Finite Group Databasebeta

← C2×#13082397 #15662186

Subgroups — C2×#13082397 #15662186

Order 2816.

11126 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C211yesmaximal, characteristic, complemented
2#13082397C2132yesmaximal, direct product factor
3C2×Q8×C22⋊D11C214yesmaximal, complemented
4C2×#10623355C2112yesmaximal, complemented
5C2×#10623347C213yesmaximal, complemented
6C2×#10623356C213yesmaximal, complemented
7C2×#10623363C213yesmaximal, complemented
8C22×#66997C213yesmaximal, complemented
9C2×#41×Dic11C211yesmaximal, characteristic, complemented
10C22×C11×2−1+4C211yesmaximal, characteristic, complemented
11C2×C11×2−1+4—216no—
12C2×C11×2−1+4C22116yescomplemented
13C22×C11×#41C2213yes—
14C22×C11×#41C2216yes—
15C22×C11×#41C2211yescharacteristic
16C23×Q8×C11C2213yes—
17C23×Q8×C11C2212yes—
18C2×#67043—216no—
19C2×#67043C22116yescomplemented
20C22×Q8×D11C2212yes—
21C22×#4341C2216yes—
22C22×#4339C2213yes—
23C23×Dic22C2213yes—
24#10623363C22148yescomplemented
25#41×Dic11C22116yescomplemented
26#10623356C22148yescomplemented
27#10623355C221192yescomplemented
28#10623347C22148yescomplemented
29Q8×C22⋊D11C22164yescomplemented
30C2×#67000C2213yes—
31C2×#66999C22112yes—
32C2×Q8×Dic11C2212yes—
33C2×#66997C2213yes—
34C2×#66997C2216yes—
35C2×#66997C22112yes—
36C2×#66997C22148yescomplemented
37C2×#66993C2211yescharacteristic
38C2×#66992C22112yes—
39C2×#66989C2213yes—
40C2×#66988C22112yes—
41C2×D4×Dic11C2216yes—
42C2×#66982C22112yes—
43C2×C4×C22⋊D11C22112yes—
44C2×#66979C2213yes—
45C2×#66977C22112yes—
46C22×Dic11⋊C4C22112yes—
47C22×C4×Dic11C2213yes—
48C11×2−1+4—2128no—
49C2×C11×#41—248no—
50C2×C11×#41—224no—
51C2×C11×#41D4116yescomplemented
52C2×C11×#41C23148yes—
53C2×C11×#41C23124yes—
54C2×C11×#41C2318yes—
55C22×Q8×C11—216no—
56C22×Q8×C11—224no—
57C22×Q8×C11C2313yes—
58C22×Q8×C11C2316yes—
59C22×Q8×C11C23124yes—
60C22×Q8×C11C23116yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2316yes—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2313yes—
65C23×C4×C11C2316yes—
66C23×C4×C11C2316yes—
67C23×C4×C11C2313yes—
68C22×C22⋊D11C2314yes—
69C22×C22⋊D11C2316yes—
70C23×Dic11C2316yes—
71C23×Dic11C2316yes—
72#67043—2128no—
73C2×Q8×D11—216no—
74C2×Q8×D11C23116yes—
75C2×#4341—248no—
76C2×#4341C23148yes—
77C2×#4339—224no—
78C2×#4339C23124yes—
79C22×D44C2311yescharacteristic
80C22×C4×D11C2316yes—
81C22×Dic22—224no—
82C22×Dic22C2316yes—
83C22×Dic22C2313yes—
84C22×Dic22C23124yes—
85C2×C22⋊Dic11C23112yes—
86C2×C22⋊Dic11C2316yes—
87#67000C23124yes—
88#66999C23196yes—
89Q8×Dic11C23116yes—
90#66997C23124yes—
91#66997C23196yes—
92#66997C23148yes—
93#66993C2318yes—
94#66992C23196yes—
95#66989C23124yes—
96#66988C23196yes—
97D4×Dic11C23148yes—
98#66982C23196yes—
99C4×C22⋊D11C23196yes—
100C2×(C2×D11)⋊C4C23112yes—
101#66979C23124yes—
102C2×C4⋊Dic11C2316yes—
103#66977C23196yes—
104C2×Dic11⋊C4C23112yes—
105C2×Dic11⋊C4C23124yes—
106C2×Dic11⋊C4C23196yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2313yes—
109C2×C4×Dic11C2316yes—
110C2×C4×Dic11C23124yes—
111C2×#3499—111nomaximal, Sylow
112C24×C11C2412yes—
113C24×C11C2413yes—
114C23×D11C2412yes—
115C11×#41—2192no—
116C11×#41—296no—
117C11×#41C2×D4164yescomplemented
118C2×Q8×C11—264no—
119C2×Q8×C11—212no—
120C2×Q8×C11—224no—
121C2×Q8×C11—296no—
122C2×Q8×C11C2×D418yes—
123C2×Q8×C11C24112yes—
124C2×Q8×C11C24124yes—
125C2×Q8×C11C2414yes—
126C2×D4×C11—224no—
127C2×D4×C11—24no—
128C2×D4×C11C2×D4124yes—
129C2×D4×C11C24124yes—
130C2×D4×C11C2414yes—
131C2×D4×C11C24112yes—
