Finite Group Databasebeta

← #34013777

Subgroups — #34013777

Order 18688.

394 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×#17989508C211yesmaximal, characteristic, complemented
2C2×C22⋊#11924031C211yesmaximal, characteristic
3C2×C22⋊#11924031C211yesmaximal, characteristic
4C2×#17989473C211yesmaximal, characteristic, complemented
5#22624970C211yesmaximal, characteristic, complemented
6#22624970C211yesmaximal, characteristic, complemented
7#22609705C211yesmaximal, characteristic
8C22×#11924031C2211yescharacteristic
9C22×#11924031C2211yescharacteristic
10C22×#11924031C2211yescharacteristic
11C22×#11924031C2211yescharacteristic
12#17989508—22no—
13C22⋊#11924031—22no—
14C22⋊#11924031—22no—
15#17989473—22no—
16C23×#10596831C2211yescharacteristic
17C2×C8×Dic73C2211yescharacteristic
18C2×C8×Dic73C2211yescharacteristic
19C4×C22⋊Dic73C411yescharacteristic
20#17988341C411yescharacteristic
21#17988341C411yescharacteristic
22C2×C22⋊C8×C73C411yescharacteristic
23C2×#11924031—21no—
24C2×#11924031—21no—
25C2×#11924031—21no—
26C2×#11924031—21no—
27C2×#11924031—21no—
28C2×#11924031—21no—
29C2×#11924031—21no—
30C2×#11924031—21no—
31C2×#11924031—21no—
32C2×#11924031—21no—
33C2×#11924031D412yes—
34C2×#11924031D412yes—
35C22×#10596831—21no—
36C22×#10596831—21no—
37C22×#10596831—21no—
38C22×#10596831—21no—
39C22×#10596831—21no—
40C22×#10596831—21no—
41C22×#10596831C2×C411yescharacteristic
42C22×#10596831C2311yescharacteristic
43C2×C22⋊Dic73C811yescharacteristic
44C2×C22⋊Dic73C811yescharacteristic
45C2×C4×Dic73C2×C411yescharacteristic
46C2×C4×Dic73C2×C411yescharacteristic
47C8×Dic73—21no—
48C8×Dic73—21no—
49C8×Dic73—21no—
50C8×Dic73—21no—
51#14556498C811yescharacteristic
52#14556498C811yescharacteristic
53C23×C4×C73C2×C411yescharacteristic
54C22×C8×C73C2×C411yescharacteristic
55C22×C8×C73C2×C411yescharacteristic
56C22⋊C8×C73—22no—
57#11924031—22no—
58#11924031—22no—
59#11924031—41no—
60#11924031—41no—
61C22×Dic73C2×C811yescharacteristic
62C22×Dic73C2×C811yescharacteristic
63C22×Dic73C2×C811yescharacteristic
64C22×Dic73C2×C811yescharacteristic
65C2×#10596831—21no—
66C2×#10596831—21no—
67C2×#10596831—21no—
68C2×#10596831—41no—
69C2×#10596831—41no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C2×#10596831C2×D411yescharacteristic
73C2×#10596831C2×D411yescharacteristic
74C2×#10596831#4111yescharacteristic
75C2×#10596831#4111yescharacteristic
76C2×#10596831#4111yescharacteristic
77C2×#10596831#4111yescharacteristic
78C22⋊Dic73—22no—
79C22⋊Dic73C1614yescomplemented
80C4×Dic73—21no—
81C4×Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84C24×C73C2×C811yescharacteristic
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73C2×C811yescharacteristic
92C22×C4×C73C22×C411yescharacteristic
93C2×C8×C73—21no—
94C2×C8×C73—21no—
95C2×C8×C73—21no—
96C2×C8×C73—21no—
97C2×C8×C73—21no—
98C2×C8×C73M1612yes—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73C2×C1612yes—
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×Dic73C2×C1612yes—
130C2×Dic73C2×C1612yes—
131C2×Dic73M3212yes—
132C8×C73—22no—
133C8×C73—41no—
134#10596831—41no—
135#10596831#12111yescharacteristic
136#10596831#12311yescharacteristic
137#10596831#12411yescharacteristic
138#10596831#12611yescharacteristic
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×C73C22×C1611yescharacteristic
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—22no—
160Dic73—22no—
161Dic73—41no—
162#13120—731nomaximal, Sylow
163C2×C73—42no—
164C2×C73#192311yescharacteristic
165C2×C73#216211yescharacteristic
166C2×C73#216411yescharacteristic
167C2×C73D4×C1611yescharacteristic
168C2×C73D4×C1611yescharacteristic
169C2×C73#216811yescharacteristic
