Finite Group Databasebeta

← C2×#13082434 #15662104

Subgroups — C2×#13082434 #15662104

Order 2816.

7478 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082434C2132yesmaximal, direct product factor
2C2×Q8×Dic22C211yesmaximal, characteristic, complemented
3C2×#10623100C212yesmaximal, complemented
4C2×#10623261C213yesmaximal, complemented
5C2×#10623110C213yesmaximal, complemented
6C2×#10623258C216yesmaximal, complemented
7C2×#10623260C216yesmaximal, complemented
8C2×#10623109C213yesmaximal, complemented
9C2×D11×C4⋊Q8C213yesmaximal, complemented
10C2×#10623105C212yesmaximal
11C2×C4×#4343C211yesmaximal, characteristic
12C2×Q82×C11C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×Q8×D11C2216yes—
15Q82×C11C22116yescomplemented
16C2×C11×C4⋊Q8C2213yes—
17C2×C11×C4⋊Q8C2216yes—
18C2×C4×Q8×C11C2213yes—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#66999C2213yes—
22C2×#66999C22112yes—
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2212yes—
25C2×#66997C2216yes—
26C2×#66997C2211yescharacteristic
27#10623261C22148yescomplemented
28#10623260C22196yescomplemented
29#10623258C22196yescomplemented
30D11×C4⋊Q8C22148yescomplemented
31#10623110C22148yescomplemented
32#10623109C22148yescomplemented
33#10623105C22132yes—
34C4×#4343C22116yes—
35#10623100C22132yescomplemented
36Q8×Dic22C22116yescomplemented
37C2×#66950C2213yes—
38C2×#66949C22112yes—
39C2×#66949C2216yes—
40C2×#66946C2216yes—
41C2×#66946C2213yes—
42C2×#66945C2213yes—
43C2×C4⋊C4×D11C2216yes—
44C2×C4⋊C4×D11C2216yes—
45C2×#66943C2216yes—
46C2×#66942C2216yes—
47C2×#66941C2213yes—
48C2×#66941C2216yes—
49C2×#66941C2216yes—
50C2×C4×D44C2213yes—
51C2×C4×D44C2216yes—
52C2×#66925C2216yes—
53C2×C42×D11C2213yes—
54C2×#66923C2216yes—
55C2×#66922C2213yes—
56C2×C4×Dic22C2213yes—
57C2×C4×Dic22C2216yes—
58C22×Q8×C11C2311yescharacteristic
59C22×Q8×C11C2316yes—
60C22×Q8×C11C2311yescharacteristic
61C2×#4343Q8116yescomplemented
62C2×#4343C2318yes—
63C2×Q8×D11—424no—
64C2×Q8×D11C23148yes—
65C22×D44C2313yes—
66C22×C4×D11C2313yes—
67C22×C4×D11C2313yes—
68C22×C4×D11C23112yes—
69C22×C4×D11C2313yes—
70C22×Dic22C2311yescharacteristic
71C22×Dic22C2316yes—
72C22×Dic22C2316yes—
73C11×C4⋊Q8C23124yes—
74C11×C4⋊Q8C23148yes—
75C4×Q8×C11C2318yes—
76C4×Q8×C11C23116yes—
77C4×Q8×C11C23124yes—
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2316yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C4⋊C4C2316yes—
82C2×C42×C11C2313yes—
83C2×C42×C11C2316yes—
84#66999C23196yes—
