Finite Group Databasebeta

← C2×#22610145 #33086792

Subgroups — C2×#22610145 #33086792

Order 18688.

1402 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989065C211yesmaximal, characteristic
2C2×#17988627C212yesmaximal
3C22×#14556510C211yesmaximal, characteristic
4#22610145C218yesmaximal, direct product factor
5C2×#17988347C212yesmaximal
6C2×#391×C73C211yesmaximal, characteristic
7C22×#11924012C2212yes—
8#17989065—24no—
9#17989065—22no—
10#17989065C2214yes—
11C2×Q8×Dic73—22no—
12C2×Q8×Dic73—22no—
13C2×#14556550—22no—
14C2×#14556550C2212yes—
15#17988627—24no—
16#17988627C2218yes—
17C2×#14556524—22no—
18C2×#14556522—22no—
19C2×#14556510C418yescomplemented
20C2×#14556510C2214yes—
21#17988347C2218yes—
22C23×Q8×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C42×C73C2211yescharacteristic
25#391×C73—22no—
26#391×C73C2214yes—
27C2×#95×C73—22no—
28C2×#11924012—22no—
29C2×#11924012—24no—
30C2×#11924012C2×C418yes—
31C2×#11924012C2314yes—
32C22×#10596831—22no—
33Q8×Dic73—28no—
34Q8×Dic73—28no—
35Q8×Dic73—28no—
36Q8×Dic73—28no—
37#14556550—28no—
38#14556550—28no—
39#14556550—22no—
40#14556550—22no—
41#14556550D414yes—
42#14556550C2314yes—
43C2×C4⋊Dic73—22no—
44C2×C4⋊Dic73—22no—
45C2×C4⋊Dic73D412yes—
46C2×C4⋊Dic73D412yes—
47C2×C22⋊Dic73—22no—
48C2×C4×Dic73—24no—
49C2×C4×Dic73—22no—
50#14556524—28no—
51#14556522—28no—
52#14556510C2×C4116yescomplemented
53C22×Q8×C73—22no—
54C22×Q8×C73—22no—
55C22×Q8×C73—24no—
56C22×Q8×C73C2×C414yes—
57C22×Q8×C73D412yes—
58C22×Q8×C73Q814yes—
59C22×Q8×C73C2312yes—
60C23×C4×C73—21no—
61C23×C4×C73—21no—
62C23×C4×C73D412yes—
63C23×C4×C73C2311yescharacteristic
64C2×C4⋊C4×C73—22no—
65C2×C4⋊C4×C73—22no—
66C2×C4⋊C4×C73—21no—
67C2×C4⋊C4×C73C2312yes—
68C2×C42×C73—24no—
69C2×C42×C73—21no—
70C2×C42×C73C2312yes—
71#95×C73—28no—
72C22×Dic73—22no—
73C22×Dic73—22no—
74#11924012—28no—
75#11924012—24no—
76#11924012C22×C418yes—
77C2×#10596831—28no—
78C2×#10596831—24no—
79C4⋊Dic73—28no—
80C4⋊Dic73—28no—
81C4⋊Dic73—22no—
82C4⋊Dic73—22no—
83C4⋊Dic73C2×D414yes—
84C4⋊Dic73C2×D414yes—
85C22⋊Dic73—24no—
86C22⋊Dic73—24no—
87C4×Dic73—216no—
88C4×Dic73—24no—
89C4×Dic73—24no—
90C24×C73C2×D411yescharacteristic
91C2×Q8×C73—28no—
92C2×Q8×C73—28no—
93C2×Q8×C73—24no—
94C2×Q8×C73—28no—
95C2×Q8×C73—28no—
96C2×Q8×C73—24no—
97C2×Q8×C73—24no—
98C2×Q8×C73—24no—
99C2×Q8×C73C4⋊C418yes—
100C2×Q8×C73C22×C414yes—
101C2×Q8×C73C2×Q814yes—
102C22×C4×C73—22no—
103C22×C4×C73—22no—
104C22×C4×C73—24no—
105C22×C4×C73—24no—
106C22×C4×C73—22no—
107C22×C4×C73—22no—
108C22×C4×C73—42no—
109C22×C4×C73—42no—
110C22×C4×C73—44no—
111C22×C4×C73—41no—
112C22×C4×C73—41no—
113C22×C4×C73C4⋊C418yes—
114C22×C4×C73C22×C412yes—
115C22×C4×C73C2×D412yes—
116C22×C4×C73C2×D412yes—
117C22×C4×C73C2×D414yes—
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73C2×Q812yes—
120C22×C4×C73#4114yes—
121C22×C4×C73C2411yescharacteristic
122C4⋊C4×C73—24no—
