Finite Group Databasebeta

← #14648943

Subgroups — #14648943

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic
2#13071351C211yesmaximal, characteristic
3#13068707C211yesmaximal, characteristic
4#13066883C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622843—21no—
13C2×#66899—21no—
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622657—22no—
20#10622657C414yescomplemented
21#10622598—21no—
22#10622594—21no—
23#10622594—21no—
24C2×#66871—21no—
25#10622563—21no—
26C22⋊C4×Dic11—21no—
27C11×#328—22no—
28#10622189—21no—
29#10622189—21no—
30C22×Q8×C11D411yescharacteristic
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C23×Dic11D411yescharacteristic
36C22×C8×C11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8C2×C412yes—
40C11×C22⋊Q8D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11C2×C412yes—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4×Dic11—21no—
56C2×C4×Dic11—21no—
57C22×C11⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62#66899—24no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)C2×C412yes—
74#66871—24no—
75#9046—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11C22⋊C412yes—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11Q1612yes—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4C22⋊C412yes—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—22no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—81no—
135C4⋊Dic11—81no—
136C4×Dic11—81no—
137C4×Dic11—81no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141C2×#484—111no—
142#2329—111no—
143#1824—111no—
144C2×#328D1111yescharacteristic
145#1445—111no—
146#1294—111no—
147#1280—111no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11C4×D411yescharacteristic
153C23×C11#12011yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11C2×Q1611yescharacteristic
156C23×C11#13511yescharacteristic
157C23×C11#13711yescharacteristic
158C23×C11#13711yescharacteristic
159Q8×C11—42no—
160Q8×C11—81no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C2×Dic11—22no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C8×C11—81no—
210C11⋊C8—42no—
211C2×C22⋊Q8C2×D1111yescharacteristic
212C22×C4⋊C4—111no—
213#484—114no—
214#484—222no—
215C2×#107—221no—
216C2×#103—221no—
217C2×C22⋊C8—111no—
218C2×C22⋊C8C2×D1111yescharacteristic
219#391—221no—
220#389—221no—
221#387—221no—
222#387—221no—
223#385—221no—
224#380—111no—
225C4×C22⋊C4—221no—
226C2×#95—111no—
227C2×#95—221no—
228C2×#95—221no—
229C2×#95C2×D1111yescharacteristic
230#340—221no—
231#340—221no—
232#328—22no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11#38611yescharacteristic
246C22×C11C4×Q1611yescharacteristic
247C22×C11#44111yescharacteristic
248C22×C11#45111yescharacteristic
249C22×C11#45211yescharacteristic
250C22×C11#45311yescharacteristic
251C22×C11#45411yescharacteristic
252C22×C11#45811yescharacteristic
253C22×C11#45811yescharacteristic
254C22×C11#46211yescharacteristic
255C22×C11#46411yescharacteristic
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—82no—
263Dic11—42no—
264Dic11—81no—
265Dic11—81no—
266Dic11—81no—
267Dic11—82no—
268C22×Q8D4411yescharacteristic
269C23×C4—21no—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—221no—
273C23×C4C22×D1111yescharacteristic
274C22×C8—21no—
275C22×C8—221no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8C4×D1112yes—
279C22⋊Q8C22⋊D1112yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4D4411yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—221no—
294C2×C42—221no—
295C2×C42—221no—
296#107—224no—
297#103—224no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—112no—
301C22⋊C8—221no—
302#95—21no—
303#95—21no—
304#95—221no—
305#95—221no—
306#95—221no—
307#95—221no—
308#95—221no—
309#95—221no—
310#95—221no—
311#95—442no—
312#95—442no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11#161411yescharacteristic
318C2×C11#161511yescharacteristic
319C2×C11#161711yescharacteristic
320C2×C11#161811yescharacteristic
321C2×C11#187811yescharacteristic
322C2×C11#188311yescharacteristic
323C2×C11#189011yescharacteristic
324C24D4×D1111yescharacteristic
325C2×Q8—21no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8(C2×D11)⋊C412yes—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—112no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—222no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4#434111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—222no—
369C2×C8—441no—
370C2×C8—441no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—881no—
381C4⋊C4—881no—
382C4⋊C4(C2×D11)⋊C412yes—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—881no—
388C42—881no—
389C11#904611yescharacteristic, complemented, Sylow
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23(C22⋊D11)⋊C411yescharacteristic
395C23#6693511yescharacteristic
396C23#6696811yescharacteristic
397C23#6696911yescharacteristic
398C23Q16×D1111yescharacteristic
399C23#6697111yescharacteristic
400C23#6699211yescharacteristic
401Q8—42no—
402Q8—81no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—222no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—881no—
442C2×C4—881no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4(C22⋊D11)⋊C411yescharacteristic
448C2×C4#6693911yescharacteristic
449C2×C4C2×(C2×D11)⋊C411yescharacteristic
450C2×C4#6699211yescharacteristic
451C8—81no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22#1062235511yescharacteristic
466C22#1062235511yescharacteristic
467C22#1062240211yescharacteristic
468C22#1062240311yescharacteristic
469C22#1062242111yescharacteristic
470C22#1062242311yescharacteristic
471C22#1062243511yescharacteristic
472C22#1062244011yescharacteristic
473C22#1062257111yescharacteristic
474C22#1062277911yescharacteristic
475C22#1062279511yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—42no—
481C4—42no—
482C4—82no—
483C4—442no—
484C4—881no—
485C4—881no—
486C4—881no—
487C4—882no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2#1306764211yescharacteristic
493C2#1306765011yescharacteristic
494C2#1306765911yescharacteristic
495C2#1306766711yescharacteristic
496C2#1306895511yescharacteristic
497C2#1306899011yescharacteristic
498C2#1306902711yescharacteristic
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11#120
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9046
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
20. #10622657C4semidirect
389. C11#9046semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130713512
#130687072
#130668832
#130664952
#130664582
C2×C11×#3282
#904611