Finite Group Databasebeta

← C2×#20276839 #27538654

Subgroups — C2×#20276839 #27538654

Order 13568.

638 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133163C211yesmaximal, characteristic, complemented
2C2×#16811041C211yesmaximal, characteristic
3C2×#16810899C211yesmaximal, characteristic
4C2×#16810895C211yesmaximal, characteristic
5#20276839C218yesmaximal, direct product factor
6C2×#16810452C211yesmaximal, characteristic, complemented
7C2×#16810440C211yesmaximal, characteristic, complemented
8C2×C53×#362C211yesmaximal, characteristic, complemented
9C2×#13133250—21no—
10C2×#13133248—21no—
11C22×Dic212C2211yescharacteristic
12C2×#13133223C2211yescharacteristic
13C2×#13133163—21no—
14C2×#13133163—21no—
15C2×#13133163—22no—
16C2×#13133163C2214yescomplemented
17#16811041—22no—
18#16811041C2214yes—
19C2×#13133156—21no—
20C22×#11719908C2211yescharacteristic
21C2×C16×D53—21no—
22#16810899—22no—
23#16810899C2214yes—
24#16810895—22no—
25#16810895C2214yes—
26C2×#13133153C2211yescharacteristic
27C2×#13133136—21no—
28C2×#13133135—21no—
29#16810452C2214yescomplemented
30#16810440C2214yescomplemented
31C22×Q16×C53C2211yescharacteristic
32C2×M32×C53C2211yescharacteristic
33C2×#108×C53C2211yescharacteristic
34C53×#362C2214yescomplemented
35C2×#11719945D411yescharacteristic
36C22×Dic106—21no—
37#13133250—24no—
38#13133250—42no—
39#13133248—24no—
40#13133248—42no—
41C2×Dic212—21no—
42C2×Dic212—21no—
43C2×Dic212—21no—
44C2×Dic212—21no—
45C2×Dic212—21no—
46C2×Dic212—41no—
47C2×Dic212C2312yes—
48C2×#11719925—41no—
49C2×#11719913—41no—
50C2×#11719924—41no—
51#13133223—21no—
52#13133223—21no—
53#13133223D412yes—
54#13133223C2312yes—
55C2×#11719917—21no—
56C2×#11719917D411yescharacteristic
57C2×#11719912—21no—
58C2×C8×D53—21no—
59#13133163—24no—
60#13133163—24no—
61#13133156—24no—
62C2×#11719908D411yescharacteristic
63C2×#11719908D411yescharacteristic
64C2×#11719908D412yes—
65C2×#11719908C2312yes—
66C16×D53—24no—
67#13133153—21no—
68#13133153C2312yes—
69#13133136—24no—
70#13133135—24no—
71C22×Q8×C53—21no—
72C2×Q16×C53—21no—
73C2×Q16×C53—21no—
74C2×Q16×C53—21no—
75C2×Q16×C53—21no—
76C2×Q16×C53—21no—
77C2×Q16×C53C2312yes—
78C2×M16×C53—21no—
79C22×C8×C53C2311yescharacteristic
80M32×C53—21no—
81M32×C53C2312yes—
82C2×C16×C53—21no—
83#108×C53—21no—
84#108×C53C2312yes—
85C2×Q8×C53—22no—
86C2×Q8×C53—41no—
87C2×Q8×C53—41no—
88C2×Q8×C53—41no—
89C2×Q8×C53—41no—
90C2×Q8×C53—41no—
91C22×C4×C53—41no—
92C22×C4×C53C2×D411yescharacteristic
93C2×C22⋊D53—21no—
94C22×Dic53—41no—
95#11719945—21no—
96#11719945—21no—
97#11719945D812yes—
98#11719945C2×D412yes—
99C2×D212D811yescharacteristic
100C2×C4×D53—21no—
101C2×Dic106—22no—
102C2×Dic106—41no—
103C2×Dic106—41no—
104C2×Dic106—41no—
105C2×Dic106—41no—
106C2×Dic106—41no—
107C2×Dic106D811yescharacteristic
108Q16×C53—22no—
109Q16×C53—22no—
110Q16×C53—41no—
111Q16×C53—41no—
112M16×C53—22no—
113M16×C53—41no—
114C2×C8×C53—41no—
115C2×C8×C53C2×D411yescharacteristic
116C2×C8×C53C2×D411yescharacteristic
117C2×C8×C53C2×D411yescharacteristic
118C2×C8×C53#4111yescharacteristic
119C2×C8×C53#4111yescharacteristic
120C2×C8×C53C2411yescharacteristic
121#11719925—44no—
