Finite Group Databasebeta

← C2×#13067575 #14725857

Subgroups — C2×#13067575 #14725857

Order 2816.

1308 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1308 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic
2C2×#10622352C212yesmaximal, complemented
3C2×#10622560C211yesmaximal, characteristic
4#13067575C218yesmaximal, direct product factor
5C2×#10622105C212yesmaximal, complemented
6C2×C11×#323C211yesmaximal, characteristic
7C23×Dic22C2211yescharacteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11—21no—
10C22×C22⋊Dic11—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13C22×Dic44—22no—
14#10623014—22no—
15#10623014—24no—
16#10623014C2214yes—
17C2×#66931—22no—
18C2×#66931—22no—
19C2×C11×C22⋊C8C2212yes—
20C2×C11⋊#95—21no—
21C2×C11⋊#95C2211yescharacteristic
22C2×#66880—22no—
23#10622560—22no—
24#10622560C2214yes—
25#10622352—24no—
26#10622352C2218yescomplemented
27C11×#323C2214yes—
28#10622105C2218yescomplemented
29C25×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11—21no—
34C23×Dic11—21no—
35C23×Dic11—21no—
36C22×Dic22—22no—
37C22×Dic22—21no—
38C22×Dic22—22no—
39C22×Dic22—21no—
40C22×Dic22—44no—
41C22×Dic22D412yes—
42C22×Dic22C2312yes—
43C22×C8×C11—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4D412yes—
47C2×C11×C22⋊C4C2312yes—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11—24no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—44no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D412yes—
56#66977—24no—
57#66977—22no—
58#66977—22no—
59#66977—24no—
60#66977D414yes—
61#66977C2314yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic44—28no—
65C2×Dic44—48no—
66#66931—28no—
67#66931—28no—
68#66931—28no—
69#66931—28no—
70C11×C22⋊C8—22no—
71C11×C22⋊C8C2314yes—
72C11⋊#95—21no—
73C11⋊#95—24no—
74C11⋊#95C2312yes—
75#66880—28no—
76C2×#1602—111nomaximal, Sylow
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—22no—
80C24×C11—42no—
81C24×C11—42no—
82C24×C11Q1614yescomplemented
83C24×C11C2×D411yescharacteristic
84C24×C11C2×D412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—42no—
107C22×Dic11—82no—
108C22×Dic11—82no—
109C2×Dic22—28no—
110C2×Dic22—24no—
111C2×Dic22—22no—
112C2×Dic22—24no—
113C2×Dic22—44no—
114C2×Dic22—44no—
115C2×Dic22—44no—
116C2×Dic22—48no—
117C2×Dic22—44no—
118C2×Dic22—42no—
119C2×Dic22—82no—
120C2×Dic22C2×D414yes—
121C2×C8×C11—24no—
122C2×C8×C11—44no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C22⋊Dic11—28no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C22⋊Dic11—48no—
129C4⋊Dic11—24no—
130C4⋊Dic11—22no—
131C4⋊Dic11C2×D414yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—24no—
134Dic11⋊C4—24no—
135Dic44—416no—
136C2×#543—111no—
137C2×#451—112no—
138C2×#393—111no—
139#1602—118no—
140C2×#328—112no—
141C2×#323D1111yescharacteristic
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—42no—
149C23×C11—48no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—84no—
154C23×C11—81no—
155C23×C11—81no—
156C23×C11#12011yescharacteristic
157C23×C11#12011yescharacteristic
158C23×C11C2×Q1612yes—
159C23×C11C2×Q1614yescomplemented
160C23×C11#13712yes—
161C23×C11C22×D411yescharacteristic
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—81no—
170C2×C4×C11#12012yes—
171C2×C4×C11C22×D412yes—
172C2×Dic11—24no—
173C2×Dic11—24no—
174C2×Dic11—24no—
175C2×Dic11—42no—
176C2×Dic11—44no—
177C2×Dic11—42no—
178C2×Dic11—44no—
179C2×Dic11—44no—
180C2×Dic11—44no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—84no—
185C2×Dic11—84no—
186C2×Dic11—84no—
187Dic22—28no—
188Dic22—48no—
189Dic22—44no—
190Dic22—44no—
191Dic22—82no—
192Dic22—84no—
193C8×C11—44no—
194C23×Q8—111no—
195C22×Q16—222no—
196#543—114no—
197#543—224no—
198#543—222no—
199C2×C22⋊Q8—112no—
200C2×C22⋊Q8—222no—
201C2×C22⋊Q8—222no—
202C2×C22⋊Q8—221no—
203C22×C22⋊C4—221no—
204C22×C22⋊C4—221no—
205C22×C22⋊C4C2×D1111yescharacteristic
206#451—118no—
207#451—224no—
208C2×#103—222no—
209C2×C22⋊C8C2×D1112yes—
210#393—114no—
211#393—222no—
212C2×#95—111no—
213C2×#95—221no—
214#328—118no—
215#323C2×D1114yes—
216C22×C11—24no—
217C22×C11—24no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—24no—
223C22×C11—44no—
224C22×C11—48no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—82no—
228C22×C11—84no—
229C22×C11#45112yes—
230C22×C11#45112yes—
231C22×C11#45512yes—
232C22×C11B(4,𝔽2)12yes—
