Finite Group Databasebeta

← #14650810

Subgroups — #14650810

Order 2816.

576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 103 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#13071773C211yesmaximal, characteristic, complemented
2#13069453C211yesmaximal, characteristic, complemented
3#13067145C211yesmaximal, characteristic, complemented
4#13067132C211yesmaximal, characteristic, complemented
5#13066523C211yesmaximal, characteristic, complemented
6#13066470C211yesmaximal, characteristic, complemented
7C11×#3192C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C11×#481—21no—
11C11×#481C412yescomplemented
12C11×#469—22no—
13C11×#447—21no—
14C11×#447C412yescomplemented
15C11×#407C2211yescharacteristic
16#10622834—21no—
17#10622833—21no—
18#10622833—21no—
19C2×#66898—21no—
20C2×#66898—21no—
21#10622825C2211yescharacteristic
22#10622824C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24#10622820C2211yescharacteristic
25#10622594—21no—
26#10622564—21no—
27#10622563—21no—
28#10622175—22no—
29#10622175—21no—
30#10622175—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11C2×C411yescharacteristic, complemented
34C22×D4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C2×C11×D8—22no—
38C2×C11×M16—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121C2×C412yes—
46C11×#121D412yes—
47C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11D411yescharacteristic
57C2×C22⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C2×#4318—21no—
63C11×#106—22no—
64C11×#102—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8C2×C412yescomplemented
68#66898—42no—
69#66898—42no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95D411yescharacteristic
76C11⋊#95D411yescharacteristic
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79#9343—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11C2×D411yescharacteristic
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—81no—
95C2×D4×C11—81no—
96C2×D4×C11—81no—
97C2×D4×C11—81no—
98C2×D4×C11C22⋊C412yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—81no—
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—41no—
113C22×Dic11—81no—
114C22×Dic11—81no—
115C22×Dic11—81no—
116C11×D8—82no—
117C11×M16—81no—
118C2×C8×C11—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4C22⋊C412yes—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C22⋊Dic11—22no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131C22⋊Dic11—81no—
132C22⋊Dic11—81no—
133C22⋊Dic11—81no—
134C22⋊Dic11—81no—
135C4⋊Dic11—81no—
136C4⋊Dic11—81no—
137C4×Dic11—81no—
138C4×Dic11—81no—
139#4318—81no—
140C2×C11⋊C8—41no—
141#3192D1111yescharacteristic
142#2377—111no—
143#1964—111no—
144#1510—111no—
145#1507—111no—
146#1305—111no—
147#1284—111no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—22no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11C4×D411yescharacteristic
165C23×C11#12011yescharacteristic
166C23×C11#12111yescharacteristic
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—82no—
172D4×C11—82no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
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×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12311yescharacteristic
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11—84no—
209C8×C11—42no—
210C11⋊C8—81no—
211C2×#121C2×D1111yescharacteristic
212C2×#121C2×D1111yescharacteristic
213#481—21no—
214#481Dic1112yescomplemented
215#469—22no—
216#447—21no—
217#447Dic1112yescomplemented
218C2×#99—221no—
219C2×#99—221no—
220#407—111no—
221#407C2×D1111yescharacteristic
222#390—221no—
223#388—221no—
224#387—221no—
225#386—221no—
226#386—221no—
227#385—221no—
228#381—111no—
229#380—111no—
230C4×C22⋊C4—111no—
231#327—221no—
232#327—221no—
233#327—222no—
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—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—161no—
255C22×C11—161no—
256C22×C11#38611yescharacteristic
257C22×C11#45311yescharacteristic
258C22×C11#45411yescharacteristic
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—81no—
265Dic11—81no—
266Dic11—81no—
267Dic11—81no—
268Dic11—81no—
269Dic11—82no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4C2×Dic1111yescharacteristic, complemented
273C22×D4C22⋊D1111yescharacteristic
274C23×C4—221no—
275C23×C4C22×D1111yescharacteristic
276C2×D8—22no—
277C2×M16—21no—
278C2×M16—221no—
279#121—21no—
280#121—21no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121C2×Dic1112yes—
286#121C22⋊D1112yes—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
290C2×C4⋊C4C22⋊D1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C42—221no—
301C2×C42—221no—
302#106—22no—
303#102—22no—
304#102—22no—
305#99—442no—
306#99—442no—
307C22⋊C8—21no—
308C22⋊C8—221no—
309C22⋊C8—221no—
310C22⋊C8C2×Dic1112yescomplemented
311#95—111no—
312#95—111no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95—221no—
317#95—221no—
318C2×C11—21no—
319C2×C11—21no—
320C2×C11—41no—
321C2×C11—41no—
322C2×C11—82no—
323C2×C11—161no—
324C2×C11#188311yescharacteristic
325C2×C11#190411yescharacteristic
326C2×C11#191311yescharacteristic
327C24—21no—
328C24—21no—
329C24D4×D1111yescharacteristic
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—81no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4C22⋊Dic1112yes—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—81no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—441no—
354C22×C4—881no—
355C22×C4—881no—
356C22×C4—881no—
357C22×C4D4×D1111yescharacteristic
358C22×C4#434111yescharacteristic
359C22×C4#434111yescharacteristic
360C22×C4C22×Dic1111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363D8—82no—
364M16—81no—
365M16—881no—
366C2×C8—22no—
367C2×C8—441no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—881no—
372C4⋊C4—881no—
373C4⋊C4C22⋊Dic1112yes—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—222no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—881no—
383C22⋊C4—881no—
384C22⋊C4—881no—
385C22⋊C4—881no—
386C42—881no—
387C42—881no—
388C11#934311yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—22no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23D4×Dic1111yescharacteristic
406C23#6699011yescharacteristic
407C23#6699211yescharacteristic
408D4—42no—
409D4—42no—
410D4—81no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
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—441no—
442C2×C4—441no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—884no—
446C2×C4D4×Dic1111yescharacteristic
447C2×C4#6698811yescharacteristic
448C2×C4#6699211yescharacteristic
449C2×C4C2×C22⋊Dic1111yescharacteristic
450C8—42no—
451C8—881no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—161no—
473C22—161no—
474C22#1062281111yescharacteristic
475C22#1062281411yescharacteristic
476C22#1062283311yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—81no—
483C4—881no—
484C4—881no—
485C4—881no—
486C4—881no—
487C4—882no—
488C2—21no—
489C2—21no—
490C2—41no—
491C2—41no—
492C2—82no—
493C2—161no—
494C2#1306899411yescharacteristic
495C2#1306910511yescharacteristic
496C2#1306915911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3192C2
socleC22×C11#386
cosocleC23×C4×C11C23
hypercenter#3192D11
hypocenterC11#9343
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3192

Complements

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

NH ≅ G/Ntype
1. #13071773C2semidirect
2. #13069453C2semidirect
3. #13067145C2semidirect
4. #13067132C2semidirect
5. #13066523C2semidirect
6. #13066470C2semidirect
11. C11×#481C4semidirect
14. C11×#447C4semidirect
33. C22×D4×C11C2×C4semidirect
47. C2×C11×C4⋊C4C2×C4semidirect
67. C11×C22⋊C8C2×C4semidirect
214. #481Dic11semidirect
217. #447Dic11semidirect
272. C22×D4C2×Dic11semidirect
289. C2×C4⋊C4C2×Dic11semidirect
310. C22⋊C8C2×Dic11semidirect
388. C11#9343semidirect

Maximal subgroups

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

subgroupindex
#130717732
#130694532
#130671452
#130671322
#130665232
#130664702
C11×#31922
#934311