Finite Group Databasebeta

← C2×#22612848 #33245289

Subgroups — C2×#22612848 #33245289

Order 18688.

3158 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic146C211yesmaximal, characteristic
2C22×#14556556C212yesmaximal
3#22612848C2116yesmaximal, direct product factor
4C2×#17988484C214yesmaximal
5C2×#17988483C212yesmaximal
6C2×#17988451C212yesmaximal
7C2×C4×C4⋊Dic73C211yesmaximal, characteristic
8C2×#17988438C212yesmaximal
9C2×#382×C73C211yesmaximal, characteristic
10C23×Dic146C2211yescharacteristic
11C2×C4×Dic146C4116yescomplemented
12C2×C4×Dic146C2218yes—
13C2×#14556556—216no—
14C2×#14556556C22116yes—
15C22×C4⋊Dic73C2212yes—
16C22×C4⋊Dic73C2211yescharacteristic
17C22×#11924007C2214yes—
18C22×#11924007C2214yes—
19C22×#11924007C2212yes—
20C22×C4×Dic73C2214yes—
21C22×C4×Dic73C2212yes—
22C22×C4×Dic73C2212yes—
23#17988484C22132yes—
24#17988483C22116yes—
25#17988451C22116yes—
26C4×C4⋊Dic73C2218yes—
27#17988438C22116yes—
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2214yes—
31C22×C4⋊C4×C73C2212yes—
32C22×C42×C73C2211yescharacteristic
33#382×C73C2218yes—
34C2×#95×C73C2212yes—
35C2×#95×C73C2212yes—
36C22×Dic146C2×C418yes—
37C22×Dic146D418yes—
38C22×Dic146Q818yes—
39C22×Dic146C2314yes—
40C23×Dic73C2312yes—
41C23×Dic73C2312yes—
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C4×Dic146C2×C4164yescomplemented
45#14556556—264no—
46C2×C4⋊Dic73—28no—
47C2×C4⋊Dic73C2×C418yes—
48C2×C4⋊Dic73C2318yes—
49C2×C4⋊Dic73C2314yes—
50C2×#11924007—216no—
51C2×#11924007—216no—
52C2×#11924007C2×C4116yes—
53C2×#11924007C23116yes—
54C2×#11924007C23116yes—
55C2×#11924007C2318yes—
56C2×C4×Dic73—216no—
57C2×C4×Dic73—28no—
58C2×C4×Dic73C2×C4116yes—
59C2×C4×Dic73C23116yes—
60C2×C4×Dic73C2318yes—
61C2×C4×Dic73C2318yes—
62#14556498C2314yes—
63#14556498C2314yes—
64#14556498C23116yes—
65C23×C4×C73C2314yes—
66C23×C4×C73C2311yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C23×C4×C73C2311yescharacteristic
69C2×C4⋊C4×C73—28no—
70C2×C4⋊C4×C73C2318yes—
71C2×C42×C73C2×C418yes—
72C2×C42×C73C2314yes—
73#95×C73C2318yes—
74#95×C73C2318yes—
75C2×Dic146C4⋊C4164yescomplemented
76C2×Dic146C22×C4116yes—
77C2×Dic146C2×D4116yes—
78C2×Dic146C2×Q8116yes—
79C22×Dic73—24no—
80C22×Dic73—28no—
81C22×Dic73—24no—
82C22×Dic73—24no—
83C22×Dic73—24no—
84C22×Dic73—24no—
85C22×Dic73C22×C418yes—
86C22×Dic73C22×C418yes—
87C22×Dic73C2×D418yes—
88C22×Dic73C2×Q818yes—
89C22×Dic73#4118yes—
90C22×Dic73C2414yes—
91C22×Dic73C2414yes—
92C22×Dic73C2414yes—
93C22×Dic73C2414yes—
94C4⋊Dic73—216no—
95C4⋊Dic73C22×C4116yes—
96#11924007—232no—
97#11924007—232no—
98#11924007C22×C4132yes—
99C4×Dic73—216no—
100C4×Dic73—232no—
101C4×Dic73C22×C4132yes—
102C24×C73C2411yescharacteristic
103C22×C4×C73—24no—
104C22×C4×C73—24no—
105C22×C4×C73—28no—
106C22×C4×C73—28no—
107C22×C4×C73—28no—
108C22×C4×C73C22×C414yes—
109C22×C4×C73C22×C414yes—
110C22×C4×C73C22×C414yes—
111C22×C4×C73C2×D414yes—
112C22×C4×C73C2×Q814yes—