132C22×C4×C11—224no—
133C22×C4×C11—224no—
134C22×C4×C11C2×D4124yes—
135C22×C4×C11C2416yes—
136C22×C4×C11C24124yes—
137C22×C4×C11C24124yes—
138C22×C4×C11C2411yescharacteristic
139C22×C4×C11C2413yes—
140C22×C4×C11C24112yes—
141C2×C22⋊D11—216no—
142C2×C22⋊D11—224no—
143C2×C22⋊D11C24116yes—
144C2×C22⋊D11C24124yes—
145C22×Dic11—224no—
146C22×Dic11—224no—
147C22×Dic11C2416yes—
148C22×Dic11C24124yes—
149C22×Dic11C2416yes—
150C22×Dic11C24124yes—
151C22×Dic11C2412yes—
152Q8×D11—264no—
153#4341—2192no—
154#4339—296no—
155C2×D44—24no—
156C2×D44C2414yes—
157C2×C4×D11—224no—
158C2×C4×D11C24124yes—
159C2×Dic22—212no—
160C2×Dic22—224no—
161C2×Dic22—296no—
162C2×Dic22C24124yes—
163C2×Dic22C24112yes—
164C22⋊Dic11C24148yes—
165C22⋊Dic11C24124yes—
166(C2×D11)⋊C4C24148yes—
167C4⋊Dic11C24124yes—
168Dic11⋊C4C24148yes—
169Dic11⋊C4C24196yes—
170C4×Dic11C2414yes—
171C4×Dic11C24112yes—
172C4×Dic11C24124yes—
173C22×2−1+4—111no—
174C22×2−1+4D1111yescharacteristic, complemented
175#3499—1132no—
176C2×D4×Q8—114no—
177C2×#547—1112no—
178C2×#536—113no—
179C2×#536—113no—
180C2×#532—113no—
181C22×C4⋊Q8—113no—
182C2×C4×#41—111no—
183C23×C11—212no—
184C23×C11—24no—
185C23×C11—28no—
186C23×C11C22×D4112yes—
187C23×C11C2514yes—
188C23×C11C2516yes—
189C23×C11C2511yescharacteristic
190C22×D11—24no—
191C22×D11—28no—
192C22×D11C2514yes—
193Q8×C11—248no—
194Q8×C11—224no—
195Q8×C11C22×D4116yes—
196D4×C11—248no—
197D4×C11—28no—
198D4×C11C22×D4148yes—
199C2×C4×C11—212no—
200C2×C4×C11—248no—
201C2×C4×C11—248no—
202C2×C4×C11C22×D414yes—
203C2×C4×C11C22×D4112yes—
204C2×C4×C11C22×D4148yes—
205C2×C4×C11C25112yes—
206C2×C4×C11C2512yes—
207C2×C4×C11C2516yes—
208C22⋊D11—248no—
209C22⋊D11—232no—
210C2×Dic11—212no—
211C2×Dic11—248no—
212C2×Dic11—212no—
213C2×Dic11—248no—
214C2×Dic112−1+418yescomplemented
215C2×Dic11C25112yes—
216C2×Dic11C25112yes—
217C2×Dic11C2514yes—
218D44—28no—
219C4×D11—248no—
220Dic22—224no—
221Dic22—248no—
222C2×2−1+4—216no—
223C2×2−1+4—1116no—
224C2×2−1+4—2216no—
225C2×2−1+4C2×D11116yescomplemented
226C22×#41—116no—
227C22×#41—113no—
228C22×#41C2×D1113yes—
229C22×#41C2×D1116yes—
230C22×#41C2×D1111yescharacteristic
231C23×Q8—112no—
232C23×Q8—113no—
233C23×Q8C2×D1113yes—
234C23×Q8C2×D1112yes—
235D4×Q8—1164no—
236#547—11192no—
237#536—1148no—
238#536—1148no—
239#532—1148no—
240C2×C4⋊Q8—113no—
241C2×C4⋊Q8—116no—
242C2×C4⋊Q8—1112no—
243C2×C4⋊Q8—1148no—
244C2×#127—111no—
245C2×#124—113no—
246C2×#124—113no—
247C2×#123—1112no—
248C2×#123—1112no—
249C2×C22⋊Q8—1112no—
250C2×C22⋊Q8—1112no—
251C2×#121—1112no—
252C4×#41—1116no—
253C2×C4×Q8—112no—
254C2×C4×D4—116no—
255C2×C4×D4—1112no—
256C2×#117—113no—
257C22×C4⋊C4—1112no—
258C22×C42—113no—
259C22×C11—212no—
260C22×C11—224no—
261C22×C11—24no—
262C22×C11—28no—
263C22×C11—48no—
264C22×C11C23×D4112yes—
265C22×C11C23×D412yes—
266C22×C11C2×2−1+414yes—
267C22×C11C2611yescharacteristic
268C2×D11—24no—
269C2×D11—28no—
270C2×D11—48no—
271C4×C11—212no—
272C4×C11C23×D4112yes—
273C4×C11C23×D414yes—
274Dic11—212no—
275Dic11—212no—
276Dic11C2×2−1+418yescomplemented
2772−1+4—2128no—
2782−1+4—22128no—
279C2×#41—248no—
280C2×#41—224no—
281C2×#41—1148no—
282C2×#41—1124no—
283C2×#41—2248no—
284C2×#41—2224no—
285C2×#41C22⋊D11116yescomplemented
286C2×#41C22×D11124yes—
287C2×#41C22×D11148yes—
288C2×#41C22×D1118yes—
289C22×Q8—216no—
290C22×Q8—224no—
291C22×Q8—1116no—
292C22×Q8—116no—
293C22×Q8—113no—
294C22×Q8—1124no—
295C22×Q8—2216no—
296C22×Q8—2224no—
297C22×Q8C22×D1116yes—
298C22×Q8C22×D1113yes—
