Finite Group Databasebeta

← #14808294

Subgroups — #14808294

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079163C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic
3#13073828C211yesmaximal, characteristic, complemented
4#13069830C214yesmaximal, complemented
5#13069561C211yesmaximal, characteristic, complemented
6#13069536C211yesmaximal, characteristic
7#13068849C214yesmaximal, complemented
8C4×#66900C211yesmaximal, characteristic, complemented
9C11×#3507C211yesmaximal, characteristic
10C11×#559—21no—
11C11×#557—21no—
12C11×#556—21no—
13C11×#556—22no—
14C11×#554—21no—
15C11×#552—22no—
16C11×#539—22no—
17C11×#536C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529—22no—
21C11×#520C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×#66901C2214yes—
25#10622845C2214yes—
26#10622843C2212yes—
27C2×#66900C2212yes—
28#10622694—21no—
29#10622692—21no—
30#10622691—21no—
31#10622683—21no—
32#10622678—22no—
33#10622668—22no—
34#10622608C2214yes—
35#10622599—22no—
36#10622590C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622542—22no—
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622170C2214yes—
42#10622168C2212yes—
43C2×C11×#41C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Dic22—21no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8D411yescharacteristic
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×#127D411yescharacteristic
51C11×#126—24no—
52C11×#126—24no—
53C11×#125—22no—
54C11×#125—24no—
55C11×#125D412yes—
56C11×#124—22no—
57C11×#124—22no—
58C11×#124D412yes—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×#121—21no—
67C11×#121—21no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—24no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C11×#117—24no—
82C11×#117—22no—
83C11×#117C2312yes—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C42×C11D412yes—
88C2×C42×C11C2311yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2312yes—
92C2×C4×Dic11C2312yes—
93C2×#4318C2312yes—
94C2×#4318C2312yes—
95#66922—21no—
96#66922—21no—
97#66922—21no—
98#66922—21no—
99#66901—28no—
100#66900—24no—
101#66899—24no—
102#66896—24no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—21no—
106#66872—24no—
107#66871—24no—
108#66867—21no—
109#66867—21no—
110C4×C11⋊C8—21no—
111C4×C11⋊C8—21no—
112#25696—111nomaximal, Sylow
113C11×#41—24no—
114C11×#41—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11—22no—
135C2×Dic22—44no—
136C2×Dic22—41no—
137C2×Dic22—41no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172C4×Dic11—24no—
173#4318—22no—
174#4318—22no—
175#4318—22no—
176#4318#4114yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179#3507D1111yescharacteristic
180#3165—111no—
181#3141—111no—
182#2568—111no—
183#2038—114no—
184#1986—111no—
185#1980—111no—
186#1860—114no—
187C4×#101—111no—
188C23×C11—22no—
189C23×C11C22×D411yescharacteristic
190Q8×C11—24no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—81no—
195D4×C11—24no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—81no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—84no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4112yes—
219C2×C4×C112−1+412yes—
220C2×Dic11—42no—
221C2×Dic11—44no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225Dic22—82no—
226Dic22—82no—
227C11⋊C8—24no—
228C11⋊C8—42no—
229#559—21no—
230#557—21no—
231#556—21no—
232#556—22no—
233#554—21no—
234#552—22no—
235#539—22no—
236#536C2×D1112yes—
237#533C2×D1111yescharacteristic
238#532C2×D1111yescharacteristic
239C2×C4⋊Q8—111no—
240#529—22no—
241#520C2×D1112yes—
242C2×C4×Q8C2×D1111yescharacteristic
243#501—222no—
244#500—221no—
245#498—221no—
246#489—222no—
247#487—221no—
248#486—221no—
249#428—114no—
250C2×#104—114no—
251#417—114no—
252C2×#101—112no—
253C4×M16—111no—
254C4×M16—111no—
255#400—222no—
256#391—112no—
257#391—222no—
258#382—112no—
259C4×C4⋊C4—111no—
260#343—112no—
