Finite Group Databasebeta

← C2×#20276842 #27538658

Subgroups — C2×#20276842 #27538658

Order 13568.

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
1C2×#16811039C211yesmaximal, characteristic, complemented
2C2×#16810895C211yesmaximal, characteristic, complemented
3C2×#16810890C211yesmaximal, characteristic
4#20276842C218yesmaximal, direct product factor
5C2×#16810453C211yesmaximal, characteristic, complemented
6C2×#16810439C211yesmaximal, characteristic, complemented
7C2×#16810436C211yesmaximal, characteristic, complemented
8C22×SD32×C53C211yesmaximal, characteristic, complemented
9C2×#13133248—21no—
10C2×#13133243—21no—
11C2×#13133223C2211yescharacteristic
12#16811039—22no—
13#16811039C2214yescomplemented
14C2×#13133157C2211yescharacteristic
15C2×#13133156—21no—
16C2×C16×D53—21no—
17#16810895—22no—
18#16810895C2214yescomplemented
19#16810890—22no—
20#16810890C2214yes—
21C2×#13133153C2211yescharacteristic
22C2×#13133153C2211yescharacteristic
23C2×#13133136—21no—
24C2×#13133134—21no—
25#16810453C2214yescomplemented
26#16810439C2214yescomplemented
27#16810436C2214yescomplemented
28C22×Q16×C53C2211yescharacteristic
29C22×D8×C53C2211yescharacteristic
30C2×SD32×C53—21no—
31C2×SD32×C53—21no—
32C2×SD32×C53—22no—
33C2×SD32×C53C2214yescomplemented
34C22×C16×C53C2211yescharacteristic
35C2×#11719945D411yescharacteristic
36#13133248—24no—
37#13133248—42no—
38#13133243—24no—
39#13133243—42no—
40C2×#11719925—41no—
41C2×#11719923—41no—
42C2×#11719924—41no—
43C2×#11719922—41no—
44#13133223—21no—
45#13133223—21no—
46#13133223D412yes—
47#13133223C2312yes—
48C2×#11719917—21no—
49C2×#11719917—21no—
50C2×#11719917D411yescharacteristic
51C2×#11719912—21no—
52C2×C8×D53—21no—
53#13133157—21no—
54#13133157C2312yes—
55#13133156—24no—
56C2×#11719908—21no—
57C16×D53—24no—
58#13133153—21no—
59#13133153—21no—
60#13133153C2312yes—
61#13133153C2312yes—
62#13133136—24no—
63#13133134—24no—
64C22×Q8×C53—21no—
65C22×D4×C53—21no—
66C2×Q16×C53—21no—
67C2×Q16×C53—21no—
68C2×Q16×C53—21no—
69C2×Q16×C53—21no—
70C2×Q16×C53—21no—
71C2×Q16×C53C2312yes—
72C2×D8×C53—21no—
73C2×D8×C53—21no—
74C2×D8×C53—21no—
75C2×D8×C53—21no—
76C2×D8×C53—21no—
77C2×D8×C53C2312yes—
78C22×C8×C53C2311yescharacteristic
79SD32×C53—24no—
80SD32×C53—24no—
81C2×C16×C53D411yescharacteristic
82C2×C16×C53D411yescharacteristic
83C2×C16×C53D412yes—
84C2×C16×C53C2312yes—
85C24×C53—41no—
86C2×Q8×C53—22no—
87C2×Q8×C53—41no—
88C2×Q8×C53—41no—
89C2×Q8×C53—41no—
90C2×Q8×C53—41no—
91C2×Q8×C53—41no—
92C2×D4×C53—22no—
93C2×D4×C53—41no—
94C2×D4×C53—41no—
95C2×D4×C53—41no—
96C2×D4×C53—41no—
97C2×D4×C53—41no—
98C22×C4×C53—41no—
99C22×C4×C53C2×D411yescharacteristic
100C2×C22⋊D53—21no—
101#11719945—21no—
102#11719945—21no—
103#11719945D812yes—
104#11719945C2×D412yes—
105C2×D212D811yescharacteristic
106C2×C4×D53—21no—
107C2×Dic106D811yescharacteristic
108Q16×C53—22no—
109Q16×C53—22no—
110Q16×C53—41no—
111Q16×C53—41no—
112D8×C53—22no—
113D8×C53—22no—
114D8×C53—41no—
115D8×C53—41no—
116C2×C8×C53C2×D411yescharacteristic
117C2×C8×C53C2×D411yescharacteristic
118C2×C8×C53C2×D411yescharacteristic
119C2×C8×C53#4111yescharacteristic
120C2×C8×C53#4111yescharacteristic
121C2×C8×C53C2411yescharacteristic
122#11719925—44no—
123#11719924—44no—
124#11719923—44no—
