Finite Group Databasebeta

← C4×#17989667 #34031089

Subgroups — C4×#17989667 #34031089

Order 18688.

3250 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989667C212yesmaximal
2#22626503C218yesmaximal, complemented
3C4×#14556679C218yesmaximal, complemented
4#22626497C216yesmaximal, complemented
5C4×D73⋊M16C216yesmaximal, complemented
6C2×C4×#11924029C211yesmaximal, characteristic
7#17989667C4132yesdirect product factor
8C2×#14556679C22116yes—
9C2×D73⋊M16C22112yes—
10#17989552C22148yescomplemented
11C4×#11924038C22112yescomplemented
12C4×#11924038C22112yescomplemented
13C4×#11924037C2214yes—
14C4×#11924037C22112yes—
15#17989546C22112yescomplemented
16C4×#11924036C22112yescomplemented
17C22×#11924029C2211yescharacteristic
18C4×#11924029C414yes—
19C4×#11924029C414yes—
20C4×#11924029C2214yes—
21C4×#11924029C2214yes—
22C2×Q8×Dic73C411yescharacteristic
23C2×C4×D292C413yes—
24C2×#14556553C413yes—
25C2×#14556549C2213yes—
26C2×C42×D73C2213yes—
27C2×C4×Q8×C73C411yescharacteristic
28#14556679C2×C41128yescomplemented
29C2×#11924038C23124yes—
30D73⋊M16C2×C4196yescomplemented
31C2×#11924037C2318yes—
32C2×#11924036C23124yes—
33#14556646C2318yes—
34#14556646C23124yes—
35C4×#10596833C2318yes—
36C4×#10596833C23124yes—
37C2×#11924029C2×C4116yes—
38C2×#11924029C2×C414yes—
39C2×#11924029C2314yes—
40C22×D292C2×C413yes—
41C22×C4×D73C2×C413yes—
42C22×C4×D73C2×C413yes—
43C22×C4×D73C2313yes—
44Q8×Dic73C2×C414yes—
45Q8×Dic73C2×C414yes—
46C4×D292C2×C4112yes—
47C4×D292C2×C4112yes—
48#14556553C2×C4112yes—
49#14556553C2×C4112yes—
50#14556549C2×C4112yes—
51#14556549C23112yes—
52C2×C4⋊Dic73C2×C413yes—
53C2×#11924005C2×C416yes—
54C2×C4×Dic73C2×C413yes—
55C2×C4×Dic73C2311yescharacteristic
56C2×C4×Dic73C2313yes—
57C42×D73C2×C416yes—
58C42×D73C2×C416yes—
59C42×D73C2316yes—
60C42×D73C2316yes—
61C22×Q8×C73C2×C411yescharacteristic
62C4×Q8×C73C2×C414yes—
63C4×Q8×C73C2×C414yes—
64C2×C4⋊C4×C73C2×C413yes—
65C2×C42×C73C2×C413yes—
66#11924038C22×C4196yescomplemented
67#11924037C22×C4132yes—
68#11924036C22×C4196yescomplemented
69C2×#10596833C24116yes—
70C23×D73C22×C413yes—
71#11924029C42132yes—
72#11924029C22×C4132yes—
73C2×D292C42124yes—
74C2×D292C22×C4112yes—
75C22×Dic73C22×C411yescharacteristic
76C22×Dic73C22×C413yes—
77C22×Dic73C2411yescharacteristic
78C2×C4×D73—46no—
79C2×C4×D73—46no—
80C2×C4×D73C22×C416yes—
81C2×C4×D73C22×C416yes—
82C2×C4×D73C22×C416yes—
83C2×C4×D73C22×C416yes—
84C2×C4×D73C22×C416yes—
85C2×C4×D73C22×C4124yes—
86C2×C4×D73C2416yes—
87C4⋊Dic73C22×C4112yes—
88#11924005C22×C4124yes—
89C4×Dic73C22×C411yescharacteristic
90C4×Dic73C22×C411yescharacteristic
91C4×Dic73C22×C416yes—
92C4×Dic73C22×C416yes—
93C4×Dic73C22×C416yes—
94C4×Dic73C2411yescharacteristic
