Finite Group Databasebeta

← #14654336

Subgroups — #14654336

Order 2816.

772 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#10622581C211yesmaximal, characteristic, complemented
2#13074720C211yesmaximal, characteristic
3C2×#10622108C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066884C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C2×C11×#481C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66992—22no—
11C2×#66983C2211yescharacteristic
12C11×#481—22no—
13C11×#481—22no—
14C2×C11×#106—21no—
15C2×C11×#102—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622836—21no—
18C2×C11⋊#95—22no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622605—21no—
23#10622581—22no—
24#10622581—22no—
25C2×#66873—21no—
26C2×#66872—21no—
27#10622573—21no—
28#10622562—21no—
29#10622175—22no—
30#10622108—22no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C22×C22⋊D11—22no—
37C23×Dic11—21no—
38C23×Dic11D412yes—
39C22×D44D411yescharacteristic
40C22×C8×C11—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D412yescomplemented
52C2×C11×C22⋊C4—21no—
53C2×C22⋊Dic11—22no—
54#66992—44no—
55#66992—44no—
56#66983—21no—
57#66983—21no—
58#66983—21no—
59#66983—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×Dic11⋊C4—22no—
64C22×C11⋊C8—21no—
65C11×#106—24no—
66C11×#102—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8D412yescomplemented
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—44no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)D412yescomplemented
76#66873—24no—
77#66872—24no—
78#9968—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×C22⋊D11—44no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—42no—
107C2×C22⋊D11—82no—
108C2×C22⋊D11—82no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11—41no—
116C22×Dic11—42no—
117C22×Dic11—41no—
118C22×Dic11—42no—
119C22×Dic11SD1614yes—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—42no—
123C2×C8×C11—22no—
124C2×C8×C11—42no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C22⋊Dic11—44no—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139Dic11⋊C4—44no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—42no—
142C2×#481—111no—
143C2×#481D1111yescharacteristic, complemented
144#2656—111no—
145C2×#327—111no—
146C2×#327—111no—
147#1445—111no—
148#1280—111no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11#12011yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12711yescharacteristic
160C23×C11C2×SD1612yes—
161C23×C11AGL(1,ℤ/8)12yes—
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—42no—
167D4×C11—42no—
168D4×C11—81no—
169D4×C11—82no—
170D4×C11—81no—
171D4×C11—81no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—44no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C22⋊D11—88no—
190C22⋊D11—82no—
191C22⋊D11—81no—
192C22⋊D11—81no—
193C2×Dic11—24no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—82no—
202C2×Dic11—82no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205D44—42no—
206D44—81no—
207C8×C11—42no—
208C11⋊C8—42no—
209C2×#121—111no—
210C2×#121—222no—
211C2×#121C2×D1111yescharacteristic
212C22×C4⋊C4C2×D1111yescharacteristic
213#481—22no—
214#481—22no—
215#481—222no—
216#481—222no—
217C2×#106—21no—
218C2×#106—221no—
219C2×#102—21no—
220C2×#102—221no—
221C2×C22⋊C8—111no—
222C2×C22⋊C8C2×D1111yescharacteristic
223#399—221no—
224#399—221no—
225#392—221no—
226#392—221no—
227C2×#95—111no—
228C2×#95—111no—
229C2×#95—222no—
230#327—222no—
231#327—222no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11#39211yescharacteristic
246C22×C11#45012yes—
247C22×C11#45311yescharacteristic
248C22×C11#45411yescharacteristic
249C22×C11#45812yes—
250C22×C11#46012yes—
251C22×C11#49211yescharacteristic
252C22×C11#49611yescharacteristic
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—82no—
263C4×C11—81no—
264Dic11—44no—
265Dic11—82no—
266Dic11—81no—
267C22×D4—21no—
268C22×D4—111no—
269C22×D4—221no—
270C22×D4—222no—
271C22×D4C22⋊D1111yescharacteristic
272C23×C4—21no—