113C22×C4×C73C2418yes—
114C22×C4×C73C2412yes—
115C22×C4×C73C2412yes—
116C22×C4×C73C2412yes—
117C4⋊C4×C73—216no—
118C42×C73C22×C4116yes—
119C23×C73C23×C412yes—
120C23×C73C22×D412yes—
121C23×C73C22×Q812yes—
122C23×C73C2×#4114yes—
123C23×C732−1+414yes—
124C23×C73C2511yescharacteristic
125C2×C4×C73—28no—
126C2×C4×C73—28no—
127C2×C4×C73—24no—
128C2×C4×C73—24no—
129C2×C4×C73—28no—
130C2×C4×C73—28no—
131C2×C4×C73—28no—
132C2×C4×C73—416no—
133C2×C4×C73C2×C4⋊C4116yes—
134C2×C4×C73C23×C414yes—
135C2×C4×C73C23×C414yes—
136C2×C4×C73C23×C414yes—
137C2×C4×C73C22×D414yes—
138C2×C4×C73C22×Q814yes—
139C2×Dic73—216no—
140C2×Dic73—216no—
141C2×Dic73—24no—
142C2×Dic73—28no—
143C2×Dic73—24no—
144C2×Dic73—24no—
145C2×Dic73—24no—
146C2×Dic73—24no—
147C2×Dic73—48no—
148C2×Dic73C2×C4⋊C4132yes—
149C2×Dic73C23×C418yes—
150C2×Dic73C23×C418yes—
151C2×Dic73C22×D418yes—
152C2×Dic73C22×Q818yes—
153C2×Dic73C2×#4118yes—
154Dic146C2×C4⋊C4164yescomplemented
155C22×C73C22×C4⋊C414yes—
156C22×C73C4×#4114yes—
157C22×C73#51914yes—
158C22×C73#54818yes—
159C22×C73#55718yes—
160C22×C73C24×C411yescharacteristic
161C22×C73C23×D411yescharacteristic
162C22×C73C23×Q811yescharacteristic
163C22×C73C22×#4112yes—
164C22×C73C2×2−1+412yes—
165C4×C73—24no—
166C4×C73—24no—
167C4×C73—48no—
168C4×C73C22×C4⋊C418yes—
169Dic73—28no—
170Dic73—28no—
171Dic73—44no—
172Dic73C22×C4⋊C4116yes—
173C2×#2351—731nomaximal, Sylow
174C2×C73#235118yescomplemented
175C2×C73C23×C4⋊C411yescharacteristic
176C2×C73C2×C4×#4111yescharacteristic
177C2×C73C2×#51911yescharacteristic
178C2×C73C2×#54812yes—
179C2×C73C2×#55712yes—
180C22×C4×Q8—731no—
181C22×C4×Q8—732no—
182#2351—7316no—
183C2×#389—734no—
184C2×#389—732no—
185C2×#382—732no—
186C2×#382D7311yescharacteristic
187C2×C4×C4⋊C4—731no—
188C2×C4×C4⋊C4—732no—
189C73C2×#235111yescharacteristic, complemented, Sylow
190C23×Q8—731no—
191C2×C4×Q8—7316no—
192C2×C4×Q8—7316no—
193C2×C4×Q8—738no—
194C2×C4×Q8—14616no—
195C22×C4⋊C4—732no—
196C22×C4⋊C4—731no—
197C22×C4⋊C4—734no—
198C22×C4⋊C4—734no—
199C22×C4⋊C4—732no—
200C22×C4⋊C4C2×D7312yes—
201C22×C42—732no—
202C22×C42—734no—
203C22×C42—732no—
204C22×C42C2×D7311yescharacteristic
205#389—7316no—
206#389—7332no—
207#382—7316no—
208#382C2×D7318yes—
209C4×C4⋊C4—738no—
210C4×C4⋊C4—7316no—
211C2×#95—731no—
212C2×#95—731no—
213C2×#95—734no—
214C2×#95C2×D7312yes—
215C2×#95C2×D7312yes—
216C22×Q8—738no—
217C22×Q8—738no—
218C22×Q8—738no—
219C22×Q8—734no—
220C23×C4—732no—
221C23×C4—732no—
222C23×C4—732no—
223C23×C4—732no—
224C23×C4C22×D7314yes—
225C23×C4C22×D7311yescharacteristic
226C23×C4C22×D7311yescharacteristic
227C23×C4C22×D7311yescharacteristic
228C4×Q8—7364no—
229C4×Q8—14664no—
230C2×C4⋊C4—28no—
231C2×C4⋊C4—7316no—
232C2×C4⋊C4—738no—
233C2×C4⋊C4—738no—
234C2×C4⋊C4—734no—
235C2×C4⋊C4—7316no—
236C2×C4⋊C4—7316no—
237C2×C4⋊C4—738no—
238C2×C4⋊C4—14616no—
239C2×C4⋊C4—14616no—
240C2×C4⋊C4—1468no—
241C2×C4⋊C4C22×D7318yes—
