Finite Group Databasebeta

← C2×#13116959 #16017480

Subgroups — C2×#13116959 #16017480

Order 3328.

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×#88069C211yesmaximal, characteristic, complemented
2C2×#11718801C211yesmaximal, characteristic
3C2×#11718804C211yesmaximal, characteristic
4#13116959C218yesmaximal, direct product factor
5C2×#11718085C211yesmaximal, characteristic, complemented
6C2×#11718157C211yesmaximal, characteristic, complemented
7C2×#11718088C211yesmaximal, characteristic, complemented
8C2×C13×#473C211yesmaximal, characteristic
9C2×C13×#137—21no—
10C22×C13×Q16C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C2×#88205—21no—
13C22×Dic52C2211yescharacteristic
14C13×#473—22no—
15C13×#473C2214yes—
16C2×C13×#108C2211yescharacteristic
17C2×C13×#101—21no—
18C2×#88069—21no—
19C2×#88069—21no—
20C2×#88069—22no—
21C2×#88069C2214yescomplemented
22#11718804—22no—
23#11718804C2214yes—
24#11718801—22no—
25#11718801C2214yes—
26C2×#88064—21no—
27C2×#88059C2211yescharacteristic
28C2×#88052—21no—
29C2×#88052C2211yescharacteristic
30C22×#6090—21no—
31C22×#6090C2211yescharacteristic
32#11718157C2214yescomplemented
33#11718088C2214yescomplemented
34#11718085C2214yescomplemented
35C2×C13×#41D411yescharacteristic
36C22×Q8×C13—21no—
37C22×Dic26—21no—
38C13×#137—24no—
39C13×#137—42no—
40C2×C13×Q16—21no—
41C2×C13×Q16—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16—21no—
44C2×C13×Q16—21no—
45C2×C13×Q16—41no—
46C2×C13×Q16C2312yes—
47C2×C13×SD16—41no—
48C13×#131—21no—
49C13×#131—21no—
50C13×#131D412yes—
51C13×#131C2312yes—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16D411yescharacteristic
55C22×C8×C13—21no—
56C22×C8×C13C2311yescharacteristic
57#88205—24no—
58#88205—42no—
59C2×#6107—41no—
60C2×#6105—41no—
61C2×#6099—21no—
62C2×Dic52—21no—
63C2×Dic52—21no—
64C2×Dic52—21no—
65C2×Dic52—21no—
66C2×Dic52—21no—
67C2×Dic52C2312yes—
68C13×#108—21no—
69C13×#108C2312yes—
70C13×#101—24no—
71#88069—24no—
72#88069—24no—
73#88064—24no—
74#88059—21no—
75#88059C2312yes—
76#88052—21no—
77#88052—24no—
78#88052C2312yes—
79C2×#6090—21no—
80C2×#6090—24no—
81C2×#6090D411yescharacteristic
82C2×#6090D411yescharacteristic
83C2×#6090D412yes—
84C2×#6090C2312yes—
85C2×#2222—131nomaximal, Sylow
86C13×#41—21no—
87C13×#41—21no—
88C13×#41D812yes—
89C13×#41C2×D412yes—
90C2×Q8×C13—22no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×Q8×C13—41no—
95C2×Q8×C13—41no—
96C2×Q8×C13D811yescharacteristic
97C2×D4×C13—21no—
98C2×D4×C13D811yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—41no—
101C22×C4×C13C2×D411yescharacteristic
102C22×Dic13—41no—
103C2×Dic26—22no—
104C2×Dic26—41no—
105C2×Dic26—41no—
106C2×Dic26—41no—
107C2×Dic26—41no—
108C2×Dic26—41no—
109C13×Q16—22no—
110C13×Q16—22no—
111C13×Q16—44no—
112C13×Q16—41no—
113C13×Q16—41no—
114C13×SD16—44no—
115C13×M16—21no—
116C13×M16—22no—
117C13×M16—22no—
118C13×M16—22no—
119C13×M16—41no—
120C13×M16C2×D412yes—
121C2×C8×C13—21no—
122C2×C8×C13—22no—
123C2×C8×C13—22no—