85#66999C23124yes—
86Q8×Dic11C23116yes—
87Q8×Dic11C2318yes—
88#66997C23148yes—
89#66997C2318yes—
90C2×(C2×D11)⋊C4C2316yes—
91C2×(C2×D11)⋊C4C2316yes—
92C2×(C2×D11)⋊C4C2316yes—
93C2×C4⋊Dic11C2313yes—
94C2×C4⋊Dic11C2316yes—
95C2×C4⋊Dic11C2316yes—
96C2×C4⋊Dic11C2313yes—
97C2×Dic11⋊C4C2312yes—
98C2×Dic11⋊C4C2316yes—
99C2×Dic11⋊C4C2316yes—
100C2×Dic11⋊C4C23112yes—
101C2×Dic11⋊C4C2312yes—
102C2×Dic11⋊C4C2316yes—
103C2×C4×Dic11C2313yes—
104C2×C4×Dic11C2316yes—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2313yes—
107#66950C23124yes—
108#66949C23148yes—
109#66949C23196yes—
110#66946C23124yes—
111#66946C23148yes—
112#66945C23124yes—
113C4⋊C4×D11C23148yes—
114C4⋊C4×D11C23148yes—
115#66943C23148yes—
116#66942C23148yes—
117#66941C23124yes—
118#66941C23148yes—
119#66941C23148yes—
120C4×D44C23148yes—
121C4×D44C23124yes—
122#66925C23148yes—
123C42×D11C23124yes—
124#66923C23148yes—
125#66922C23124yes—
126C4×Dic22C23148yes—
127C4×Dic22C23124yes—
128C2×#3503—111nomaximal, Sylow
129C23×D11C2413yes—
130C2×Q8×C11—24no—
131C2×Q8×C11—412no—
132C2×Q8×C11C2×Q818yescomplemented
133C2×Q8×C11C2414yes—
134C2×Q8×C11C24124yes—
135C2×Q8×C11C2414yes—
136C22×C4×C11C2413yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2416yes—
139C22×C4×C11C2413yes—
140C22×C4×C11C2411yescharacteristic
141C22×Dic11C2412yes—
142C22×Dic11C2413yes—
143C22×Dic11C2416yes—
144C22×Dic11C2411yescharacteristic
145C22×Dic11C2411yescharacteristic
146#4343C2×Q8164yescomplemented
147Q8×D11—496no—
148C2×D44C2×Q8124yescomplemented
149C2×D44C24112yes—
150C2×C4×D11—212no—
151C2×C4×D11—212no—
152C2×C4×D11—424no—
153C2×C4×D11C2×Q8124yescomplemented
154C2×C4×D11C24112yes—
155C2×C4×D11C24112yes—
156C2×C4×D11C24148yes—
157C2×C4×D11C24112yes—
158C2×Dic22—224no—
159C2×Dic22—24no—
160C2×Dic22—412no—
161C2×Dic22C2414yes—
162C2×Dic22C24124yes—
163C2×Dic22C24124yes—
164C11×C4⋊C4C24112yes—
165C11×C4⋊C4C24124yes—
166C11×C4⋊C4C24112yes—
167C11×C4⋊C4C24124yes—
168C42×C11C24112yes—
169C42×C11C24124yes—
170(C2×D11)⋊C4C24124yes—
171(C2×D11)⋊C4C24124yes—
172(C2×D11)⋊C4C24124yes—
173C4⋊Dic11C24112yes—
174C4⋊Dic11C24124yes—
175C4⋊Dic11C24124yes—
176C4⋊Dic11C24112yes—
177Dic11⋊C4C2418yes—
178Dic11⋊C4C24124yes—
179Dic11⋊C4C24124yes—
180Dic11⋊C4C24148yes—
181Dic11⋊C4C2418yes—
182Dic11⋊C4C24124yes—
183C4×Dic11C24112yes—
184C4×Dic11C24124yes—
185C4×Dic11C2414yes—
186C4×Dic11C24112yes—
187#3503—1132no—
188C2×Q82—111no—
189C2×Q82D1111yescharacteristic, complemented
190C2×#557—112no—