122#11719924—44no—
123#11719917—21no—
124#11719917—22no—
125#11719917—41no—
126#11719917C2×D412yes—
127C2×#88322—21no—
128C2×#88322—41no—
129Dic212—22no—
130Dic212—22no—
131Dic212—44no—
132Dic212—41no—
133Dic212—41no—
134#11719913—44no—
135#11719912—22no—
136#11719912—22no—
137C8×D53—22no—
138C8×D53—22no—
139C16×C53—22no—
140#11719908C2×D412yes—
141#11719908C2×D412yes—
142C23×C53#13511yescharacteristic
143C22×D53—21no—
144Q8×C53—42no—
145Q8×C53—42no—
146Q8×C53—81no—
147Q8×C53—81no—
148C2×C4×C53—42no—
149C2×C4×C53—81no—
150C2×C4×C53—81no—
151C2×C4×C53#12111yescharacteristic
152C2×C4×C53#12111yescharacteristic
153C2×C4×C53C2×D811yescharacteristic
154C2×C4×C53C2×D811yescharacteristic
155C2×C4×C53#13511yescharacteristic
156C2×C4×C53C22×D411yescharacteristic
157C22⋊D53—22no—
158C22⋊D53—22no—
159C2×Dic53—21no—
160C2×Dic53—42no—
161C2×Dic53—81no—
162C2×Dic53—81no—
163D212—21no—
164D212C2×D812yes—
165C4×D53—22no—
166C4×D53—22no—
167Dic106—21no—
168Dic106—42no—
169Dic106—42no—
170Dic106—81no—
171Dic106—81no—
172Dic106C2×D812yes—
173C8×C53—42no—
174C8×C53#12111yescharacteristic
175C8×C53#12111yescharacteristic
176C8×C53C22×D411yescharacteristic
177C8×C53C2×#4111yescharacteristic
178#88322—22no—
179#88322—42no—
180C2×#2222—531nomaximal, Sylow
181C22×C53—22no—
182C22×C53#46611yescharacteristic
183C22×C53#46611yescharacteristic
184C22×C53C2×#13511yescharacteristic
185C2×D53—22no—
186C2×D53—42no—
187C4×C53—82no—
188C4×C53#46611yescharacteristic
189C4×C53#46611yescharacteristic
190C4×C53C2×#12111yescharacteristic
191C4×C53C22×D811yescharacteristic
192Dic53—22no—
193Dic53—82no—
194C22×Q32—531no—
195C2×#504—531no—
196C2×#473—531no—
197C2×#473—531no—
198#2222—538no—
199C2×#368—531no—
200C2×#362—531no—
201C2×#362D5311yescharacteristic, complemented
202C2×C53—21no—
203C2×C53—21no—
204C2×C53#222212yescomplemented
205C2×C53C2×#46611yescharacteristic
206D53—42no—
207C2×#137—1061no—
208C2×#137—1061no—
209C22×Q16—531no—
210C22×Q16C2×D5311yescharacteristic
211C2×#131—531no—
212C2×Q32—534no—
213C2×Q32—1061no—
214C2×Q32—1061no—
215C2×Q32—1062no—
216#504—534no—
217#504—1062no—
218C2×M32—1061no—
219C2×M32C2×D5311yescharacteristic
220C22×C16—531no—
221C22×C16—1061no—
222#473—534no—
223#473—534no—
224#473—1062no—
225#473—1062no—
226C2×#108—531no—
227C2×#108C2×D5311yescharacteristic
228C2×#101—1061no—
229C2×#101—1061no—
230#368—534no—
231#362—534no—
232#362C2×D5314yescomplemented
233C53C2×#222211yescharacteristic, complemented, Sylow
234C2×#41—531no—
235C22×Q8—21no—
236C22×Q8—1061no—
237#137—1064no—
238#137—1064no—
239#137—2122no—
240#137—2122no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—532no—
247C2×Q16—1061no—
248C2×Q16—1061no—
249C2×Q16—1061no—
250C2×Q16—1061no—
251C2×Q16—1061no—
252C2×Q16—2121no—
253C2×Q16—2121no—
254C2×Q16C22×D5312yes—
255C2×SD16—2121no—
256C2×SD16—2121no—
257#131—532no—
258#131—532no—
259#131—1061no—
260#131—1061no—
261C2×M16—21no—
262C2×M16—531no—
263C2×M16—1061no—
264C2×M16—1061no—
265C22×C8—1061no—
266C22×C8C22×D5311yescharacteristic
267Q32—1064no—
268Q32—1064no—
269M32—21no—
270M32—1064no—
271M32C22×D5312yes—
272C2×C16—21no—
273C2×C16—531no—
274C2×C16—531no—
275C2×C16—532no—
