Finite Group Databasebeta

← C2×#22618642 #33949857

Subgroups — C2×#22618642 #33949857

Order 18688.

2894 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×#14556599C212yesmaximal, complemented
2C2×#17989137C211yesmaximal, characteristic
3#22618642C2116yesmaximal, direct product factor
4C2×#17988664C214yesmaximal, complemented
5C2×#17988652C214yesmaximal, complemented
6C2×#17988555C212yesmaximal, complemented
7C22×C4×#10596831C211yesmaximal, characteristic, complemented
8C2×#423×C73C211yesmaximal, characteristic, complemented
9C22×#11924028C2212yes—
10C2×#14556599—216no—
11C2×#14556599C22116yescomplemented
12C22×#11924011C2214yes—
13C23×#10596831C2211yescharacteristic
14C23×#10596831C2211yescharacteristic
15C22×C8×D73C2214yes—
16#17989137C418yes—
17#17989137C2218yes—
18C2×#14556591C411yescharacteristic
19C2×#14556588C411yescharacteristic
20C2×#14556579C412yes—
21C2×#14556565C414yes—
22C2×C4×D292C2214yes—
23#17988664C22132yescomplemented
24#17988652C22132yescomplemented
25#17988555C22116yescomplemented
26C2×#14556503C2218yes—
27C2×C4×#10596831C2212yes—
28C2×C4×#10596831C2212yes—
29C2×C4×#10596831C2218yescomplemented
30C22×M16×C73C2212yes—
31C22×C42×C73C2211yescharacteristic
32#423×C73C2218yescomplemented
33C2×C4⋊C8×C73C2214yes—
34C2×#11924028—28no—
35C2×#11924028—28no—
36C2×#11924028C2×C418yes—
37C2×#11924028C2318yes—
38C22×Dic146C2×C412yes—
39C22×D292C2×C412yes—
40C22×D292C2×C414yes—
41C22×C22⋊D73C2×C414yes—
42C22×C4×D73C2314yes—
43#14556599—264no—
44C2×#11924011—216no—
45C2×#11924011C23116yes—
46C22×#10596831—24no—
47C22×#10596831D418yescomplemented
48C22×#10596831C2312yes—
49C22×#10596831C2314yes—
50C22×#10596831C2311yescharacteristic
51C22×#10596831C2311yescharacteristic
52C22×#10596831C2314yes—
53C2×C8×D73—216no—
54C2×C8×D73C23116yes—
55#14556591C2×C418yes—
56#14556588C2×C418yes—
57#14556579C2×C4116yes—
58#14556565C2×C4132yes—
59C4×D292C2×C4116yes—
60C4×D292C23116yes—
61C2×C4⋊Dic73C2×C414yes—
62C2×#11924005C2×C418yes—
63#14556503C23132yes—
64C4×#10596831C2318yes—
65C4×#10596831C2318yes—
66C23×C4×C73C2×C412yes—
67C23×C4×C73C2311yescharacteristic
68C2×M16×C73—28no—
69C2×M16×C73C2318yes—
70C22×C8×C73C2314yes—
71C2×C42×C73C2×C411yescharacteristic
72C2×C42×C73C2×C414yes—
73C2×C42×C73C2×C411yescharacteristic
74C2×C42×C73C2314yes—
75C2×C42×C73C2312yes—
76C4⋊C8×C73C23116yes—
77C23×D73C22×C414yes—
78#11924028—232no—
79#11924028—216no—
80#11924028—216no—
81C2×Dic146—28no—
82C2×Dic146C22×C418yes—
83C2×D292—28no—
84C2×D292—216no—
85C2×D292C22×C4116yes—
86C2×D292C22×C418yes—
87C2×C22⋊D73—216no—
88C2×C22⋊D73C22×C4116yes—
89C22×Dic73C22×C414yes—
90C2×C4×D73—28no—
91C2×C4×D73—28no—
92C2×C4×D73C22×C418yes—
93C2×C4×D73C2418yes—
94#11924011—232no—
95C2×#10596831—24no—
96C2×#10596831—28no—
97C2×#10596831C2×D414yes—
98C2×#10596831C2×D414yes—
99C2×#10596831C2×D4116yescomplemented
100C2×#10596831C2414yes—
101C2×#10596831C2412yes—
102C2×#10596831C2412yes—
103C8×D73—232no—
104C4⋊Dic73C22×C4116yes—
105#11924005C22×C4132yes—
106C24×C73C22×C411yescharacteristic
107C22×C4×C73—28no—
108C22×C4×C73C22×C412yes—
109C22×C4×C73C22×C418yes—
110C22×C4×C73C22×C411yescharacteristic
111C22×C4×C73C22×C412yes—
112C22×C4×C73C22×C412yes—