125#11719922—44no—
126#11719917—21no—
127#11719917—22no—
128#11719917—22no—
129#11719917—41no—
130#11719917—41no—
131#11719917C2×D412yes—
132C2×#88322—21no—
133C2×#88322—41no—
134C2×#88322—41no—
135#11719912—22no—
136#11719912—22no—
137C8×D53—22no—
138C8×D53—22no—
139C16×C53C2×D412yes—
140C16×C53C2×D412yes—
141#11719908—22no—
142C23×C53—42no—
143C23×C53—81no—
144C23×C53—81no—
145C23×C53—162no—
146C23×C53#13511yescharacteristic
147C22×D53—21no—
148Q8×C53—42no—
149Q8×C53—42no—
150Q8×C53—81no—
151Q8×C53—81no—
152D4×C53—42no—
153D4×C53—42no—
154D4×C53—81no—
155D4×C53—81no—
156C2×C4×C53—42no—
157C2×C4×C53—81no—
158C2×C4×C53—81no—
159C2×C4×C53#12111yescharacteristic
160C2×C4×C53#12111yescharacteristic
161C2×C4×C53C2×D811yescharacteristic
162C2×C4×C53C2×D811yescharacteristic
163C2×C4×C53#13511yescharacteristic
164C2×C4×C53C22×D411yescharacteristic
165C22⋊D53—22no—
166C22⋊D53—22no—
167C2×Dic53—21no—
168D212—21no—
169D212C2×D812yes—
170C4×D53—22no—
171C4×D53—22no—
172Dic106—21no—
173Dic106C2×D812yes—
174C8×C53#12111yescharacteristic
175C8×C53#12111yescharacteristic
176C8×C53C22×D411yescharacteristic
177C8×C53C2×#4111yescharacteristic
178#88322—22no—
179#88322—42no—
180#88322—42no—
181C2×#2223—531nomaximal, Sylow
182C22×C53—22no—
183C22×C53—82no—
184C22×C53—162no—
185C22×C53—162no—
186C22×C53—162no—
187C22×C53#46611yescharacteristic
188C22×C53#46611yescharacteristic
189C22×C53C2×#13511yescharacteristic
190C2×D53—22no—
191C2×D53—42no—
192C4×C53—82no—
193C4×C53#46611yescharacteristic
194C4×C53#46611yescharacteristic
195C4×C53C2×#12111yescharacteristic
196C4×C53C22×D811yescharacteristic
197Dic53—22no—
198C22×SD32D5311yescharacteristic, complemented
199C2×#504—531no—
200C2×#473—531no—
201C2×#472—531no—
202#2223—538no—
203C2×#368—531no—
204C2×#362—531no—
205C2×#361—531no—
206C2×C53—21no—
207C2×C53—21no—
208C2×C53—162no—
209C2×C53#222312yescomplemented
210C2×C53C2×#46611yescharacteristic
211D53—42no—
212C2×#137—1061no—
213C2×AGL(1,ℤ/8)—1061no—
214C22×Q16C2×D5311yescharacteristic
215C22×D8C2×D5311yescharacteristic
216C2×#131—531no—
217C2×SD32—21no—
218C2×SD32—21no—
219C2×SD32—22no—
220C2×SD32C2×D5314yescomplemented
221#504—534no—
222#504—1062no—
223C2×M32—531no—
224C2×M32—1061no—
225C22×C16—1061no—
226C22×C16C2×D5311yescharacteristic
227#473—534no—
228#473—1062no—
229#472—534no—
230#472—1062no—
231C2×#108—531no—
232C2×#108—531no—
233C2×#101—1061no—
234C2×#100—1061no—
235#368—534no—
236#362—534no—
237#361—534no—
238C53C2×#222311yescharacteristic, complemented, Sylow
239C2×#41—531no—
240C22×Q8—21no—
241C22×D4—21no—
242#137—1064no—
243#137—2122no—
244AGL(1,ℤ/8)—1064no—
245AGL(1,ℤ/8)—2122no—
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—2121no—
252C2×Q16C22×D5312yes—
253C2×SD16—2121no—
254C2×SD16—2121no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—2121no—
261C2×D8C22×D5312yes—
262#131—532no—
263#131—532no—
264#131—1061no—
265#131—1061no—
266C2×M16—531no—
267C2×M16—1061no—
268C2×M16—1061no—
269C2×M16—1061no—
270C22×C8—1061no—
271C22×C8C22×D5311yescharacteristic
272SD32—24no—
273SD32—24no—
274M32—532no—
275M32—1061no—
276M32—1064no—
277C2×C16—1061no—
278C2×C16—1064no—
279C2×C16C22⋊D5311yescharacteristic
280C2×C16C22⋊D5311yescharacteristic
281C2×C16C22⋊D5312yes—
