Finite Group Databasebeta

← #14654338

Subgroups — #14654338

Order 2816.

772 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10622348C211yesmaximal, characteristic, complemented
2C2×#10622647C211yesmaximal, characteristic, complemented
3#13074720C211yesmaximal, characteristic
4C2×#10622089C211yesmaximal, characteristic, complemented
5#13066883C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66992—22no—
10C2×#66983C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622836—21no—
15C2×#66896—21no—
16C2×C11⋊#95—22no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66885—21no—
20C2×#66881—21no—
21#10622647—22no—
22#10622647—22no—
23#10622605—21no—
24C2×#66872—21no—
25#10622573—21no—
26#10622562—21no—
27#10622348—22no—
28#10622348—22no—
29C11×#327—22no—
30#10622089—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⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—22no—
48#66992—44no—
49#66992—44no—
50#66983—21no—
51#66983—21no—
52#66983—21no—
53#66983—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11D412yescomplemented
63C2×Dic11⋊C4—22no—
64C22×C11⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8D412yescomplemented
67C11×#95—21no—
68C11×#95—21no—
69#66896—24no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—44no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yescomplemented
75#66885—24no—
76#66881—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—22no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—41no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11—42no—
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—21no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11SD1614yes—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—42no—
123C2×C8×C11—22no—
124C2×C8×C11—42no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C22⋊Dic11—44no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139Dic11⋊C4—44no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—42no—
142C2×#481—111no—
143C2×#481—111no—
144#2656—111no—
145C2×#327—111no—
146C2×#327D1111yescharacteristic, complemented
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—42no—
180C2×C4×C11—41no—
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⋊C4—111no—
213#481—222no—
214#481—222no—
215#481—222no—
216#481—222no—
217C2×#106—221no—
218C2×#106—221no—
219C2×#102—221no—
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—222no—
229C2×#95C2×D1111yescharacteristic
230#327—22no—
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×D4D4411yescharacteristic
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—112no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4D4411yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301#106—224no—
302#106—224no—
303#102—224no—
304#102—224no—
305C22⋊C8—21no—
306C22⋊C8—112no—
307C22⋊C8—221no—
308C22⋊C8C22⋊D1112yescomplemented
309#95—21no—
310#95—21no—
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—41no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—442no—
337C2×D4—444no—
338C2×D4—441no—
339C2×D4—442no—
340C2×D4—442no—
341C2×D4—441no—
342C2×D4—882no—
343C2×D4—882no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—41no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—114no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—442no—
357C22×C4—442no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4C2×D4411yescharacteristic
363C22×C4#433911yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—222no—
371C2×C8—442no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—222no—
375C4⋊C4—221no—
376C4⋊C4—222no—
377C4⋊C4—221no—
378C4⋊C4—444no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—444no—
384C22⋊C4—444no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C11#996811yescharacteristic, complemented, Sylow
388C23—22no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23—441no—
397C23—442no—
398C23—442no—
399C23—441no—
400C23—441no—
401C23#6693511yescharacteristic
402C23#6693711yescharacteristic
403C23#6696412yes—
404C23SD16×D1112yes—
405C23#6699311yescharacteristic
406D4—42no—
407D4—81no—
408D4—81no—
409D4—81no—
410D4—82no—
411D4—442no—
412D4—881no—
413D4—888no—
414D4—881no—
415D4—881no—
416D4—882no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—44no—
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—444no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—882no—
439C2×C4—882no—
440C2×C4—881no—
441C2×C4—881no—
442C2×C4#6693511yescharacteristic
443C2×C4#6693711yescharacteristic
444C2×C4#6698311yescharacteristic
445C2×C4#6699011yescharacteristic
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#1062235512yes—
467C22#1062237512yes—
468C22#1062238912yes—
469C22#1062243511yescharacteristic
470C22#1062244011yescharacteristic
471C22#1062257311yescharacteristic
472C22#1062276711yescharacteristic
473C22#1062278811yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—81no—
480C4—444no—
481C4—882no—
482C4—881no—
483C2—21no—
484C2—21no—
485C2—22no—
486C2—161no—
487C2—1761no—
488C2#1306763712yes—
489C2#1306765412yes—
490C2#1306965911yescharacteristic
491C2#1306970511yescharacteristic
492C2#1306974611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11#120
prime radical#13074720C2
hypercenterC2×#327D11
hypocenterC11#9968
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
1. C2×#10622348C2semidirect
2. C2×#10622647C2semidirect
4. C2×#10622089C2semidirect
5. #13066883C2semidirect
6. #13066458C2semidirect
7. C2×C11×#327C2semidirect
62. C2×C4⋊Dic11D4semidirect
66. C11×C22⋊C8D4semidirect
74. C22⋊(C11⋊C8)D4semidirect
146. C2×#327D11semidirect
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×#106223482
C2×#106226472
#130747202
C2×#106220892
#130668832
#130664582
C2×C11×#3272
#996811