Finite Group Databasebeta

← #33003715

Subgroups — #33003715

Order 18688.

382 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988405C211yesmaximal, characteristic, complemented
2C2×C22⋊#11924003C211yesmaximal, characteristic
3C2×#17988362C211yesmaximal, characteristic, complemented
4C8×C22⋊Dic73C211yesmaximal, characteristic
5#22608008C211yesmaximal, characteristic, complemented
6#22608008C211yesmaximal, characteristic, complemented
7C2×C22⋊C16×C73C211yesmaximal, characteristic
8C22×#11924003C2211yescharacteristic
9C22×#11924003C2211yescharacteristic
10C2×C22⋊#10596831C411yescharacteristic
11C2×C8×Dic73C2211yescharacteristic
12C2×C8×Dic73C2211yescharacteristic
13C4×C22⋊Dic73C411yescharacteristic
14#17988405—22no—
15C22⋊#11924003—22no—
16#17988362—22no—
17#17988341C411yescharacteristic
18#17988341C411yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C22×C16×C73C2211yescharacteristic
21C22×C16×C73C2211yescharacteristic
22C22⋊C16×C73—22no—
23C22×#10596831C2×C411yescharacteristic
24C22×#10596831C2×C411yescharacteristic
25C2×C22⋊Dic73C811yescharacteristic
26C2×C22⋊Dic73C811yescharacteristic
27C2×C4×Dic73C2×C411yescharacteristic
28C2×C4×Dic73C2×C411yescharacteristic
29C2×#11924003—21no—
30C2×#11924003—21no—
31C2×#11924003—21no—
32C2×#11924003—21no—
33C2×#11924003—21no—
34C2×#11924003D412yes—
35C22⋊#10596831—22no—
36C8×Dic73—21no—
37C8×Dic73—21no—
38C8×Dic73—21no—
39C8×Dic73—21no—
40#14556498C811yescharacteristic
41#14556498C811yescharacteristic
42C23×C4×C73C2×C411yescharacteristic
43C22×C8×C73—21no—
44C22×C8×C73—21no—
45C22×C8×C73—21no—
46C22×C8×C73—21no—
47C22×C8×C73—21no—
48C22×C8×C73—21no—
49C22×C8×C73C2×C411yescharacteristic
50C22×C8×C73C2311yescharacteristic
51C2×C16×C73—21no—
52C2×C16×C73—21no—
53C2×C16×C73—21no—
54C2×C16×C73—21no—
55C2×C16×C73—21no—
56C2×C16×C73D412yes—
57C22×Dic73C2×C811yescharacteristic
58C22×Dic73C2×C811yescharacteristic
59C22×Dic73C2×C811yescharacteristic
60C22×Dic73C2×C811yescharacteristic
61C2×#10596831—21no—
62C2×#10596831—21no—
63C2×#10596831—21no—
64C2×#10596831—21no—
65C2×#10596831—21no—
66C2×#10596831M1612yes—
67C22⋊Dic73—22no—
68C22⋊Dic73—22no—
69C4×Dic73—21no—
70C4×Dic73—21no—
71C4×Dic73—21no—
72C4×Dic73—21no—
73#11924003—22no—
74#11924003—41no—
75C24×C73C2×C811yescharacteristic
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73C2×C811yescharacteristic
83C22×C4×C73C22×C411yescharacteristic
84C2×C8×C73—21no—
85C2×C8×C73—21no—
86C2×C8×C73—21no—
87C2×C8×C73—41no—
88C2×C8×C73—41no—
89C2×C8×C73—41no—
90C2×C8×C73—41no—
91C2×C8×C73C2×D411yescharacteristic
92C2×C8×C73C2×D411yescharacteristic
93C2×C8×C73#4111yescharacteristic
94C2×C8×C73#4111yescharacteristic
95C2×C8×C73#4111yescharacteristic
96C2×C8×C73#4111yescharacteristic
97C16×C73—22no—
98C16×C73—41no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73M3212yes—
106C23×C73C22×C811yescharacteristic
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73#11711yescharacteristic
115C2×C4×C73C4×D411yescharacteristic
116C2×C4×C73C4×D411yescharacteristic
117C2×C4×C73C2×M1611yescharacteristic
118C2×C4×C73#13111yescharacteristic
119C2×C4×C73#13111yescharacteristic
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73M3212yes—
132C8×C73—41no—
133C8×C73#12111yescharacteristic
134C8×C73#12311yescharacteristic
135C8×C73#12411yescharacteristic
136C8×C73#12611yescharacteristic
137#10596831—22no—
138#10596831—41no—
139C22×C73—22no—
140C22×C73—22no—
141C22×C73—22no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73#43111yescharacteristic
147C22×C73C8×D411yescharacteristic
148C22×C73C8×D411yescharacteristic
149C22×C73C2×M3211yescharacteristic
150C22×C73C2×M3211yescharacteristic
151C22×C73#50411yescharacteristic
152C22×C73#50411yescharacteristic
153C4×C73—41no—
154C4×C73#38811yescharacteristic
155C4×C73#43311yescharacteristic
156C4×C73#43511yescharacteristic
157C4×C73#43611yescharacteristic
158Dic73—22no—
159Dic73—41no—
160Dic73—41no—
161Dic73—41no—