124C2×C8×C13—41no—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13#4111yescharacteristic
129C2×C8×C13#4111yescharacteristic
130C2×C8×C13C2411yescharacteristic
131#6107—44no—
132#6105—44no—
133#6099—22no—
134#6099—41no—
135C2×#1055—41no—
136Dic52—22no—
137Dic52—22no—
138Dic52—41no—
139Dic52—41no—
140#6090—22no—
141#6090C2×D412yes—
142#6090C2×D412yes—
143C22×Q32—131no—
144C2×#504—131no—
145C2×#473—131no—
146C2×#473D1311yescharacteristic
147#2222—138no—
148C2×#368—131no—
149C2×#362—131no—
150C2×#362—131no—
151C23×C13—21no—
152C23×C13#13511yescharacteristic
153Q8×C13—21no—
154Q8×C13—42no—
155Q8×C13—42no—
156Q8×C13—81no—
157Q8×C13—81no—
158Q8×C13C2×D812yes—
159D4×C13—22no—
160D4×C13—22no—
161D4×C13—21no—
162D4×C13C2×D812yes—
163C2×C4×C13—21no—
164C2×C4×C13—22no—
165C2×C4×C13—22no—
166C2×C4×C13—42no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13C2×D811yescharacteristic
172C2×C4×C13C2×D811yescharacteristic
173C2×C4×C13#13511yescharacteristic
174C2×C4×C13C22×D411yescharacteristic
175C2×Dic13—42no—
176C2×Dic13—81no—
177C2×Dic13—81no—
178Dic26—42no—
179Dic26—42no—
180Dic26—81no—
181Dic26—81no—
182C8×C13—22no—
183C8×C13—42no—
184C8×C13#12111yescharacteristic
185C8×C13#12111yescharacteristic
186C8×C13C22×D411yescharacteristic
187C8×C13C2×#4111yescharacteristic
188#1055—42no—
189C2×#137—21no—
190C2×#137—261no—
191C22×Q16—131no—
192C22×Q16C2×D1311yescharacteristic
193C2×#131C2×D1311yescharacteristic
194C2×Q32—134no—
195C2×Q32—261no—
196C2×Q32—261no—
197C2×Q32—262no—
198#504—134no—
199#504—262no—
200C2×M32—131no—
201C2×M32—261no—
202C22×C16—131no—
203C22×C16—261no—
204#473—22no—
205#473—134no—
206#473—262no—
207#473C2×D1314yes—
208C2×#108—131no—
209C2×#108C2×D1311yescharacteristic
210C2×#101—21no—
211C2×#101—261no—
212#368—134no—
213#362—134no—
214#362—134no—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—42no—
218C22×C13#46611yescharacteristic
219C22×C13#46611yescharacteristic
220C22×C13C2×#13511yescharacteristic
221C4×C13—22no—
222C4×C13—82no—
223C4×C13#46611yescharacteristic
224C4×C13#46611yescharacteristic
225C4×C13C2×#12111yescharacteristic
226C4×C13C22×D811yescharacteristic
227Dic13—82no—
228C2×#41C22⋊D1311yescharacteristic
229C22×Q8—21no—
230C22×Q8—261no—
231#137—24no—
232#137—42no—
233#137—264no—
234#137—522no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—41no—
241C2×Q16—132no—
242C2×Q16—261no—
243C2×Q16—261no—
244C2×Q16—261no—
245C2×Q16—261no—
246C2×Q16—261no—
247C2×Q16—521no—
248C2×Q16C22×D1312yes—
249C2×SD16—41no—
250C2×SD16—521no—
251#131—21no—
252#131—21no—
253#131C22⋊D1312yes—
254#131C22×D1312yes—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—261no—
258C2×M16C22⋊D1311yescharacteristic
259C22×C8—21no—
260C22×C8C22×D1311yescharacteristic
261Q32—264no—
262Q32—264no—
263M32—132no—
264M32—264no—
265M32—261no—
266C2×C16—131no—
267C2×C16—131no—
268C2×C16—132no—
269C2×C16—132no—
270C2×C16—264no—
271C2×C16—261no—
272#108—21no—
273#108—132no—
274#108—261no—
275#108C22×D1312yes—
276#101—24no—
277#101—264no—
278C2×C13—21no—
279C2×C13—21no—
