Finite Group Databasebeta

← C2×#13116676 #16016151

Subgroups — C2×#13116676 #16016151

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718562C211yesmaximal, characteristic, complemented
2C2×#11718805C211yesmaximal, characteristic
3#13116676C218yesmaximal, direct product factor
4C2×#11718103C211yesmaximal, characteristic, complemented
5C2×#11718107C211yesmaximal, characteristic, complemented
6C2×#11718153C211yesmaximal, characteristic, complemented
7C2×#11718094C211yesmaximal, characteristic, complemented
8C2×C13×#504C211yesmaximal, characteristic, complemented
9C2×C13×#131C2211yescharacteristic
10C2×#88204C411yescharacteristic
11C2×#88155C2211yescharacteristic
12C13×#504—22no—
13C13×#504C2214yescomplemented
14C2×C13×M32—21no—
15C2×C13×M32C2211yescharacteristic
16C22×C13×C16—21no—
17C22×C13×C16C2211yescharacteristic
18C2×#88077C411yescharacteristic
19#11718805C414yes—
20#11718805C2214yes—
21C2×#88065C411yescharacteristic
22C2×#88062C411yescharacteristic
23C2×C8×Dic13C2211yescharacteristic
24C2×#88052C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26#11718562—22no—
27#11718562C2214yescomplemented
28C2×#88038—21no—
29C2×C16×D13—21no—
30#11718153C2214yescomplemented
31#11718107C2214yescomplemented
32#11718103C2214yescomplemented
33#11718094C2214yescomplemented
34C2×C13×#41C2×C411yescharacteristic
35C2×#6127C2×C411yescharacteristic
36C13×#131—21no—
37C13×#131—21no—
38C13×#131C2×C412yes—
39C13×#131C2312yes—
40C2×C13×M16—21no—
41C2×C13×M16C2×C411yescharacteristic
42C22×C8×C13—21no—
43C22×C8×C13C2311yescharacteristic
44#88204C814yes—
45#88204C2×C414yes—
46C2×#6107C811yescharacteristic
47C2×#6106C811yescharacteristic
48C2×#6105C811yescharacteristic
49C2×#6104C811yescharacteristic
50C2×C4×Dic13C2×C411yescharacteristic
51C2×#6099C2×C411yescharacteristic
52C22×#1055C2×C411yescharacteristic
53#88155—21no—
54#88155—21no—
55#88155C2×C412yes—
56#88155C2312yes—
57C2×#6094—21no—
58C2×C8×D13—21no—
59C13×M32—21no—
60C13×M32—24no—
61C13×M32C2312yes—
62C2×C13×C16—21no—
63C2×C13×C16—24no—
64C2×C13×C16D411yescharacteristic
65C2×C13×C16D411yescharacteristic
66C2×C13×C16D412yes—
67C2×C13×C16C2312yes—
68#88077C2×C414yes—
69#88065C2×C414yes—
70#88062C2×C414yes—
71C8×Dic13C2×C412yes—
72C8×Dic13C2312yes—
73#88052—21no—
74#88052C2312yes—
75C2×#6090—21no—
76C2×#6090—21no—
77C2×#6090—21no—
78C2×#6090C2312yes—
79#88038—24no—
80C16×D13—24no—
81C2×#2171—131nomaximal, Sylow
82C13×#41—21no—
83C13×#41—21no—
84C13×#41C2×C812yes—
85C13×#41C22×C412yes—
86C2×Q8×C13C2×C811yescharacteristic
87C2×D4×C13—21no—
88C2×D4×C13C2×C811yescharacteristic
89C22×C4×C13—21no—
90C22×C4×C13C22×C411yescharacteristic
91C2×C22⋊D13—21no—
92C22×Dic13—21no—
93#6127—21no—
94#6127—21no—
95#6127C2×C812yes—
96#6127C22×C412yes—
97C2×D52C2×C811yescharacteristic
98C2×C4×D13—21no—
99C2×Dic26C2×C811yescharacteristic
100C13×M16—21no—
101C13×M16—22no—
102C13×M16—22no—
103C13×M16C22×C412yes—
104C2×C8×C13—21no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13C22×C411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13#4111yescharacteristic
111C2×C8×C13#4111yescharacteristic
112C2×C8×C13C2411yescharacteristic
113#6107C2×C814yes—
114#6106C2×C814yes—
115#6105C2×C814yes—
116#6104C2×C814yes—
117C4×Dic13—21no—