170C2×C73#216911yescharacteristic
171C2×C4⋊C16—731no—
172C2×C22⋊C16—731no—
173C2×C22⋊C16—731no—
174C2×C4×C16—731no—
175C8×C22⋊C4—731no—
176#1374—731no—
177#1374—731no—
178C73#1312011yescharacteristic, complemented, Sylow
179C23×C8—731no—
180C22×C16—731no—
181C22×C16—731no—
182C22×C16—731no—
183C22×C16—731no—
184C2×C22⋊C8#6440811yescharacteristic
185C2×C4×C8—731no—
186C2×C4×C8—731no—
187C4×C22⋊C4—731no—
188C4⋊C16—1462no—
189C22⋊C16—1462no—
190C22⋊C16—1462no—
191C4×C16—1462no—
192#336—731no—
193#336—731no—
194C23×C4C2×#6440811yescharacteristic
195C22×C8—731no—
196C22×C8—731no—
197C22×C8—1461no—
198C22×C8—1461no—
199C22×C8—1461no—
200C22×C8—1461no—
201C22×C8—1461no—
202C22×C8—1461no—
203C22×C8C2×#6440811yescharacteristic
204C22×C8C2×#6440811yescharacteristic
205C2×C22⋊C4—731no—
206C2×C22⋊C4—731no—
207C2×C42—731no—
208C2×C42—731no—
209C2×C16—732no—
210C2×C16—732no—
211C2×C16—1461no—
212C2×C16—1461no—
213C2×C16—1461no—
214C2×C16—1461no—
215C2×C16—1461no—
216C2×C16—1461no—
217C2×C16—1461no—
218C2×C16—1461no—
219C2×C16—1461no—
220C2×C16—1461no—
221C22⋊C8—22no—
222C4×C8—1461no—
223C4×C8—1461no—
224C4×C8—1461no—
225C4×C8—1461no—
226#95—731no—
227#95—731no—
228C24#1192403611yescharacteristic
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×C4#1192403611yescharacteristic
240C22×C4C22×#6440811yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—2921no—
247C2×C8—2921no—
248C2×C8—2921no—
249C2×C8—2921no—
250C2×C8—731no—
251C2×C8—731no—
252C2×C8—731no—
253C2×C8—731no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—1461no—
257C2×C8—1461no—
258C2×C8—1461no—
259C2×C8#1192403712yes—
260C22⋊C4—734no—
261C22⋊C4—1462no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42—1461no—
266C16—2921no—
267C16—2921no—
268C16—1462no—
269C16—1462no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#1455666412yes—
277C23C2×#1192403611yescharacteristic
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—732no—
287C2×C4—732no—
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#1455667011yescharacteristic
298C2×C4D4×#6440811yescharacteristic
299C2×C4D4×#6440811yescharacteristic
300C2×C4C2×#1192403711yescharacteristic
301C2×C4#1455667811yescharacteristic
302C2×C4#1455667811yescharacteristic
303C8—22no—
304C8—41no—
305C8—2921no—
306C8—731no—
307C8—731no—
308C8—731no—
309C8—731no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1798960411yescharacteristic
318C22#1798961411yescharacteristic
319C22#1798961411yescharacteristic
320C22C2×#1455666411yescharacteristic
321C22#1798964311yescharacteristic
322C22#1798964611yescharacteristic
323C22#1798964611yescharacteristic
324C4—41no—
325C4—2921no—
326C4—1462no—
327C4—1462no—
328C4—1462no—
329C4#1798953711yescharacteristic
330C4#1798961111yescharacteristic
331C4#1798961811yescharacteristic
332C4#1798962211yescharacteristic
333C2—42no—
334C2#2262600111yescharacteristic
335C2#2262628911yescharacteristic
336C2#2262629711yescharacteristic
337C2#2262630911yescharacteristic
338C2#2262630911yescharacteristic
339C2#2262631211yescharacteristic
340C2#2262631611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#64408
commutatorC22×C73C22×C16
FittingC2×C22⋊C8×C73C4
socleC23×C73C22×C8
prime radicalC24×C73C2×C8
cosocleC22×#10596831C23
hypercenterC2×C22⋊C8#64408
hypocenterC73#13120
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#17989508C2semidirect
4. C2×#17989473C2semidirect
5. #22624970C2semidirect
6. #22624970C2semidirect
79. C22⋊Dic73C16semidirect
178. C73#13120semidirect

Maximal subgroups

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

subgroupindex
C2×#179895082
C2×C22⋊#119240312
C2×#179894732
#226249702
#226097052
#1312073