Finite Group Databasebeta

← C2×#13131238 #16807208

Subgroups — C2×#13131238 #16807208

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719111C211yesmaximal, characteristic, complemented
2C2×#11719103C211yesmaximal, characteristic, complemented
3#13131238C218yesmaximal, direct product factor
4C2×#11718223C211yesmaximal, characteristic, complemented
5C2×#11718281C211yesmaximal, characteristic, complemented
6C2×#11718277C211yesmaximal, characteristic, complemented
7C2×#11718216C211yesmaximal, characteristic, complemented
8C2×#11718577C211yesmaximal, characteristic
9C2×#88240—21no—
10C2×#88238—21no—
11C2×#88173C2211yescharacteristic
12C2×#88166C2211yescharacteristic
13C2×#88118—21no—
14C2×#88116—21no—
15#11719111—22no—
16#11719111C2214yescomplemented
17#11719103—22no—
18#11719103C2214yescomplemented
19C2×#88104C2211yescharacteristic
20C2×#88104C2211yescharacteristic
21C2×C8×#261C2211yescharacteristic
22C2×D13⋊C16C2211yescharacteristic
23C2×C13×SD32C411yescharacteristic, complemented
24C2×#88069C411yescharacteristic, complemented
25C2×#88066C411yescharacteristic, complemented
26#11718577C414yescomplemented
27#11718577C2214yes—
28C2×#88040C411yescharacteristic, complemented
29C2×C16×D13C2211yescharacteristic
30#11718281C2214yescomplemented
31#11718277C2214yescomplemented
32#11718223C2214yescomplemented
33#11718216C2214yescomplemented
34C2×#6131—21no—
35C2×#6129—21no—
36C2×#6122—41no—
37C22×#1057—41no—
38#88240—24no—
39#88240—42no—
40#88238—24no—
41#88238—42no—
42C2×C4×#261D411yescharacteristic
43C2×#6118—21no—
44C2×#6118—21no—
45C2×#6118—41no—
46C2×D13⋊C8—41no—
47C2×D13⋊C8D411yescharacteristic
48C2×C13×Q16C2×C411yescharacteristic
49C2×C13×D8C2×C411yescharacteristic
50C2×#6106—21no—
51C2×#6105—21no—
52#88173—21no—
53#88173—21no—
54#88173C2×C412yes—
55#88173C2312yes—
56#88166—21no—
57#88166—21no—
58#88166C2×C412yes—
59#88166C2312yes—
60C2×Dic52C2×C411yescharacteristic
61C2×D104C2×C411yescharacteristic
62C2×C8×D13C2311yescharacteristic
63#88118—24no—
64#88116—24no—
65C2×#6092—21no—
66#88104—21no—
67#88104—21no—
68#88104C2312yes—
69#88104C2312yes—
70C8×#261D412yes—
71C8×#261C2312yes—
72D13⋊C16—21no—
73D13⋊C16C2312yes—
74C13×SD32C2×C414yescomplemented
75C2×C13×C16C2×C411yescharacteristic
76#88069C2×C414yescomplemented
77#88066C2×C414yescomplemented
78C2×#6090C2×C411yescharacteristic
79#88040C2×C414yescomplemented
80C16×D13C2×C412yes—
81C16×D13C2312yes—
82C2×#2179—131nomaximal, Sylow
83C22×#261—21no—
84C2×Q8×C13—21no—
85C2×D4×C13—21no—
86C2×C22⋊D13—41no—
87C22×Dic13—41no—
88#6131—22no—
89#6131—22no—
90#6131—41no—
91#6131—41no—
92#6129—22no—
93#6129—22no—
94#6129—41no—
95#6129—41no—
96C2×D52—21no—
97C2×D52—41no—
98C2×C4×D13—41no—
99C2×C4×D13C2×D411yescharacteristic
100C2×Dic26—21no—
101#6122—44no—
102C2×#1057—41no—
103C2×#1057—41no—
104C2×#1057—44no—
105C2×#1057D811yescharacteristic
106C2×#1057D811yescharacteristic
107C4×#261—21no—
108C4×#261C2×D412yes—
109#6118—22no—
110#6118—22no—
111#6118—41no—
112#6118—41no—
113#6118—44no—
114D13⋊C8—44no—
115D13⋊C8D812yes—
116D13⋊C8C2×D412yes—