299C22×Q8C22×D11124yes—
300C22×Q8C22×D11116yes—
301C22×Q8C22×D1111yescharacteristic
302C22×D4—114no—
303C22×D4—116no—
304C22×D4—111no—
305C22×D4C22×D1116yes—
306C22×D4C22×D1111yescharacteristic
307C22×D4C22×D1113yes—
308C23×C4—116no—
309C23×C4—116no—
310C23×C4—116no—
311C23×C4C22×D1116yes—
312C23×C4C22×D1116yes—
313C23×C4C22×D1113yes—
314C4⋊Q8—1124no—
315C4⋊Q8—1148no—
316C4⋊Q8—1196no—
317#127—118no—
318#124—1124no—
319#124—1124no—
320#123—1196no—
321#123—1196no—
322C22⋊Q8—1196no—
323C22⋊Q8—1196no—
324#121—1196no—
325C4×Q8—1116no—
326C4×D4—1148no—
327C4×D4—1196no—
328#117—1124no—
329C2×C4⋊C4—1112no—
330C2×C4⋊C4—1124no—
331C2×C4⋊C4—1196no—
332C2×C4⋊C4—116no—
333C2×C22⋊C4—116no—
334C2×C22⋊C4—1112no—
335C2×C22⋊C4—1112no—
336C2×C42—113no—
337C2×C42—116no—
338C2×C42—1124no—
339C2×C42—111no—
340C2×C11—212no—
341C2×C11—44no—
342C2×C11#349914yescomplemented
343C2×C11C24×D411yescharacteristic
344C2×C11C22×2−1+412yes—
345D11—44no—
346C24—112no—
347C24C23×D1112yes—
348C24C23×D1113yes—
349#41—2192no—
350#41—296no—
351#41—22192no—
352#41—2296no—
353#41C2×C22⋊D11164yescomplemented
354C2×Q8—264no—
355C2×Q8—224no—
356C2×Q8—212no—
357C2×Q8—296no—
358C2×Q8—1124no—
359C2×Q8—1112no—
360C2×Q8—2264no—
361C2×Q8—2224no—
362C2×Q8—2212no—
363C2×Q8—2296no—
364C2×Q8C2×C22⋊D1118yes—
365C2×Q8C23×D11124yes—
366C2×Q8C23×D11112yes—
367C2×Q8C23×D1114yes—
368C2×D4—224no—
369C2×D4—24no—
370C2×D4—1116no—
371C2×D4—1124no—
372C2×D4—114no—
373C2×D4—2216no—
374C2×D4—2224no—
375C2×D4—224no—
376C2×D4C2×C22⋊D11124yes—
377C2×D4C23×D11124yes—
378C2×D4C23×D1114yes—
379C2×D4C23×D11112yes—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—112no—
383C22×C4—1124no—
384C22×C4—1124no—
385C22×C4—116no—
386C22×C4—116no—
387C22×C4—1124no—
388C22×C4—2224no—
389C22×C4—2224no—
390C22×C4—2224no—
391C22×C4C2×C22⋊D11124yes—
392C22×C4C23×D11124yes—
393C22×C4C23×D11124yes—
394C22×C4C23×D1116yes—
395C22×C4C23×D11112yes—
396C22×C4C23×D1111yescharacteristic
397C22×C4C23×D1113yes—
398C4⋊C4—1148no—
399C4⋊C4—1196no—
400C4⋊C4—1124no—
401C22⋊C4—1124no—
402C22⋊C4—1148no—
403C22⋊C4—1148no—
404C42—114no—
405C42—1112no—
406C42—1124no—
407C11C2×#349911yescharacteristic, complemented, Sylow
408C23—212no—
409C23—28no—
410C23—24no—
411C23—114no—
412C23—228no—
413C23—224no—
414C23C22×C22⋊D11112yes—
415C23C24×D1114yes—
416C23C24×D1116yes—
417C23C24×D1111yescharacteristic
418Q8—248no—
419Q8—224no—
420Q8—2248no—
421Q8—2224no—
422Q8C22×C22⋊D11116yes—
423D4—248no—
424D4—28no—
425D4—2232no—
426D4—2248no—
427D4—228no—
428D4C22×C22⋊D11148yes—
429C2×C4—212no—
430C2×C4—248no—
431C2×C4—248no—
432C2×C4—118no—
433C2×C4—114no—
434C2×C4—1112no—
435C2×C4—1112no—
436C2×C4—2248no—
437C2×C4—2212no—
438C2×C4—2212no—
439C2×C4—2248no—
440C2×C4—2248no—
441C2×C4C22×C22⋊D11112yes—
442C2×C4C22×C22⋊D1114yes—
443C2×C4C22×C22⋊D11148yes—
444C2×C4C24×D11112yes—
445C2×C4C24×D1112yes—
446C2×C4C24×D1116yes—
447C22—212no—
448C22—224no—
449C22—24no—
450C22—28no—
451C22—48no—
452C22—224no—
453C22—228no—
454C22—448no—
455C22D11×2−1+414yes—
456C22C23×C22⋊D11112yes—
457C22C23×C22⋊D1112yes—
458C22C25×D1111yescharacteristic
459C4—212no—
460C4—118no—
461C4—2212no—
462C4—2212no—
463C4C23×C22⋊D11112yes—
464C4C23×C22⋊D1114yes—
465C2—212no—
466C2—44no—
467C2—444no—
468C2#1308239714yesdirect product factor
469C2C24×C22⋊D1111yescharacteristic
470C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×2−1+4C2
socleC23×C11C25
hypercenterC22×2−1+4D11
hypocenterC11C2×#3499
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×2−1+4

