Finite Group Databasebeta

← C2×#13131241 #16807221

Subgroups — C2×#13131241 #16807221

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719104C211yesmaximal, characteristic
2C2×#11719110C211yesmaximal, characteristic, complemented
3#13131241C218yesmaximal, direct product factor
4C2×#11718220C211yesmaximal, characteristic, complemented
5C2×#11718282C211yesmaximal, characteristic, complemented
6C2×#11718275C211yesmaximal, characteristic
7C2×#11718218C211yesmaximal, characteristic, complemented
8C2×#11718576C211yesmaximal, characteristic
9C2×Q8×#261—21no—
10C2×#88238—21no—
11C2×Q16×D13C2211yescharacteristic
12C2×#88166C2211yescharacteristic
13C2×#88117—21no—
14C2×#88116—21no—
15#11719110—22no—
16#11719110C2214yescomplemented
17#11719104—22no—
18#11719104C2214yes—
19C2×#88103C2211yescharacteristic
20C2×#88101C2211yescharacteristic
21C2×#88100C2211yescharacteristic
22C2×#88098C2211yescharacteristic
23C2×C13×SD32C411yescharacteristic, complemented
24C2×#88069C411yescharacteristic, complemented
25C2×#88067C411yescharacteristic, complemented
26#11718576C414yescomplemented
27#11718576C2214yes—
28C2×Dic104C411yescharacteristic, complemented
29C2×#88038C2211yescharacteristic
30#11718282C2214yescomplemented
31#11718275C2214yes—
32#11718220C2214yescomplemented
33#11718218C2214yescomplemented
34C2×Q8×D13—21no—
35C2×#6129—21no—
36C2×#6122—41no—
37C22×#1057—41no—
38Q8×#261—24no—
39Q8×#261—42no—
40#88238—24no—
41#88238—42no—
42C2×C4⋊#261—21no—
43C2×C4⋊#261—41no—
44C2×C4×#261—41no—
45C2×C4×#261D411yescharacteristic
46C2×#6118—21no—
47C2×D13⋊C8D411yescharacteristic
48C2×C13×Q16C2×C411yescharacteristic
49C2×C13×D8C2×C411yescharacteristic
50C2×#6107—21no—
51C2×#6105—21no—
52Q16×D13—21no—
53Q16×D13—21no—
54Q16×D13C2×C412yes—
55Q16×D13C2312yes—
56#88166—21no—
57#88166—21no—
58#88166C2×C412yes—
59#88166C2312yes—
60C2×Dic52C2×C411yescharacteristic
61C2×Dic52C2×C411yescharacteristic
62C2×C8×D13C2311yescharacteristic
63#88117—24no—
64#88116—24no—
65C2×#6092—21no—
66#88103—21no—
67#88103C2312yes—
68#88101—21no—
69#88101C2312yes—
70#88100D412yes—
71#88100C2312yes—
72#88098—21no—
73#88098C2312yes—
74C13×SD32C2×C414yescomplemented
75C2×C13×C16C2×C411yescharacteristic
76#88069C2×C414yescomplemented
77#88067C2×C414yescomplemented
78C2×#6090C2×C411yescharacteristic
79Dic104C2×C414yescomplemented
80#88038C2×C412yes—
81#88038C2312yes—
82C2×#2180—131nomaximal, Sylow
83C22×#261—21no—
84C22×#261—41no—
85C2×Q8×C13—21no—
86C2×D4×C13—21no—
87C2×C22⋊D13—41no—
88C22×Dic13—41no—
89Q8×D13—22no—
90Q8×D13—22no—
91Q8×D13—41no—
92Q8×D13—41no—
93#6129—22no—
94#6129—22no—
95#6129—41no—
96#6129—41no—
97C2×C4×D13—41no—
98C2×C4×D13C2×D411yescharacteristic
99C2×Dic26—21no—
100C2×Dic26—21no—
101C2×Dic26—41no—
102#6122—44no—
103C2×#1057—21no—
104C2×#1057—44no—
105C2×#1057—41no—
106C4⋊#261—22no—
107C4⋊#261—44no—
108C4⋊#261—41no—
109C4×#261—21no—
110C4×#261—44no—
111C4×#261C2×D412yes—
112#6118—22no—
113#6118—41no—
114D13⋊C8—21no—
115D13⋊C8C2×D412yes—
116C13×Q16—21no—
117C13×Q16C22×C412yes—
