Finite Group Databasebeta

← C2×#22610770 #33089747

Subgroups — C2×#22610770 #33089747

Order 18688.

2206 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556588C211yesmaximal, characteristic
2C22×#14556507C214yesmaximal, complemented
3C2×C4×#11924012C211yesmaximal, characteristic, complemented
4#22610770C218yesmaximal, direct product factor
5C2×#423×C73C211yesmaximal, characteristic, complemented
6C23×D292C414yes—
7C23×D292C2212yes—
8C22×#11924012C2212yes—
9C2×#14556588—21no—
10C2×#14556588—21no—
11C2×#14556588—22no—
12C2×#14556588—22no—
13C2×#14556588—22no—
14C2×#14556588C414yes—
15C2×#14556588C2214yes—
16C2×#14556507—216no—
17C2×#14556507C22116yescomplemented
18C4×#11924012—22no—
19C4×#11924012C2214yescomplemented
20C2×#14556502—21no—
21C2×C4×#10596831—21no—
22C22×M16×C73C2212yes—
23C22×C42×C73C2211yescharacteristic
24#423×C73—22no—
25#423×C73C2214yescomplemented
26C2×C4⋊C8×C73—22no—
27C24×D73C2×C414yes—
28C22×D292—28no—
29C22×D292—24no—
30C22×D292—24no—
31C22×D292—22no—
32C22×D292—22no—
33C22×D292—22no—
34C22×D292—22no—
35C22×D292—28no—
36C22×D292—28no—
37C22×D292—416no—
38C22×D292C2×C414yes—
39C22×D292C2×C4116yes—
40C22×D292C2314yes—
41C2×#11924012—22no—
42C2×#11924012—24no—
43C2×#11924012D418yescomplemented
44C2×#11924012C2314yes—
45C22×#10596831—22no—
46#14556588—24no—
47#14556588—28no—
48#14556588—24no—
49#14556588—28no—
50#14556588—24no—
51#14556588—24no—
52#14556507—232no—
53#14556502—24no—
54C4×#10596831—24no—
55C23×C4×C73C2×C412yes—
56C23×C4×C73C2311yescharacteristic
57C2×M16×C73—22no—
58C2×M16×C73—28no—
59C2×M16×C73C2314yes—
60C22×C8×C73—22no—
61C2×C42×C73C2×C412yes—
62C2×C42×C73D411yescharacteristic
63C2×C42×C73D411yescharacteristic
64C2×C42×C73D412yes—
65C2×C42×C73D412yes—
66C2×C42×C73D412yes—
67C2×C42×C73C2312yes—
68C4⋊C8×C73—28no—
69C23×D73—24no—
70C23×D73—24no—
71C23×D73—216no—
72C23×D73—416no—
73C23×D73C22×C418yes—
74C2×D292—216no—
75C2×D292—24no—
76C2×D292—24no—
77C2×D292—216no—
78C2×D292—216no—
79C2×D292—28no—
80C2×D292—24no—
81C2×D292—24no—
82C2×D292—28no—
83C2×D292—416no—
84C2×D292—432no—
85C2×D292—416no—
86C2×D292—48no—
87C2×D292—48no—
88C2×D292—44no—
89C2×D292—44no—
90C2×D292—44no—
91C2×D292—44no—
92C2×D292—432no—
93#11924012—28no—
94#11924012—24no—
95#11924012C2×D418yescomplemented
96C2×#10596831—28no—
97C2×#10596831—24no—
98C24×C73C22×C411yescharacteristic
99C22×C4×C73—28no—
100C22×C4×C73C22⋊C414yes—
101C22×C4×C73C22⋊C412yes—
102C22×C4×C73C22⋊C412yes—
103C22×C4×C73C22×C414yes—
104C22×C4×C73C22×C411yescharacteristic
105C22×C4×C73C2×D414yes—
106C22×C4×C73C2×D411yescharacteristic
107C22×C4×C73C2×D411yescharacteristic
108C22×C4×C73C2×D411yescharacteristic
109C22×C4×C73C2×D411yescharacteristic
110C22×C4×C73#4114yes—
111C22×C4×C73C2411yescharacteristic
112M16×C73—28no—
113M16×C73—44no—
114C2×C8×C73—24no—
115C2×C8×C73—44no—
116C42×C73C22⋊C412yes—
117C42×C73C22⋊C414yes—
118C42×C73C22⋊C412yes—
119C42×C73C2×D414yes—
120C42×C73C2×D412yes—
121C42×C73C2×D412yes—
122C23×C73—24no—
123C23×C73C2×C22⋊C411yescharacteristic
124C23×C73C2×C22⋊C411yescharacteristic
125C23×C73C4×D414yes—
126C23×C73C23×C411yescharacteristic
127C22×D73—28no—
128C22×D73—216no—
