Finite Group Databasebeta

← C2×#22612059 #33240551

Subgroups — C2×#22612059 #33240551

Order 18688.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556535C211yesmaximal, characteristic, complemented
2C2×#17989004C211yesmaximal, characteristic, complemented
3C2×#17988862C211yesmaximal, characteristic, complemented
4#22612059C218yesmaximal, direct product factor
5C2×#17988416C211yesmaximal, characteristic, complemented
6C2×#17988402C211yesmaximal, characteristic, complemented
7C2×#17988400C211yesmaximal, characteristic, complemented
8C2×#472×C73C211yesmaximal, characteristic
9C2×#14556621—21no—
10C22×Dic292C2211yescharacteristic
11C2×#14556535—21no—
12C2×#14556535—21no—
13C2×#14556535—22no—
14C2×#14556535C2214yescomplemented
15#17989004—22no—
16#17989004C2214yescomplemented
17C2×#14556531—21no—
18C2×#14556531C2211yescharacteristic
19C22×#11924003—21no—
20C22×#11924003C2211yescharacteristic
21#17988862—22no—
22#17988862C2214yescomplemented
23C2×#14556527C2211yescharacteristic
24C2×#14556509—21no—
25#17988416C2214yescomplemented
26#17988402C2214yescomplemented
27#17988400C2214yescomplemented
28C2×AGL(1,ℤ/8)×C73—21no—
29C22×D8×C73C2211yescharacteristic
30C2×#131×C73C2211yescharacteristic
31#472×C73—22no—
32#472×C73C2214yes—
33C2×#108×C73C2211yescharacteristic
34C2×#100×C73—21no—
35C22×Dic146—21no—
36#14556621—24no—
37#14556621—42no—
38C2×Dic292—21no—
39C2×Dic292—21no—
40C2×Dic292—21no—
41C2×Dic292—21no—
42C2×Dic292—21no—
43C2×Dic292C2312yes—
44C2×#11924018—41no—
45C2×#11924016—41no—
46C2×#11924012—21no—
47#14556535—24no—
48#14556535—24no—
49#14556531—24no—
50#14556531—21no—
51#14556531C2312yes—
52C2×#11924003—24no—
53C2×#11924003—21no—
54C2×#11924003D411yescharacteristic
55C2×#11924003D411yescharacteristic
56C2×#11924003D412yes—
57C2×#11924003C2312yes—
58#14556527—21no—
59#14556527C2312yes—
60#14556509—24no—
61C2×#41×C73D411yescharacteristic
62C22×D4×C73—21no—
63AGL(1,ℤ/8)×C73—24no—
64AGL(1,ℤ/8)×C73—42no—
65C2×SD16×C73—41no—
66C2×D8×C73—21no—
67C2×D8×C73—21no—
68C2×D8×C73—21no—
69C2×D8×C73—21no—
70C2×D8×C73—21no—
71C2×D8×C73—41no—
72C2×D8×C73C2312yes—
73#131×C73—21no—
74#131×C73—21no—
75#131×C73D412yes—
76#131×C73C2312yes—
77C2×M16×C73—21no—
78C2×M16×C73—21no—
79C2×M16×C73D411yescharacteristic
80C22×C8×C73—21no—
81C22×C8×C73C2311yescharacteristic
82#108×C73—21no—
83#108×C73C2312yes—
84#100×C73—24no—
85C2×Dic146—22no—
86C2×Dic146—41no—
87C2×Dic146—41no—
88C2×Dic146—41no—
89C2×Dic146—41no—
90C2×Dic146—41no—
91C22×Dic73—41no—
92Dic292—22no—
93Dic292—22no—
94Dic292—41no—
95Dic292—41no—
96#11924018—44no—
97#11924016—44no—
98#11924012—22no—
99#11924012—41no—
100C2×#10596831—41no—
101#11924003—22no—
102#11924003C2×D412yes—
103#11924003C2×D412yes—
104C24×C73—41no—
105#41×C73—21no—
106#41×C73—21no—
107#41×C73D812yes—
108#41×C73C2×D412yes—
109C2×Q8×C73D811yescharacteristic
110C2×D4×C73—21no—
111C2×D4×C73—22no—
112C2×D4×C73—41no—
113C2×D4×C73—41no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C2×D4×C73—41no—
117C2×D4×C73D811yescharacteristic
118C22×C4×C73—21no—
119C22×C4×C73C2×D411yescharacteristic
120SD16×C73—44no—
121D8×C73—22no—
122D8×C73—22no—
123D8×C73—44no—
124D8×C73—41no—
125D8×C73—41no—
126M16×C73—21no—
127M16×C73—22no—
128M16×C73—22no—