273C23×C4—112no—
274C23×C4—221no—
275C23×C4C22×D1111yescharacteristic
276C22×C8—21no—
277C22×C8—221no—
278#121—21no—
279#121—21no—
280#121—21no—
281#121—21no—
282#121—221no—
283#121—221no—
284#121—221no—
285#121—221no—
286#121—444no—
287#121—444no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22⋊D1111yescharacteristic
296C2×C4⋊C4C22⋊D1112yescomplemented
297C2×C22⋊C4—21no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301#106—24no—
302#106—224no—
303#102—24no—
304#102—224no—
305C22⋊C8—21no—
306C22⋊C8—112no—
307C22⋊C8—221no—
308C22⋊C8C22⋊D1112yescomplemented
309#95—221no—
310#95—221no—
311#95—221no—
312#95—221no—
313#95—444no—
314C2×C11—21no—
315C2×C11—22no—
316C2×C11—21no—
317C2×C11—161no—
318C2×C11#161312yes—
319C2×C11#161612yes—
320C2×C11#200611yescharacteristic
321C2×C11#201411yescharacteristic
322C2×C11#202211yescharacteristic
323D11—161no—
324C24—21no—
325C24—221no—
326C24D4×D1111yescharacteristic
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—442no—
337C2×D4—444no—
338C2×D4—442no—
339C2×D4—442no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—882no—
343C2×D4—882no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—114no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—221no—
356C22×C4—442no—
357C22×C4—442no—
358C22×C4—441no—
359C22×C4—442no—
360C22×C4—442no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—222no—
371C2×C8—442no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—444no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—444no—
384C22⋊C4—444no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C11#996811yescharacteristic, complemented, Sylow
388C23—21no—
389C23—21no—
390C23—22no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—42no—
396C23—442no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23—442no—
401C23SD16×D1112yes—
402C23#6696712yes—
403C23#6699011yescharacteristic
404C23#6699211yescharacteristic
405C23#6699311yescharacteristic
406D4—42no—
407D4—81no—
408D4—82no—
409D4—81no—
410D4—81no—
411D4—442no—
412D4—881no—
413D4—888no—
414D4—882no—
415D4—881no—
416D4—881no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—224no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—444no—
434C2×C4—442no—
435C2×C4—444no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—882no—
439C2×C4—882no—
440C2×C4—881no—
441C2×C4—881no—
442C2×C4#6699011yescharacteristic
443C2×C4#6699111yescharacteristic
444C2×C4#6699211yescharacteristic
445C2×C4#6700611yescharacteristic
446C8—42no—
447C8—442no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—21no—
455C22—21no—
456C22—81no—
457C22—82no—
458C22—82no—
459C22—81no—
460C22—81no—
461C22—881no—
462C22—882no—
463C22—882no—
464C22—881no—
465C22—881no—
466C22#1062266612yes—
467C22#1062277612yes—
468C22#1062278212yes—
469C22#1062278811yescharacteristic
470C22#1062278911yescharacteristic
471C22#1062281111yescharacteristic
472C22#1062281411yescharacteristic
473C22#1062283611yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—81no—
480C4—444no—
481C4—882no—
482C4—881no—
483C2—21no—
484C2—22no—
485C2—21no—
486C2—161no—
487C2—1761no—
488C2#1306763412yes—
489C2#1306765112yes—
490C2#1306965611yescharacteristic
491C2#1306970211yescharacteristic
492C2#1306974411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#481C2
socleC23×C11#120
prime radical#13074720C2
hypercenterC2×#481D11
hypocenterC11#9968
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#10622581C2semidirect
3. C2×#10622108C2semidirect
4. C2×#10622175C2semidirect
5. #13066884C2semidirect
6. #13066458C2semidirect
7. C2×C11×#481C2semidirect
51. C2×C11×C4⋊C4D4semidirect
68. C11×C22⋊C8D4semidirect
75. C22⋊(C11⋊C8)D4semidirect
143. C2×#481D11semidirect
296. C2×C4⋊C4C22⋊D11semidirect
308. C22⋊C8C22⋊D11semidirect
387. C11#9968semidirect

Maximal subgroups

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

subgroupindex
C2×#106225812
#130747202
C2×#106221082
C2×#106221752
#130668842
#130664582
C2×C11×#4812
#996811