129C22×D73—416no—
130C22×D73—48no—
131C22×D73—48no—
132C22×D73—416no—
133C22×D73—416no—
134C22×D73—832no—
135C2×C4×C73—24no—
136C2×C4×C73—28no—
137C2×C4×C73—28no—
138C2×C4×C73#10018yescomplemented
139C2×C4×C73C2×C22⋊C414yes—
140C2×C4×C73C2×C22⋊C411yescharacteristic
141C2×C4×C73C2×C22⋊C411yescharacteristic
142C2×C4×C73C2×C22⋊C414yes—
143C2×C4×C73C4×D414yes—
144C2×C4×C73#12114yes—
145C2×C4×C73#12114yes—
146C2×C4×C73#12412yes—
147C2×C4×C73#12412yes—
148C2×C4×C73#12712yes—
149C2×C4×C73#12712yes—
150C2×C4×C73C22×D412yes—
151C2×C4×C73C22×D411yescharacteristic
152C2×C4×C73C22×D411yescharacteristic
153C2×C4×C73C2×#4112yes—
154D292—432no—
155D292—48no—
156D292—44no—
157D292—44no—
158D292—48no—
159D292—48no—
160D292—432no—
161C8×C73—44no—
162#10596831—28no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—28no—
166C22×C73#39012yes—
167C22×C73#39012yes—
168C22×C73C2×#10014yes—
169C22×C73C22×C22⋊C411yescharacteristic
170C22×C73C2×C4×D412yes—
171C2×D73—416no—
172C2×D73—48no—
173C2×D73—816no—
174C2×D73—816no—
175C2×D73—816no—
176C4×C73—24no—
177C4×C73#39012yes—
178C4×C73#39012yes—
179C4×C73C2×#10018yescomplemented
180C4×C73C2×#12112yes—
181C4×C73C2×#12411yescharacteristic
182C4×C73C2×#12711yescharacteristic
183C2×#1965—731nomaximal, Sylow
184C2×C73—22no—
185C2×C73—22no—
186C2×C73#196514yescomplemented
187C2×C73C2×#39011yescharacteristic
188C2×C73C22×#10012yes—
189D73—88no—
190C22×#127—731no—
191C2×#423D7311yescharacteristic, complemented
192C22×#100—734no—
193C2×C4×M16—731no—
194#1965—738no—
195C73C2×#196511yescharacteristic, complemented, Sylow
196C23×D4—734no—
197C23×D4—732no—
198C22×M16—732no—
199C22×M16C2×D7312yes—
200C2×#127—734no—
201C2×#127—734no—
202C2×#127—1461no—
203C2×#127—1461no—
204C2×#127—1462no—
205C2×#127—1462no—
206C2×#127—1462no—
207C22×C42C2×D7311yescharacteristic
208#423—22no—
209#423C2×D7314yescomplemented
210C2×C4⋊C8—22no—
211C2×#100—7316no—
212C2×#100—14616no—
213C4×M16—734no—
214C4×M16—1462no—
215C2×#97—1461no—
216C2×C4×C8—1461no—
217C25—734no—
218C22×D4—29216no—
219C22×D4—7316no—
220C22×D4—734no—
221C22×D4—734no—
222C22×D4—1468no—
223C22×D4—1464no—
224C22×D4—1464no—
225C22×D4—1468no—
226C22×D4—1462no—
227C22×D4—1462no—
228C22×D4—1462no—
229C22×D4—1462no—
230C22×D4—1468no—
231C23×C4C4×D7312yes—
232C23×C4C22×D7311yescharacteristic
233C2×M16—22no—
234C2×M16—28no—
235C2×M16—738no—
236C2×M16—734no—
237C2×M16—1462no—
238C2×M16—1464no—
239C2×M16C22×D7314yes—
240C22×C8—22no—
241C22×C8—1462no—
242#127—1464no—
243#127—1468no—
244#127—1464no—
245#127—1468no—
246#127—1464no—
247#127—1464no—
248C2×C42C4×D7312yes—
249C2×C42D29211yescharacteristic
250C2×C42D29211yescharacteristic
251C2×C42D29212yes—
252C2×C42C22⋊D7312yes—
253C2×C42C22⋊D7312yes—
254C2×C42C22×D7312yes—
255C4⋊C8—28no—
256#100—14632no—
257#97—1464no—
258C4×C8—1464no—
259C24—29216no—
260C24—738no—
261C24—1464no—
262C24—1464no—
263C24—14616no—
264C24C2×C4×D7311yescharacteristic
265C2×D4—29216no—
266C2×D4—29232no—
267C2×D4—29232no—
268C2×D4—29216no—
269C2×D4—2928no—
270C2×D4—2928no—
271C2×D4—2924no—
272C2×D4—2924no—
273C2×D4—2924no—
274C2×D4—2924no—
275C2×D4—14616no—
276C2×D4—1464no—
277C2×D4—1464no—
278C2×D4—14616no—