280C2×C13—42no—
281C2×C13#222212yescomplemented
282C2×C13C2×#46611yescharacteristic
283#41—21no—
284#41—21no—
285#41#610412yes—
286#41C2×C22⋊D1312yes—
287C2×Q8—22no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—262no—
294C2×Q8—521no—
295C2×Q8—521no—
296C2×Q8—521no—
297C2×Q8—521no—
298C2×Q8—521no—
299C2×Q8#610411yescharacteristic
300C2×D4—21no—
301C2×D4#610411yescharacteristic
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—521no—
305C22×C4C2×C22⋊D1311yescharacteristic
306Q16—22no—
307Q16—22no—
308Q16—44no—
309Q16—41no—
310Q16—41no—
311Q16—262no—
312Q16—262no—
313Q16—524no—
314Q16—521no—
315Q16—521no—
316SD16—44no—
317SD16—524no—
318M16—21no—
319M16—22no—
320M16—22no—
321M16—22no—
322M16—41no—
323M16—262no—
324M16—521no—
325M16C2×C22⋊D1312yes—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—521no—
331C2×C8D4×D1311yescharacteristic
332C2×C8D4×D1311yescharacteristic
333C2×C8#612911yescharacteristic
334C2×C8#612911yescharacteristic
335C2×C8C2×C22⋊D1311yescharacteristic
336C2×C8C23×D1311yescharacteristic
337C16—132no—
338C16—132no—
339C16—262no—
340C13C2×#222211yescharacteristic, complemented, Sylow
341C23—21no—
342C23#8820411yescharacteristic
343Q8—21no—
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348Q8—522no—
349Q8—522no—
350Q8—1041no—
351Q8—1041no—
352Q8C2×#610412yes—
353D4—22no—
354D4—22no—
355D4—21no—
356D4C2×#610412yes—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—522no—
364C2×C4—1041no—
365C2×C4—1041no—
366C2×C4C2×#610411yescharacteristic
367C2×C4C2×#610411yescharacteristic
368C2×C4#8819311yescharacteristic
369C2×C4#8819311yescharacteristic
370C2×C4#8820411yescharacteristic
371C2×C4C22×C22⋊D1311yescharacteristic
372C8—22no—
373C8—42no—
374C8—522no—
375C8#8819311yescharacteristic
376C8#8819311yescharacteristic
377C8C2×D4×D1311yescharacteristic
378C8C2×#612911yescharacteristic
379C22—22no—
380C22—22no—
381C22—42no—
382C22#1171869911yescharacteristic
383C22#1171869911yescharacteristic
384C22C2×#8820411yescharacteristic
385C4—22no—
386C4—82no—
387C4—1042no—
388C4#1171869911yescharacteristic
389C4#1171869911yescharacteristic
390C4C22×#610411yescharacteristic
391C4C2×#8819311yescharacteristic
392C2—21no—
393C2—21no—
394C2—42no—
395C2#1311695912yesdirect product factor
396C2C2×#1171869911yescharacteristic
subgroupG/H
centerC22#11718699
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#473C2
socleC22×C13#466
prime radicalC2×C13×#41D4
hypercenterC2×#473D13
hypocenterC13C2×#2222
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
1. C22×#88069C2semidirect
4. #13116959C2direct (N × H)
5. C2×#11718085C2semidirect
6. C2×#11718157C2semidirect
7. C2×#11718088C2semidirect
21. C2×#88069C22semidirect
32. #11718157C22semidirect
33. #11718088C22semidirect
34. #11718085C22semidirect
281. C2×C13#2222semidirect
340. C13C2×#2222semidirect
395. C2#13116959direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880692
C2×#117188012
C2×#117188042
#131169592
C2×#117180852
C2×#117181572
C2×#117180882
C2×C13×#4732
C2×#222213