113C22×C4×C73C2×D414yes—
114C22×C4×C73#4114yes—
115C22×C4×C73C2412yes—
116C22×C4×C73C2411yescharacteristic
117M16×C73—216no—
118C2×C8×C73—28no—
119C2×C8×C73C2418yes—
120C42×C73C22×C414yes—
121C42×C73C22×C414yes—
122C42×C73C22×C414yes—
123C42×C73C2414yes—
124C23×C73—24no—
125C23×C73C4×D414yes—
126C23×C73C23×C412yes—
127C23×C73C23×C411yescharacteristic
128C22×D73—28no—
129C22×D73—216no—
130C22×D73C23×C418yes—
131C2×C4×C73—24no—
132C2×C4×C73—216no—
133C2×C4×C73C4×D414yes—
134C2×C4×C73C4×D418yes—
135C2×C4×C73#13118yescomplemented
136C2×C4×C73C23×C414yes—
137C2×C4×C73C23×C411yescharacteristic
138C2×C4×C73C23×C412yes—
139C2×C4×C73C23×C414yes—
140C2×C4×C73C22×D412yes—
141C2×C4×C73C22×D414yes—
142C2×C4×C73C2×#4112yes—
143C2×C4×C73C2×#4114yes—
144C2×C4×C73C2511yescharacteristic
145C22⋊D73—232no—
146C2×Dic73—28no—
147C2×Dic73C23×C418yes—
148D292—216no—
149D292—232no—
150C4×D73—216no—
151C4×D73—28no—
152C4×D73—28no—
153Dic146—216no—
154C8×C73—28no—
155#10596831—24no—
156#10596831C22×D414yes—
157#10596831C22×D414yes—
158C22×C73—28no—
159C22×C73—24no—
160C22×C73C2×C4×D414yes—
161C22×C73C2×C4×D412yes—
162C22×C73C2×#13114yes—
163C22×C73C24×C411yescharacteristic
164C2×D73—28no—
165C2×D73—216no—
166C2×D73—416no—
167C4×C73—24no—
168C4×C73C2×C4×D414yes—
169C4×C73C2×C4×D412yes—
170C4×C73C2×#13118yescomplemented
171C4×C73C23×D411yescharacteristic
172C4×C73C22×#4111yescharacteristic
173Dic73—28no—
174C2×#2931—731nomaximal, Sylow
175C2×C73—24no—
176C2×C73#293114yescomplemented
177C2×C73C22×C4×D411yescharacteristic
178C2×C73C22×#13112yes—
179D73—48no—
180C22×#131—732no—
181C2×#532—731no—
182#2931—7316no—
183C2×#436—734no—
184C2×C8×D4—734no—
185C2×#423D7311yescharacteristic, complemented
186C2×#408—732no—
187C22×C4×C8—731no—
188C73C2×#293111yescharacteristic, complemented, Sylow
189C22×#41—732no—
190C2×#131—7316no—
191C2×#131—14616no—
192C22×M16—734no—
193C22×M16C2×D7312yes—
194C23×C8—731no—
195C23×C8—731no—
196C23×C8—734no—
197#532—738no—
198#532—738no—
199C2×C4⋊Q8—731no—
200C2×#127—731no—
201C2×#124—732no—
202C2×#121—734no—
203C2×C4×D4—734no—
204C22×C42C2×D7311yescharacteristic
205#436—7332no—
206C8×D4—7332no—
207#423C2×D7318yescomplemented
208C2×C4⋊C8C2×D7314yes—
209#408—7316no—
210C2×C22⋊C8—738no—
211C2×C4×C8—732no—
212C2×C4×C8—732no—
213C2×C4×C8—738no—
214C2×#41—738no—
215C2×#41—738no—
216C2×#41—1468no—
217C2×#41—1468no—
218C22×Q8—732no—
219C22×D4—734no—
220C22×D4—734no—
221C22×D4—732no—
222C23×C4—734no—
223C23×C4C4×D7312yes—
224C23×C4C22×D7311yescharacteristic
225#131—14664no—
226C2×M16—28no—
227C2×M16—7316no—
228C2×M16—14616no—
229C2×M16C22×D7318yes—
230C22×C8—738no—
231C22×C8—734no—
232C22×C8—731no—
233C22×C8—731no—
234C22×C8—734no—
235C22×C8—732no—
236C22×C8—7316no—
237C22×C8—14616no—
238C22×C8—1464no—
239C22×C8C22×D7314yes—
240C4⋊Q8—738no—
241#127—738no—
242#124—7316no—
243#121—7332no—
244C4×D4—7316no—
245C4×D4—7316no—
246C2×C4⋊C4—734no—
247C2×C22⋊C4—738no—
248C2×C42C4×D7311yescharacteristic
249C2×C42C4×D7311yescharacteristic
250C2×C42C4×D7314yes—
251C2×C42C22×D7314yes—
252C2×C42C22×D7312yes—
253C4⋊C8C22×D73116yes—
254C22⋊C8—7332no—
255C4×C8—738no—
256C4×C8—738no—
257C24—734no—
258C24C2×C4×D7311yescharacteristic