129M16×C73—22no—
130M16×C73—41no—
131M16×C73C2×D412yes—
132C2×C8×C73—21no—
133C2×C8×C73—22no—
134C2×C8×C73—22no—
135C2×C8×C73—41no—
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73#4111yescharacteristic
140C2×C8×C73#4111yescharacteristic
141C2×C8×C73C2411yescharacteristic
142C23×C73—21no—
143C23×C73—42no—
144C23×C73—81no—
145C23×C73—81no—
146C23×C73—162no—
147C23×C73#13511yescharacteristic
148Q8×C73—21no—
149Q8×C73C2×D812yes—
150D4×C73—22no—
151D4×C73—22no—
152D4×C73—21no—
153D4×C73—42no—
154D4×C73—42no—
155D4×C73—81no—
156D4×C73—81no—
157D4×C73C2×D812yes—
158C2×C4×C73—21no—
159C2×C4×C73—22no—
160C2×C4×C73—22no—
161C2×C4×C73#12111yescharacteristic
162C2×C4×C73#12111yescharacteristic
163C2×C4×C73C2×D811yescharacteristic
164C2×C4×C73C2×D811yescharacteristic
165C2×C4×C73#13511yescharacteristic
166C2×C4×C73C22×D411yescharacteristic
167C2×Dic73—42no—
168C2×Dic73—81no—
169C2×Dic73—81no—
170Dic146—42no—
171Dic146—42no—
172Dic146—81no—
173Dic146—81no—
174C8×C73—22no—
175C8×C73—42no—
176C8×C73#12111yescharacteristic
177C8×C73#12111yescharacteristic
178C8×C73C22×D411yescharacteristic
179C8×C73C2×#4111yescharacteristic
180#10596831—42no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—42no—
184C22×C73—82no—
185C22×C73—162no—
186C22×C73—162no—
187C22×C73—162no—
188C22×C73#46611yescharacteristic
189C22×C73#46611yescharacteristic
190C22×C73C2×#13511yescharacteristic
191C4×C73—22no—
192C4×C73#46611yescharacteristic
193C4×C73#46611yescharacteristic
194C4×C73C2×#12111yescharacteristic
195C4×C73C22×D811yescharacteristic
196Dic73—82no—
197C2×#2223—731nomaximal, Sylow
198C2×C73—21no—
199C2×C73—21no—
200C2×C73—42no—
201C2×C73—162no—
202C2×C73#222312yescomplemented
203C2×C73C2×#46611yescharacteristic
204C22×SD32—731no—
205C2×#504—731no—
206C2×#473—731no—
207C2×#472D7311yescharacteristic
208#2223—738no—
209C2×#368—731no—
210C2×#362—731no—
211C2×#361—731no—
212C73C2×#222311yescharacteristic, complemented, Sylow
213C2×#137—1461no—
214C2×AGL(1,ℤ/8)—21no—
215C22×Q16—731no—
216C22×D8C2×D7311yescharacteristic
217C2×#131C2×D7311yescharacteristic
218C2×SD32—734no—
219C2×SD32—1461no—
220C2×SD32—1461no—
221C2×SD32—1462no—
222#504—734no—
223#504—1462no—
224C2×M32—731no—
225C2×M32—1461no—
226C22×C16—731no—
227C22×C16—1461no—
228#473—734no—
229#473—1462no—
230#472—22no—
231#472C2×D7314yes—
232C2×#108—731no—
233C2×#108C2×D7311yescharacteristic
234C2×#101—1461no—
235C2×#100—21no—
236#368—734no—
237#362—734no—
238#361—734no—
239C2×#41C22⋊D7311yescharacteristic
240C22×Q8—1461no—
241C22×D4—21no—
242#137—2922no—
243#137—1464no—
244AGL(1,ℤ/8)—24no—
245AGL(1,ℤ/8)—42no—
246C2×Q16—2921no—
247C2×Q16—732no—
248C2×Q16—1461no—
249C2×Q16—1461no—
250C2×Q16—1461no—
251C2×Q16—1461no—
252C2×Q16—1461no—
253C2×SD16—41no—
254C2×SD16—2921no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—41no—
261C2×D8C22×D7312yes—
262#131—21no—
263#131—21no—
264#131C22⋊D7312yes—
265#131C22×D7312yes—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—1461no—
269C2×M16C22⋊D7311yescharacteristic
270C22×C8—21no—
271C22×C8C22×D7311yescharacteristic
272SD32—1464no—
273SD32—1464no—
274M32—732no—
275M32—1464no—
276M32—1461no—
277C2×C16—731no—
278C2×C16—731no—
279C2×C16—732no—
280C2×C16—732no—
