Finite Group Databasebeta

← #14651097

Subgroups — #14651097

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077642C211yesmaximal, characteristic
2#13073796C211yesmaximal, characteristic
3#13068601C211yesmaximal, characteristic
4#13067189C211yesmaximal, characteristic, complemented
5#13067187C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622826—21no—
14#10622825—21no—
15#10622825C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622724—22no—
18C2×#66870—21no—
19#10622343—22no—
20#10622339—21no—
21#10622332—21no—
22#10622290C411yescharacteristic, complemented
23#10622286C411yescharacteristic, complemented
24#10622281—21no—
25#10622272C411yescharacteristic, complemented
26#10622269C411yescharacteristic, complemented
27#10622266—21no—
28#10622165—21no—
29#10622105—22no—
30#10622090—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11D411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×Dic22C2×C411yescharacteristic
36C22×C8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45C4×C22⋊D11—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4C2×C411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53#66977—21no—
54#66977—21no—
55#66977—21no—
56#66977—21no—
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4C2×C411yescharacteristic
59C2×C4×Dic11D411yescharacteristic
60C22×C11⋊C8—21no—
61C2×#4313—22no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8D412yes—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95C2×C411yescharacteristic
67C11×#95C2×C411yescharacteristic
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yes—
75(C2×D11)⋊C8—22no—
76#66879—22no—
77Dic11⋊C8—22no—
78#66870—42no—
79#9385—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11C22⋊C411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—81no—
89C22×C4×C11—81no—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—21no—
97C2×C22⋊D11—21no—
98C2×C22⋊D11—21no—
99C2×C22⋊D11—21no—
100C2×C22⋊D11—21no—
101C2×C22⋊D11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—41no—
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—81no—
111C2×Dic22—21no—
112C2×Dic22—21no—
113C2×Dic22—81no—
114C2×C8×C11—22no—
115C2×C8×C11—81no—
116C11×C4⋊C4—81no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C22⋊Dic11—21no—
120C22⋊Dic11—21no—
121C22⋊Dic11—41no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124C22⋊Dic11—41no—
125(C2×D11)⋊C4—21no—
126(C2×D11)⋊C4—21no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—81no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—42no—
132C4⋊Dic11—81no—
133C4⋊Dic11—81no—
134Dic11⋊C4—21no—
135Dic11⋊C4—21no—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—81no—
142#4313—82no—
143#2973—111no—
144#2564—111no—
145#1799—111no—
146#1520—111no—
147#1520—111no—
148#1294—111no—
149#1294D1111yescharacteristic, complemented
150C23×C11—41no—
151C23×C11—41no—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11#12111yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11AGL(1,ℤ/8)11yescharacteristic
156C23×C11#13711yescharacteristic
157C23×C11#13711yescharacteristic
158C23×C11#13711yescharacteristic
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—41no—
163C22×D11—41no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
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—41no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11C4×D411yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12311yescharacteristic
185C22⋊D11—41no—
186C22⋊D11—41no—
187C22⋊D11—41no—
188C22⋊D11—41no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
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—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C4×D11—42no—
206C4×D11—81no—
207Dic22—81no—
208Dic22—81no—
209C8×C11—42no—
210C11⋊C8—42no—
211C2×C22⋊Q8—111no—
212C2×C4×D4—111no—
213#435—222no—
214#435—222no—
215#432—221no—
216C2×#99—221no—
217#407—221no—
218C2×C22⋊C8—111no—
219C2×C22⋊C8C2×D1111yescharacteristic
220#400—111no—
221#399—111no—
222#395—111no—
223#393—111no—
224#387—221no—
225#386—221no—
226#385—221no—
227#380—111no—
228#380—221no—
229#380C2×D1111yescharacteristic
230C2×#95C2×D1111yescharacteristic
231#342—221no—
232#328—222no—
233#328—222no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11#38611yescharacteristic
