Finite Group Databasebeta

← C2×#13130904 #16798764

Subgroups — C2×#13130904 #16798764

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719079C211yesmaximal, characteristic
2C2×#11719072C211yesmaximal, characteristic
3#13130904C218yesmaximal, direct product factor
4C2×#11718268C211yesmaximal, characteristic
5C2×#11718247C211yesmaximal, characteristic
6C2×#11718247C211yesmaximal, characteristic
7C2×(C2×#261)⋊C8C211yesmaximal, characteristic
8C2×#11718541C211yesmaximal, characteristic
9C22×C4×#261C2211yescharacteristic
10C22×#6118C2211yescharacteristic
11C22×#6118C2211yescharacteristic
12C22×D13⋊C8C2211yescharacteristic
13C22×C8×D13C2211yescharacteristic
14C2×#88146C2211yescharacteristic
15C2×#88146C2211yescharacteristic
16C2×#88112—21no—
17C2×#88110—21no—
18C2×C4⋊#1057—21no—
19C2×C4×#1057—21no—
20#11719079—22no—
21#11719079C2214yes—
22#11719072—22no—
23#11719072C2214yes—
24C2×C13×#107C411yescharacteristic, complemented
25C2×#88058C411yescharacteristic, complemented
26C2×#88048C411yescharacteristic, complemented
27C2×#88048C411yescharacteristic, complemented
28#11718541C414yescomplemented
29#11718541C2214yes—
30#11718268C2214yes—
31(C2×#261)⋊C8C2214yes—
32#11718247C2214yes—
33#11718247C2214yes—
34C23×#261—21no—
35C22×C4×D13C2311yescharacteristic
36C22×#1057—21no—
37C22×#1057—21no—
38C22×#1057D411yescharacteristic
39C22×#1057D411yescharacteristic
40C2×C4×#261—22no—
41C2×C4×#261—22no—
42C2×C4×#261—21no—
43C2×C4×#261C2312yes—
44C2×#6118—21no—
45C2×#6118—22no—
46C2×#6118—22no—
47C2×#6118—22no—
48C2×#6118—21no—
49C2×#6118Q814yes—
50C2×#6118C2312yes—
51C2×#6118C2312yes—
52C2×D13⋊C8—22no—
53C2×D13⋊C8—22no—
54C2×D13⋊C8D412yes—
55C2×D13⋊C8C2312yes—
56C22×C8×C13C2×C411yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×#6103—21no—
60C2×#6103—21no—
61C2×C4⋊Dic13C2×C411yescharacteristic
62C2×C4⋊Dic13C2×C411yescharacteristic
63C2×C4×Dic13—21no—
64C2×C4×Dic13—21no—
65C22×#1055C2×C411yescharacteristic
66C2×C8×D13—22no—
67C2×C8×D13—22no—
68C2×C8×D13C2×C412yes—
69C2×C8×D13C2312yes—
70#88146—21no—
71#88146—21no—
72#88146—21no—
73#88146—21no—
74#88146C2×C412yes—
75#88146C2×C412yes—
76#88146C2312yes—
77#88146C2312yes—
78#88112—24no—
79#88110—24no—
80C4⋊#1057—24no—
81C4×#1057—24no—
82C13×#107C2×C414yescomplemented
83#88058C2×C414yescomplemented
84#88048C2×C414yescomplemented
85#88048C2×C414yescomplemented
86C2×#1922—131nomaximal, Sylow
87C23×D13#4111yescharacteristic
88C22×#261—24no—
89C22×#261—22no—
90C22×#261—42no—
91C22×#261—42no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13C22×C411yescharacteristic
95C22×Dic13—21no—
96C22×Dic13—21no—
97C22×Dic13C2×D411yescharacteristic
98C2×C4×D13C22×C411yescharacteristic
99C2×C4×D13C2×D411yescharacteristic
100C2×C4×D13C2×Q812yes—
101C2×C4×D13#4112yes—
102C2×C4×D13#4112yes—
103C2×C4×D13#4112yes—
104C2×C4×D13#4111yescharacteristic
105C2×C4×D13C2411yescharacteristic
106C2×#1057—24no—
107C2×#1057—22no—
108C2×#1057—22no—
109C2×#1057—22no—
110C2×#1057—22no—
111C2×#1057—42no—
112C2×#1057C2×D412yes—
113C2×#1057C2×D412yes—
114C4×#261—22no—
115C4×#261—22no—
116C4×#261—42no—
117#6118—24no—
118#6118—22no—
119#6118—22no—
120#6118—22no—
121#6118—42no—
122#6118C2×Q814yes—
123D13⋊C8—24no—
124D13⋊C8—22no—
125D13⋊C8—22no—
126C2×C8×C13—22no—
127C2×C8×C13C22×C412yes—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4C22×C412yes—
131C13×C4⋊C4C22×C412yes—
132#6103—22no—
