Finite Group Databasebeta

← C2×#13067890 #14729586

Subgroups — C2×#13067890 #14729586

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic
2C2×#10622707C211yesmaximal, characteristic
3C2×#10622703C211yesmaximal, characteristic
4#13067890C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic
6C2×#10622094C211yesmaximal, characteristic
7C2×#10622094C211yesmaximal, characteristic
8C2×C11×#498C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×Q8×Dic11—21no—
12C2×#66997—21no—
13C22×#4326—21no—
14#10623252—22no—
15#10623252—22no—
16#10623252—22no—
17#10623252C2214yes—
18C2×#66943—21no—
19C2×#66942—22no—
20C2×#66940—21no—
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#498—22no—
24C11×#498C2214yes—
25C2×C11×#106—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899—21no—
28#10622707—22no—
29#10622707C2214yes—
30#10622703—22no—
31#10622703C2214yes—
32C2×#66874—21no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622185C2214yes—
37#10622094C2214yes—
38#10622094C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Dic22D411yescharacteristic
42C22×Dic22D411yescharacteristic
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8D412yes—
50C11×C4⋊Q8C2312yes—
51C11×C4⋊Q8C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11C2311yescharacteristic
57Q8×Dic11—24no—
58Q8×Dic11—24no—
59#66997—24no—
60#66997—24no—
61C2×#4326—24no—
62C2×#4326—44no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D411yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75#66943—24no—
76#66943—24no—
77#66942—28no—
78#66942—28no—
79#66940—24no—
80#66940—24no—
81C4×Dic22—21no—
82C4×Dic22—21no—
83C4×Dic22—21no—
84C4×Dic22—21no—
85C4×Dic22D412yes—
86C4×Dic22D412yes—
87C4×Dic22C2312yes—
88C4×Dic22C2312yes—
89C11×#106—28no—
90C4×C8×C11—21no—
91C4×C8×C11C2312yes—
92#66899—24no—
93#66874—24no—
94#66872—24no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1653—111nomaximal, Sylow
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—41no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C22×C4×C11—22no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22SD1614yes—
123C2×Dic22C2×D412yes—
124C2×Dic22C2×D412yes—
125C2×C8×C11—24no—
126C2×C8×C11—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4C2×D414yes—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2411yescharacteristic
139#4326—48no—
140C4⋊Dic11—28no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11C2×D412yes—
144C4⋊Dic11C2×D412yes—
145Dic11⋊C4—28no—
146Dic11⋊C4—28no—
147Dic11⋊C4—22no—
148Dic11⋊C4—22no—
149Dic11⋊C4—22no—
150Dic11⋊C4—22no—
151C4×Dic11—28no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—42no—
159C2×C11⋊C8—42no—
160C2×#557—111no—
161C2×#498D1111yescharacteristic
162C2×#475—111no—
163C2×#462—111no—
164#1653—118no—
165C2×#332—111no—
166C2×Q8⋊C8—111no—
167C2×Q8⋊C8—111no—
168C23×C11#12011yescharacteristic
169Q8×C11—42no—
170Q8×C11—42no—
171Q8×C11—44no—
172Q8×C11—42no—
173Q8×C11—42no—
174Q8×C11—82no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—44no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11C2×SD1612yes—
184C2×C4×C11#13512yes—
185C2×C4×C11#13712yes—
186C2×C4×C11#13712yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—24no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198Dic22—22no—
199Dic22—24no—
200Dic22—22no—
201Dic22—22no—
202Dic22—42no—
203Dic22C2×SD1614yes—
204C8×C11—24no—
205C11⋊C8—42no—
206C11⋊C8—42no—
207C22×Q16—221no—
208#557—114no—
209#557—222no—
210#557—222no—
211#557—222no—
212C2×C4⋊Q8—221no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#125—221no—
216C2×#125—222no—
217C2×C4×Q8—111no—
218C2×C4×Q8—111no—
219C2×C4×Q8—221no—
220C2×C4×Q8—221no—
221#498—22no—
222#498C2×D1114yes—
223#475—114no—
224#475—222no—
225#462—114no—
226#462—222no—
227C2×#106—22no—
228C2×#106—221no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8—111no—
231C2×#103—221no—
232C2×#103—221no—
233C2×C4×C8C2×D1111yescharacteristic
234#332—114no—
235Q8⋊C8—114no—
236Q8⋊C8—114no—
237C22×C11#44812yes—
