Finite Group Databasebeta

← #14657189

Subgroups — #14657189

Order 2816.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073611C211yesmaximal, characteristic
2#13069576C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×#10622124C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C2×#66928—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×#107—21no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622600—21no—
16#10622600—21no—
17C2×#66873—21no—
18#10622542—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622287—22no—
22C11×#340—21no—
23#10622167—22no—
24#10622167—21no—
25#10622124—22no—
26#10622121—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×C4⋊Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66928—42no—
47#66928—42no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56C11×#107—42no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62#66873—42no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8—21no—
67#10416—111nomaximal, Sylow
68C23×D11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—22no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44D812yes—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—44no—
114(C2×D11)⋊C4—44no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129#2547—111no—
130#1990—111no—
131#1947D1111yescharacteristic, complemented
132#1802—111no—
133C2×#332—111no—
134C2×D4⋊C8—111no—
135#1279—111no—
136C23×C11#12011yescharacteristic
137C22×D11—22no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×C4×C11#12411yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11#13511yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175D44—22no—
176D44—22no—
177D44—41no—
178D44—41no—
179C4×D11—81no—
180C4×D11—81no—
181C4×D11—81no—
182C4×D11—81no—
183Dic22—81no—
184Dic22—81no—
185Dic22—81no—
186Dic22—81no—
187C8×C11—42no—
188C11⋊C8—42no—
189C11⋊C8—81no—
190C2×C4⋊Q8—111no—
191C2×#124—221no—
192C2×C4×D4—111no—
193C2×#107—21no—
194C2×C4⋊C8—111no—
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×#102—221no—
197C2×C4×C8—111no—
198#397—222no—
199#391—221no—
200#384C2×D1111yescharacteristic
201#380—221no—
202#380—221no—
203C4×C4⋊C4C2×D1111yescharacteristic
204#340—21no—
205#340—221no—
206#340—222no—
207#332—222no—
208D4⋊C8—222no—
209C22×C11#39411yescharacteristic
210C22×C11#44711yescharacteristic
211C22×C11#44911yescharacteristic
212C22×C11#45211yescharacteristic
213C22×C11#45211yescharacteristic
214C22×C11#45411yescharacteristic
215C22×C11#45611yescharacteristic
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—161no—
228C4×C11#46311yescharacteristic
229C4×C11#46411yescharacteristic
230C4×C11#46611yescharacteristic
231C4×C11#46811yescharacteristic
232C4×C11#48011yescharacteristic
233C4×C11#48211yescharacteristic
234C4×C11#48811yescharacteristic
235C4×C11#48911yescharacteristic
236Dic11—82no—
237Dic11—81no—
238C22×Q8—221no—
239C22×D4—111no—
240C23×C4—221no—
241C22×C8—21no—
242C22×C8—221no—
243C22×C8—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248#124—442no—
249#124—442no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4C22⋊D1111yescharacteristic
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—222no—
263C2×C22⋊C4—222no—
264C2×C22⋊C4—221no—
265C2×C42—21no—
266C2×C42C22×D1111yescharacteristic
267#107—42no—
268C4⋊C8—21no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C4⋊C8D4412yes—
272#102—442no—
273C4×C8—221no—
274C4×C8—221no—
275#95—21no—
276#95—222no—
277#95—222no—
278C2×C11#162511yescharacteristic
279C2×C11#163811yescharacteristic
280C2×C11#164711yescharacteristic
281C2×C11#165211yescharacteristic
282C2×C11#203311yescharacteristic
283C2×C11#203811yescharacteristic
284C2×C11#204211yescharacteristic
285D11—82no—
286C24—221no—
287C2×Q8—441no—
288C2×Q8—441no—
289C2×Q8—441no—
290C2×Q8—441no—
291C2×Q8—441no—
292C2×Q8—441no—
293C2×D4—112no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—221no—
303C22×C4—222no—
304C22×C4—441no—
305C22×C4—441no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—222no—
317C2×C8—441no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—221no—
334C4⋊C4—222no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C22⋊C4—444no—
338C22⋊C4—444no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C42—41no—
342C42—41no—
343C42C2×D4411yescharacteristic
344C42#433911yescharacteristic
345C42#434311yescharacteristic
346C42#434311yescharacteristic
347C11#1041611yescharacteristic, complemented, Sylow
348C23—222no—
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23#6699011yescharacteristic
356Q8—881no—
357Q8—881no—
358Q8—881no—
359Q8—881no—
360D4—222no—
361D4—222no—
362D4—441no—
363D4—441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4#6694711yescharacteristic
386C2×C4#6694711yescharacteristic
387C2×C4#6694811yescharacteristic
388C2×C4#6694811yescharacteristic
389C2×C4D8×D1111yescharacteristic
390C2×C4#6696411yescharacteristic
391C2×C4#6697111yescharacteristic
392C2×C4#6697211yescharacteristic
393C2×C4#6698311yescharacteristic
394C2×C4#6698511yescharacteristic
395C2×C4#6699511yescharacteristic
396C2×C4#6700011yescharacteristic
397C2×C4#6700311yescharacteristic
398C2×C4#6700311yescharacteristic
399C8—42no—
400C8—442no—
401C8—881no—
402C22—442no—
403C22—442no—
404C22—442no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22—881no—
409C22#1062260411yescharacteristic
410C22#1062265011yescharacteristic
411C22#1062266011yescharacteristic
412C22#1062276911yescharacteristic
413C22#1062280011yescharacteristic
414C22#1062281411yescharacteristic
415C22#1062281811yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—161no—
421C4—881no—
422C4—882no—
423C4#1062249511yescharacteristic
424C4#1062249611yescharacteristic
425C4#1062249811yescharacteristic
426C4#1062249911yescharacteristic
427C4#1062262911yescharacteristic
428C4#1062264111yescharacteristic
429C4#1062268111yescharacteristic
430C4#1062270211yescharacteristic
431C2—882no—
432C2#1306770411yescharacteristic
433C2#1306778711yescharacteristic
434C2#1306785011yescharacteristic
435C2#1306788411yescharacteristic
436C2#1306980011yescharacteristic
437C2#1306983511yescharacteristic
438C2#1306985711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1947C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1947D11
hypocenterC11#10416
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #13069576C2semidirect
4. C2×#10622124C2semidirect
6. #13066457C2semidirect
7. C11×#1947C2semidirect
131. #1947D11semidirect
347. C11#10416semidirect

Maximal subgroups

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

subgroupindex
#130736112
#130695762
#130686132
C2×#106221242
C2×#106221212
#130664572
C11×#19472
#1041611