Finite Group Databasebeta

← C2×#22612049 #33240539

Subgroups — C2×#22612049 #33240539

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556532C211yesmaximal, characteristic, complemented
2C2×#17989004C211yesmaximal, characteristic, complemented
3C2×#17988857C211yesmaximal, characteristic, complemented
4#22612049C218yesmaximal, direct product factor
5C2×#17988416C211yesmaximal, characteristic, complemented
6C2×#17988400C211yesmaximal, characteristic, complemented
7C2×#17988399C211yesmaximal, characteristic, complemented
8C2×#472×C73C211yesmaximal, characteristic, complemented
9C2×#14556616—21no—
10C22×D584C2211yescharacteristic
11C2×#14556532—21no—
12C2×#14556532—21no—
13C2×#14556532—22no—
14C2×#14556532C2214yescomplemented
15#17989004—22no—
16#17989004C2214yescomplemented
17C2×#14556531—21no—
18C2×#14556531C2211yescharacteristic
19C22×#11924003—21no—
20C22×#11924003C2211yescharacteristic
21#17988857—22no—
22#17988857C2214yescomplemented
23C2×#14556527C2211yescharacteristic
24C2×#14556507—21no—
25#17988416C2214yescomplemented
26#17988400C2214yescomplemented
27#17988399C2214yescomplemented
28C2×AGL(1,ℤ/8)×C73—21no—
29C22×D8×C73C2211yescharacteristic
30C2×#131×C73C2211yescharacteristic
31#472×C73—22no—
32#472×C73C2214yescomplemented
33C2×#108×C73C2211yescharacteristic
34C2×#100×C73—21no—
35C22×D292—21no—
36#14556616—24no—
37#14556616—42no—
38C2×#11924015—41no—
39C2×D584—21no—
40C2×D584—21no—
41C2×D584—21no—
42C2×D584—21no—
43C2×D584—21no—
44C2×D584C2312yes—
45C2×#11924013—41no—
46C2×#11924012—21no—
47#14556532—24no—
48#14556532—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#14556507—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—
85C23×D73—41no—
86C2×D292—22no—
87C2×D292—41no—
88C2×D292—41no—
89C2×D292—41no—
90C2×D292—41no—
91C2×D292—41no—
92#11924015—44no—
93D584—22no—
94D584—22no—
95D584—41no—
96D584—41no—
97#11924013—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
148C22×D73—42no—
149C22×D73—81no—
150C22×D73—81no—
151C22×D73—162no—
152Q8×C73—21no—
153Q8×C73C2×D812yes—
154D4×C73—22no—
155D4×C73—22no—
156D4×C73—21no—
157D4×C73—42no—
158D4×C73—42no—
159D4×C73—81no—
160D4×C73—81no—
161D4×C73C2×D812yes—
162C2×C4×C73—21no—
163C2×C4×C73—22no—
164C2×C4×C73—22no—
165C2×C4×C73#12111yescharacteristic
166C2×C4×C73#12111yescharacteristic
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73C2×D811yescharacteristic
169C2×C4×C73#13511yescharacteristic
170C2×C4×C73C22×D411yescharacteristic
171D292—42no—
172D292—42no—
173D292—81no—
174D292—81no—
175C8×C73—22no—
176C8×C73—42no—
177C8×C73#12111yescharacteristic
178C8×C73#12111yescharacteristic
179C8×C73C22×D411yescharacteristic
180C8×C73C2×#4111yescharacteristic
181#10596831—42no—
182C22×C73—22no—
183C22×C73—22no—
184C22×C73—42no—
185C22×C73—82no—
186C22×C73—162no—
187C22×C73—162no—
188C22×C73—162no—
189C22×C73#46611yescharacteristic
190C22×C73#46611yescharacteristic
191C22×C73C2×#13511yescharacteristic
192C2×D73—82no—
193C2×D73—162no—
194C2×D73—162no—
195C2×D73—162no—
196C4×C73—22no—
197C4×C73#46611yescharacteristic
198C4×C73#46611yescharacteristic
199C4×C73C2×#12111yescharacteristic
200C4×C73C22×D811yescharacteristic
201C2×#2221—731nomaximal, Sylow
202C2×C73—21no—
203C2×C73—21no—
204C2×C73—42no—
205C2×C73—162no—
206C2×C73#222112yescomplemented
207C2×C73C2×#46611yescharacteristic
208D73—162no—
209C22×D16—731no—
210C2×#504—731no—
211C2×#472—731no—
212C2×#472D7311yescharacteristic, complemented
213#2221—738no—
214C2×#368—731no—
215C2×#361—731no—
216C2×#361—731no—
217C73C2×#222111yescharacteristic, complemented, Sylow
218C2×AGL(1,ℤ/8)—21no—
219C2×AGL(1,ℤ/8)—1461no—
220C22×D8—731no—
221C22×D8C2×D7311yescharacteristic
222C2×#131C2×D7311yescharacteristic
223C2×D16—734no—
224C2×D16—1461no—
225C2×D16—1461no—
226C2×D16—1462no—
227#504—734no—
228#504—1462no—
229C2×M32—731no—
230C2×M32—1461no—
231C22×C16—731no—
232C22×C16—1461no—
233#472—22no—
234#472—734no—
235#472—1462no—
236#472C2×D7314yescomplemented
237C2×#108—731no—
238C2×#108C2×D7311yescharacteristic
239C2×#100—21no—
240C2×#100—1461no—
241#368—734no—
242#361—734no—
243#361—734no—
244C2×#41C22⋊D7311yescharacteristic
