Finite Group Databasebeta

← #14657013

Subgroups — #14657013

Order 2816.

594 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 75 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#13074283C211yesmaximal, characteristic, complemented
2#13068560C211yesmaximal, characteristic
3#13068534C211yesmaximal, characteristic
4#13066525C211yesmaximal, characteristic, complemented
5#13066470C211yesmaximal, characteristic, complemented
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1789C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×C11×#104—21no—
10C2×C11×#104—21no—
11C11×#407C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C2×#66901—21no—
14C2×#66901—21no—
15C2×#66898—21no—
16C2×#66898—21no—
17#10622824C2211yescharacteristic
18#10622824C2211yescharacteristic
19C4×C22⋊Dic11C2211yescharacteristic
20#10622820C2211yescharacteristic
21#10622561—21no—
22#10622561—21no—
23#10622546—21no—
24#10622541—21no—
25#10622268—21no—
26#10622260—21no—
27C2×C11×#41—21no—
28C2×C11×#41—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—42no—
32C2×C11×#41—42no—
33C22×Q8×C11Q811yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11Q811yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11C2311yescharacteristic
38C2×C11×M16—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11D411yescharacteristic
45C2×C22⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11D411yescharacteristic
53C2×C4×Dic11D411yescharacteristic
54C2×#4318—21no—
55C11×#104—42no—
56C11×#104—42no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60#66901—42no—
61#66901—42no—
62#66898—42no—
63#66898—42no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#10388—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11C2×D411yescharacteristic
76C11×#41—22no—
77C11×#41—22no—
78C11×#41—22no—
79C11×#41—22no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—42no—
85C11×#41—42no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—42no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×Q811yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—41no—
120C11×M16—41no—
121C11×M16—41no—
122C2×C8×C11—41no—
123C11×C22⋊C4—42no—
124C42×C11—41no—
125C42×C11—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—42no—
131C4⋊Dic11—42no—
132C4⋊Dic11—81no—
133Dic11⋊C4—42no—
134Dic11⋊C4—42no—
135Dic11⋊C4—42no—
136Dic11⋊C4—81no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139#4318—41no—
140#4318—41no—
141C2×C11⋊C8—41no—
142#2608—111no—
143#1789—111no—
144#1789D1111yescharacteristic
145#1782—111no—
146#1306—111no—
147#1284—111no—
148#1284—111no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11#12011yescharacteristic
159C23×C11C22⋊Q811yescharacteristic
160C23×C11#12411yescharacteristic
161Q8×C11—22no—
162Q8×C11—22no—
163Q8×C11—41no—
164Q8×C11—41no—
165D4×C11—22no—
166D4×C11—22no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11C22⋊Q811yescharacteristic
195C2×C4×C11C22⋊Q811yescharacteristic
196C2×C4×C11#12411yescharacteristic
197C2×C4×C11#12411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—81no—
211C2×Dic11—81no—
212C2×Dic11—81no—
213C8×C11—81no—
214C11⋊C8—81no—
215C22×#41C2×D1111yescharacteristic
216C2×#104—21no—
217C2×#104—21no—
218C2×#104—221no—
219C2×#104—221no—
220C2×#99—221no—
221C2×#99—221no—
222#407—111no—
223#407C2×D1111yescharacteristic
224#396—221no—
225#396—221no—
226#389—221no—
227#389—221no—
228#387—221no—
229#387—221no—
230#381—111no—
231#381—111no—
232C4×C22⋊C4—111no—
233C4×C22⋊C4C2×D1111yescharacteristic
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—81no—
244C22×C11—81no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11#39311yescharacteristic
250C22×C11B(4,𝔽2)11yescharacteristic
251C22×C11B(4,𝔽2)11yescharacteristic
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—81no—
259Dic11—42no—
260Dic11—81no—
261Dic11—81no—
262Dic11—81no—
263Dic11—161no—
264C2×#41—21no—
265C2×#41—21no—
266C2×#41—21no—
267C2×#41—21no—
268C2×#41—42no—
269C2×#41—42no—
270C22×Q8Dic2211yescharacteristic
271C22×D4—21no—
272C22×D4Dic2211yescharacteristic
273C23×C4—21no—
274C23×C4C22×D1111yescharacteristic
275C2×M16—21no—
276C2×M16—221no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C42—111no—
289C2×C42—111no—
290C2×C42C22⋊D1111yescharacteristic
291C2×C42C22⋊D1111yescharacteristic
292#104—42no—
293#104—42no—
294#104—442no—
295#104—442no—
296#99—442no—
297#99—442no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—221no—
301C22⋊C8—221no—
302#95—21no—
303#95—221no—
304#95—221no—
305#95—221no—
306#95—221no—
307#95—221no—
308#95—221no—
309#95—221no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—41no—
313C2×C11—41no—
314C2×C11—82no—
315C2×C11#202911yescharacteristic
316C2×C11#203111yescharacteristic
317C2×C11#203111yescharacteristic
318C24—21no—
319C24D4×D1111yescharacteristic
320#41—22no—
321#41—22no—
322#41—22no—
323#41—22no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—42no—
329#41—42no—
330#41—42no—
331#41—42no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—42no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—441no—
358C22×C4C2×Dic2211yescharacteristic
359C22×C4#433911yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4#434111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364M16—41no—
365M16—41no—
366M16—441no—
367M16—441no—
368C2×C8—41no—
369C2×C8—441no—
370C4⋊C4—442no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4—881no—
375C4⋊C4—881no—
376C22⋊C4—42no—
377C22⋊C4—442no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C42—41no—
383C42—41no—
384C42—441no—
385C42—441no—
386C11#1038811yescharacteristic, complemented, Sylow
387C23—21no—
388C23—21no—
389C23—22no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—81no—
395C23—81no—
396C23#6693111yescharacteristic
397C23#6693811yescharacteristic
398C23#6699011yescharacteristic
399Q8—22no—
400Q8—22no—
401Q8—41no—
402Q8—41no—
403D4—22no—
404D4—22no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—222no—
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—441no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4#6693111yescharacteristic
448C2×C4#6693811yescharacteristic
449C2×C4#6697711yescharacteristic
450C2×C4#6698911yescharacteristic
451C8—81no—
452C8—881no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—81no—
463C22—81no—
464C22—82no—
465C22—82no—
466C22—81no—
467C22—81no—
468C22#1062256011yescharacteristic
469C22#1062264511yescharacteristic
470C22#1062264511yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—442no—
479C4—881no—
480C4—881no—
481C4—881no—
482C4—1761no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—41no—
487C2—82no—
488C2#1306978011yescharacteristic
489C2#1306978611yescharacteristic
490C2#1306978811yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1789C2
socleC22×C11#393
prime radicalC22×C11×#41C22
hypercenter#1789D11
hypocenterC11#10388
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #13074283C2semidirect
4. #13066525C2semidirect
5. #13066470C2semidirect
6. #13066469C2semidirect
386. C11#10388semidirect

Maximal subgroups

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

subgroupindex
#130742832
#130685602
#130685342
#130665252
#130664702
#130664692
C11×#17892
#1038811