Finite Group Databasebeta

← #14666153

Subgroups — #14666153

Order 2816.

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

normal subgroups only

This group has 622 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#13067533C211yesmaximal, characteristic, complemented
3#13067533C211yesmaximal, characteristic, complemented
4#13066613C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2675C211yesmaximal, characteristic, complemented
8C2×C11×#121—21no—
9C2×C11×#121—21no—
10C2×C11×#121—21no—
11#10623024C2211yescharacteristic
12C11×#396—21no—
13C11×#392—21no—
14C11×#392C2211yescharacteristic
15C11×#392C2211yescharacteristic
16C11×#385—21no—
17C11×#385C2211yescharacteristic
18#10622830—21no—
19#10622830—21no—
20#10622826—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11D411yescharacteristic
35C22×C22⋊D11—21no—
36C11×#121—44no—
37C11×#121—44no—
38C11×#121—42no—
39C11×#121—42no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C2×C22⋊Dic11—21no—
51C2×#4323—41no—
52C2×#4323—41no—
53#66983—21no—
54#66983—21no—
55C2×(C2×D11)⋊C4—41no—
56#66939—41no—
57#66935—41no—
58C11×#95—21no—
59C11×#95D411yescharacteristic
60C11×#95D411yescharacteristic
61#66896—41no—
62#66896—41no—
63C11⋊#95—41no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66870—42no—
67#12148—111nomaximal, Sylow
68C24×C11—21no—
69C24×C11—21no—
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C2×D4×C11—81no—
88C2×D4×C11—81no—
89C2×D4×C11—81no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11—81no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C22×Dic11—21no—
108C22×Dic11—41no—
109C2×D44—21no—
110C2×D44—21no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—42no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—21no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—42no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—81no—
121C11×C22⋊C4D812yescomplemented
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124#4323—82no—
125#4323—82no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—82no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#2675D1111yescharacteristic, complemented
134#2044—111no—
135#1595—111no—
136#1595—111no—
137#1343—111no—
138#1343—111no—
139#1326—111no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11#12011yescharacteristic
159C23×C11C2×D811yescharacteristic
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—81no—
165C22×D11—81no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—81no—
169D4×C11—82no—
170D4×C11—82no—
171D4×C11—84no—
172D4×C11—84no—
173D4×C11—81no—
174D4×C11—82no—
175D4×C11—82no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—81no—
194C2×C4×C11—84no—
195C22⋊D11—81no—
196C22⋊D11—81no—
197C22⋊D11—81no—
198C22⋊D11—81no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205D44—81no—
206D44—81no—
207C11⋊C8—81no—
208C11⋊C8—81no—
209#534—111no—
210C2×#121—21no—
211C2×#121—21no—
212C2×#121—21no—
213#447—221no—
214#447—221no—
215C2×#99—221no—
216#396—21no—
217#392—21no—
218#392C2×D1111yescharacteristic
219#392C2×D1111yescharacteristic
220#386—221no—
221#385—21no—
222#385C2×D1111yescharacteristic
223#342—111no—
224#327—221no—
225#327—221no—
226#323—111no—
227#323—111no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11#44711yescharacteristic
252C22×C11#45411yescharacteristic
253C22×C11B(4,𝔽2)11yescharacteristic
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—161no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—41no—
263C4×C11—41no—
264C4×C11—81no—
265Dic11—81no—
266Dic11—161no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—221no—
272C22×D4C22⋊D1111yescharacteristic
273C22×D4C22⋊D1111yescharacteristic
274C23×C4—21no—
275C23×C4C22⋊D1111yescharacteristic
276C2×D8—441no—
277C2×D8—441no—
278#123—441no—
279#121—44no—
280#121—44no—
281#121—42no—
282#121—42no—
283#121—221no—
284#121—221no—
285#120—441no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—441no—
296C2×C22⋊C4C22⋊D1111yescharacteristic
297C2×C22⋊C4C22×D1111yescharacteristic
298#102—441no—
299#102—441no—
300#99—442no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303#95—21no—
304#95—441no—
305#95C22⋊D1111yescharacteristic
306#95C22⋊D1111yescharacteristic
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—41no—
310C2×C11—41no—
311C2×C11—82no—
312C2×C11—161no—
313C2×C11#159811yescharacteristic
314C2×C11#219611yescharacteristic
315C2×C11#220011yescharacteristic
316D11—161no—
317C24—21no—
318C24—21no—
319C24—221no—
320C24C2×C22⋊D1111yescharacteristic
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—81no—
335C2×D4—81no—
336C2×D4—81no—
337C2×D4—81no—
338C2×D4—81no—
339C2×D4—221no—
340C2×D4—221no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—81no—
356C22×C4—221no—
357C22×C4—441no—
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360D8—882no—
361D8—882no—
362C2×C8—441no—
363C2×C8—441no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C22⋊C4—24no—
370C22⋊C4—21no—
371C22⋊C4—41no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—81no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—882no—
381C22⋊C4#432312yescomplemented
382C11#1214811yescharacteristic, complemented, Sylow
383C23—21no—
384C23—21no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—881no—
405C23—881no—
406C23C2×#432311yescharacteristic
407C23#6698511yescharacteristic
408C23#6700611yescharacteristic
409D4—42no—
410D4—42no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—84no—
415D4—84no—
416D4—81no—
417D4—82no—
418D4—82no—
419D4—881no—
420D4—881no—
421D4—881no—
422D4—881no—
423D4—881no—
424D4—881no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—84no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4—881no—
450C8—881no—
451C8—881no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—42no—
459C22—42no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—882no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22—1761no—
480C22#1062283011yescharacteristic
481C22#1062285711yescharacteristic
482C22#1062285811yescharacteristic
483C4—42no—
484C4—42no—
485C4—41no—
486C4—42no—
487C4—41no—
488C4—81no—
489C4—881no—
490C4—1761no—
491C2—21no—
492C2—21no—
493C2—41no—
494C2—41no—
495C2—82no—
496C2—161no—
497C2—1761no—
498C2#1306755111yescharacteristic
499C2#1307060011yescharacteristic
500C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2675C2
socleC22×C11B(4,𝔽2)
hypercenter#2675D11
hypocenterC11#12148
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2675

Complements

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

NH ≅ G/Ntype
1. #13069867C2semidirect
2. #13067533C2semidirect
3. #13067533C2semidirect
4. #13066613C2semidirect
5. #13066613C2semidirect
6. #13066564C2semidirect
7. C11×#2675C2semidirect
121. C11×C22⋊C4D8semidirect
133. #2675D11semidirect
381. C22⋊C4#4323semidirect
382. C11#12148semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130675332
#130666132
#130665642
C11×#26752
#1214811