281C2×C16—1464no—
282C2×C16—1461no—
283#108—21no—
284#108—732no—
285#108—1461no—
286#108C22×D7312yes—
287#101—1464no—
288#100—24no—
289C24—41no—
290#41—21no—
291#41—21no—
292#41#1192401312yes—
293#41C2×C22⋊D7312yes—
294C2×Q8—2921no—
295C2×Q8—2921no—
296C2×Q8—2921no—
297C2×Q8—2921no—
298C2×Q8—2921no—
299C2×Q8—1462no—
300C2×Q8#1192401311yescharacteristic
301C2×D4—21no—
302C2×D4—22no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4#1192401311yescharacteristic
309C22×C4—21no—
310C22×C4—2921no—
311C22×C4C2×C22⋊D7311yescharacteristic
312Q16—2924no—
313Q16—2921no—
314Q16—2921no—
315Q16—1462no—
316Q16—1462no—
317SD16—44no—
318SD16—2924no—
319D8—22no—
320D8—22no—
321D8—44no—
322D8—41no—
323D8—41no—
324M16—21no—
325M16—22no—
326M16—22no—
327M16—22no—
328M16—41no—
329M16—2921no—
330M16—1462no—
331M16C2×C22⋊D7312yes—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—2921no—
337C2×C8D4×D7311yescharacteristic
338C2×C8D4×D7311yescharacteristic
339C2×C8C2×C22⋊D7311yescharacteristic
340C2×C8#1192402711yescharacteristic
341C2×C8#1192402711yescharacteristic
342C2×C8C23×D7311yescharacteristic
343C16—732no—
344C16—732no—
345C16—1462no—
346C23—21no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—162no—
351C23#1455661111yescharacteristic
352Q8—21no—
353Q8—2922no—
354Q8—2922no—
355Q8—5841no—
356Q8—5841no—
357Q8C2×#1192401312yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—81no—
365D4C2×#1192401312yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—2922no—
370C2×C4—5841no—
371C2×C4—5841no—
372C2×C4#1455656311yescharacteristic
373C2×C4#1455656311yescharacteristic
374C2×C4C2×#1192401311yescharacteristic
375C2×C4C2×#1192401311yescharacteristic
376C2×C4#1455661111yescharacteristic
377C2×C4C22×C22⋊D7311yescharacteristic
378C8—22no—
379C8—42no—
380C8—2922no—
381C8#1455656311yescharacteristic
382C8#1455656311yescharacteristic
383C8C2×D4×D7311yescharacteristic
384C8C2×#1192402711yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22—162no—
392C22#1798882111yescharacteristic
393C22#1798882111yescharacteristic
394C22C2×#1455661111yescharacteristic
395C4—22no—
396C4—5842no—
397C4#1798882111yescharacteristic
398C4#1798882111yescharacteristic
399C4C2×#1455656311yescharacteristic
400C4C22×#1192401311yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—162no—
405C2#2261205912yesdirect product factor
406C2C2×#1798882111yescharacteristic
subgroupG/H
centerC22#17988821
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
Fitting, prime radicalC2×#472×C73C2
socleC22×C73#466
hypercenterC2×#472D73
hypocenterC73C2×#2223
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C22×#14556535C2semidirect
2. C2×#17989004C2semidirect
3. C2×#17988862C2semidirect
4. #22612059C2direct (N × H)
5. C2×#17988416C2semidirect
6. C2×#17988402C2semidirect
7. C2×#17988400C2semidirect
14. C2×#14556535C22semidirect
16. #17989004C22semidirect
22. #17988862C22semidirect
25. #17988416C22semidirect
26. #17988402C22semidirect
27. #17988400C22semidirect
202. C2×C73#2223semidirect
212. C73C2×#2223semidirect
405. C2#22612059direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565352
C2×#179890042
C2×#179888622
#226120592
C2×#179884162
C2×#179884022
C2×#179884002
C2×#472×C732
C2×#222373