Complements

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

NH ≅ G/Ntype
1. C22×#67043C2semidirect
2. #13082397C2direct (N × H)
3. C2×Q8×C22⋊D11C2semidirect
4. C2×#10623355C2semidirect
5. C2×#10623347C2semidirect
6. C2×#10623356C2semidirect
7. C2×#10623363C2semidirect
8. C22×#66997C2semidirect
9. C2×#41×Dic11C2semidirect
10. C22×C11×2−1+4C2semidirect
12. C2×C11×2−1+4C22semidirect
19. C2×#67043C22semidirect
24. #10623363C22semidirect
25. #41×Dic11C22semidirect
26. #10623356C22semidirect
27. #10623355C22semidirect
28. #10623347C22semidirect
29. Q8×C22⋊D11C22semidirect
36. C2×#66997C22semidirect
51. C2×C11×#41D4semidirect
117. C11×#41C2×D4semidirect
174. C22×2−1+4D11semidirect
214. C2×Dic112−1+4semidirect
225. C2×2−1+4C2×D11semidirect
276. Dic11C2×2−1+4semidirect
285. C2×#41C22⋊D11semidirect
342. C2×C11#3499semidirect
353. #41C2×C22⋊D11semidirect
407. C11C2×#3499semidirect
468. C2#13082397direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670432
#130823972
C2×Q8×C22⋊D112
C2×#106233552
C2×#106233472
C2×#106233562
C2×#106233632
C22×#669972
C2×#41×Dic112
C22×C11×2−1+42
C2×#349911