245C22×D4—21no—
246C22×D4—1461no—
247AGL(1,ℤ/8)—24no—
248AGL(1,ℤ/8)—42no—
249AGL(1,ℤ/8)—2922no—
250AGL(1,ℤ/8)—1464no—
251C2×SD16—41no—
252C2×SD16—2921no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—41no—
259C2×D8—2921no—
260C2×D8—732no—
261C2×D8—1461no—
262C2×D8—1461no—
263C2×D8—1461no—
264C2×D8—1461no—
265C2×D8—1461no—
266C2×D8C22×D7312yes—
267#131—21no—
268#131—21no—
269#131C22⋊D7312yes—
270#131C22×D7312yes—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—1461no—
274C2×M16C22⋊D7311yescharacteristic
275C22×C8—21no—
276C22×C8C22×D7311yescharacteristic
277D16—1464no—
278D16—1464no—
279M32—732no—
280M32—1464no—
281M32—1461no—
282C2×C16—731no—
283C2×C16—731no—
284C2×C16—732no—
285C2×C16—732no—
286C2×C16—1464no—
287C2×C16—1461no—
288#108—21no—
289#108—732no—
290#108—1461no—
291#108C22×D7312yes—
292#100—24no—
293#100—1464no—
294C24—41no—
295C24—2921no—
296#41—21no—
297#41—21no—
298#41#1192401312yes—
299#41C2×C22⋊D7312yes—
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—2921no—
309C2×D4—2921no—
310C2×D4—2921no—
311C2×D4—2921no—
312C2×D4—2921no—
313C2×D4—1462no—
314C2×D4#1192401311yescharacteristic
315C22×C4—21no—
316C22×C4C2×C22⋊D7311yescharacteristic
317SD16—44no—
318SD16—2924no—
319D8—22no—
320D8—22no—
321D8—44no—
322D8—41no—
323D8—41no—
324D8—2924no—
325D8—2921no—
326D8—2921no—
327D8—1462no—
328D8—1462no—
329M16—21no—
330M16—22no—
331M16—22no—
332M16—22no—
333M16—41no—
334M16—2921no—
335M16—1462no—
336M16C2×C22⋊D7312yes—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—2921no—
342C2×C8D4×D7311yescharacteristic
343C2×C8D4×D7311yescharacteristic
344C2×C8C2×C22⋊D7311yescharacteristic
345C2×C8#1192402711yescharacteristic
346C2×C8#1192402711yescharacteristic
347C2×C8C23×D7311yescharacteristic
348C16—732no—
349C16—732no—
350C16—1462no—
351C23—21no—
352C23—42no—
353C23—81no—
354C23—81no—
355C23—162no—
356C23—2922no—
357C23—5841no—
358C23—5841no—
359C23—11682no—
360C23#1455661111yescharacteristic
361Q8—21no—
362Q8C2×#1192401312yes—
363D4—22no—
364D4—22no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—81no—
369D4—81no—
370D4—2922no—
371D4—2922no—
372D4—5841no—
373D4—5841no—
374D4C2×#1192401312yes—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4#1455656311yescharacteristic
379C2×C4#1455656311yescharacteristic
380C2×C4C2×#1192401311yescharacteristic
381C2×C4C2×#1192401311yescharacteristic
382C2×C4#1455661111yescharacteristic
383C2×C4C22×C22⋊D7311yescharacteristic
384C8—22no—
385C8—42no—
386C8—2922no—
387C8#1455656311yescharacteristic
388C8#1455656311yescharacteristic
389C8C2×D4×D7311yescharacteristic
390C8C2×#1192402711yescharacteristic
391C22—22no—
392C22—22no—
393C22—42no—
394C22—82no—
395C22—162no—
396C22—162no—
397C22—162no—
398C22—5842no—
399C22—11682no—
400C22—11682no—
401C22—11682no—
402C22#1798882111yescharacteristic
403C22#1798882111yescharacteristic
404C22C2×#1455661111yescharacteristic
405C4—22no—
406C4#1798882111yescharacteristic
407C4#1798882111yescharacteristic
408C4C2×#1455656311yescharacteristic
409C4C22×#1192401311yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—162no—
414C2—11682no—
415C2#2261204912yesdirect product factor
416C2C2×#1798882111yescharacteristic
subgroupG/H
centerC22#17988821
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#472×C73C2
socleC22×C73#466
hypercenterC2×#472D73
hypocenterC73C2×#2221
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×#14556532C2semidirect
2. C2×#17989004C2semidirect
3. C2×#17988857C2semidirect
4. #22612049C2direct (N × H)
5. C2×#17988416C2semidirect
6. C2×#17988400C2semidirect
7. C2×#17988399C2semidirect
8. C2×#472×C73C2semidirect
14. C2×#14556532C22semidirect
16. #17989004C22semidirect
22. #17988857C22semidirect
25. #17988416C22semidirect
26. #17988400C22semidirect
27. #17988399C22semidirect
32. #472×C73C22semidirect
206. C2×C73#2221semidirect
212. C2×#472D73semidirect
217. C73C2×#2221semidirect
236. #472C2×D73semidirect
415. C2#22612049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565322
C2×#179890042
C2×#179888572
#226120492
C2×#179884162
C2×#179884002
C2×#179883992
C2×#472×C732
C2×#222173