242C2×C42—7316no—
243C2×C42—738no—
244C2×C42—7316no—
245C2×C42—738no—
246C2×C42—14616no—
247C2×C42—1468no—
248C2×C42C4×D7318yes—
249C2×C42C22×D7314yes—
250#95—734no—
251#95—734no—
252#95—7316no—
253#95C22×D7318yes—
254#95C22×D7318yes—
255C24C23×D7311yescharacteristic
256C2×Q8—7364no—
257C2×Q8—7316no—
258C2×Q8—7316no—
259C2×Q8—7316no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—738no—
266C22×C4—738no—
267C22×C4—738no—
268C22×C4—734no—
269C22×C4—738no—
270C22×C4—738no—
271C22×C4—734no—
272C22×C4—734no—
273C22×C4—734no—
274C22×C4—1464no—
275C22×C4—1464no—
276C22×C4—1464no—
277C22×C4—1464no—
278C22×C4—1468no—
279C22×C4—1464no—
280C22×C4C2×C4×D7314yes—
281C22×C4C2×C4×D7314yes—
282C22×C4C2×C4×D7314yes—
283C22×C4D4×D7314yes—
284C22×C4Q8×D7314yes—
285C22×C4C23×D7318yes—
286C22×C4C23×D7312yes—
287C22×C4C23×D7312yes—
288C22×C4C23×D7312yes—
289C4⋊C4—216no—
290C4⋊C4—7332no—
291C4⋊C4—7316no—
292C4⋊C4—14632no—
293C4⋊C4—14632no—
294C4⋊C4—14616no—
295C42—7332no—
296C42—14632no—
297C42—14616no—
298C42C2×C4×D73116yes—
299C23C22×C4×D7312yes—
300C23C2×D4×D7312yes—
301C23C2×Q8×D7312yes—
302C23#41×D7314yes—
303C23#1455663814yes—
304C23C24×D7311yescharacteristic
305Q8—7364no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—28no—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—416no—
314C2×C4—2928no—
315C2×C4—738no—
316C2×C4—738no—
317C2×C4—738no—
318C2×C4—7332no—
319C2×C4—738no—
320C2×C4—738no—
321C2×C4—1464no—
322C2×C4—1464no—
323C2×C4—1464no—
324C2×C4—1464no—
325C2×C4—1468no—
326C2×C4—1464no—
327C2×C4—14616no—
328C2×C4—14616no—
329C2×C4C4⋊C4×D73116yes—
330C2×C4C22×C4×D7314yes—
331C2×C4C22×C4×D7314yes—
332C2×C4C22×C4×D7314yes—
333C2×C4C2×D4×D7314yes—
334C2×C4C2×Q8×D7314yes—
335C22C2×C4⋊C4×D7314yes—
336C22#1798905514yes—
337C22#1798906414yes—
338C22#1798924518yes—
339C22#1798931418yes—
340C22C23×C4×D7311yescharacteristic
341C22C22×D4×D7311yescharacteristic
342C22C22×Q8×D7311yescharacteristic
343C22C2×#41×D7312yes—
344C22C2×#1455663812yes—
345C4—24no—
346C4—24no—
347C4—48no—
348C4—2924no—
349C4—7316no—
350C4—1468no—
351C4—1468no—
352C4C2×C4⋊C4×D7318yes—
353C2#2261284818yesdirect product factor
354C2C22×C4⋊C4×D7311yescharacteristic
355C2C2×#1798905511yescharacteristic
356C2C2×#1798906411yescharacteristic
357C2C2×#1798924512yes—
358C2C2×#1798931412yes—
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#382×C73C2
socle, prime radicalC24×C73C24
cosocleC23×C73C25
hypercenterC2×#382D73
hypocenterC73C2×#2351
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. #22612848C2direct (N × H)
11. C2×C4×Dic146C4semidirect
44. C4×Dic146C2×C4semidirect
75. C2×Dic146C4⋊C4semidirect
154. Dic146C2×C4⋊C4semidirect
174. C2×C73#2351semidirect
189. C73C2×#2351semidirect
353. C2#22612848direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic1462
C22×#145565562
#226128482
C2×#179884842
C2×#179884832
C2×#179884512
C2×C4×C4⋊Dic732
C2×#179884382
C2×#382×C732
C2×#235173