233C22×C11C2×#12011yescharacteristic
234C22×C11C22×Q1611yescharacteristic
235C22×C11C2×#13711yescharacteristic
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—42no—
239Dic11—44no—
240Dic11—44no—
241Dic11—44no—
242Dic11—82no—
243C25D4411yescharacteristic
244C22×Q8—112no—
245C22×Q8—112no—
246C22×Q8—221no—
247C22×Q8—221no—
248C22×Q8—222no—
249C22×Q8—222no—
250C22×Q8—444no—
251C23×C4—221no—
252C23×C4—221no—
253C23×C4—221no—
254C23×C4—221no—
255C23×C4D4411yescharacteristic
256C23×C4C22×D1111yescharacteristic
257C2×Q16—228no—
258C2×Q16—448no—
259C22×C8—22no—
260C22⋊Q8—114no—
261C22⋊Q8—114no—
262C22⋊Q8—228no—
263C22⋊Q8—228no—
264C22⋊Q8—228no—
265C22⋊Q8—228no—
266C22⋊Q8—224no—
267C22⋊Q8—222no—
268C22⋊Q8—224no—
269C22⋊Q8—222no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—224no—
278C2×C22⋊C4—222no—
279C2×C22⋊C4—224no—
280C2×C22⋊C4—224no—
281C2×C22⋊C4—444no—
282C2×C22⋊C4D4412yes—
283C2×C22⋊C4C22×D1112yes—
284#103—228no—
285C22⋊C8—22no—
286C22⋊C8C22×D1114yes—
287#95—112no—
288#95—221no—
289#95—224no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—22no—
293C2×C11—44no—
294C2×C11#160214yescomplemented
295C2×C11C2×#45111yescharacteristic
296C2×C11C2×#45511yescharacteristic
297C2×C11C2×B(4,𝔽2)11yescharacteristic
298C24—21no—
299C24—21no—
300C24—22no—
301C24—42no—
302C24—42no—
303C24Dic4414yescomplemented
304C24C2×D4411yescharacteristic
305C24C2×D4412yes—
306C2×Q8—114no—
307C2×Q8—224no—
308C2×Q8—228no—
309C2×Q8—222no—
310C2×Q8—224no—
311C2×Q8—444no—
312C2×Q8—444no—
313C2×Q8—444no—
314C2×Q8—444no—
315C2×Q8—448no—
316C2×Q8—442no—
317C2×Q8—882no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—224no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—222no—
329C22×C4—442no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4—442no—
333C22×C4—442no—
334C22×C4—442no—
335C22×C4—882no—
336C22×C4—882no—
337C22×C4C2×D4412yes—
338C22×C4C2×D4411yescharacteristic
339C22×C4D4×D1112yes—
340C22×C4D4×D1112yes—
341C22×C4C23×D1111yescharacteristic
342Q16—4416no—
343C2×C8—24no—
344C2×C8—44no—
345C4⋊C4—114no—
346C4⋊C4—228no—
347C4⋊C4—224no—
348C4⋊C4—222no—
349C4⋊C4—224no—
350C4⋊C4—224no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—228no—
354C22⋊C4—224no—
355C22⋊C4—224no—
356C22⋊C4—448no—
357C11C2×#160211yescharacteristic, complemented, Sylow
358C23—22no—
359C23—22no—
360C23—22no—
361C23—24no—
362C23—22no—
363C23—24no—
364C23—42no—
365C23—48no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—84no—
370C23—81no—
371C23—81no—
372C23#6693511yescharacteristic
373C23#6693511yescharacteristic
374C23C2×Dic4412yes—
375C23C2×Dic4414yescomplemented
376C23#6696212yes—
377C23C22×D4411yescharacteristic
378Q8—228no—
379Q8—444no—
380Q8—444no—
381Q8—448no—
382Q8—882no—
383Q8—884no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—224no—
393C2×C4—224no—
394C2×C4—224no—
395C2×C4—442no—
396C2×C4—444no—
397C2×C4—442no—
398C2×C4—444no—
399C2×C4—444no—
400C2×C4—444no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—884no—
405C2×C4—884no—
406C2×C4—884no—
407C2×C4#6693512yes—
408C2×C4C2×D4×D1112yes—
409C8—44no—
410C22—24no—
411C22—24no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—24no—
417C22—44no—
418C22—48no—
419C22—42no—
420C22—42no—
421C22—82no—
422C22—84no—
423C22#1062235212yes—
424C22#1062235212yes—
425C22#1062235412yes—
426C22#1062235912yes—
427C22C2×#6693511yescharacteristic
428C22C22×Dic4411yescharacteristic
429C22C2×#6696211yescharacteristic
430C4—22no—
431C4—22no—
432C4—42no—
433C4—444no—
434C4—444no—
435C4—444no—
436C4—882no—
437C2—21no—
438C2—21no—
439C2—22no—
440C2—44no—
441C2#1306757514yesdirect product factor
442C2C2×#1062235211yescharacteristic
443C2C2×#1062235911yescharacteristic
444C2C2×#1062235411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11#120
prime radicalC25×C11D4
hypercenterC2×#323D11
hypocenterC11C2×#1602
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622352C2semidirect
4. #13067575C2direct (N × H)
5. C2×#10622105C2semidirect
26. #10622352C22semidirect
28. #10622105C22semidirect
82. C24×C11Q16semidirect
159. C23×C11C2×Q16semidirect
294. C2×C11#1602semidirect
303. C24Dic44semidirect
357. C11C2×#1602semidirect
375. C23C2×Dic44semidirect
441. C2#13067575direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230142
C2×#106223522
C2×#106225602
#130675752
C2×#106221052
C2×C11×#3232
C2×#160211