279C2×D4—14616no—
280C2×D4—1468no—
281C2×D4—1464no—
282C2×D4—1464no—
283C2×D4—1468no—
284C22×C4—28no—
285C22×C4#1192400514yes—
286C22×C4#1192400512yes—
287C22×C4#1192400512yes—
288C22×C4C2×C4×D7314yes—
289C22×C4C2×C4×D7311yescharacteristic
290C22×C4D4×D7314yes—
291C22×C4C2×C22⋊D7311yescharacteristic
292C22×C4C2×C22⋊D7311yescharacteristic
293C22×C4C2×D29211yescharacteristic
294C22×C4C2×D29211yescharacteristic
295C22×C4#1192402914yes—
296C22×C4C23×D7311yescharacteristic
297M16—28no—
298M16—44no—
299M16—738no—
300M16—1468no—
301M16—1464no—
302C2×C8—24no—
303C2×C8—44no—
304C2×C8—1468no—
305C2×C8—1464no—
306C42#1192400512yes—
307C42#1192400514yes—
308C42#1192400512yes—
309C42C2×C22⋊D7314yes—
310C42C2×D29212yes—
311C42C2×D29212yes—
312C23—24no—
313C23—29216no—
314C23—29216no—
315C23—2928no—
316C23—2928no—
317C23—29216no—
318C23—58432no—
319C23—1468no—
320C23—14616no—
321C23C2×#1192400511yescharacteristic
322C23C2×#1192400511yescharacteristic
323C23#1455655314yes—
324C23C22×C4×D7311yescharacteristic
325D4—29232no—
326D4—2924no—
327D4—2928no—
328D4—2928no—
329D4—29232no—
330D4—2928no—
331D4—2924no—
332C2×C4—24no—
333C2×C4—28no—
334C2×C4—28no—
335C2×C4#1455650718yescomplemented
336C2×C4C2×#1192400514yes—
337C2×C4C2×#1192400511yescharacteristic
338C2×C4C2×#1192400511yescharacteristic
339C2×C4C2×#1192400514yes—
340C2×C4#1455655314yes—
341C2×C4#1455656614yes—
342C2×C4#1455656614yes—
343C2×C4#1455658012yes—
344C2×C4#1455658012yes—
345C2×C4#1455658712yes—
346C2×C4#1455658712yes—
347C2×C4C2×D4×D7312yes—
348C2×C4C22×C22⋊D7311yescharacteristic
349C2×C4C22×D29211yescharacteristic
350C2×C4C2×#1192402912yes—
351C8—44no—
352C8—1468no—
353C22—22no—
354C22—22no—
355C22—28no—
356C22—29216no—
357C22—2928no—
358C22—58416no—
359C22—58416no—
360C22—58416no—
361C22#1798848812yes—
362C22#1798848812yes—
363C22C2×#1455650714yes—
364C22C22×#1192400511yescharacteristic
365C22C2×#1455655312yes—
366C4—24no—
367C4#1798848812yes—
368C4#1798848812yes—
369C4C2×#1455650718yescomplemented
370C4C2×#1455656612yes—
371C4C2×#1455658011yescharacteristic
372C4C2×#1455658711yescharacteristic
373C2—22no—
374C2—22no—
375C2—5848no—
376C2#2261077014yesdirect product factor
377C2C2×#1798848811yescharacteristic
378C2C22×#1455650712yes—
subgroupG/H
centerC23C2×#11924005
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#423×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC22×#14556588C2
cosocleC22×C4×C73C24
hypercenterC2×#423D73
hypocenterC73C2×#1965
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
2. C22×#14556507C2semidirect
3. C2×C4×#11924012C2semidirect
4. #22610770C2direct (N × H)
5. C2×#423×C73C2semidirect
17. C2×#14556507C22semidirect
19. C4×#11924012C22semidirect
25. #423×C73C22semidirect
43. C2×#11924012D4semidirect
95. #11924012C2×D4semidirect
138. C2×C4×C73#100semidirect
179. C4×C73C2×#100semidirect
186. C2×C73#1965semidirect
191. C2×#423D73semidirect
195. C73C2×#1965semidirect
209. #423C2×D73semidirect
335. C2×C4#14556507semidirect
369. C4C2×#14556507semidirect
376. C2#22610770direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565882
C22×#145565072
C2×C4×#119240122
#226107702
C2×#423×C732
C2×#196573