Finite Group Databasebeta

← #14909278

Subgroups — #14909278

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079153C211yesmaximal, characteristic
2#13079149C211yesmaximal, characteristic
3#13070902C211yesmaximal, characteristic, complemented
4#13070901C211yesmaximal, characteristic, complemented
5#13070900C211yesmaximal, characteristic, complemented
6#13070894C211yesmaximal, characteristic, complemented
7#13070892C211yesmaximal, characteristic, complemented
8#13070890C211yesmaximal, characteristic, complemented
9#13070889C211yesmaximal, characteristic, complemented
10#13070403C211yesmaximal, characteristic
11#13070401C211yesmaximal, characteristic
12#13070399C211yesmaximal, characteristic
13D11×#366C211yesmaximal, characteristic
14#13070214C211yesmaximal, characteristic
15C11×#2255C211yesmaximal, characteristic, complemented
16#10623260—21no—
17#10623220—21no—
18C11×#500C2211yescharacteristic
19C11×#499C2211yescharacteristic
20#10622693—21no—
21#10622678—21no—
22C2×#66862C2211yescharacteristic
23C2×C16×D11C2211yescharacteristic
24#10622494—21no—
25#10622493C2211yescharacteristic
26#10622493C2211yescharacteristic
27D11×#107C2211yescharacteristic
28D11×#107C2211yescharacteristic
29#10622491C2211yescharacteristic
30#10622491C2211yescharacteristic
31#10622489—21no—
32#10622487C2211yescharacteristic
33#10622487C2211yescharacteristic
34#10622474—21no—
35#10622469—21no—
36#10622302C2211yescharacteristic
37#10622296C2211yescharacteristic
38#10622295C2211yescharacteristic
39C11×#367C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622143C2211yescharacteristic
45#10622143C2211yescharacteristic
46#10622142C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622140C2211yescharacteristic
49C16×Dic11C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622127C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C11×C4⋊Q8—21no—
60C11×#125—21no—
61#66999—41no—
62#66997—41no—
63C2×#4313D411yescharacteristic
64C2×C8×D11C2311yescharacteristic
65#66950—41no—
66#66949—41no—
67#66949—41no—
68#66945—21no—
69#66945—21no—
70C4⋊C4×D11—21no—
71C4⋊C4×D11—21no—
72#66943—21no—
73#66943—21no—
74#66942—41no—
75#66942—41no—
76#66941—21no—
77#66941—21no—
78#66941—41no—
79#66925D411yescharacteristic
80#66923—21no—
81#66922—21no—
82C2×C11×C16C2311yescharacteristic
83C2×C11×C16C2311yescharacteristic
84C11×#107—21no—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#106—21no—
90C4×C8×C11C2311yescharacteristic
91#66882—21no—
92#66882C2311yescharacteristic
93#66882C2311yescharacteristic
94#66882C2311yescharacteristic
95#66882C2311yescharacteristic
96#66881—21no—
97#66879D411yescharacteristic
98C8×Dic11C2311yescharacteristic
99C2×C11⋊C16C2311yescharacteristic
100C2×C11⋊C16C2311yescharacteristic
101#66872—21no—
102#66872—21no—
103#66872—21no—
104#66872—21no—
105#66871—21no—
106#66871—21no—
107#66871—21no—
108#66871—21no—
109#66867D411yescharacteristic
110#66862Q814yescomplemented
111C16×D11Q814yescomplemented
112#33729—111nomaximal, Sylow
113C2×Q8×C11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C4×D11C2×D411yescharacteristic
117C2×Dic22—41no—
118C2×Dic22—41no—
119C2×Dic22—41no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C42×C11C2×D411yescharacteristic
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4D811yescharacteristic
133(C2×D11)⋊C4D811yescharacteristic
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144Dic11⋊C4—41no—
145Dic11⋊C4—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4D811yescharacteristic
150Dic11⋊C4D811yescharacteristic
151C4×Dic11—41no—
152C4×Dic11—41no—
153C4×Dic11C2×D411yescharacteristic
154C2×C11⋊C8C2×D411yescharacteristic
155C2×C11⋊C8C2×D411yescharacteristic
156#4313Q1614yes—
157C8×D11C2×Q812yes—
158C8×D11C2×Q812yes—
159C11×C16C2×Q812yes—
160C11×C16C2×Q812yes—
161C11⋊C16C2×Q812yes—
162C11⋊C16C2×Q812yes—
163#3164—111no—
164#3164—111no—
165#2255—111no—
166#2255—111no—
167#2255—111no—
168#2255D1111yescharacteristic, complemented
169#2253—111no—
170#2253—111no—
171#2252—111no—
172#2252—111no—
173#2159—111no—
174#2159—111no—
175#2158—111no—
176C2×#366—111no—
177#2108—111no—
178C22×D11C2×D811yescharacteristic
179Q8×C11—161no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11C2×D811yescharacteristic
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194C4×D11—161no—
195C4×D11—161no—
196C4×D11C4⋊Q812yes—
197C4×D11C2×Q1612yes—
198Dic22—161no—
199Dic22—161no—
200Dic22—161no—
201C8×C11C2×Q1612yes—
202C8×C11C22×Q811yescharacteristic