162#13121—731nomaximal, Sylow
163C2×C73—42no—
164C2×C73#192311yescharacteristic
165C2×C73#216311yescharacteristic
166C2×C73#216411yescharacteristic
167C2×C73#216811yescharacteristic
168C2×C73#216811yescharacteristic
169C2×C73#216811yescharacteristic
170C2×C73#216911yescharacteristic
171C2×C4⋊C16—731no—
172C2×C22⋊C16—731no—
173C2×C22⋊C16D7311yescharacteristic
174C2×#346—731no—
175C8×C22⋊C4—731no—
176#1374—731no—
177#1374—731no—
178C73#1312111yescharacteristic, complemented, Sylow
179C23×C8C2×D7311yescharacteristic
180C22×C16—731no—
181C22×C16—731no—
182C22×C16C2×D7311yescharacteristic
183C22×C16C2×D7311yescharacteristic
184C2×C22⋊C8—731no—
185C2×C4×C8—731no—
186C2×C4×C8—731no—
187C4×C22⋊C4—731no—
188C4⋊C16—1462no—
189C22⋊C16—22no—
190C22⋊C16—1462no—
191#346—1462no—
192#336—731no—
193#336—731no—
194C23×C4C4×D7311yescharacteristic
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—731no—
202C22×C8—731no—
203C22×C8C4×D7311yescharacteristic
204C22×C8C22×D7311yescharacteristic
205C2×C22⋊C4—731no—
206C2×C22⋊C4—731no—
207C2×C42—731no—
208C2×C42—731no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—21no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—732no—
215C2×C16—1461no—
216C2×C16—1461no—
217C2×C16—1461no—
218C2×C16—1461no—
219C2×C16—1461no—
220C2×C16C22⋊D7312yes—
221C22⋊C8—1462no—
222C4×C8—1461no—
223C4×C8—1461no—
224C4×C8—1461no—
225C4×C8—1461no—
226#95—731no—
227#95—731no—
228C24C8×D7311yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4C8×D7311yescharacteristic
240C22×C4C2×C4×D7311yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—732no—
249C2×C8—1461no—
250C2×C8—1461no—
251C2×C8—1461no—
252C2×C8—1461no—
253C2×C8—1461no—
254C2×C8D4×D7311yescharacteristic
255C2×C8C2×C22⋊D7311yescharacteristic
256C2×C8#1192402711yescharacteristic
257C2×C8#1192402711yescharacteristic
258C2×C8#1192402711yescharacteristic
259C2×C8#1192402811yescharacteristic
260C22⋊C4—1462no—
261C22⋊C4—1462no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42—1461no—
266C16—22no—
267C16—41no—
268C16—2921no—
269C16—1462no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#1455653012yes—
277C23C2×C8×D7311yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—732no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4#1455654711yescharacteristic
298C2×C4#1455655111yescharacteristic
299C2×C4C4×C22⋊D7311yescharacteristic
300C2×C4M16×D7311yescharacteristic
301C2×C4#1455659711yescharacteristic
302C2×C4#1455659911yescharacteristic
303C8—41no—
304C8—2921no—
305C8—1462no—
306C8#1455656211yescharacteristic
307C8#1455657211yescharacteristic
308C8#1455657711yescharacteristic
309C8#1455658411yescharacteristic
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1798863711yescharacteristic
318C22#1798865011yescharacteristic
319C22C8×C22⋊D7311yescharacteristic
320C22M32×D7311yescharacteristic
321C22C2×#1455653011yescharacteristic
322C22#1798900311yescharacteristic
323C22#1798900511yescharacteristic
324C4—41no—
325C4—2921no—
326C4—2921no—
327C4—2921no—
328C4—1462no—
329C4#1798847511yescharacteristic
330C4#1798864511yescharacteristic
331C4#1798865611yescharacteristic
332C4#1798866211yescharacteristic
333C2—42no—
334C2#2261053411yescharacteristic
335C2#2261173111yescharacteristic
336C2#2261173511yescharacteristic
337C2#2261175311yescharacteristic
338C2#2261175611yescharacteristic
339C2#2261175911yescharacteristic
340C2#2261176111yescharacteristic
subgroupG/H
center, FrattiniC22×C8C22×D73
commutator, socleC23×C73C22×C8
FittingC2×C22⋊C16×C73C2
prime radicalC24×C73C2×C8
cosocleC22×C8×C73C23
hypercenterC2×C22⋊C16D73
hypocenterC73#13121
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×#17988405C2semidirect
3. C2×#17988362C2semidirect
5. #22608008C2semidirect
6. #22608008C2semidirect
178. C73#13121semidirect

Maximal subgroups

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

subgroupindex
C2×#179884052
C2×C22⋊#119240032
C2×#179883622
C8×C22⋊Dic732
#226080082
C2×C22⋊C16×C732
#1312173