245C22×C11#41711yescharacteristic
246C22×C11#41911yescharacteristic
247C22×C11#46811yescharacteristic
248C22×C11#46811yescharacteristic
249C22×C11#47011yescharacteristic
250C22×C11#47011yescharacteristic
251C2×D11—42no—
252C2×D11—41no—
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—81no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11—161no—
263Dic11—41no—
264Dic11—41no—
265Dic11—41no—
266Dic11—81no—
267Dic11—81no—
268Dic11—161no—
269C22×Q8—111no—
270C22×D4—111no—
271C23×C4—21no—
272C23×C4—111no—
273C23×C4C22×D1111yescharacteristic
274C2×M16—222no—
275C22×C8—21no—
276C22×C8—221no—
277C22⋊Q8—221no—
278C22⋊Q8—221no—
279C22⋊Q8—221no—
280C22⋊Q8—221no—
281C4×D4—221no—
282C4×D4—221no—
283C4×D4—221no—
284C4×D4—221no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
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×C42—111no—
300C4⋊C8—222no—
301#99—442no—
302C22⋊C8—21no—
303C22⋊C8—112no—
304C22⋊C8—222no—
305C22⋊C8—221no—
306C22⋊C8D4412yes—
307#97—222no—
308#95—21no—
309#95—21no—
310#95—221no—
311#95—221no—
312#95—221no—
313#95—221no—
314#95—221no—
315#95C4×D1111yescharacteristic
316#95C4×D1111yescharacteristic
317C2×C11—21no—
318C2×C11—21no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11#188411yescharacteristic
324C2×C11#189411yescharacteristic
325C2×C11#191311yescharacteristic
326D11—81no—
327C24—111no—
328C24D4×D1111yescharacteristic
329C2×Q8—221no—
330C2×Q8—221no—
331C2×Q8—881no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—81no—
345C22×C4—81no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—441no—
354C22×C4—881no—
355C22×C4C2×C4×D1111yescharacteristic
356C22×C4C2×D4411yescharacteristic
357C22×C4#433911yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4#434311yescharacteristic
361M16—882no—
362C2×C8—22no—
363C2×C8—81no—
364C2×C8—222no—
365C2×C8—881no—
366C4⋊C4—81no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—442no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—881no—
375C4⋊C4—881no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—221no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—442no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—881no—
388C42—221no—
389C42—221no—
390C11#938511yescharacteristic, complemented, Sylow
391C23—41no—
392C23—41no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—441no—
397C23—441no—
398C23C22⋊C4×D1111yescharacteristic
399C23#6693711yescharacteristic
400C23#6694811yescharacteristic
401C23#6696411yescharacteristic
402C23#6696811yescharacteristic
403C23#6696811yescharacteristic
404C23#6697111yescharacteristic
405Q8—881no—
406Q8—881no—
407D4—441no—
408D4—441no—
409D4—441no—
410D4—441no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—442no—
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—881no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4C4×D4411yescharacteristic
447C2×C4#6693511yescharacteristic
448C2×C4#6694611yescharacteristic
449C2×C4#6694711yescharacteristic
450C8—42no—
451C8—442no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—442no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—881no—
467C22#1062227811yescharacteristic
468C22#1062238411yescharacteristic
469C22#1062239311yescharacteristic
470C22#1062241511yescharacteristic
471C22#1062242911yescharacteristic
472C22#1062248111yescharacteristic
473C22#1062249911yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—81no—
480C4—161no—
481C4—441no—
482C4—441no—
483C4—441no—
484C4—881no—
485C4—881no—
486C4—1761no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—881no—
494C2#1306899811yescharacteristic
495C2#1306904811yescharacteristic
496C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC22×C11#386
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9385
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #13067189C2semidirect
5. #13067187C2semidirect
6. #13066495C2semidirect
7. C11×#1294C2semidirect
22. #10622290C4semidirect
23. #10622286C4semidirect
25. #10622272C4semidirect
26. #10622269C4semidirect
149. #1294D11semidirect
390. C11#9385semidirect

Maximal subgroups

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

subgroupindex
#130776422
#130737962
#130686012
#130671892
#130671872
#130664952
C11×#12942
#938511