Finite Group Databasebeta

← #14812689

Subgroups — #14812689

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078463C212yesmaximal
2#13077213C211yesmaximal, characteristic
3#13070124C212yesmaximal, complemented
4#13069958C212yesmaximal, complemented
5#13069401C211yesmaximal, characteristic, complemented
6#13069365C211yesmaximal, characteristic, complemented
7#13068839C212yesmaximal
8#13068774C211yesmaximal, characteristic, complemented
9#13068681C211yesmaximal, characteristic
10#13068455C211yesmaximal, characteristic
11C11×#3164C211yesmaximal, characteristic, complemented
12C11×#544C2212yes—
13C2×#66954C2211yescharacteristic
14#10623054C2212yes—
15C11×#501—22no—
16C11×#500—21no—
17C11×#499—21no—
18C11×#428C2212yes—
19C11×#427C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C11×#405C2211yescharacteristic
22C2×#66889C2211yescharacteristic
23C2×#66883C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×C8×Dic11C2211yescharacteristic
26#10622704—22no—
27#10622700—22no—
28#10622679—22no—
29#10622676—22no—
30#10622615C2211yescharacteristic
31#10622612C2212yes—
32#10622608C2212yes—
33#10622608C2212yes—
34#10622589C2212yes—
35#10622579C2212yes—
36C2×#66871C2212yes—
37#10622493—21no—
38D11×#107—21no—
39#10622474—22no—
40#10622196C2211yescharacteristic
41#10622192C2212yes—
42#10622170C2212yes—
43#10622170C2211yescharacteristic
44#10622168C2212yes—
45C2×#4339C2311yescharacteristic
46C2×C11×M16C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C11×#125—22no—
51C11×#125—22no—
52C11×C22⋊Q8—42no—
53C11×#117C2312yes—
54C11×#117C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—42no—
58C2×C4×Dic11C2311yescharacteristic
59C2×#4318C2312yes—
60C2×#4318C2311yescharacteristic
61C22×C11⋊C8C2311yescharacteristic
62#66954—22no—
63#66954Q814yescomplemented
64C2×#4313—21no—
65C2×C8×D11—21no—
66#66945—22no—
67C4⋊C4×D11—22no—
68(C22⋊D11)⋊C4—42no—
69C4×D44—22no—
70C4×Dic22—22no—
71C11×#107—21no—
72C11×#107—21no—
73C11×#107—22no—
74C11×#107D411yescharacteristic
75C11×#107D411yescharacteristic
76C11×#106—22no—
77C11×#106D412yes—
78C11×#97—21no—
79C4×C8×C11—21no—
80#66889Q814yescomplemented
81#66883—22no—
82#66882—21no—
83#66882—21no—
84C8×Dic11—22no—
85#66874—22no—
86#66874D411yescharacteristic
87#66874D411yescharacteristic
88#66873—22no—
89#66873D411yescharacteristic
90#66873D411yescharacteristic
91#66872—22no—
92#66872—22no—
93#66871—22no—
94#66871—22no—
95#66871—22no—
96#66871—22no—
97C4⋊(C11⋊C8)—22no—
98C4⋊(C11⋊C8)—22no—
99#26083—111nomaximal, Sylow
100C2×Q8×C11—42no—
101C22×C4×C11—22no—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106#4339—21no—
107#4339—21no—
108#4339C2×Q812yes—
109#4339C2×Q812yes—
110C2×D44C2×D411yescharacteristic
111C2×C4×D11—21no—
112C2×C4×D11—42no—
113C2×Dic22C2×D411yescharacteristic
114C11×M16—21no—
115C11×M16C2×Q812yes—
116C2×C8×C11—21no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×Q812yes—
120C2×C8×C11#4112yes—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C4⋊C4C2×D412yes—
129C11×C4⋊C4C2×D412yes—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—21no—
132C42×C11—22no—
133C42×C11—21no—