238C22×C11#45212yes—
239C22×C11#45612yes—
240C22×C11C2×#12011yescharacteristic
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—44no—
244C4×C11—82no—
245C4×C11#44812yes—
246C4×C11#45212yes—
247C4×C11C22×SD1611yescharacteristic
248C4×C11C2×#13511yescharacteristic
249C4×C11C2×#13711yescharacteristic
250C4×C11C2×#13711yescharacteristic
251Dic11—24no—
252Dic11—42no—
253Dic11—42no—
254Dic11—42no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—111no—
258C22×Q8—111no—
259C2×Q16—224no—
260C2×Q16—444no—
261C22×C8—21no—
262C22×C8—221no—
263C22×C8—221no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—224no—
270C4⋊Q8—224no—
271C4⋊Q8C22⋊D1112yes—
272C4⋊Q8C22×D1112yes—
273C4⋊Q8C22×D1112yes—
274#125—224no—
275#125—228no—
276#125—224no—
277#125—228no—
278C4×Q8—112no—
279C4×Q8—112no—
280C4×Q8—112no—
281C4×Q8—112no—
282C4×Q8—224no—
283C4×Q8—224no—
284C4×Q8—224no—
285C4×Q8—224no—
286C4×Q8—221no—
287C4×Q8—221no—
288C4×Q8—221no—
289C4×Q8—221no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4C22⋊D1112yes—
301C2×C42—222no—
302C2×C42—221no—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305#106—28no—
306#106—224no—
307C4⋊C8—112no—
308C4⋊C8—112no—
309C4⋊C8—221no—
310C4⋊C8—221no—
311#103—224no—
312#103—224no—
313C4×C8—21no—
314C4×C8C22×D1112yes—
315C2×C11#165314yescomplemented
316C2×C11C2×#44811yescharacteristic
317C2×C11C2×#45211yescharacteristic
318C2×C11C2×#45611yescharacteristic
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—41no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8—114no—
328C2×Q8—112no—
329C2×Q8—112no—
330C2×Q8—222no—
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—222no—
334C2×Q8—222no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4D4×D1111yescharacteristic
342C22×C4D4×D1111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344Q16—448no—
345C2×C8—24no—
346C2×C8—22no—
347C2×C8—222no—
348C2×C8—222no—
349C2×C8—442no—
350C2×C8—442no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—112no—
359C4⋊C4—112no—
360C4⋊C4—228no—
361C4⋊C4—228no—
362C4⋊C4—228no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4C2×C22⋊D1114yes—
370C42—228no—
371C42—222no—
372C42—222no—
373C42—222no—
374C42—222no—
375C42D4×D1111yescharacteristic
376C42D4×D1111yescharacteristic
377C42C2×C22⋊D1111yescharacteristic
378C42C23×D1111yescharacteristic
379C11C2×#165311yescharacteristic, complemented, Sylow
380C23#6699011yescharacteristic
381Q8—42no—
382Q8—42no—
383Q8—44no—
384Q8—42no—
385Q8—42no—
386Q8—82no—
387Q8—114no—
388Q8—222no—
389Q8—224no—
390Q8—222no—
391Q8—222no—
392Q8—442no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—82no—
398C2×C4—224no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4SD16×D1112yes—
407C2×C4#6696812yes—
408C2×C4#6696812yes—
409C2×C4#6696912yes—
410C2×C4#6699011yescharacteristic
411C2×C4#6699011yescharacteristic
412C2×C4#6699011yescharacteristic
413C2×C4C2×D4×D1111yescharacteristic
414C2×C4C2×D4×D1111yescharacteristic
415C2×C4C22×C22⋊D1111yescharacteristic
416C8—24no—
417C8—442no—
418C8—442no—
419C22#1062270812yes—
420C22#1062278312yes—
421C22#1062278612yes—
422C22C2×#6699011yescharacteristic
423C4—21no—
424C4—21no—
425C4—44no—
426C4—82no—
427C4—224no—
428C4—442no—
429C4—442no—
430C4—442no—
431C4#1062278312yes—
432C4#1062278612yes—
433C4C2×SD16×D1111yescharacteristic
434C4C2×#6696811yescharacteristic
435C4C2×#6696811yescharacteristic
436C4C2×#6696911yescharacteristic
437C2#1306789014yesdirect product factor
438C2C2×#1062278311yescharacteristic
439C2C2×#1062278611yescharacteristic
440C2C2×#1062270811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#498C2
socle, prime radicalC23×C11#120
hypercenterC2×#498D11
hypocenterC11C2×#1653
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
4. #13067890C2direct (N × H)
315. C2×C11#1653semidirect
379. C11C2×#1653semidirect
437. C2#13067890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106227072
C2×#106227032
#130678902
C2×#106221852
C2×#106220942
C2×C11×#4982
C2×#165311