Finite Group Databasebeta

← C16×#11924027 #33239499

Subgroups — C16×#11924027 #33239499

Order 18688.

602 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#11924027C211yesmaximal, characteristic
2C16×Dic146C211yesmaximal, characteristic, complemented
3#22611833C211yesmaximal, characteristic, complemented
4D4×#11924003C211yesmaximal, characteristic, complemented
5C16×C22⋊D73C212yesmaximal, complemented
6#22611748C212yesmaximal, complemented
7#22611729C211yesmaximal, characteristic, complemented
8#22611727C212yesmaximal, complemented
9C2×C16×Dic73C212yesmaximal, complemented
10C4×C16×D73C211yesmaximal, characteristic, complemented
11D4×C16×C73C211yesmaximal, characteristic, complemented
12C4×#11924027C411yescharacteristic
13C22×#11924003C2212yes—
14C2×C16×D73C2211yescharacteristic
15C2×C16×D73C2211yescharacteristic
16C8×Dic146C2211yescharacteristic
17#17988711C411yescharacteristic
18D4×#10596831C411yescharacteristic
19C8×C22⋊D73C2212yes—
20#17988650C412yes—
21#17988639C411yescharacteristic
22#17988637C412yes—
23C2×C8×Dic73C2212yes—
24C4×C8×D73C2211yescharacteristic
25C4⋊#11924003C2211yescharacteristic
26#17988405C2212yes—
27#17988405C2212yes—
28C22⋊#11924003C2212yes—
29#17988366C2212yes—
30C4×#11924003C2211yescharacteristic
31C16×Dic73C2211yescharacteristic
32C16×Dic73C2212yes—
33C16×Dic73C2212yes—
34C16×Dic73C2212yes—
35C16×Dic73C2211yescharacteristic
36C22×C16×C73C2212yes—
37C8×D4×C73C2211yescharacteristic
38C4⋊C16×C73C2211yescharacteristic
39C22⋊C16×C73C2212yes—
40C4×C16×C73C2211yescharacteristic
41C2×#11924027C811yescharacteristic
42C22×#10596831C2×C412yes—
43C2×C8×D73C2×C411yescharacteristic
44C2×C8×D73C2311yescharacteristic
45C4×Dic146C2×C411yescharacteristic
46#14556556C811yescharacteristic
47D4×Dic73C811yescharacteristic
48C4×C22⋊D73C2×C412yes—
49#14556551C812yes—
50#14556549C811yescharacteristic
51#14556547C812yes—
52C2×C4×Dic73C2×C412yes—
53C42×D73C2×C411yescharacteristic
54C2×#11924003—24no—
55C2×#11924003C2312yes—
56C2×#11924003C2311yescharacteristic
57C2×#11924003C2311yescharacteristic
58C16×D73—22no—
59C16×D73—22no—
60C4⋊#10596831C2×C411yescharacteristic
61#14556520C2×C412yes—
62#14556520C2×C412yes—
63C22⋊#10596831C2×C412yes—
64#14556503C2×C412yes—
65C4×#10596831C2×C411yescharacteristic
66C8×Dic73C2×C411yescharacteristic
67C8×Dic73C2×C412yes—
68C8×Dic73C2×C412yes—
69C8×Dic73C2311yescharacteristic
70C8×Dic73C2312yes—
71C22×C8×C73C2312yes—
72C4×D4×C73C2×C411yescharacteristic
73C2×C16×C73—24no—
74C2×C16×C73C2312yes—
75C2×C16×C73C2311yescharacteristic
76C2×C16×C73C2311yescharacteristic
77C4⋊C8×C73C2×C411yescharacteristic
78C22⋊C8×C73C2×C412yes—
79C4×C8×C73C2311yescharacteristic
80#11924027C1618yesdirect product factor
81C2×Dic146C2×C811yescharacteristic
82C2×C22⋊D73C2×C812yes—
83C22×Dic73C2×C812yes—
84C22×Dic73C2×C812yes—
85C2×C4×D73C2×C811yescharacteristic
86C2×C4×D73C2×C811yescharacteristic
87C2×C4×D73C22×C411yescharacteristic
88C2×#10596831—24no—
89C2×#10596831C22×C412yes—
90C2×#10596831C22×C411yescharacteristic
91C2×#10596831C22×C411yescharacteristic
92C8×D73—21no—
93C8×D73—21no—
94C8×D73—22no—
95C4⋊Dic73C2×C811yescharacteristic
96#11924007C2×C812yes—
97#11924007C2×C812yes—
98C22⋊Dic73C2×C812yes—
99#11924005C2×C812yes—
100C4×Dic73C2×C811yescharacteristic