203C8×C11C22×Q811yescharacteristic
204C11⋊C8C4⋊Q812yes—
205C11⋊C8C2×Q1612yes—
206#544—221no—
207#544—221no—
208C2×M32—111no—
209C22×C16—111no—
210#501—221no—
211#501—221no—
212#501—221no—
213#501—221no—
214#500—111no—
215#500—111no—
216#500—111no—
217#500C2×D1111yescharacteristic
218#499—111no—
219#499—111no—
220#499—111no—
221#499C2×D1111yescharacteristic
222#428—221no—
223#428—221no—
224#427—111no—
225#427—111no—
226C2×#107—111no—
227C2×#107—111no—
228#405—111no—
229#367—111no—
230#367—111no—
231#367—111no—
232#367—111no—
233#367C2×D1111yescharacteristic
234#367C2×D1111yescharacteristic
235#366—111no—
236#366—111no—
237#366—111no—
238#366—111no—
239#366—111no—
240#366—111no—
241#366—111no—
242#366—111no—
243#366C2×D1111yescharacteristic
244#366C2×D1111yescharacteristic
245#346—111no—
246#346C2×D1111yescharacteristic
247C4×C16—111no—
248C4×C16—111no—
249C22×C11C22×D811yescharacteristic
250C2×D11—21no—
251C2×D11—21no—
252C2×D11#50012yes—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11C2×C4⋊Q811yescharacteristic
260C4×C11C22×Q1611yescharacteristic
261Dic11—21no—
262Dic11—21no—
263Dic11—81no—
264Dic11—81no—
265Dic11—81no—
266Dic11—81no—
267Dic11#50012yes—
268C2×M16—111no—
269C22×C8—111no—
270C4⋊Q8—21no—
271C4⋊Q8—221no—
272C4⋊Q8—221no—
273C4⋊Q8—221no—
274C4⋊Q8—441no—
275C4⋊Q8—441no—
276#125—21no—
277#125—221no—
278#125—221no—
279#125—221no—
280#125—441no—
281#125—441no—
282C22⋊Q8—441no—
283C22⋊Q8—441no—
284C22⋊Q8—441no—
285C22⋊Q8—441no—
286#117—111no—
287#117—221no—
288#117—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291M32—114no—
292C2×C16—111no—
293C2×C16—111no—
294C2×C16—114no—
295C2×C16C22×D1111yescharacteristic
296C2×C16C22×D1111yescharacteristic
297#107—21no—
298#107—111no—
299#107—111no—
300#107—111no—
301#107—111no—
302#107—221no—
303#107—221no—
304#107—221no—
305#107—221no—
306#107—221no—
307#107C22×D1111yescharacteristic
308#107C22×D1111yescharacteristic
309#107C22×D1111yescharacteristic
310#107C22×D1111yescharacteristic
311#106—21no—
312#106—221no—
313#106—221no—
314#106—221no—
315#106—221no—
316#106—221no—
317#97—111no—
318#97—111no—
319C4×C8—111no—
320C4×C8C22×D1111yescharacteristic
321C2×C11C2×#50011yescharacteristic
322C2×C11#341511yescharacteristic
323C2×C11#341711yescharacteristic
324D11—22no—
325C2×Q8—41no—
326C2×Q8—441no—
327C2×Q8—441no—
328C2×Q8—441no—
329C22×C4—111no—
330C22×C4—441no—
331C22×C4—441no—
332M16—114no—
333C2×C8—111no—
334C2×C8—111no—
335C2×C8—112no—
336C2×C8—112no—
337C2×C8D4×D1111yescharacteristic
338C2×C8C23×D1111yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—111no—
347C4⋊C4—111no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C22⋊C4—111no—
364C22⋊C4—111no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C42—111no—
368C42—441no—
369C42—441no—
370C42D4×D1111yescharacteristic
371C16—112no—
372C16—112no—
373C16Q8×D1112yes—
374C16Q8×D1112yes—
375C11#3372911yescharacteristic, complemented, Sylow
376C23—111no—
377Q8—161no—
378Q8—1761no—
379Q8—1761no—
380Q8—1761no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—111no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—1761no—
395C2×C4—1761no—
396C2×C4D8×D1111yescharacteristic
397C2×C4D8×D1111yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C8—112no—
400C8—112no—
401C8Q16×D1112yes—
402C8C2×Q8×D1111yescharacteristic
403C8C2×Q8×D1111yescharacteristic
404C22—112no—
405C22—221no—
406C22—221no—
407C22C2×D8×D1111yescharacteristic
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—81no—
414C4—112no—
415C4—221no—
416C4—221no—
417C4—881no—
418C4—881no—
419C4—881no—
420C4—881no—
421C4D11×C4⋊Q811yescharacteristic
422C4C2×Q16×D1111yescharacteristic
423C2—222no—
424C2D11×#50011yescharacteristic
425C2#1308175611yescharacteristic
426C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2255C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2255D11
hypocenterC11#33729
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13070902C2semidirect
4. #13070901C2semidirect
5. #13070900C2semidirect
6. #13070894C2semidirect
7. #13070892C2semidirect
8. #13070890C2semidirect
9. #13070889C2semidirect
15. C11×#2255C2semidirect
110. #66862Q8semidirect
111. C16×D11Q8semidirect
168. #2255D11semidirect
375. C11#33729semidirect

Maximal subgroups

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

subgroupindex
#130791532
#130791492
#130709022
#130709012
#130709002
#130708942
#130708922
#130708902
#130708892
#130704032
#130704012
#130703992
D11×#3662
#130702142
C11×#22552
#3372911