123C4⋊C4×C73—42no—
124C42×C73—24no—
125C42×C73—42no—
126C23×C73—22no—
127C23×C73—22no—
128C23×C73C2×C4⋊C412yes—
129C23×C73#12011yescharacteristic
130C23×C73#12011yescharacteristic
131C23×C73#12312yes—
132C23×C73C22×D411yescharacteristic
133Q8×C73—28no—
134Q8×C73—28no—
135Q8×C73—216no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—28no—
139C2×C4×C73—28no—
140C2×C4×C73—24no—
141C2×C4×C73—48no—
142C2×C4×C73—42no—
143C2×C4×C73—42no—
144C2×C4×C73—44no—
145C2×C4×C73—42no—
146C2×C4×C73—82no—
147C2×C4×C73—82no—
148C2×C4×C73C2×C4⋊C418yes—
149C2×C4×C73C2×C4⋊C412yes—
150C2×C4×C73C4×D414yes—
151C2×C4×C73C4×D414yes—
152C2×C4×C73#12012yes—
153C2×C4×C73C22⋊Q814yes—
154C2×C4×C73C22⋊Q814yes—
155C2×C4×C73#12312yes—
156C2×C4×C73C23×C411yescharacteristic
157C2×C4×C73C22×D412yes—
158C2×C4×C73C22×Q811yescharacteristic
159C2×C4×C73C2×#4112yes—
160C2×Dic73—24no—
161C2×Dic73—24no—
162C2×Dic73—44no—
163C2×Dic73—44no—
164#10596831—28no—
165C22×C73—24no—
166C22×C73—24no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73#38512yes—
172C22×C73#38512yes—
173C22×C73#45412yes—
174C22×C73#45612yes—
175C22×C73C22×C4⋊C411yescharacteristic
176C22×C73C2×#12011yescharacteristic
177C22×C73C2×#12311yescharacteristic
178C4×C73—28no—
179C4×C73—44no—
180C4×C73—82no—
181C4×C73#38514yes—
182C4×C73C2×C4×D412yes—
183C4×C73C2×C22⋊Q812yes—
184Dic73—44no—
185Dic73—44no—
186C2×#1857—731nomaximal, Sylow
187C2×C73—21no—
188C2×C73—21no—
189C2×C73—22no—
190C2×C73#185714yescomplemented
191C2×C73C2×#38511yescharacteristic
192C2×C73C2×#45411yescharacteristic
193C2×C73C2×#45611yescharacteristic
194C2×#519—731no—
195C2×#428—732no—
196C22×#101—731no—
197C2×#391D7311yescharacteristic
198#1857—738no—
199C2×#339—732no—
200C73C2×#185711yescharacteristic, complemented, Sylow
201C23×Q8C2×D7311yescharacteristic
202C22×M16—732no—
203#519—734no—
204#519—1464no—
205#519—1462no—
206C2×C4×Q8—1462no—
207C2×C4×Q8—1462no—
208C2×#117—732no—
209C2×#117—1462no—
210C22×C4⋊C4C2×D7311yescharacteristic
211C22×C42C2×D7311yescharacteristic
212#428—738no—
213#428—1464no—
214C2×#107—1462no—
215C2×#106—1462no—
216C2×#101—738no—
217C2×#101—734no—
218#391—22no—
219#391C2×D7314yes—
220C2×#95—22no—
221#339—738no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8Dic14614yes—
226C22×Q8C4×D7314yes—
227C22×Q8C22⋊D7312yes—
228C22×Q8C22×D7312yes—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4C22⋊D7312yes—
232C23×C4C22×D7311yescharacteristic
233C2×M16—738no—
234C2×M16—734no—
235C2×M16—1462no—
236C2×M16—1464no—
237C22×C8—1462no—
238C4×Q8—1468no—
239C4×Q8—1468no—
240C4×Q8—1468no—
241C4×Q8—1468no—
242#117—734no—
243#117—734no—
244#117—1468no—
245#117—1462no—
246#117—1462no—
247#117—1468no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—732no—
252C2×C4⋊C4—732no—
253C2×C4⋊C4—1462no—
254C2×C4⋊C4—1462no—
255C2×C4⋊C4C22×D7312yes—
256C2×C22⋊C4—1462no—
257C2×C42—24no—
258C2×C42—21no—