191C2×#554—113no—
192C2×#554—113no—
193C2×D4×Q8—116no—
194C2×#544—116no—
195C2×#533—113no—
196C22×C4⋊Q8—113no—
197C2×#520—112no—
198C2×C4×#41—111no—
199C23×C11C2511yescharacteristic
200C22×D11—26no—
201C22×D11—26no—
202C22×D11C22×Q8112yes—
203C22×D11C2516yes—
204Q8×C11—28no—
205Q8×C11—424no—
206Q8×C11C22×Q8116yescomplemented
207C2×C4×C11—212no—
208C2×C4×C11—26no—
209C2×C4×C11—24no—
210C2×C4×C11C22×Q8112yes—
211C2×C4×C112−1+414yes—
212C2×C4×C11C2516yes—
213C2×C4×C11C2514yes—
214C2×C4×C11C25112yes—
215C2×C4×C11C2516yes—
216C2×C4×C11C2512yes—
217C2×Dic11—212no—
218C2×Dic11—24no—
219C2×Dic11—26no—
220C2×Dic11C22×Q814yes—
221C2×Dic11H(5,𝔽2)14yes—
222C2×Dic11C2514yes—
223C2×Dic11C2516yes—
224C2×Dic11C25112yes—
225C2×Dic11C2512yes—
226C2×Dic11C2512yes—
227D44C22×Q8148yescomplemented
228C4×D11—224no—
229C4×D11—224no—
230C4×D11—448no—
231C4×D11C22×Q8148yescomplemented
232Dic22—28no—
233Dic22—248no—
234Dic22—424no—
235C22×#41—111no—
236C23×Q8—116no—
237Q82—1116no—
238Q82C2×D11116yescomplemented
239#557—1132no—
240#554—1148no—
241#554—1148no—
242D4×Q8—1196no—
243#544—1196no—
244#533—1148no—
245C2×C4⋊Q8—116no—
246C2×C4⋊Q8—111no—
247C2×C4⋊Q8—1148no—
248C2×C4⋊Q8—113no—
249C2×C4⋊Q8—116no—
250C2×C4⋊Q8—116no—
251C2×C4⋊Q8—113no—
252C2×C4⋊Q8C2×D1113yes—
253C2×C4⋊Q8C2×D1116yes—
254C2×#125—116no—
255C2×#125—116no—
256C2×#125—116no—
257C2×C22⋊Q8—113no—
258C2×C22⋊Q8—1112no—
259C2×C22⋊Q8—116no—
260C2×C22⋊Q8—1112no—
261C2×C22⋊Q8—113no—
262#520—1132no—
263C4×#41—1116no—
264C2×C4×Q8—111no—
265C2×C4×Q8—112no—
266C2×C4×Q8—116no—
267C2×C4×Q8—113no—
268C2×C4×Q8C2×D1111yescharacteristic
269C2×C4×Q8C2×D1112yes—
270C2×C4×Q8C2×D1113yes—
271C2×C4×D4—113no—
272C2×C4×D4—116no—
273C2×C4×D4—113no—
274C2×C4×D4—116no—
275C2×#117—113no—
276C2×#117—116no—
277C22×C4⋊C4—116no—
278C22×C4⋊C4—116no—
279C22×C42—113no—
280C22×C11C23×Q812yes—
281C22×C11C2×H(5,𝔽2)12yes—
282C22×C11C2×2−1+412yes—
283C22×C11C2611yescharacteristic
284C2×D11—26no—
285C2×D11—26no—
286C2×D11—224no—
287C2×D11C23×Q8112yes—
288C4×C11—212no—
289C4×C11—26no—
290C4×C11—24no—
291C4×C11C23×Q8112yes—
292C4×C11C2×2−1+414yes—
293Dic11—212no—
294Dic11—24no—
295Dic11—26no—
296Dic11C23×Q814yes—
297Dic11C2×H(5,𝔽2)14yes—
298C2×#41—1116no—
299C2×#41—118no—
300C22×Q8—1148no—
301C22×Q8—111no—
302C22×Q8—116no—
303C22×Q8—116no—
304C22×Q8—4424no—
305C22×Q8C22×D1111yescharacteristic
306C22×Q8C22×D1116yes—
307C22×Q8C22×D1111yescharacteristic
308C22×D4—113no—
309C23×C4—113no—
310C23×C4—113no—