118C4×Dic13C22×C412yes—
119#6099—21no—
120#6099C22×C412yes—
121C2×#1055—21no—
122C2×#1055C2×C811yescharacteristic
123C2×#1055C2×C811yescharacteristic
124C2×#1055C2×C812yes—
125C2×#1055C22×C412yes—
126#6094—22no—
127#6094—22no—
128C8×D13—22no—
129C8×D13—22no—
130C13×C16—22no—
131C13×C16C2×D412yes—
132C13×C16C2×D412yes—
133#6090—22no—
134#6090—22no—
135C2×#504—131no—
136C2×#504D1311yescharacteristic, complemented
137C2×#443—131no—
138#2171—138no—
139C2×#364—131no—
140C2×#350—131no—
141C2×#350—131no—
142C2×#346—131no—
143C23×C13—21no—
144C23×C13#13111yescharacteristic
145C22×D13—21no—
146Q8×C13—21no—
147Q8×C13C22×C812yes—
148D4×C13—22no—
149D4×C13—22no—
150D4×C13—21no—
151D4×C13C22×C812yes—
152C2×C4×C13—21no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13C4×D411yescharacteristic
157C2×C4×C13C22×C811yescharacteristic
158C2×C4×C13C22×C811yescharacteristic
159C2×C4×C13#13111yescharacteristic
160C2×C4×C13C23×C411yescharacteristic
161C22⋊D13—22no—
162C22⋊D13—22no—
163C2×Dic13—21no—
164C2×Dic13—22no—
165C2×Dic13—42no—
166D52—21no—
167D52C22×C812yes—
168C4×D13—22no—
169C4×D13—22no—
170Dic26—21no—
171Dic26C22×C812yes—
172C8×C13—22no—
173C8×C13C4×D411yescharacteristic
174C8×C13C4×D411yescharacteristic
175C8×C13C22×D411yescharacteristic
176C8×C13C2×#4111yescharacteristic
177#1055—22no—
178#1055C22×C812yes—
179#1055C22×C812yes—
180C2×#135—131no—
181C2×#131—131no—
182C2×#131C2×D1311yescharacteristic
183#504—22no—
184#504—134no—
185#504—262no—
186#504C2×D1314yescomplemented
187C2×M32—21no—
188C2×M32—131no—
189C2×M32—261no—
190C2×M32C2×D1311yescharacteristic
191C22×C16—21no—
192C22×C16—131no—
193C22×C16—261no—
194C22×C16C2×D1311yescharacteristic
195#443—134no—
196#443—134no—
197C2×#108—131no—
198C2×#104—131no—
199C2×#104—131no—
200C2×C4×C8—131no—
201#364—134no—
202#350—134no—
203#350—134no—
204#346—134no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—42no—
208C22×C13C8×D411yescharacteristic
209C22×C13C8×D411yescharacteristic
210C22×C13C2×#13111yescharacteristic
211C2×D13—22no—
212C2×D13—42no—
213C4×C13—22no—
214C4×C13C8×D411yescharacteristic
215C4×C13C8×D411yescharacteristic
216C4×C13C2×C4×D411yescharacteristic
217C4×C13C23×C811yescharacteristic
218Dic13—22no—
219Dic13—42no—
220C2×#41—131no—
221C2×#41C4×D1311yescharacteristic
222#135—134no—
223#135—134no—
224C2×Q16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×D8—131no—
228#131—21no—
229#131—21no—
230#131—132no—
231#131—132no—
232#131—261no—
233#131—261no—
234#131C4×D1312yes—
235#131C22×D1312yes—
236C2×M16—21no—
237C2×M16—131no—
238C2×M16—261no—
239C2×M16C4×D1311yescharacteristic
240C22×C8—21no—
241C22×C8—131no—
242C22×C8—261no—
243C22×C8C22×D1311yescharacteristic
244C2×C42—131no—
245M32—21no—
246M32—24no—
247M32—132no—
248M32—261no—
249M32—264no—
250M32C22×D1312yes—
251C2×C16—21no—
252C2×C16—24no—
253C2×C16—132no—
254C2×C16—261no—
255C2×C16—261no—
256C2×C16—261no—
257C2×C16—264no—
258C2×C16C22⋊D1312yes—
259C2×C16C22⋊D1311yescharacteristic
260C2×C16C22⋊D1311yescharacteristic
261C2×C16C22×D1312yes—
262#108—134no—
263#104—134no—
264#104—134no—
265C4×C8—132no—
266C4×C8—132no—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—42no—
270C2×C13#217112yescomplemented
271C2×C13C2×C8×D411yescharacteristic
272D13—42no—