276C2×C16—532no—
277C2×C16—1064no—
278#108—21no—
279#108—532no—
280#108—1061no—
281#108C22×D5312yes—
282#101—1064no—
283#101—1064no—
284#41—532no—
285#41—532no—
286#41—1061no—
287#41—1061no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—531no—
295C2×Q8—1062no—
296C2×Q8—2121no—
297C2×Q8—2121no—
298C2×Q8—2121no—
299C2×Q8—2121no—
300C2×Q8—2121no—
301C2×D4—531no—
302C2×D4—1061no—
303C22×C4—41no—
304C22×C4—1061no—
305C22×C4—2121no—
306C22×C4D4×D5311yescharacteristic
307Q16—22no—
308Q16—22no—
309Q16—41no—
310Q16—41no—
311Q16—1062no—
312Q16—1062no—
313Q16—2124no—
314Q16—2124no—
315Q16—2121no—
316Q16—2121no—
317SD16—2124no—
318SD16—2124no—
319M16—22no—
320M16—41no—
321M16—532no—
322M16—1061no—
323M16—1062no—
324M16—1062no—
325M16—1062no—
326M16—2121no—
327C2×C8—41no—
328C2×C8—1061no—
329C2×C8—1062no—
330C2×C8—1062no—
331C2×C8—2121no—
332C2×C8#1171994511yescharacteristic
333C2×C8#1171994511yescharacteristic
334C2×C8D4×D5311yescharacteristic
335C2×C8D4×D5311yescharacteristic
336C2×C8D4×D5311yescharacteristic
337C2×C8C23×D5311yescharacteristic
338C16—22no—
339C16—532no—
340C16—532no—
341C23—1061no—
342C23#1313323811yescharacteristic
343Q8—42no—
344Q8—42no—
345Q8—81no—
346Q8—81no—
347Q8—532no—
348Q8—1061no—
349Q8—4241no—
350Q8—4241no—
351Q8—2122no—
352Q8—2122no—
353D4—532no—
354D4—1062no—
355D4—1062no—
356D4—1061no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—1061no—
361C2×C4—1062no—
362C2×C4—1062no—
363C2×C4—4241no—
364C2×C4—4241no—
365C2×C4—2122no—
366C2×C4#1313319011yescharacteristic
367C2×C4#1313319011yescharacteristic
368C2×C4D8×D5311yescharacteristic
369C2×C4D8×D5311yescharacteristic
370C2×C4#1313323811yescharacteristic
371C2×C4C2×D4×D5311yescharacteristic
372C8—42no—
373C8—1062no—
374C8—2122no—
375C8#1313319011yescharacteristic
376C8#1313319011yescharacteristic
377C8C2×D4×D5311yescharacteristic
378C8C2×#1171994511yescharacteristic
379C22—22no—
380C22—1062no—
381C22—2122no—
382C22#1681085811yescharacteristic
383C22#1681085811yescharacteristic
384C22C2×#1313323811yescharacteristic
385C4—82no—
386C4—1062no—
387C4—4242no—
388C4#1681085811yescharacteristic
389C4#1681085811yescharacteristic
390C4C2×#1313319011yescharacteristic
391C4C2×D8×D5311yescharacteristic
392C2—21no—
393C2—21no—
394C2—2122no—
395C2#2027683912yesdirect product factor
396C2C2×#1681085811yescharacteristic
subgroupG/H
centerC22#16810858
commutator, cosocleC2×C8×C53C24
FrattiniC2×C8C23×D53
FittingC2×C53×#362C2
socleC22×C53#466
prime radicalC2×#11719945D4
hypercenterC2×#362D53
hypocenterC53C2×#2222
LCSG ▷ C2×C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
1. C22×#13133163C2semidirect
5. #20276839C2direct (N × H)
6. C2×#16810452C2semidirect
7. C2×#16810440C2semidirect
8. C2×C53×#362C2semidirect
16. C2×#13133163C22semidirect
29. #16810452C22semidirect
30. #16810440C22semidirect
34. C53×#362C22semidirect
201. C2×#362D53semidirect
204. C2×C53#2222semidirect
232. #362C2×D53semidirect
233. C53C2×#2222semidirect
395. C2#20276839direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331632
C2×#168110412
C2×#168108992
C2×#168108952
#202768392
C2×#168104522
C2×#168104402
C2×C53×#3622
C2×#222253