Finite Group Databasebeta

← #14812678

Subgroups — #14812678

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078474C212yesmaximal
2#13077213C211yesmaximal, characteristic
3#13070129C212yesmaximal, complemented
4#13069963C212yesmaximal, complemented
5#13069401C211yesmaximal, characteristic, complemented
6#13069365C211yesmaximal, characteristic, complemented
7#13068846C212yesmaximal
8#13068779C211yesmaximal, 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#10622707—22no—
27#10622697—22no—
28#10622679—22no—
29#10622676—22no—
30#10622615C2211yescharacteristic
31#10622612C2212yes—
32#10622608C2212yes—
33#10622608C2212yes—
34#10622590C2212yes—
35#10622579C2212yes—
36C2×#66872C2212yes—
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×C4×Dic11C2311yescharacteristic
58C2×#4318C2312yes—
59C2×#4318C2311yescharacteristic
60C22×C11⋊C8C2311yescharacteristic
61#66954—22no—
62#66954Q814yescomplemented
63C2×#4313—21no—
64C2×C8×D11—21no—
65#66945—22no—
66C4⋊C4×D11—22no—
67(C22⋊D11)⋊C4—42no—
68C4×D44—22no—
69C4×Dic22—22no—
70C11×#107—21no—
71C11×#107—21no—
72C11×#107—22no—
73C11×#107D411yescharacteristic
74C11×#107D411yescharacteristic
75C11×#106—22no—
76C11×#106D412yes—
77C11×#97—21no—
78C4×C8×C11—21no—
79C11⋊#95—42no—
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#66872—22no—
94#66872—22no—
95#66871—22no—
96#66871—22no—
97C4⋊(C11⋊C8)—22no—
98C4⋊(C11⋊C8)—22no—
99#26082—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—
138C4×Dic11—21no—
139C4×Dic11—42no—
140C4×Dic11C2×Q812yes—
141#4318—21no—
142#4318—22no—
143#4318—22no—
144#4318C2×Q812yes—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8C2×D411yescharacteristic
150C2×C11⋊C8C2×D411yescharacteristic
151#4313—24no—
152C8×D11—24no—
153#3164D1111yescharacteristic, complemented
154#3084—112no—
155#2913—111no—
156#2090—112no—
157#2061—112no—
158#1952—111no—
159#1945—111no—
160#1860—112no—
161#1846—111no—
162#1816—111no—
163#1764—111no—
164C23×C11H(5,𝔽2)11yescharacteristic
165C22×D11—21no—
166Q8×C11—162no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11C22×Q811yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C22⋊D11—22no—
180C22⋊D11—22no—
181C2×Dic11—21no—
182C2×Dic11—22no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—82no—
187D44—21no—
188D44C4⋊Q812yes—
189C4×D11—22no—
190C4×D11—22no—
191C4×D11—162no—
192Dic22—21no—
193Dic22C4⋊Q812yes—
194C8×C11—22no—
195C8×C11C22⋊Q812yes—
196C8×C11C22⋊Q812yes—
197C11⋊C8—22no—
198C11⋊C8—21no—
199C11⋊C8—21no—
200C11⋊C8—42no—
201C2×#131—111no—
202#544C2×D1112yes—
203#520—112no—
204#501—22no—
205#500—21no—
206#499—21no—
207#479—222no—
208#478—222no—
209#476—222no—
210#475—222no—
211C2×#108—111no—
212#428—112no—
213#428—112no—
214#428—222no—
215#428C2×D1112yes—
216#427—221no—
217#427C2×D1111yescharacteristic
218C2×#107—111no—
219C2×#107—221no—
220C2×#107C2×D1111yescharacteristic
221C2×#106—112no—
222#424—112no—
223C2×#104—111no—
224#417—112no—
225#416—111no—
226#405C2×D1111yescharacteristic
227C2×C4×C8—111no—
228#382—112no—
229#343—112no—
230#343—112no—
231#341—111no—
232#339—111no—
233#339—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11#54411yescharacteristic
237C22×C11D4211yescharacteristic
238C22×C11#55411yescharacteristic
239C2×D11—22no—
240C2×D11—41no—
241C2×D11—41no—
242C4×C11—41no—
243C4×C11—42no—
244C4×C11—41no—
245C4×C11—42no—
246C4×C11—82no—
247C4×C11C2×C22⋊Q811yescharacteristic
248C4×C11C2×C4⋊Q811yescharacteristic
249C4×C11#54711yescharacteristic
250C4×C11D4×Q811yescharacteristic
251Dic11—22no—
252Dic11—42no—
253Dic11—82no—
254C2×#41—111no—
255#131—114no—
256#131—222no—
257C2×M16—111no—
258C2×M16—112no—
259C2×M16—221no—
260C2×M16C22×D1111yescharacteristic