134(C2×D11)⋊C4—42no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137Dic11⋊C4—42no—
138Dic11⋊C4—84no—
139C4×Dic11—21no—
140C4×Dic11—42no—
141C4×Dic11C2×Q812yes—
142#4318—21no—
143#4318—22no—
144#4318—22no—
145#4318C2×Q812yes—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C2×D411yescharacteristic
151C2×C11⋊C8C2×D411yescharacteristic
152#4313—24no—
153C8×D11—24no—
154#3164D1111yescharacteristic, complemented
155#3083—112no—
156#2913—111no—
157#2089—112no—
158#2060—112no—
159#1952—111no—
160#1945—111no—
161#1859—112no—
162#1845—111no—
163#1816—111no—
164#1764—111no—
165C23×C11H(5,𝔽2)11yescharacteristic
166C22×D11—21no—
167Q8×C11—162no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—42no—
173C2×C4×C11—82no—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×Q811yescharacteristic
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C112−1+411yescharacteristic
180C22⋊D11—22no—
181C22⋊D11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—21no—
185C2×Dic11—22no—
186C2×Dic11—42no—
187C2×Dic11—82no—
188D44—21no—
189D44C4⋊Q812yes—
190C4×D11—22no—
191C4×D11—22no—
192C4×D11—162no—
193Dic22—21no—
194Dic22C4⋊Q812yes—
195C8×C11—22no—
196C8×C11C22⋊Q812yes—
197C8×C11C22⋊Q812yes—
198C11⋊C8—22no—
199C11⋊C8—21no—
200C11⋊C8—21no—
201C11⋊C8—42no—
202C2×#131—111no—
203#544C2×D1112yes—
204#520—112no—
205#501—22no—
206#500—21no—
207#499—21no—
208#479—222no—
209#478—222no—
210#477—222no—
211#474—222no—
212C2×#108—111no—
213#428—112no—
214#428—112no—
215#428—222no—
216#428C2×D1112yes—
217#427—221no—
218#427C2×D1111yescharacteristic
219C2×#107—111no—
220C2×#107—112no—
221C2×#107—221no—
222C2×#107C2×D1111yescharacteristic
223#424—112no—
224C2×#104—111no—
225#417—112no—
226#416—111no—
227#405C2×D1111yescharacteristic
228C2×C4×C8—111no—
229#384—112no—
230#343—112no—
231#343—112no—
232#341—111no—
233#339—111no—
234#339—112no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11#54411yescharacteristic
238C22×C11D4211yescharacteristic
239C22×C11#55411yescharacteristic
240C2×D11—22no—
241C2×D11—41no—
242C2×D11—41no—
243C4×C11—41no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—41no—
247C4×C11—82no—
248C4×C11C2×C22⋊Q811yescharacteristic
249C4×C11C2×C4⋊Q811yescharacteristic
250C4×C11#54711yescharacteristic
251C4×C11D4×Q811yescharacteristic
252Dic11—24no—
253Dic11—22no—
254Dic11—82no—
255C2×#41—111no—
256#131—114no—
257#131—222no—
258C2×M16—111no—
259C2×M16—112no—
260C2×M16—221no—
261C2×M16C22×D1111yescharacteristic
262C22×C8—111no—
263C22×C8—221no—
264C22×C8C22×D1111yescharacteristic
265C4⋊Q8—22no—
266C4⋊Q8—22no—
267#125—22no—
268#125—22no—
269C22⋊Q8—42no—
270C4×Q8—222no—
271C4×D4—222no—
272C4×D4—442no—
273#117—222no—
274#117C22×D1111yescharacteristic
275#117C22×D1112yes—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—442no—
279C2×C4⋊C4C22×D1112yes—
280C2×C42—111no—
281#108—222no—
282#107—21no—
283#107—21no—
284#107—22no—
285#107—222no—
286#107—222no—
287#107—221no—
288#107—221no—
289#107—222no—
290#107—222no—
291#107C22⋊D1111yescharacteristic
292#107C22⋊D1111yescharacteristic
293#106—22no—
294#106—222no—
295#106—222no—
296#106C22⋊D1112yes—
297C4⋊C8—222no—
298C4⋊C8—222no—
299#104—114no—
300#103—111no—