133#6103—22no—
134#6103—22no—
135#6103—22no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13C22×C412yes—
139C4⋊Dic13C22×C412yes—
140C4×Dic13—22no—
141C4×Dic13—22no—
142C4×Dic13—22no—
143C4×Dic13—22no—
144C2×#1055—22no—
145C2×#1055C22×C412yes—
146C8×D13—24no—
147C8×D13—22no—
148C8×D13—22no—
149C2×#427—131no—
150C2×#424—131no—
151C2×#405—131no—
152#1922—138no—
153C2×#341—131no—
154C2×#339—131no—
155C2×#339—131no—
156C2×#336—131no—
157C23×C13C4×D411yescharacteristic
158C22×D13—22no—
159C22×D13—22no—
160C22×D13C4×D411yescharacteristic
161C22×D13#12512yes—
162C22×D13#12612yes—
163C22×D13C2×#4111yescharacteristic
164C2×#261—24no—
165C2×#261—48no—
166C2×#261—42no—
167C2×#261—42no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13#11712yes—
173C2×C4×C13C4×D411yescharacteristic
174C2×C4×C13C4×Q812yes—
175C2×C4×C13C23×C411yescharacteristic
176C2×Dic13—22no—
177C2×Dic13—22no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13C4×D411yescharacteristic
181C2×Dic13C22⋊Q812yes—
182C2×Dic13#12312yes—
183C2×Dic13C22×D411yescharacteristic
184C4×D13#11712yes—
185C4×D13C4×Q812yes—
186C4×D13C22⋊Q812yes—
187C4×D13#12312yes—
188C4×D13#12512yes—
189C4×D13#12612yes—
190C4×D13C22×Q811yescharacteristic
191C4×D13C2×#4111yescharacteristic
192C4×D13C2×#4111yescharacteristic
193C4×D13C2×#4111yescharacteristic
194#1057—24no—
195#1057—22no—
196#1057—22no—
197#1057—42no—
198C8×C13—22no—
199#1055—22no—
200C22×M16—131no—
201C22×M16—131no—
202C23×C8—131no—
203C23×C8—131no—
204C2×#117—131no—
205C2×#117—131no—
206C22×C42—131no—
207#427—134no—
208#427—134no—
209C2×#107—131no—
210C2×#107#26111yescharacteristic, complemented
211C2×#106—131no—
212C2×#106—131no—
213#424—134no—
214#424—262no—
215C2×C4⋊C8—261no—
216C2×C4⋊C8—261no—
217#405—134no—
218#405—262no—
219C2×#97—261no—
220C2×C4×C8—261no—
221#341—134no—
222#339—134no—
223#339—134no—
224#336—134no—
225C22×C13#38712yes—
226C22×C13#44312yes—
227C22×C13#44412yes—
228C22×C13C2×C4×D411yescharacteristic
229C2×D13—24no—
230C2×D13—24no—
231C2×D13—21no—
232C2×D13—21no—
233C2×D13—21no—
234C2×D13—21no—
235C2×D13#38712yes—
236C2×D13C2×#12511yescharacteristic
237C2×D13C2×#12611yescharacteristic
238#261—44no—
239C4×C13—42no—
240C4×C13—42no—
241C4×C13#38712yes—
242C4×C13C2×#11711yescharacteristic
243C4×C13C2×C4×Q811yescharacteristic
244Dic13—42no—
245Dic13—42no—
246Dic13#38712yes—
247Dic13C2×C22⋊Q811yescharacteristic
248Dic13C2×#12311yescharacteristic
249C23×C4—131no—
250C23×C4—261no—
251C2×M16—132no—
252C2×M16—134no—
253C2×M16—132no—
254C2×M16—261no—
255C2×M16—262no—
256C2×M16—261no—
257C2×M16—262no—
258C2×M16—262no—
259C22×C8—132no—
260C22×C8—131no—
261C22×C8—131no—
262C22×C8—132no—
263C22×C8—131no—
264C22×C8—132no—
265C22×C8—132no—
266C22×C8—262no—
267C22×C8—262no—
268C22×C8—262no—
269C22×C8—262no—
270C22×C8—261no—
271C22×C8—261no—
272C22×C8C2×#26111yescharacteristic
273#117—132no—
274#117—132no—
275#117—132no—
276#117—132no—
277#117—261no—
278#117—261no—
279#117—261no—
280#117—261no—
281C2×C4⋊C4—131no—
282C2×C4⋊C4—131no—
283C2×C4⋊C4C2×#26111yescharacteristic
284C2×C4⋊C4C2×#26111yescharacteristic
285C2×C22⋊C4—261no—
286C2×C22⋊C4—261no—
287C2×C42—132no—
288C2×C42—261no—
289C2×C42—261no—
290C2×C42—262no—
291C2×C42—262no—
292C2×C42—261no—
293#107—134no—
294#107C2×#26114yescomplemented
295#106—134no—
296#106—134no—
297C4⋊C8—264no—
298C4⋊C8—264no—
299#97—264no—
300C4×C8—264no—