261C22×C8—111no—
262C22×C8—221no—
263C22×C8C22×D1111yescharacteristic
264C4⋊Q8—22no—
265C4⋊Q8—22no—
266#125—22no—
267#125—22no—
268C22⋊Q8—42no—
269C4×Q8—222no—
270C4×D4—222no—
271C4×D4—442no—
272#117—222no—
273#117C22×D1111yescharacteristic
274#117C22×D1112yes—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4C22×D1112yes—
278C2×C42—111no—
279#108—222no—
280#107—21no—
281#107—21no—
282#107—22no—
283#107—221no—
284#107—221no—
285#107—222no—
286#107—222no—
287#107C22⋊D1111yescharacteristic
288#107C22⋊D1111yescharacteristic
289#106—22no—
290#106—222no—
291#106—222no—
292#106—222no—
293#106—222no—
294#106C22⋊D1112yes—
295C4⋊C8—222no—
296C4⋊C8—222no—
297#104—114no—
298#103—111no—
299#103—111no—
300#103—222no—
301#102—111no—
302#102—111no—
303#102—222no—
304#97—21no—
305C4×C8—21no—
306C4×C8—222no—
307#95—442no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11#244011yescharacteristic
311C2×C11#329011yescharacteristic
312C2×C11#329011yescharacteristic
313D11—42no—
314#41—112no—
315#41—112no—
316#41—221no—
317#41—221no—
318C2×Q8—42no—
319C2×Q8—111no—
320C2×D4—111no—
321C2×D4—221no—
322C22×C4—22no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—442no—
327C22×C4C23×D1111yescharacteristic
328M16—21no—
329M16—112no—
330M16—221no—
331M16—224no—
332M16—222no—
333M16—222no—
334M16Q8×D1112yes—
335C2×C8—21no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—224no—
342C2×C8—222no—
343C2×C8Q8×D1112yes—
344C2×C8#434312yes—
345C2×C8C2×C22⋊D1111yescharacteristic
346C2×C8C2×C22⋊D1111yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—442no—
355C4⋊C4D4×D1111yescharacteristic
356C4⋊C4D4×D1111yescharacteristic
357C4⋊C4C2×C22⋊D1112yes—
358C4⋊C4C2×C22⋊D1112yes—
359C22⋊C4—22no—
360C22⋊C4—21no—
361C22⋊C4—442no—
362C42—22no—
363C42—21no—
364C42—112no—
365C42—221no—
366C42—442no—
367C11#2608211yescharacteristic, complemented, Sylow
368C23—221no—
369C23#6703711yescharacteristic
370Q8—112no—
371Q8—162no—
372Q8—221no—
373D4—112no—
374D4—222no—
375D4—222no—
376D4—221no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—221no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—442no—
390C2×C4—882no—
391C2×C4—1762no—
392C2×C4C2×D4×D1111yescharacteristic
393C2×C4C2×Q8×D1111yescharacteristic
394C2×C4C2×Q8×D1111yescharacteristic
395C2×C4C2×#434311yescharacteristic
396C2×C4#6704011yescharacteristic
397C2×C4C22×C22⋊D1111yescharacteristic
398C8—22no—
399C8—221no—
400C8—221no—
401C8—222no—
402C8—442no—
403C8#6699912yes—
404C8#6699912yes—
405C22—21no—
406C22—21no—
407C22—222no—
408C22—441no—
409C22—441no—
410C22#1062326011yescharacteristic
411C22#1062326111yescharacteristic
412C22D4×C22⋊D1111yescharacteristic
413C4—41no—
414C4—42no—
415C4—42no—
416C4—41no—
417C4—82no—
418C4—222no—
419C4—442no—
420C4—882no—
421C4D11×C4⋊Q811yescharacteristic
422C4#1062325711yescharacteristic
423C4C2×#6699911yescharacteristic
424C4Q8×C22⋊D1111yescharacteristic
425C2—21no—
426C2—21no—
427C2—442no—
428C2#1307231411yescharacteristic
429C2#1308039811yescharacteristic
430C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3164C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#3164D11
hypocenterC11#26082
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. #13070129C2semidirect
4. #13069963C2semidirect
5. #13069401C2semidirect
6. #13069365C2semidirect
8. #13068779C2semidirect
11. C11×#3164C2semidirect
62. #66954Q8semidirect
80. #66889Q8semidirect
153. #3164D11semidirect
367. C11#26082semidirect

Maximal subgroups

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

subgroupindex
#130784742
#130772132
#130701292
#130699632
#130694012
#130693652
#130688462
#130687792
#130686812
#130684552
C11×#31642
#2608211