117C13×Q16—21no—
118C13×Q16C22×C412yes—
119C13×D8—21no—
120C13×D8C22×C412yes—
121C2×C8×C13C22×C411yescharacteristic
122#6106—22no—
123#6106—22no—
124#6105—22no—
125#6105—22no—
126C2×#1055#4111yescharacteristic
127Dic52—21no—
128Dic52C22×C412yes—
129D104—21no—
130D104C22×C412yes—
131C8×D13C22×C411yescharacteristic
132C8×D13C2×D411yescharacteristic
133C8×D13#4111yescharacteristic
134C8×D13C2411yescharacteristic
135#6092—22no—
136C13×C16C22×C412yes—
137#6090C22×C412yes—
138C2×#508—131no—
139C2×#443—131no—
140C2×#443—131no—
141#2179—138no—
142C2×#368—131no—
143C2×#359—131no—
144C2×#359—131no—
145C2×#346—131no—
146C23×C13—41no—
147C22×D13—41no—
148C22×D13#13511yescharacteristic
149C2×#261—22no—
150C2×#261—42no—
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—42no—
161C2×Dic13—42no—
162C2×Dic13C2×D811yescharacteristic
163D52—22no—
164D52—42no—
165D52—42no—
166D52—41no—
167C4×D13—42no—
168C4×D13—42no—
169C4×D13C4×D411yescharacteristic
170C4×D13C2×D811yescharacteristic
171C4×D13#13511yescharacteristic
172C4×D13C22×D411yescharacteristic
173Dic26—22no—
174Dic26—41no—
175#1057—42no—
176#1057—42no—
177#1057C2×D812yes—
178#1057C2×D812yes—
179C8×C13C4×D411yescharacteristic
180C8×C13C23×C411yescharacteristic
181#1055C4×D411yescharacteristic
182#1055C2×#4111yescharacteristic
183C2×#135—131no—
184C2×#135—131no—
185C2×#131—261no—
186C2×#131—261no—
187#508—134no—
188#508—134no—
189C2×Q32—131no—
190C2×SD32—131no—
191C2×SD32#26111yescharacteristic, complemented
192C2×D16—131no—
193C22×C16—131no—
194C22×C16—131no—
195#443—134no—
196#443—134no—
197#443—262no—
198#443—262no—
199C2×#108—131no—
200C2×#108—131no—
201C2×#104—261no—
202C2×#104—261no—
203C2×C4×C8—131no—
204#368—134no—
205#359—134no—
206#359—134no—
207#346—134no—
208C22×C13—42no—
209C22×C13—82no—
210C22×C13C4×D811yescharacteristic
211C2×D13—22no—
212C2×D13—42no—
213C2×D13—82no—
214C2×D13C4×D811yescharacteristic
215C2×D13C2×#13511yescharacteristic
216#261—42no—
217C4×C13—42no—
218C4×C13C4×D811yescharacteristic
219C4×C13C2×C4×D411yescharacteristic
220Dic13—42no—
221Dic13C4×D811yescharacteristic
222Dic13C22×D811yescharacteristic
223C2×#41—261no—
224C2×#41—261no—
225#135—132no—
226#135—132no—
227#135—132no—
228#135—132no—
229#135—261no—
230#135—261no—
231#135—261no—
232#135—261no—
233C2×Q16—131no—
234C2×Q16C2×#26111yescharacteristic
235C2×SD16—261no—
236C2×SD16—261no—
237C2×D8—131no—
238C2×D8C2×#26111yescharacteristic
239#131—264no—
240#131—264no—
241#131—522no—
242#131—522no—
243C2×M16—261no—
244C2×M16—261no—
245C2×M16—521no—
246C2×M16—521no—
247C22×C8—131no—
248C22×C8—131no—
249C22×C8—521no—
250C22×C8—521no—
251C2×C42—131no—
252Q32—134no—
253SD32—134no—
254SD32C2×#26114yescomplemented
255D16—134no—
256C2×C16—131no—
257C2×C16—132no—
258C2×C16—132no—
259C2×C16—132no—
260C2×C16—261no—
261C2×C16—261no—
262C2×C16C2×#26111yescharacteristic
263#108—132no—
264#108—132no—
265#108—261no—
266#108—261no—
267#104—264no—
268#104—264no—
269C4×C8—132no—
270C4×C8—132no—
271C2×C13—82no—
272C2×C13#217912yescomplemented
273C2×C13C2×C4×D811yescharacteristic