301C2×C13#192214yescomplemented
302C2×C13C2×#38711yescharacteristic
303C2×C13C2×#44311yescharacteristic
304C2×C13C2×#44411yescharacteristic
305D13—21no—
306D13—21no—
307D13—22no—
308C24—131no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—131no—
312C22×C4—132no—
313C22×C4—132no—
314C22×C4—131no—
315C22×C4—131no—
316C22×C4—132no—
317C22×C4—132no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—262no—
321C22×C4—264no—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—522no—
325C22×C4—522no—
326C22×C4C22×#26111yescharacteristic
327M16—134no—
328M16—264no—
329M16—262no—
330M16—262no—
331M16—262no—
332M16—522no—
333C2×C8—22no—
334C2×C8—132no—
335C2×C8—132no—
336C2×C8—132no—
337C2×C8—262no—
338C2×C8—262no—
339C2×C8—264no—
340C2×C8—262no—
341C2×C8—264no—
342C2×C8—262no—
343C2×C8—262no—
344C2×C8—262no—
345C2×C8—262no—
346C2×C8—264no—
347C2×C8—262no—
348C2×C8—262no—
349C2×C8—522no—
350C2×C8C22×#26112yes—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—132no—
354C4⋊C4—132no—
355C4⋊C4—261no—
356C4⋊C4—261no—
357C4⋊C4C22×#26112yes—
358C4⋊C4C22×#26112yes—
359C22⋊C4—262no—
360C22⋊C4—262no—
361C22⋊C4—262no—
362C22⋊C4—262no—
363C42—262no—
364C42—262no—
365C42—262no—
366C42—262no—
367C42—262no—
368C42—262no—
369C42—522no—
370C13C2×#192211yescharacteristic, complemented, Sylow
371C23—132no—
372C23—132no—
373C23—131no—
374C23—131no—
375C23—262no—
376C23—262no—
377C23D4×#26111yescharacteristic
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—132no—
383C2×C4—132no—
384C2×C4—131no—
385C2×C4—131no—
386C2×C4—132no—
387C2×C4—132no—
388C2×C4—132no—
389C2×C4—132no—
390C2×C4—131no—
391C2×C4—131no—
392C2×C4—132no—
393C2×C4—131no—
394C2×C4—131no—
395C2×C4—132no—
396C2×C4—264no—
397C2×C4—262no—
398C2×C4—262no—
399C2×C4—522no—
400C2×C4—522no—
401C2×C4—528no—
402C2×C4—522no—
403C2×C4—522no—
404C2×C4#8823712yes—
405C2×C4D4×#26111yescharacteristic
406C2×C4Q8×#26112yes—
407C2×C4C23×#26111yescharacteristic
408C8—22no—
409C8—262no—
410C8—262no—
411C8—264no—
412C8—262no—
413C8—522no—
414C22—131no—
415C22—131no—
416C22—132no—
417C22—261no—
418C22—261no—
419C22—261no—
420C22—261no—
421C22—264no—
422C22—264no—
423C22#1171908212yes—
424C22#1171910412yes—
425C22#1171911112yes—
426C22C2×D4×#26111yescharacteristic
427C4—42no—
428C4—42no—
429C4—131no—
430C4—131no—
431C4—132no—
432C4—524no—
433C4—522no—
434C4—522no—
435C4#1171908212yes—
436C4C2×#8823711yescharacteristic
437C4C2×Q8×#26111yescharacteristic
438C2—261no—
439C2—261no—
440C2—262no—
441C2#1313090414yesdirect product factor
442C2C2×#1171908211yescharacteristic
443C2C2×#1171911111yescharacteristic
444C2C2×#1171910411yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#107C4
socleC23×C13C4×D4
prime radicalC23×D13#41
cosocleC2×C4×D13C24
hypercenterC2×#107#261
hypocenterC13C2×#1922
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #13130904C2direct (N × H)
24. C2×C13×#107C4semidirect
25. C2×#88058C4semidirect
26. C2×#88048C4semidirect
27. C2×#88048C4semidirect
28. #11718541C4semidirect
82. C13×#107C2×C4semidirect
83. #88058C2×C4semidirect
84. #88048C2×C4semidirect
85. #88048C2×C4semidirect
210. C2×#107#261semidirect
294. #107C2×#261semidirect
301. C2×C13#1922semidirect
370. C13C2×#1922semidirect
441. C2#13130904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190792
C2×#117190722
#131309042
C2×#117182682
C2×#117182472
C2×(C2×#261)⋊C82
C2×#117185412
C2×#192213