311C23×C4—113no—
312C23×C4—1112no—
313C4⋊Q8—1148no—
314C4⋊Q8—118no—
315C4⋊Q8—1124no—
316C4⋊Q8—1148no—
317C4⋊Q8—1148no—
318C4⋊Q8—1124no—
319C4⋊Q8C22×D11124yes—
320C4⋊Q8C22×D11148yes—
321#125—1148no—
322#125—1148no—
323#125—1148no—
324C22⋊Q8—1124no—
325C22⋊Q8—1196no—
326C22⋊Q8—1148no—
327C22⋊Q8—1124no—
328C22⋊Q8—1196no—
329C4×Q8—118no—
330C4×Q8—1116no—
331C4×Q8—1148no—
332C4×Q8—1124no—
333C4×Q8C22×D1118yes—
334C4×Q8C22×D11116yes—
335C4×Q8C22×D11124yes—
336C4×D4—1124no—
337C4×D4—1148no—
338C4×D4—1124no—
339C4×D4—1148no—
340#117—1124no—
341#117—1148no—
342C2×C4⋊C4—116no—
343C2×C4⋊C4—113no—
344C2×C4⋊C4—116no—
345C2×C4⋊C4—1112no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—113no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—116no—
350C2×C4⋊C4—116no—
351C2×C4⋊C4—116no—
352C2×C4⋊C4—1148no—
353C2×C4⋊C4—1148no—
354C2×C4⋊C4C22×D1113yes—
355C2×C4⋊C4C22×D1116yes—
356C2×C4⋊C4C22×D1113yes—
357C2×C4⋊C4C22×D1116yes—
358C2×C22⋊C4—116no—
359C2×C22⋊C4—116no—
360C2×C22⋊C4—116no—
361C2×C42—113no—
362C2×C42—116no—
363C2×C42—113no—
364C2×C42—111no—
365C2×C42—1124no—
366C2×C42C22×D1116yes—
367C2×C42C22×D1113yes—
368C2×C11#350314yescomplemented
369C2×C11C24×Q811yescharacteristic
370C2×C11C22×H(5,𝔽2)11yescharacteristic
371C2×C11C22×2−1+411yescharacteristic
372D11—212no—
373C24—113no—
374#41—1164no—
375C2×Q8—24no—
376C2×Q8—412no—
377C2×Q8—114no—
378C2×Q8—1124no—
379C2×Q8—1124no—
380C2×Q8—2224no—
381C2×Q8—224no—
382C2×Q8—4412no—
383C2×Q8—4496no—
384C2×Q8Q8×D1118yescomplemented
385C2×Q8C23×D1114yes—
386C2×Q8C23×D11124yes—
387C2×Q8C23×D1114yes—
388C2×D4—1124no—
389C2×D4—1112no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—1124no—
393C22×C4—1112no—
394C22×C4—112no—
395C22×C4—113no—
396C22×C4—116no—
397C22×C4—1112no—
398C22×C4—1112no—
399C22×C4—1148no—
400C22×C4—2212no—
401C22×C4—2212no—
402C22×C4—4424no—
403C22×C4C23×D1113yes—
404C22×C4C23×D1112yes—
405C22×C4C23×D1116yes—
406C22×C4C23×D1113yes—
407C22×C4C23×D1111yescharacteristic
408C4⋊C4—1124no—
409C4⋊C4—1112no—
410C4⋊C4—1124no—
411C4⋊C4—1148no—
412C4⋊C4—118no—
413C4⋊C4—1112no—
414C4⋊C4—118no—
415C4⋊C4—1124no—
416C4⋊C4—1124no—
417C4⋊C4—1124no—
418C4⋊C4C23×D11112yes—
419C4⋊C4C23×D11124yes—
420C4⋊C4C23×D11112yes—
421C4⋊C4C23×D11124yes—
422C22⋊C4—1124no—
423C22⋊C4—1124no—
424C22⋊C4—1124no—
425C42—114no—
426C42—1112no—
427C42—1112no—
428C42—1124no—
429C42C23×D11112yes—
430C42C23×D11124yes—
431C11C2×#350311yescharacteristic, complemented, Sylow
432C23—1112no—