261#339—114no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11C2×#12011yescharacteristic
268C22×C11#53211yescharacteristic
269C22×C11#53611yescharacteristic
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11#45412yes—
279C4×C11#54712yes—
280C4×C11#54812yes—
281Dic11—82no—
282Dic11—82no—
283C2×#41C22×D1112yes—
284C22×Q8—221no—
285C22×Q8C22×D1111yescharacteristic
286C2×M16—112no—
287C2×M16—112no—
288C4⋊Q8—22no—
289C4⋊Q8—221no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293C4⋊Q8C22⋊D1111yescharacteristic
294C4⋊Q8C22⋊D1111yescharacteristic
295C4⋊Q8C22⋊D1111yescharacteristic
296#127C22⋊D1111yescharacteristic
297#126—24no—
298#126—24no—
299#125—22no—
300#125—24no—
301#125C22⋊D1112yes—
302#124—22no—
303#124—22no—
304#124C22⋊D1112yes—
305#123—24no—
306#123—24no—
307C22⋊Q8—24no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312#121—21no—
313#121—21no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—24no—
325C4×D4—21no—
326C4×D4—21no—
327#117—24no—
328#117—22no—
329#117C22×D1112yes—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22⋊D1112yes—
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C42—112no—
337C2×C42C22⋊D1112yes—
338C2×C42C22×D1111yescharacteristic
339#107—224no—
340#106—224no—
341#104—228no—
342#103—224no—
343#102—224no—
344#101—224no—
345#97—221no—
346#97—221no—
347C4×C8—221no—
348C4×C8—221no—
349#95—221no—
350#95—224no—
351#95—224no—
352C2×C11—21no—
353C2×C11—21no—
354C2×C11—82no—
355C2×C11#243211yescharacteristic
356C2×C11C2×#45411yescharacteristic
357C2×C11#302211yescharacteristic
358#41—24no—
359#41—24no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—444no—
367C2×Q8—441no—
368C2×Q8—441no—
369C2×Q8C2×C22⋊D1112yes—
370C2×D4—22no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4C2×C22⋊D1112yes—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383M16—114no—
384M16—222no—
385M16—222no—
386M16—222no—
387C2×C8—222no—
388C2×C8—222no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—442no—
405C4⋊C4—441no—
406C4⋊C4—441no—
407C4⋊C4C2×C22⋊D1112yes—
408C4⋊C4C2×C22⋊D1112yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C42—24no—
416C42—22no—
417C42—22no—
418C42—22no—
419C42—224no—
420C42C2×C22⋊D1111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C42C2×C22⋊D1111yescharacteristic
423C42C2×C22⋊D1111yescharacteristic
424C11#2569611yescharacteristic, complemented, Sylow
425C23—22no—
426C23C22×C22⋊D1111yescharacteristic
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—81no—
432Q8—882no—
433Q8—882no—
434D4—24no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—81no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—84no—
451C2×C4—442no—
452C2×C4—444no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4#6700611yescharacteristic
457C2×C4#6700611yescharacteristic
458C2×C4#6700611yescharacteristic
459C2×C4#6700611yescharacteristic
460C2×C4#41×D1112yes—
461C2×C4#6704312yes—
462C2×C4C22×C22⋊D1111yescharacteristic
463C2×C4C22×C22⋊D1111yescharacteristic
464C8—224no—
465C8—442no—
466C22—21no—
467C22—21no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22#1062335611yescharacteristic
472C22#1062336311yescharacteristic
473C22C2×#6700611yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—882no—
483C4—882no—
484C4#1062285812yes—
485C4#1062335512yes—
486C4#1062336212yes—
487C2—21no—
488C2—21no—
489C2—82no—
490C2#1307224011yescharacteristic
491C2C2×#1062285811yescharacteristic
492C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3507C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3507D11
hypocenterC11#25696
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
3. #13073828C2semidirect
4. #13069830C2semidirect
5. #13069561C2semidirect
7. #13068849C2semidirect
8. C4×#66900C2semidirect
424. C11#25696semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130790092
#130738282
#130698302
#130695612
#130695362
#130688492
C4×#669002
C11×#35072
#2569611