118C13×D8—21no—
119C13×D8C22×C412yes—
120C2×C8×C13C22×C411yescharacteristic
121#6107—22no—
122#6107—22no—
123#6105—22no—
124#6105—22no—
125C2×#1055#4111yescharacteristic
126Dic52—21no—
127Dic52—21no—
128Dic52C22×C412yes—
129Dic52C22×C412yes—
130C8×D13C22×C411yescharacteristic
131C8×D13C2×D411yescharacteristic
132C8×D13#4111yescharacteristic
133C8×D13C2411yescharacteristic
134#6092—22no—
135C13×C16C22×C412yes—
136#6090C22×C412yes—
137C2×#510—131no—
138C2×#444—131no—
139C2×#441—131no—
140#2180—138no—
141C2×#365—131no—
142C2×#362—131no—
143C2×#360—131no—
144C2×#347—131no—
145C23×C13—41no—
146C22×D13AGL(1,ℤ/8)11yescharacteristic
147C2×#261—22no—
148C2×#261—42no—
149C2×#261—42no—
150C2×#261—82no—
151Q8×C13—22no—
152Q8×C13—41no—
153D4×C13—22no—
154D4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13C4×D411yescharacteristic
157C22⋊D13—42no—
158C22⋊D13—42no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13AGL(1,ℤ/8)11yescharacteristic
164C4×D13—42no—
165C4×D13—42no—
166C4×D13C4×D411yescharacteristic
167C4×D13AGL(1,ℤ/8)11yescharacteristic
168C4×D13AGL(1,ℤ/8)11yescharacteristic
169C4×D13C22×D411yescharacteristic
170Dic26—22no—
171Dic26—22no—
172Dic26—41no—
173Dic26—41no—
174Dic26—42no—
175Dic26—42no—
176#1057—22no—
177#1057—42no—
178C8×C13C4×D411yescharacteristic
179C8×C13C23×C411yescharacteristic
180#1055C4×D411yescharacteristic
181#1055C2×#4111yescharacteristic
182C2×#135—131no—
183C22×Q16—131no—
184C2×#131—261no—
185C2×C4×Q8—261no—
186#510—134no—
187#510—134no—
188C2×Q32—131no—
189C2×Q32—131no—
190C2×SD32—131no—
191C2×SD32#26111yescharacteristic, complemented
192C2×M32—131no—
193C2×M32—131no—
194#444—134no—
195#444—262no—
196#441—134no—
197#441—262no—
198C2×#108—131no—
199C2×#106—131no—
200C2×#104—261no—
201C2×#103—261no—
202C2×#97—131no—
203#365—134no—
204#362—134no—
205#360—134no—
206#347—134no—
207C22×C13—42no—
208C22×C13—82no—
209C22×C13#44211yescharacteristic
210C2×D13—22no—
211C2×D13#44211yescharacteristic
212C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
213#261—42no—
214#261—82no—
215C4×C13—42no—
216C4×C13#44211yescharacteristic
217C4×C13C2×C4×D411yescharacteristic
218Dic13—42no—
219Dic13—42no—
220Dic13#44211yescharacteristic
221Dic13C2×AGL(1,ℤ/8)11yescharacteristic
222C2×#41—261no—
223C22×Q8—261no—
224#135—132no—
225#135—132no—
226#135—261no—
227#135—261no—
228C2×Q16—132no—
229C2×Q16—132no—
230C2×Q16—131no—
231C2×Q16—131no—
232C2×Q16—261no—
233C2×Q16—261no—
234C2×Q16—261no—
235C2×Q16C2×#26111yescharacteristic
236C2×SD16—261no—
237C2×D8C2×#26111yescharacteristic
238#131—264no—
239#131—522no—
240C2×M16—261no—
241C2×M16—521no—
242C22×C8—131no—
243C22×C8—131no—
244C22×C8—521no—
245C4×Q8—264no—
246C4×Q8—522no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—521no—
249C2×C42—131no—
250C2×C42—521no—
251Q32—134no—
252Q32—134no—
253SD32—134no—
254SD32C2×#26114yescomplemented
255M32—132no—
256M32—132no—
257M32—132no—
258M32—261no—
259C2×C16—131no—
260C2×C16—261no—
261C2×C16C2×#26111yescharacteristic
262#108—132no—
263#108—261no—