274D13—21no—
275D13—21no—
276D13—82no—
277#41—262no—
278#41—262no—
279#41—262no—
280#41—262no—
281#41—521no—
282#41—521no—
283#41—521no—
284#41—521no—
285C2×Q8—21no—
286C2×Q8—261no—
287C2×D4—21no—
288C2×D4—261no—
289C2×D4—521no—
290C2×D4—521no—
291C22×C4—131no—
292C22×C4—261no—
293C22×C4—521no—
294C22×C4—521no—
295Q16—21no—
296Q16—132no—
297Q16—261no—
298Q16C22×#26112yes—
299SD16—262no—
300SD16—262no—
301SD16—262no—
302SD16—262no—
303D8—21no—
304D8—132no—
305D8—261no—
306D8C22×#26112yes—
307M16—262no—
308M16—262no—
309M16—524no—
310M16—524no—
311M16—521no—
312M16—521no—
313C2×C8—132no—
314C2×C8—131no—
315C2×C8—131no—
316C2×C8—132no—
317C2×C8—131no—
318C2×C8—131no—
319C2×C8—131no—
320C2×C8—131no—
321C2×C8—131no—
322C2×C8—524no—
323C2×C8—524no—
324C2×C8—521no—
325C2×C8—521no—
326C2×C8C22×#26111yescharacteristic
327C42—132no—
328C42—261no—
329C16—132no—
330C16—262no—
331C16C22×#26112yes—
332C13C2×#217911yescharacteristic, complemented, Sylow
333C23—41no—
334C23—131no—
335C23—521no—
336Q8—22no—
337Q8—41no—
338Q8—262no—
339Q8—521no—
340D4—22no—
341D4—41no—
342D4—262no—
343D4—522no—
344D4—522no—
345D4—522no—
346D4—522no—
347D4—521no—
348C2×C4—41no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—131no—
353C2×C4—131no—
354C2×C4—262no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—521no—
361C2×C4D4×#26111yescharacteristic
362C8—132no—
363C8—132no—
364C8—131no—
365C8—131no—
366C8—522no—
367C8—522no—
368C8D4×#26111yescharacteristic
369C8C23×#26111yescharacteristic
370C22—42no—
371C22—82no—
372C22—131no—
373C22—131no—
374C22—262no—
375C22—522no—
376C22—1042no—
377C22D8×#26111yescharacteristic
378C4—42no—
379C4—131no—
380C4—131no—
381C4—522no—
382C4—522no—
383C4D8×#26111yescharacteristic
384C4C2×D4×#26111yescharacteristic
385C2—82no—
386C2—261no—
387C2—261no—
388C2—1042no—
389C2#1313123812yesdirect product factor
390C2C2×D8×#26111yescharacteristic
subgroupG/H
centerC22D8×#261
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×SD32C4
socleC22×C13C4×D8
prime radicalC2×#11718577C2
cosocleC8×D13C24
hypercenterC2×SD32#261
hypocenterC13C2×#2179
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
1. C2×#11719111C2semidirect
2. C2×#11719103C2semidirect
3. #13131238C2direct (N × H)
4. C2×#11718223C2semidirect
5. C2×#11718281C2semidirect
6. C2×#11718277C2semidirect
7. C2×#11718216C2semidirect
16. #11719111C22semidirect
18. #11719103C22semidirect
23. C2×C13×SD32C4semidirect
24. C2×#88069C4semidirect
25. C2×#88066C4semidirect
26. #11718577C4semidirect
28. C2×#88040C4semidirect
30. #11718281C22semidirect
31. #11718277C22semidirect
32. #11718223C22semidirect
33. #11718216C22semidirect
74. C13×SD32C2×C4semidirect
76. #88069C2×C4semidirect
77. #88066C2×C4semidirect
79. #88040C2×C4semidirect
191. C2×SD32#261semidirect
254. SD32C2×#261semidirect
272. C2×C13#2179semidirect
332. C13C2×#2179semidirect
389. C2#13131238direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191112
C2×#117191032
#131312382
C2×#117182232
C2×#117182812
C2×#117182772
C2×#117182162
C2×#117185772
C2×#217913