301#103—111no—
302#103—222no—
303#102—111no—
304#102—111no—
305#102—222no—
306#97—21no—
307C4×C8—21no—
308C4×C8—222no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11#244011yescharacteristic
312C2×C11#329211yescharacteristic
313C2×C11#329311yescharacteristic
314D11—42no—
315#41—112no—
316#41—112no—
317#41—221no—
318#41—221no—
319C2×Q8—42no—
320C2×Q8—111no—
321C2×D4—111no—
322C2×D4—221no—
323C22×C4—22no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—222no—
327C22×C4—442no—
328C22×C4C23×D1111yescharacteristic
329M16—21no—
330M16—112no—
331M16—221no—
332M16—224no—
333M16—222no—
334M16—222no—
335M16Q8×D1112yes—
336C2×C8—21no—
337C2×C8—111no—
338C2×C8—111no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—224no—
343C2×C8—222no—
344C2×C8Q8×D1112yes—
345C2×C8#434312yes—
346C2×C8C2×C22⋊D1111yescharacteristic
347C2×C8C2×C22⋊D1111yescharacteristic
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—442no—
356C4⋊C4—884no—
357C4⋊C4D4×D1111yescharacteristic
358C4⋊C4D4×D1111yescharacteristic
359C4⋊C4C2×C22⋊D1112yes—
360C4⋊C4C2×C22⋊D1112yes—
361C22⋊C4—22no—
362C22⋊C4—21no—
363C22⋊C4—442no—
364C42—22no—
365C42—21no—
366C42—112no—
367C42—221no—
368C42—442no—
369C11#2608311yescharacteristic, complemented, Sylow
370C23—221no—
371C23#6703711yescharacteristic
372Q8—112no—
373Q8—162no—
374Q8—221no—
375D4—112no—
376D4—222no—
377D4—222no—
378D4—221no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—221no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—442no—
392C2×C4—882no—
393C2×C4—1762no—
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4C2×Q8×D1111yescharacteristic
396C2×C4C2×Q8×D1111yescharacteristic
397C2×C4C2×#434311yescharacteristic
398C2×C4#6704011yescharacteristic
399C2×C4C22×C22⋊D1111yescharacteristic
400C8—22no—
401C8—221no—
402C8—221no—
403C8—222no—
404C8—442no—
405C8#6699912yes—
406C8#6699912yes—
407C22—21no—
408C22—21no—
409C22—222no—
410C22—441no—
411C22—441no—
412C22#1062326011yescharacteristic
413C22#1062326111yescharacteristic
414C22D4×C22⋊D1111yescharacteristic
415C4—42no—
416C4—41no—
417C4—42no—
418C4—41no—
419C4—82no—
420C4—224no—
421C4—222no—
422C4—882no—
423C4D11×C4⋊Q811yescharacteristic
424C4#1062325711yescharacteristic
425C4C2×#6699911yescharacteristic
426C4Q8×C22⋊D1111yescharacteristic
427C2—21no—
428C2—21no—
429C2—442no—
430C2#1307231411yescharacteristic
431C2#1308041311yescharacteristic
432C2#1308041811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3164C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#3164D11
hypocenterC11#26083
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3164

Complements

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

NH ≅ G/Ntype
3. #13070124C2semidirect
4. #13069958C2semidirect
5. #13069401C2semidirect
6. #13069365C2semidirect
8. #13068774C2semidirect
11. C11×#3164C2semidirect
63. #66954Q8semidirect
80. #66889Q8semidirect
154. #3164D11semidirect
369. C11#26083semidirect

Maximal subgroups

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

subgroupindex
#130784632
#130772132
#130701242
#130699582
#130694012
#130693652
#130688392
#130687742
#130686812
#130684552
C11×#31642
#2608311