282C2×C16C22×D5312yes—
283#108—532no—
284#108—532no—
285#108—1061no—
286#108—1061no—
287#101—1064no—
288#100—1064no—
289C24—41no—
290#41—532no—
291#41—532no—
292#41—1061no—
293#41—1061no—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—531no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—531no—
308C2×D4—1061no—
309C22×C4—41no—
310C22×C4—1061no—
311C22×C4D4×D5311yescharacteristic
312Q16—22no—
313Q16—22no—
314Q16—41no—
315Q16—41no—
316Q16—2124no—
317SD16—2124no—
318SD16—2124no—
319D8—22no—
320D8—22no—
321D8—41no—
322D8—41no—
323D8—2124no—
324M16—532no—
325M16—1061no—
326M16—1062no—
327M16—1062no—
328M16—1062no—
329M16—1062no—
330M16—2121no—
331M16—2121no—
332C2×C8—1061no—
333C2×C8—1062no—
334C2×C8—1062no—
335C2×C8—2121no—
336C2×C8—2121no—
337C2×C8D4×D5311yescharacteristic
338C2×C8#1171994711yescharacteristic
339C2×C8#1171994711yescharacteristic
340C2×C8C2×C22⋊D5311yescharacteristic
341C2×C8C2×C22⋊D5311yescharacteristic
342C2×C8C23×D5311yescharacteristic
343C16—1062no—
344C16C2×C22⋊D5312yes—
345C16C2×C22⋊D5312yes—
346C23—42no—
347C23—81no—
348C23—81no—
349C23—162no—
350C23—1061no—
351C23#1313323611yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
356Q8—532no—
357Q8—1061no—
358D4—42no—
359D4—42no—
360D4—81no—
361D4—81no—
362D4—532no—
363D4—1062no—
364D4—1062no—
365D4—1061no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—1061no—
370C2×C4—1062no—
371C2×C4—1062no—
372C2×C4#1313318811yescharacteristic
373C2×C4#1313318811yescharacteristic
374C2×C4D8×D5311yescharacteristic
375C2×C4D8×D5311yescharacteristic
376C2×C4#1313323611yescharacteristic
377C2×C4C2×D4×D5311yescharacteristic
378C8—1062no—
379C8—2122no—
380C8—2122no—
381C8#1313318811yescharacteristic
382C8#1313318811yescharacteristic
383C8C22×C22⋊D5311yescharacteristic
384C8C2×#1171994711yescharacteristic
385C22—22no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22—162no—
390C22—1062no—
391C22—2122no—
392C22#1681085611yescharacteristic
393C22#1681085611yescharacteristic
394C22C2×#1313323611yescharacteristic
395C4—82no—
396C4—1062no—
397C4#1681085611yescharacteristic
398C4#1681085611yescharacteristic
399C4C2×#1313318811yescharacteristic
400C4C2×D8×D5311yescharacteristic
401C2—21no—
402C2—21no—
403C2—162no—
404C2—2122no—
405C2#2027684212yesdirect product factor
406C2C2×#1681085611yescharacteristic
subgroupG/H
centerC22#16810856
commutator, cosocleC2×C8×C53C24
FrattiniC2×C8C23×D53
FittingC22×SD32×C53C2
socleC22×C53#466
prime radicalC2×#16810890C2
hypercenterC22×SD32D53
hypocenterC53C2×#2223
LCSG ▷ C2×C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#16811039C2semidirect
2. C2×#16810895C2semidirect
4. #20276842C2direct (N × H)
5. C2×#16810453C2semidirect
6. C2×#16810439C2semidirect
7. C2×#16810436C2semidirect
8. C22×SD32×C53C2semidirect
13. #16811039C22semidirect
18. #16810895C22semidirect
25. #16810453C22semidirect
26. #16810439C22semidirect
27. #16810436C22semidirect
33. C2×SD32×C53C22semidirect
198. C22×SD32D53semidirect
209. C2×C53#2223semidirect
220. C2×SD32C2×D53semidirect
238. C53C2×#2223semidirect
405. C2#20276842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168110392
C2×#168108952
C2×#168108902
#202768422
C2×#168104532
C2×#168104392
C2×#168104362
C22×SD32×C532
C2×#222353