101C4×Dic73C2×C811yescharacteristic
102C4×Dic73C2×C812yes—
103C4×Dic73C2×C812yes—
104C4×Dic73C22×C411yescharacteristic
105C4×Dic73C22×C412yes—
106#11924003—21no—
107#11924003—22no—
108#11924003#4112yescomplemented
109C2×D4×C73C2×C811yescharacteristic
110C22×C4×C73C22×C412yes—
111C2×C8×C73—22no—
112C2×C8×C73—22no—
113C2×C8×C73C22×C411yescharacteristic
114C2×C8×C73C22×C412yes—
115C2×C8×C73C2411yescharacteristic
116C4⋊C4×C73C2×C811yescharacteristic
117C22⋊C4×C73C2×C812yes—
118C42×C73C22×C411yescharacteristic
119C16×C73—22no—
120C16×C73—21no—
121C16×C73#4112yescomplemented
122C23×C73C22×C812yes—
123C22×D73C22×C811yescharacteristic
124D4×C73C2×C1614yescomplemented
125C2×C4×C73—22no—
126C2×C4×C73—22no—
127C2×C4×C73C22×C811yescharacteristic
128C2×C4×C73C22×C812yes—
129C2×C4×C73C22×C811yescharacteristic
130C2×C4×C73C23×C411yescharacteristic
131C22⋊D73C2×C1618yescomplemented
132C2×Dic73—24no—
133C2×Dic73C2×C1618yescomplemented
134C2×Dic73C22×C811yescharacteristic
135C2×Dic73C22×C812yes—
136C2×Dic73C22×C811yescharacteristic
137C2×Dic73C22×C812yes—
138C2×Dic73C22×C811yescharacteristic
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—22no—
142C4×D73C2×C1614yescomplemented
143Dic146C2×C1614yescomplemented
144C8×C73—22no—
145C8×C73—21no—
146C8×C73C2×#4111yescharacteristic
147C8×C73C2×#4111yescharacteristic
148#10596831—21no—
149#10596831—22no—
150#10596831#13112yes—
151C22×C73—22no—
152C22×C73—22no—
153C22×C73C22×C1614yes—
154C22×C73C23×C811yescharacteristic
155C2×D73—21no—
156C2×D73—21no—
157C2×D73C22×C1612yes—
158C4×C73—21no—
159C4×C73—22no—
160C4×C73C22×C1612yes—
161C4×C73C4×#4111yescharacteristic
162C4×C73C2×#13111yescharacteristic
163Dic73—22no—
164Dic73—21no—
165Dic73C22×C1614yes—
166Dic73C22×C1612yes—
167Dic73#50412yes—
168C16×#41—731nomaximal, Sylow
169C2×C73—24no—
170C2×C73C8×#4111yescharacteristic
171C2×C73C23×C1611yescharacteristic
172C2×C73C2×#50411yescharacteristic
173D73—22no—
174C8×#41—731no—
175Q8×C16—731no—
176Q8×C16—731no—
177D4×C16—732no—
178D4×C16—731no—
179D4×C16—732no—
180D4×C16D7311yescharacteristic, complemented
181#2162—731no—
182#2162—732no—
183C2×C4×C16—732no—
184C2×C4×C16—731no—
185C73C16×#4111yescharacteristic, complemented, Sylow
186C4×#41—731no—
187C22×C16—732no—
188C22×C16—731no—
189C22×C16—731no—
190C22×C16C2×D7312yes—
191C8×Q8—731no—
192C8×Q8—731no—
193C8×D4—732no—
194C8×D4—731no—
195C8×D4—732no—
196C8×D4C2×D7311yescharacteristic
197#431—731no—
198#431—732no—
199C2×C4×C8—732no—
200C2×C4×C8—731no—
201C4⋊C16—732no—
202C4⋊C16—732no—
203C4⋊C16—731no—
204C4⋊C16C2×D7311yescharacteristic
205C22⋊C16—732no—
206C22⋊C16—732no—
207C22⋊C16C2×D7312yes—
208C4×C16—732no—
209C4×C16—731no—
210C4×C16—732no—
211C4×C16—731no—
212C4×C16—732no—
213C4×C16—731no—
214C4×C16C2×D7311yescharacteristic
215C2×#41—731no—
216C22×C8—732no—
217C22×C8—731no—
218C22×C8—731no—
219C22×C8C22×D7312yes—
220C4×Q8—731no—
221C4×Q8—731no—
222C4×D4—731no—
223C4×D4—732no—
224C4×D4—732no—
225C4×D4C4×D7311yescharacteristic
226#117—731no—
227#117—732no—
228C2×C42—732no—
229C2×C42—731no—
230C2×C16—24no—
231C2×C16—731no—
232C2×C16—732no—
233C2×C16—731no—
234C2×C16—1462no—
235C2×C16—1464no—
236C2×C16—1462no—
237C2×C16C22×D7312yes—
238C2×C16C22×D7311yescharacteristic
239C2×C16C22×D7311yescharacteristic
240C4⋊C8—732no—
241C4⋊C8—732no—