95C4×Dic73C2411yescharacteristic
96C4×Dic73C2416yes—
97C2×Q8×C73C4218yes—
98C2×Q8×C73C22×C414yes—
99C22×C4×C73C22×C411yescharacteristic
100C22×C4×C73C22×C413yes—
101C22×C4×C73C22×C413yes—
102C4⋊C4×C73C22×C4112yes—
103C42×C73C22×C416yes—
104C42×C73C22×C416yes—
105C23×C73C23×C411yescharacteristic
106C22×D73—43no—
107C22×D73—43no—
108C22×D73C2×C42112yes—
109C22×D73C23×C416yes—
110Q8×C73C2×C42116yes—
111C2×C4×C73—22no—
112C2×C4×C73—43no—
113C2×C4×C73C2×C42112yes—
114C2×C4×C73C23×C411yescharacteristic
115C2×C4×C73C23×C416yes—
116C2×C4×C73C23×C416yes—
117C2×C4×C73C23×C411yescharacteristic
118C2×Dic73—22no—
119C2×Dic73—43no—
120C2×Dic73C23×C411yescharacteristic
121C2×Dic73C23×C416yes—
122C2×Dic73C23×C411yescharacteristic
123C2×Dic73C23×C414yes—
124C2×Dic73C23×C411yescharacteristic
125C2×Dic73C2511yescharacteristic
126D292C2×C42148yes—
127C4×D73—212no—
128C4×D73—212no—
129C4×D73—46no—
130C4×D73—46no—
131C4×D73C2×C42124yes—
132C4×D73C23×C4124yes—
133#10596833C23×C4132yes—
134C22×C73—21no—
135C22×C73—21no—
136C22×C73C22×C4212yes—
137C22×C73C24×C411yescharacteristic
138C2×D73—26no—
139C2×D73—26no—
140C2×D73—412no—
141C2×D73C22×C42112yes—
142C4×C73—26no—
143C4×C73—21no—
144C4×C73C22×C42112yes—
145C4×C73#56812yescomplemented
146Dic73—26no—
147Dic73—21no—
148Dic73C22×C4212yes—
149Dic73#56812yescomplemented
150Dic73C24×C412yes—
151C4×#568—731nomaximal, Sylow
152C2×C73—22no—
153C2×C73C23×C4211yescharacteristic
154C2×C73C2×#56811yescharacteristic
155C2×C73C2×#56811yescharacteristic
156D73—212no—
157C2×#568—732no—
158C2×C4×#41—731no—
159#2875—738no—
160C4×#131—738no—
161#2873—736no—
162C2×C4×M16—736no—
163C73C4×#56811yescharacteristic, complemented, Sylow
164C22×#41—731no—
165#568—7332no—
166C2×#131—7316no—
167C22×M16—7312no—
168C4×#41—734no—
169C4×#41—734no—
170C4×#41—734no—
171C4×#41—734no—
172C2×C4×Q8—731no—
173C2×C4×Q8#6440811yescharacteristic
174C2×C4×D4—733no—
175C2×C4×D4—733no—
176C2×#117—733no—
177C22×C42—733no—
178#405—7348no—
179C4×M16—734no—
180C4×M16—7312no—
181C4×M16—7312no—
182C4×M16—7312no—
183C2×#97—7312no—
184C2×C4×C8—7312no—
185C2×#41—7316no—
186C2×#41—734no—
187C2×#41—734no—
188C22×Q8C2×#6440811yescharacteristic
189C22×D4—733no—
190C23×C4—733no—
191C23×C4—733no—
192C23×C4—733no—
193#131—73128no—
194C2×M16—738no—
195C2×M16—7396no—
196C2×M16—7324no—
197C22×C8—7324no—
198C4×Q8—734no—
199C4×Q8—734no—
200C4×Q8C2×#6440814yes—
201C4×Q8C2×#6440814yes—
202C4×D4—7312no—
203C4×D4—7312no—
204C4×D4—7312no—
205C4×D4—7312no—
206#117—7312no—
207#117—7312no—
208C2×C4⋊C4—733no—
209C2×C4⋊C4C2×#6440813yes—
210C2×C22⋊C4—736no—
211C2×C42—733no—
212C2×C42—733no—
213C2×C42—731no—
214C2×C42—736no—
215C2×C42—736no—
216C2×C42—736no—
217C2×C42—736no—