259C2×C42—1464no—
260C2×C42—1462no—
261C2×C42C22×D7312yes—
262#107—1468no—
263#106—1468no—
264#101—7316no—
265#95—28no—
266C24C2×C22⋊D7311yescharacteristic
267C2×Q8—28no—
268C2×Q8—28no—
269C2×Q8—24no—
270C2×Q8—28no—
271C2×Q8—28no—
272C2×Q8—24no—
273C2×Q8—24no—
274C2×Q8—24no—
275C2×Q8#1192400718yes—
276C2×Q8C2×C4×D7314yes—
277C2×Q8C2×Dic14614yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—1462no—
290C22×C4—1462no—
291C22×C4#1192400718yes—
292C22×C4C2×C4×D7312yes—
293C22×C4D4×D7312yes—
294C22×C4D4×D7312yes—
295C22×C4C2×C22⋊D7314yes—
296C22×C4C2×C22⋊D7311yescharacteristic
297C22×C4C2×Dic14612yes—
298C22×C4#1192402714yes—
299C22×C4C23×D7311yescharacteristic
300M16—738no—
301M16—1468no—
302M16—1464no—
303C2×C8—1468no—
304C2×C8—1464no—
305C4⋊C4—24no—
306C4⋊C4—42no—
307C4⋊C4—734no—
308C4⋊C4—734no—
309C4⋊C4—1468no—
310C4⋊C4—1468no—
311C4⋊C4—1462no—
312C4⋊C4—1462no—
313C22⋊C4—1464no—
314C22⋊C4—1464no—
315C42—24no—
316C42—42no—
317C42—14616no—
318C42—1464no—
319C42—1464no—
320C23—22no—
321C23—22no—
322C23C2×#1192400712yes—
323C23#1455655911yescharacteristic
324C23#1455655911yescharacteristic
325C23#1455657212yes—
326C23C22×C22⋊D7311yescharacteristic
327Q8—216no—
328Q8—28no—
329Q8—28no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—42no—
336C2×C4—48no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—2924no—
343C2×C4—2924no—
344C2×C4—1464no—
345C2×C4—1464no—
346C2×C4C2×#1192400718yes—
347C2×C4C2×#1192400712yes—
348C2×C4#1455655114yes—
349C2×C4#1455655114yes—
350C2×C4#1455655912yes—
351C2×C4#1455656814yes—
352C2×C4#1455656814yes—
353C2×C4#1455657212yes—
354C2×C4C22×C4×D7311yescharacteristic
355C2×C4C2×D4×D7312yes—
356C2×C4C22×Dic14611yescharacteristic
357C2×C4C2×#1192402712yes—
358C8—1468no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22#1798845912yes—
366C22#1798845912yes—
367C22#1798875912yes—
368C22#1798876912yes—
369C22C22×#1192400711yescharacteristic
370C22C2×#1455655911yescharacteristic
371C22C2×#1455657211yescharacteristic
372C4—28no—
373C4—44no—
374C4—82no—
375C4—2924no—
376C4—2924no—
377C4#1798845914yes—
378C4C2×#1455655112yes—
379C4C2×#1455656812yes—
380C2—21no—
381C2—22no—
382C2—21no—
383C2#2261014514yesdirect product factor
384C2C2×#1798845911yescharacteristic
385C2C2×#1798875911yescharacteristic
386C2C2×#1798876911yescharacteristic
subgroupG/H
centerC23#14556559
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#391×C73C2
socleC23×C73#120
prime radicalC24×C73C2×D4
cosocleC22×C4×C73C24
hypercenterC2×#391D73
hypocenterC73C2×#1857
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
4. #22610145C2direct (N × H)
19. C2×#14556510C4semidirect
52. #14556510C2×C4semidirect
190. C2×C73#1857semidirect
200. C73C2×#1857semidirect
383. C2#22610145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890652
C2×#179886272
C22×#145565102
#226101452
C2×#179883472
C2×#391×C732
C2×#185773