273#41—21no—
274#41—21no—
275#41—132no—
276#41—132no—
277#41—261no—
278#41—261no—
279#41C8×D1312yes—
280#41C2×C4×D1312yes—
281C2×Q8—131no—
282C2×Q8C8×D1311yescharacteristic
283C2×D4—21no—
284C2×D4—131no—
285C2×D4—261no—
286C2×D4C8×D1311yescharacteristic
287C22×C4—21no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4C2×C4×D1311yescharacteristic
291Q16—134no—
292SD16—134no—
293SD16—134no—
294D8—134no—
295M16—21no—
296M16—22no—
297M16—22no—
298M16—132no—
299M16—261no—
300M16—262no—
301M16—262no—
302M16C2×C4×D1312yes—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—131no—
307C2×C8—131no—
308C2×C8—132no—
309C2×C8—132no—
310C2×C8—261no—
311C2×C8—262no—
312C2×C8—262no—
313C2×C8C2×C4×D1311yescharacteristic
314C2×C8#612711yescharacteristic
315C2×C8#612711yescharacteristic
316C2×C8C2×C22⋊D1311yescharacteristic
317C2×C8C2×C22⋊D1311yescharacteristic
318C2×C8C23×D1311yescharacteristic
319C42—132no—
320C42—261no—
321C16—22no—
322C16—262no—
323C16—262no—
324C16C2×C22⋊D1312yes—
325C16C2×C22⋊D1312yes—
326C13C2×#217111yescharacteristic, complemented, Sylow
327C23—21no—
328C23—261no—
329C23#8815511yescharacteristic
330Q8—21no—
331Q8—132no—
332Q8—261no—
333Q8C2×C8×D1312yes—
334D4—22no—
335D4—22no—
336D4—21no—
337D4—132no—
338D4—262no—
339D4—262no—
340D4—261no—
341D4C2×C8×D1312yes—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—261no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—522no—
350C2×C4C2×C8×D1311yescharacteristic
351C2×C4C2×C8×D1311yescharacteristic
352C2×C4#8815511yescharacteristic
353C2×C4C4×C22⋊D1311yescharacteristic
354C2×C4C4×C22⋊D1311yescharacteristic
355C2×C4C22×C4×D1311yescharacteristic
356C8—22no—
357C8—132no—
358C8—132no—
359C8—262no—
360C8C4×C22⋊D1311yescharacteristic
361C8C4×C22⋊D1311yescharacteristic
362C8C2×#612711yescharacteristic
363C8C22×C22⋊D1311yescharacteristic
364C22—22no—
365C22—22no—
366C22—42no—
367C22—262no—
368C22—522no—
369C22C8×C22⋊D1311yescharacteristic
370C22C8×C22⋊D1311yescharacteristic
371C22C2×#8815511yescharacteristic
372C4—22no—
373C4—262no—
374C4—522no—
375C4C8×C22⋊D1311yescharacteristic
376C4C8×C22⋊D1311yescharacteristic
377C4C22×C8×D1311yescharacteristic
378C4C2×C4×C22⋊D1311yescharacteristic
379C2—21no—
380C2—21no—
381C2—42no—
382C2—522no—
383C2#1311667612yesdirect product factor
384C2C2×C8×C22⋊D1311yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D13
commutatorC4×C13C23×C8
FrattiniC2×C8C23×D13
FittingC2×C13×#504C2
socleC22×C13C8×D4
prime radicalC2×#88204C4
cosocleC2×C8×C13C24
hypercenterC2×#504D13
hypocenterC13C2×#2171
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C2×#11718562C2semidirect
3. #13116676C2direct (N × H)
4. C2×#11718103C2semidirect
5. C2×#11718107C2semidirect
6. C2×#11718153C2semidirect
7. C2×#11718094C2semidirect
8. C2×C13×#504C2semidirect
13. C13×#504C22semidirect
27. #11718562C22semidirect
30. #11718153C22semidirect
31. #11718107C22semidirect
32. #11718103C22semidirect
33. #11718094C22semidirect
136. C2×#504D13semidirect
186. #504C2×D13semidirect
270. C2×C13#2171semidirect
326. C13C2×#2171semidirect
383. C2#13116676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117185622
C2×#117188052
#131166762
C2×#117181032
C2×#117181072
C2×#117181532
C2×#117180942
C2×C13×#5042
C2×#217113