264#106—132no—
265#106—261no—
266#104—264no—
267#103—264no—
268#97—132no—
269#97—132no—
270C2×C13—82no—
271C2×C13#218012yescomplemented
272C2×C13C2×#44211yescharacteristic
273D13—21no—
274D13—21no—
275#41—262no—
276#41—262no—
277#41—521no—
278#41—521no—
279C2×Q8—21no—
280C2×Q8—262no—
281C2×Q8—262no—
282C2×Q8—261no—
283C2×Q8—261no—
284C2×Q8—521no—
285C2×Q8—521no—
286C2×Q8—521no—
287C2×D4—21no—
288C2×D4—521no—
289C22×C4—131no—
290C22×C4—261no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294Q16—21no—
295Q16—132no—
296Q16—132no—
297Q16—262no—
298Q16—262no—
299Q16—261no—
300Q16—261no—
301Q16C22×#26112yes—
302SD16—262no—
303SD16—262no—
304D8—21no—
305D8C22×#26112yes—
306M16—262no—
307M16—524no—
308M16—521no—
309C2×C8—131no—
310C2×C8—131no—
311C2×C8—131no—
312C2×C8—131no—
313C2×C8—131no—
314C2×C8—132no—
315C2×C8—261no—
316C2×C8—261no—
317C2×C8—524no—
318C2×C8—521no—
319C2×C8C22×#26111yescharacteristic
320C4⋊C4—262no—
321C4⋊C4—521no—
322C4⋊C4—524no—
323C42—132no—
324C42—261no—
325C42—524no—
326C16—132no—
327C16—262no—
328C16C22×#26112yes—
329C13C2×#218011yescharacteristic, complemented, Sylow
330C23—41no—
331C23—131no—
332Q8—22no—
333Q8—41no—
334Q8—262no—
335Q8—262no—
336Q8—522no—
337Q8—522no—
338Q8—521no—
339Q8—521no—
340D4—22no—
341D4—41no—
342D4—522no—
343D4—522no—
344C2×C4—41no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—262no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—522no—
359C2×C4—1042no—
360C2×C4D4×#26111yescharacteristic
361C8—131no—
362C8—131no—
363C8—262no—
364C8—522no—
365C8D4×#26111yescharacteristic
366C8C23×#26111yescharacteristic
367C22—42no—
368C22—82no—
369C22—131no—
370C22—131no—
371C22—262no—
372C22#1171910211yescharacteristic
373C4—42no—
374C4—131no—
375C4—131no—
376C4—522no—
377C4—522no—
378C4—522no—
379C4—1042no—
380C4#1171910211yescharacteristic
381C4C2×D4×#26111yescharacteristic
382C2—82no—
383C2—261no—
384C2—261no—
385C2#1313124112yesdirect product factor
386C2C2×#1171910211yescharacteristic
subgroupG/H
centerC22#11719102
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×SD32C4
socleC22×C13#442
prime radicalC2×#88166C22
cosocleC8×D13C24
hypercenterC2×SD32#261
hypocenterC13C2×#2180
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. C2×#11719110C2semidirect
3. #13131241C2direct (N × H)
4. C2×#11718220C2semidirect
5. C2×#11718282C2semidirect
7. C2×#11718218C2semidirect
16. #11719110C22semidirect
23. C2×C13×SD32C4semidirect
24. C2×#88069C4semidirect
25. C2×#88067C4semidirect
26. #11718576C4semidirect
28. C2×Dic104C4semidirect
30. #11718282C22semidirect
32. #11718220C22semidirect
33. #11718218C22semidirect
74. C13×SD32C2×C4semidirect
76. #88069C2×C4semidirect
77. #88067C2×C4semidirect
79. Dic104C2×C4semidirect
191. C2×SD32#261semidirect
254. SD32C2×#261semidirect
271. C2×C13#2180semidirect
329. C13C2×#2180semidirect
385. C2#13131241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191042
C2×#117191102
#131312412
C2×#117182202
C2×#117182822
C2×#117182752
C2×#117182182
C2×#117185762
C2×#218013