Finite Group Databasebeta

← #14666160

Subgroups — #14666160

Order 2816.

498 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069867C211yesmaximal, characteristic, complemented
2#13067601C211yesmaximal, characteristic, complemented
3#13067533C211yesmaximal, characteristic
4#13066616C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2693C211yesmaximal, characteristic, complemented
8C2×C11×#123—21no—
9#10623024C2211yescharacteristic
10C11×#400—21no—
11C11×#397C2211yescharacteristic
12C11×#396—21no—
13C11×#392C2211yescharacteristic
14C11×#386—21no—
15C11×#386—21no—
16C11×#385C2211yescharacteristic
17C11×#380—21no—
18#10622830—21no—
19#10622826—21no—
20#10622580—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C22×C22⋊D11—21no—
32C11×#123—42no—
33C11×#123—42no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C11×C22⋊C4C2311yescharacteristic
45C2×C22⋊Dic11—21no—
46C2×#4323—41no—
47#66983—21no—
48#66983—21no—
49C2×(C2×D11)⋊C4—41no—
50#66939—41no—
51#66935—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58#66896—41no—
59C11⋊#95—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66871—41no—
64#66870—42no—
65#12149—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—42no—
81C22×C4×C11—41no—
82C22×C4×C11—42no—
83C22×C4×C11—81no—
84C22×C4×C11—81no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C22×Dic11—21no—
94C22×Dic11—41no—
95C2×D44—21no—
96C2×D44—21no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—21no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—81no—
108C11×C22⋊C4—81no—
109C11×C22⋊C4D812yescomplemented
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112#4323—82no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—82no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2693D1111yescharacteristic, complemented
121#2044—111no—
122#1607—111no—
123#1595—111no—
124#1344—111no—
125#1343—111no—
126#1326—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139C23×C11C2×D811yescharacteristic
140C23×C11AGL(1,ℤ/8)11yescharacteristic
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—81no—
145C22×D11—81no—
146D4×C11—42no—
147D4×C11—81no—
148D4×C11—82no—
149D4×C11—82no—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—84no—
171C2×C4×C11—81no—
172C22⋊D11—81no—
173C22⋊D11—81no—
174C22⋊D11—81no—
175C22⋊D11—81no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182D44—81no—
183D44—81no—
184C11⋊C8—81no—
185C11⋊C8—81no—
186#534—111no—
187C2×#123—21no—
188#480—221no—
189#447—221no—
190C2×#99—221no—
191#400—21no—
192#397C2×D1111yescharacteristic
193#396—21no—
194#392C2×D1111yescharacteristic
195#386—21no—
196#386—21no—
197#386—221no—
198#385C2×D1111yescharacteristic
199#380—21no—
200#342—111no—
201#327—221no—
202#327—221no—
203#323—111no—
204#323—111no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#44711yescharacteristic
222C22×C11#45411yescharacteristic
223C22×C11B(4,𝔽2)11yescharacteristic
224C2×D11—82no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—161no—
229C4×C11—42no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—81no—
236Dic11—81no—
237Dic11—161no—
238C22×D4—21no—
239C22×D4—221no—
240C22×D4C22⋊D1111yescharacteristic
241C23×C4—21no—
242C23×C4C22⋊D1111yescharacteristic
243C2×D8—441no—
244#123—42no—
245#123—42no—
246#123—441no—
247#121—221no—
248#121—221no—
249#120—441no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—441no—
261C2×C22⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4C22×D1111yescharacteristic
263#107—441no—
264#102—441no—
265#102—441no—
266#99—442no—
267C22⋊C8—221no—
268C22⋊C8—221no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—441no—
274#95C22⋊D1111yescharacteristic
275#95C22⋊D1111yescharacteristic
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11—82no—
281C2×C11#159811yescharacteristic
282C2×C11#219711yescharacteristic
283C2×C11#220011yescharacteristic
284D11—161no—
285C24—21no—
286C24—221no—
287C24C2×C22⋊D1111yescharacteristic
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—221no—
313C22×C4—441no—
314C22×C4C2×C22⋊D1111yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316D8—882no—
317C2×C8—441no—
318C2×C8—441no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—81no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C22⋊C4—21no—
326C22⋊C4—41no—
327C22⋊C4—42no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—882no—
338C22⋊C4#432312yescomplemented
339C11#1214911yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—881no—
355C23—881no—
356C23C2×#432311yescharacteristic
357C23#6698511yescharacteristic
358C23#6700611yescharacteristic
359D4—42no—
360D4—81no—
361D4—82no—
362D4—82no—
363D4—881no—
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368D4—881no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—84no—
390C2×C4—81no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4—881no—
397C8—881no—
398C8—881no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22—42no—
407C22—41no—
408C22—41no—
409C22—42no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—882no—
416C22—881no—
417C22—881no—
418C22—881no—
419C22—1761no—
420C22#1062283011yescharacteristic
421C22#1062285711yescharacteristic
422C22#1062285811yescharacteristic
423C4—42no—
424C4—41no—
425C4—41no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4—81no—
430C4—881no—
431C4—1761no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—82no—
437C2—1761no—
438C2#1306755111yescharacteristic
439C2#1307060611yescharacteristic
440C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2693C2
socleC22×C11B(4,𝔽2)
prime radical#13067533C2
hypercenter#2693D11
hypocenterC11#12149
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2693

Complements

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

NH ≅ G/Ntype
1. #13069867C2semidirect
2. #13067601C2semidirect
4. #13066616C2semidirect
5. #13066613C2semidirect
6. #13066564C2semidirect
7. C11×#2693C2semidirect
109. C11×C22⋊C4D8semidirect
120. #2693D11semidirect
338. C22⋊C4#4323semidirect
339. C11#12149semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130676012
#130675332
#130666162
#130666132
#130665642
C11×#26932
#1214911