88C2×C8×C73—41no—
89C2×C8×C73—41no—
90C2×C8×C73—41no—
91C2×C8×C73—41no—
92C4⋊C4×C73—22no—
93C4⋊C4×C73—22no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C42×C73C2×D411yescharacteristic
97C42×C73C2×Q811yescharacteristic
98C42×C73#4111yescharacteristic
99C42×C73#4111yescharacteristic
100C23×C73#12111yescharacteristic
101Q8×C73—82no—
102Q8×C73—82no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—42no—
106C2×C4×C73—81no—
107C2×C4×C73—81no—
108C2×C4×C73#12111yescharacteristic
109C2×C4×C73#12111yescharacteristic
110C2×C4×C73C22⋊Q811yescharacteristic
111C2×C4×C73C22⋊Q811yescharacteristic
112C2×C4×C73C22⋊Q811yescharacteristic
113C2×C4×C73#12611yescharacteristic
114C2×C4×C73C2×Q1611yescharacteristic
115C2×C4×C73C2×Q1611yescharacteristic
116C2×C4×C73#13511yescharacteristic
117C2×C4×C73#13511yescharacteristic
118C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C73#13711yescharacteristic
121C2×C4×C73#13711yescharacteristic
122C2×Dic73—22no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—81no—
129C2×Dic73—81no—
130C2×Dic73—81no—
131C8×C73—42no—
132C8×C73—81no—
133#10596831—22no—
134#10596831—41no—
135#10596831—81no—
136C22×C73#39611yescharacteristic
137C22×C73#46211yescharacteristic
138C22×C73#46311yescharacteristic
139C22×C73#46711yescharacteristic
140C22×C73#46811yescharacteristic
141C22×C73#47111yescharacteristic
142C22×C73#47211yescharacteristic
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—82no—
146C4×C73#46211yescharacteristic
147C4×C73#46311yescharacteristic
148C4×C73#46711yescharacteristic
149C4×C73#46811yescharacteristic
150C4×C73#47711yescharacteristic
151C4×C73#47711yescharacteristic
152C4×C73#47911yescharacteristic
153C4×C73#47911yescharacteristic
154Dic73—42no—
155Dic73—81no—
156Dic73—161no—
157#10593—731nomaximal, Sylow
158C2×C73#167611yescharacteristic
159C2×C73#168311yescharacteristic
160C2×C73#169211yescharacteristic
161C2×C73#169711yescharacteristic
162C2×C73#206311yescharacteristic
163C2×C73#206811yescharacteristic
164C2×C73#206811yescharacteristic
165#1990—731no—
166#1987—731no—
167#1947—731no—
168#1939—731no—
169C2×#335—731no—
170C2×#333D7311yescharacteristic
171#1296—731no—
172C73#1059311yescharacteristic, complemented, Sylow
173C2×C4⋊Q8C2×D7311yescharacteristic
174C2×#107—1461no—
175C2×C4⋊C8—731no—
176C2×C4⋊C8—1461no—
177C2×C4⋊C8C2×D7311yescharacteristic
178C2×C4⋊C8C2×D7311yescharacteristic
179C2×C4×C8—731no—
180#384—731no—
181C4×C4⋊C4—731no—
182#340—1461no—
183#340—1461no—
184#340—1461no—
185#340—1461no—
186#340—1461no—
187#336—1461no—
188#335—1462no—
189#333—22no—
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—731no—
194C22×C8—731no—
195C22×C8—1461no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Dic14612yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C42—1461no—
208C2×C42C22×D7311yescharacteristic
209#107—2922no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—2922no—
214C4⋊C8—1461no—
215C4⋊C8—1461no—
216C4⋊C8C22⋊D7312yes—
217C4×C8—1461no—
218C4×C8—1461no—
219#95—1461no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—41no—
225C22×C4—2921no—
226C22×C4—1461no—
227C22×C4—1461no—
228C22×C4D4×D7311yescharacteristic
229C22×C4D4×D7311yescharacteristic
230C22×C4#1192402811yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—2921no—
238C2×C8—2921no—
239C2×C8—2921no—
240C2×C8—732no—
241C2×C8—1461no—
242C2×C8—1461no—
243C2×C8—1461no—
244C2×C8—1461no—
245C2×C8—1461no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—5841no—
255C4⋊C4—732no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C42—2921no—
260C42—2921no—
261C42C2×C22⋊D7311yescharacteristic
262C42C2×Dic14611yescharacteristic
263C42#1192402711yescharacteristic
264C42#1192402711yescharacteristic
265C23#1455656411yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—2921no—
274C2×C4—2921no—
275C2×C4—2921no—
276C2×C4—2921no—
277C2×C4—2921no—
278C2×C4—5841no—
279C2×C4—5841no—
280C2×C4—5841no—
281C2×C4—1462no—
282C2×C4#1455656211yescharacteristic
283C2×C4#1455656311yescharacteristic
284C2×C4#1455656811yescharacteristic
285C2×C4#1455656811yescharacteristic
286C2×C4#1455657011yescharacteristic
287C2×C4#1455658411yescharacteristic
288C2×C4Q16×D7311yescharacteristic
289C2×C4Q16×D7311yescharacteristic
290C2×C4#1455661211yescharacteristic
291C2×C4#1455661411yescharacteristic
292C2×C4#1455661811yescharacteristic
293C2×C4#1455661811yescharacteristic
294C2×C4#1455662011yescharacteristic
295C2×C4#1455662311yescharacteristic
296C8—42no—
297C8—81no—
298C8—2921no—
299C8—5841no—
300C8—1462no—
301C22#1798851011yescharacteristic
302C22#1798879611yescharacteristic
303C22#1798880511yescharacteristic
304C22#1798882711yescharacteristic
305C22#1798883611yescharacteristic
306C22#1798884911yescharacteristic
307C22#1798885611yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—2922no—
312C4—5841no—
313C4—11681no—
314C4#1798879511yescharacteristic
315C4#1798880411yescharacteristic
316C4#1798882511yescharacteristic
317C4#1798883011yescharacteristic
318C4#1798888011yescharacteristic
319C4#1798888011yescharacteristic
320C4#1798889211yescharacteristic
321C4#1798889611yescharacteristic
322C2#2260933411yescharacteristic
323C2#2260938511yescharacteristic
324C2#2260944011yescharacteristic
325C2#2260946711yescharacteristic
326C2#2261128711yescharacteristic
327C2#2261132211yescharacteristic
328C2#2261132411yescharacteristic
subgroupG/H
centerC23#14556564
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC2×#333×C73C2
socle, prime radicalC23×C73#121
hypercenterC2×#333D73
hypocenterC73#10593
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
172. C73#10593semidirect

Maximal subgroups

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

subgroupindex
#226108932
#226108802
#226106902
#226106472
C2×#179883392
#226078152
C2×#333×C732
#1059373