242C4⋊C8—731no—
243C4⋊C8C4×D7311yescharacteristic
244C22⋊C8—732no—
245C22⋊C8—732no—
246C22⋊C8C4×D7312yes—
247C4×C8—732no—
248C4×C8—731no—
249C4×C8—732no—
250C4×C8—731no—
251C4×C8—732no—
252C4×C8—731no—
253C4×C8C22×D7311yescharacteristic
254#41—738no—
255C2×Q8—731no—
256C2×D4—732no—
257C2×D4C8×D7311yescharacteristic
258C22×C4—732no—
259C22×C4—731no—
260C22×C4—732no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4C2×C4×D7312yes—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—731no—
267C2×C8—731no—
268C2×C8—732no—
269C2×C8—1462no—
270C2×C8—1464no—
271C2×C8—1461no—
272C2×C8—1461no—
273C2×C8C2×C4×D7312yes—
274C2×C8C2×C4×D7311yescharacteristic
275C2×C8C23×D7311yescharacteristic
276C4⋊C4—732no—
277C4⋊C4—732no—
278C4⋊C4—731no—
279C4⋊C4C8×D7311yescharacteristic
280C22⋊C4—732no—
281C22⋊C4—732no—
282C22⋊C4C8×D7312yes—
283C42—732no—
284C42—731no—
285C42—732no—
286C42—731no—
287C42—731no—
288C42—732no—
289C42C2×C4×D7311yescharacteristic
290C16—21no—
291C16—22no—
292C16—732no—
293C16—1462no—
294C16—1461no—
295C16#1192402712yesdirect product factor
296C23—731no—
297C23C2×C8×D7312yes—
298Q8—734no—
299D4—738no—
300D4C16×D7314yescomplemented
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—738no—
304C2×C4—731no—
305C2×C4—731no—
306C2×C4—732no—
307C2×C4—734no—
308C2×C4—731no—
309C2×C4—732no—
310C2×C4—1462no—
311C2×C4—1464no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4C2×C8×D7312yes—
315C2×C4C2×C8×D7311yescharacteristic
316C2×C4C2×C8×D7311yescharacteristic
317C2×C4C22×C4×D7311yescharacteristic
318C8—22no—
319C8—21no—
320C8—732no—
321C8—1461no—
322C8—1462no—
323C8#41×D7311yescharacteristic
324C8C2×#1192402711yescharacteristic
325C22—22no—
326C22—22no—
327C22—732no—
328C22—1461no—
329C22—1461no—
330C22C2×C16×D7314yes—
331C22C22×C8×D7311yescharacteristic
332C4—22no—
333C4—21no—
334C4—732no—
335C4—734no—
336C4—732no—
337C4—1461no—
338C4—1462no—
339C4C2×C16×D7312yes—
340C4C4×#1192402711yescharacteristic
341C4#131×D7311yescharacteristic
342C2—24no—
343C2—1462no—
344C2C8×#1192402711yescharacteristic
345C2C22×C16×D7311yescharacteristic
346C2#504×D7311yescharacteristic
subgroupG/H
centerC2×C16C22×D73
commutatorC2×C73C23×C16
FrattiniC2×C8C23×D73
FittingD4×C16×C73C2
socleC22×C73C23×C8
prime radicalC2×#11924027C8
cosocleC2×C8×C73C24
hypercenterD4×C16D73
hypocenterC73C16×#41
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C16 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
2. C16×Dic146C2semidirect
3. #22611833C2semidirect
4. D4×#11924003C2semidirect
5. C16×C22⋊D73C2semidirect
6. #22611748C2semidirect
7. #22611729C2semidirect
8. #22611727C2semidirect
9. C2×C16×Dic73C2semidirect
10. C4×C16×D73C2semidirect
11. D4×C16×C73C2semidirect
80. #11924027C16direct (N × H)
108. #11924003#41semidirect
121. C16×C73#41semidirect
124. D4×C73C2×C16semidirect
131. C22⋊D73C2×C16semidirect
133. C2×Dic73C2×C16semidirect
142. C4×D73C2×C16semidirect
143. Dic146C2×C16semidirect
180. D4×C16D73semidirect
185. C73C16×#41semidirect
295. C16#11924027direct (N × H)
300. D4C16×D73semidirect

Maximal subgroups

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

subgroupindex
C8×#119240272
C16×Dic1462
#226118332
D4×#119240032
C16×C22⋊D732
#226117482
#226117292
#226117272
C2×C16×Dic732
C4×C16×D732
D4×C16×C732
C16×#4173