433C23—116no—
434C23—226no—
435C23—226no—
436C23C24×D1111yescharacteristic
437Q8—28no—
438Q8—424no—
439Q8—2248no—
440Q8—228no—
441Q8—4424no—
442Q8C2×Q8×D11116yescomplemented
443D4—1148no—
444C2×C4—24no—
445C2×C4—26no—
446C2×C4—212no—
447C2×C4—114no—
448C2×C4—114no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—1148no—
452C2×C4—114no—
453C2×C4—116no—
454C2×C4—1112no—
455C2×C4—2224no—
456C2×C4—226no—
457C2×C4—224no—
458C2×C4—2212no—
459C2×C4—2224no—
460C2×C4—4448no—
461C2×C4C2×Q8×D11112yes—
462C2×C4#6704014yes—
463C2×C4C24×D1116yes—
464C2×C4C24×D1114yes—
465C2×C4C24×D11112yes—
466C2×C4C24×D1116yes—
467C2×C4C24×D1112yes—
468C22—1112no—
469C22—226no—
470C22—226no—
471C22—2224no—
472C22C22×Q8×D1112yes—
473C22C2×#6704012yes—
474C22D11×H(5,𝔽2)12yes—
475C22C25×D1111yescharacteristic
476C4—26no—
477C4—212no—
478C4—24no—
479C4—114no—
480C4—114no—
481C4—2212no—
482C4—226no—
483C4—224no—
484C4C22×Q8×D11112yes—
485C4C2×#6704014yes—
486C2—2212no—
487C2#1308243414yesdirect product factor
488C2C23×Q8×D1111yescharacteristic
489C2C2×D11×H(5,𝔽2)11yescharacteristic
490C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×Q82×C11C2
socleC23×C11C25
prime radicalC22×#4343C22
hypercenterC2×Q82D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. #13082434C2direct (N × H)
2. C2×Q8×Dic22C2semidirect
3. C2×#10623100C2semidirect
4. C2×#10623261C2semidirect
5. C2×#10623110C2semidirect
6. C2×#10623258C2semidirect
7. C2×#10623260C2semidirect
8. C2×#10623109C2semidirect
9. C2×D11×C4⋊Q8C2semidirect
12. C2×Q82×C11C2semidirect
15. Q82×C11C22semidirect
27. #10623261C22semidirect
28. #10623260C22semidirect
29. #10623258C22semidirect
30. D11×C4⋊Q8C22semidirect
31. #10623110C22semidirect
32. #10623109C22semidirect
35. #10623100C22semidirect
36. Q8×Dic22C22semidirect
61. C2×#4343Q8semidirect
132. C2×Q8×C11C2×Q8semidirect
146. #4343C2×Q8semidirect
148. C2×D44C2×Q8semidirect
153. C2×C4×D11C2×Q8semidirect
189. C2×Q82D11semidirect
206. Q8×C11C22×Q8semidirect
227. D44C22×Q8semidirect
231. C4×D11C22×Q8semidirect
238. Q82C2×D11semidirect
368. C2×C11#3503semidirect
384. C2×Q8Q8×D11semidirect
431. C11C2×#3503semidirect
442. Q8C2×Q8×D11semidirect
487. C2#13082434direct (N × H)

Maximal subgroups

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

subgroupindex
#130824342
C2×Q8×Dic222
C2×#106231002
C2×#106232612
C2×#106231102
C2×#106232582
C2×#106232602
C2×#106231092
C2×D11×C4⋊Q82
C2×#106231052
C2×C4×#43432
C2×Q82×C112
C2×#350311