218C2×C42C2×#6440813yes—
219#97—738no—
220#97—7324no—
221C4×C8—738no—
222C4×C8—7324no—
223C24—733no—
224#41—7332no—
225#41—7332no—
226C2×Q8C4×#6440818yes—
227C2×Q8C22×#6440814yes—
228C2×D4—7312no—
229C2×D4—7324no—
230C22×C4—2926no—
231C22×C4—2926no—
232C22×C4—733no—
233C22×C4—736no—
234C22×C4—736no—
235C22×C4—731no—
236C22×C4—736no—
237C22×C4—736no—
238C22×C4—7324no—
239C22×C4—731no—
240C22×C4—736no—
241C22×C4—736no—
242C22×C4C22×#6440811yescharacteristic
243C22×C4C22×#6440813yes—
244C22×C4C22×#6440813yes—
245M16—7332no—
246M16—7396no—
247C2×C8—7316no—
248C2×C8—7396no—
249C4⋊C4—7312no—
250C4⋊C4C22×#64408112yes—
251C22⋊C4—7324no—
252C42—731no—
253C42—736no—
254C42—736no—
255C42—736no—
256C42—736no—
257C42—731no—
258C42—731no—
259C42—731no—
260C42C22×#6440816yes—
261C42C22×#6440816yes—
262C23—2923no—
263C23—2923no—
264C23—7312no—
265C23—736no—
266C23C23×#6440811yescharacteristic
267Q8C2×C4×#64408116yes—
268D4—7348no—
269C2×C4—22no—
270C2×C4—43no—
271C2×C4—2926no—
272C2×C4—2926no—
273C2×C4—2923no—
274C2×C4—734no—
275C2×C4—731no—
276C2×C4—731no—
277C2×C4—731no—
278C2×C4—7324no—
279C2×C4—7324no—
280C2×C4—731no—
281C2×C4—736no—
282C2×C4—14612no—
283C2×C4—1462no—
284C2×C4—14612no—
285C2×C4C2×C4×#64408112yes—
286C2×C4C23×#6440811yescharacteristic
287C2×C4C23×#6440816yes—
288C2×C4C23×#6440816yes—
289C2×C4C23×#6440811yescharacteristic
290C8—7332no—
291C22—21no—
292C22—21no—
293C22—29212no—
294C22—7312no—
295C22—1466no—
296C22—1466no—
297C22C22×C4×#6440812yes—
298C22C24×#6440811yescharacteristic
299C4—26no—
300C4—21no—
301C4—732no—
302C4—732no—
303C4—732no—
304C4—1461no—
305C4—1466no—
306C4C22×C4×#64408112yes—
307C4#1798966712yesdirect product factor
308C2—22no—
309C2—14612no—
310C2C23×C4×#6440811yescharacteristic
311C2D73⋊#56811yescharacteristic
312C2C2×#1798966711yescharacteristic
subgroupG/H
centerC2×C4C23×#64408
commutatorC2×C73C23×C42
FrattiniC22C24×#64408
FittingC2×C4×Q8×C73C4
socleC22×C73C24×C4
prime radicalC22×#11924029C22
cosocleC2×Dic73C25
hypercenterC2×C4×Q8#64408
hypocenterC73C4×#568
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #22626503C2semidirect
3. C4×#14556679C2semidirect
4. #22626497C2semidirect
5. C4×D73⋊M16C2semidirect
7. #17989667C4direct (N × H)
10. #17989552C22semidirect
11. C4×#11924038C22semidirect
12. C4×#11924038C22semidirect
15. #17989546C22semidirect
16. C4×#11924036C22semidirect
28. #14556679C2×C4semidirect
30. D73⋊M16C2×C4semidirect
66. #11924038C22×C4semidirect
68. #11924036C22×C4semidirect
145. C4×C73#568semidirect
149. Dic73#568semidirect
163. C73C4×#568semidirect
307. C4#17989667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896672
#226265032
C4×#145566792
#226264972
C4×D73⋊M162
C2×C4×#119240292
C4×#56873