259#41—14632no—
260#41—14616no—
261#41—14616no—
262C2×Q8—738no—
263C2×Q8—1468no—
264C2×D4—7316no—
265C2×D4—7316no—
266C2×D4—738no—
267C2×D4—14616no—
268C2×D4—1468no—
269C2×D4—14616no—
270C22×C4—28no—
271C22×C4—734no—
272C22×C4—738no—
273C22×C4—738no—
274C22×C4—1468no—
275C22×C4—1468no—
276C22×C4C2×C4×D7312yes—
277C22×C4C2×C4×D7318yes—
278C22×C4C2×C4×D7311yescharacteristic
279C22×C4C2×C4×D7312yes—
280C22×C4C2×C4×D7312yes—
281C22×C4D4×D7314yes—
282C22×C4#1192402914yes—
283C22×C4C23×D7312yes—
284C22×C4C23×D7311yescharacteristic
285M16—216no—
286M16—14632no—
287C2×C8—28no—
288C2×C8—734no—
289C2×C8—734no—
290C2×C8—7316no—
291C2×C8—732no—
292C2×C8—732no—
293C2×C8—734no—
294C2×C8—14632no—
295C2×C8—1464no—
296C2×C8—1468no—
297C2×C8C23×D7318yes—
298C4⋊C4—7316no—
299C22⋊C4—7332no—
300C42C2×C4×D7314yes—
301C42C2×C4×D7314yes—
302C42C2×C4×D7314yes—
303C42C23×D7314yes—
304C23—24no—
305C23—738no—
306C23—1468no—
307C23—14616no—
308C23#1455655314yes—
309C23C22×C4×D7312yes—
310C23C22×C4×D7311yescharacteristic
311Q8—14616no—
312D4—14632no—
313D4—14616no—
314D4—14632no—
315C2×C4—24no—
316C2×C4—216no—
317C2×C4—738no—
318C2×C4—1468no—
319C2×C4—1468no—
320C2×C4—1468no—
321C2×C4—14616no—
322C2×C4#1455655314yes—
323C2×C4#1455655318yes—
324C2×C4#1455659918yescomplemented
325C2×C4C22×C4×D7314yes—
326C2×C4C22×C4×D7311yescharacteristic
327C2×C4C22×C4×D7312yes—
328C2×C4C22×C4×D7314yes—
329C2×C4C2×D4×D7312yes—
330C2×C4C2×D4×D7314yes—
331C2×C4C2×#1192402912yes—
332C2×C4C2×#1192402914yes—
333C2×C4C24×D7311yescharacteristic
334C8—28no—
335C8—734no—
336C8—734no—
337C8—1464no—
338C22—28no—
339C22—24no—
340C22—29216no—
341C22—1468no—
342C22—14616no—
343C22C2×#1455655314yes—
344C22C2×#1455655312yes—
345C22C2×#1455659914yes—
346C22C23×C4×D7311yescharacteristic
347C4—24no—
348C4—1468no—
349C4C2×#1455655312yes—
350C4C2×#1455655314yes—
351C4C2×#1455659918yescomplemented
352C4C22×D4×D7311yescharacteristic
353C4C22×#1192402911yescharacteristic
354C2—24no—
355C2—2928no—
356C2#2261864214yesdirect product factor
357C2C22×#1455655311yescharacteristic
358C2C22×#1455659912yes—
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC2×C4C24×D73
FittingC2×#423×C73C2
socleC23×C73C23×C4
prime radicalC2×#17989137C2
cosocleC2×C4×C73C25
hypercenterC2×#423D73
hypocenterC73C2×#2931
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C22×#14556599C2semidirect
3. #22618642C2direct (N × H)
4. C2×#17988664C2semidirect
5. C2×#17988652C2semidirect
6. C2×#17988555C2semidirect
7. C22×C4×#10596831C2semidirect
8. C2×#423×C73C2semidirect
11. C2×#14556599C22semidirect
23. #17988664C22semidirect
24. #17988652C22semidirect
25. #17988555C22semidirect
29. C2×C4×#10596831C22semidirect
32. #423×C73C22semidirect
47. C22×#10596831D4semidirect
99. C2×#10596831C2×D4semidirect
135. C2×C4×C73#131semidirect
170. C4×C73C2×#131semidirect
176. C2×C73#2931semidirect
185. C2×#423D73semidirect
188. C73C2×#2931semidirect
207. #423C2×D73semidirect
324. C2×C4#14556599semidirect
351. C4C2×#14556599semidirect
356. C2#22618642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565992
C2×#179891372
#226186422
C2×#179886642
C2×#179886522
C2×#179885552
C22×C4×#105968312
C2×#423×C732
C2×#293173