Finite Group Databasebeta

← #14672093

Subgroups — #14672093

Order 2816.

540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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#13073616C211yesmaximal, characteristic
2C2×#10622180C211yesmaximal, characteristic, complemented
3C2×#10622115C211yesmaximal, characteristic, complemented
4C2×#10622115C211yesmaximal, characteristic, complemented
5#13068610C211yesmaximal, characteristic, complemented
6#101×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#355C211yesmaximal, characteristic, complemented
8C2×C11×#124C2211yescharacteristic
9C2×#67000C2211yescharacteristic
10C2×Q8×Dic11C2211yescharacteristic
11C2×#66993C411yescharacteristic
12C2×C11×#101C2211yescharacteristic
13C2×C11×#101C2211yescharacteristic
14C2×#66900C2211yescharacteristic
15C2×#66900C2211yescharacteristic
16#10622834C411yescharacteristic
17#10622731—21no—
18M16×Dic11—21no—
19#10622574—21no—
20#10622574—21no—
21#10622570—21no—
22#10622570—21no—
23#10622552C411yescharacteristic
24C4×Dic11⋊C4C411yescharacteristic
25C11×#355—22no—
26#10622192—21no—
27#10622192—21no—
28#10622180—22no—
29#10622115—22no—
30#10622115—22no—
31C22×Q8×C11C2311yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C22×C22⋊D11—21no—
34C22×C22⋊D11—21no—
35C22×D44C2×C411yescharacteristic
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C11×#124—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47#67000—21no—
48#67000—21no—
49#67000—21no—
50#67000—21no—
51Q8×Dic11—41no—
52Q8×Dic11—41no—
53#66993—41no—
54#66993—41no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D411yescharacteristic
62C2×Dic11⋊C4—21no—
63C2×C4×Dic11C2×C411yescharacteristic
64C2×C4×Dic11C2×C411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×#4318—21no—
68C2×#4318—21no—
69C11×#101—21no—
70C11×#101—21no—
71C11×#101—21no—
72C11×#101D412yescomplemented
73#66900—21no—
74#66900—21no—
75#66900—21no—
76#66900D412yescomplemented
77C11⋊#95—21no—
78#66879—41no—
79Dic11⋊C8—41no—
80Dic11⋊C8—41no—
81C8×Dic11—41no—
82#13226—111nomaximal, Sylow
83C24×C11—21no—
84C23×D11—21no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11C2×D411yescharacteristic
88C2×Q8×C11C2×D411yescharacteristic
89C2×Q8×C11#4111yescharacteristic
90C2×Q8×C11#4111yescharacteristic
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C22×C4×C11—21no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—42no—
100C2×C22⋊D11—42no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—81no—
105C2×C22⋊D11—81no—
106C22×Dic11—21no—
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C22×Dic11C22⋊C411yescharacteristic
110C22×Dic11C22⋊C411yescharacteristic
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—41no—
114C2×D44—41no—
115C11×M16—22no—
116C11×M16—41no—
117C11×M16—41no—
118C11×M16—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—21no—
126C42×C11—21no—
127C22⋊Dic11—81no—
128C22⋊Dic11—81no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—81no—
134(C2×D11)⋊C4—81no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138Dic11⋊C4—42no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—21no—
146C4×Dic11—21no—
147#4318—22no—
148#4318—41no—
149#4318—41no—
150#4318—41no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153#2548—111no—
154C2×#355—111no—
155C2×#355—111no—
156C2×#355—111no—
157C2×#355D1111yescharacteristic, complemented
158#1801—111no—
159C4×#101—111no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11C2×C22⋊C411yescharacteristic
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—41no—
176Q8×C11—41no—
177Q8×C11—41no—
178Q8×C11—41no—
179D4×C11—81no—
180D4×C11—81no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12411yescharacteristic
195C2×C4×C11#12711yescharacteristic
196C22⋊D11—82no—
197C22⋊D11—84no—
198C22⋊D11—82no—
199C2×Dic11—22no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11#9911yescharacteristic
210C2×Dic11#9911yescharacteristic
211D44—81no—
212D44—81no—
213C8×C11—42no—
214C8×C11—81no—
215C11⋊C8—42no—
216C11⋊C8—81no—
217C2×#127—111no—
218C2×#124—111no—
219C2×#124C2×D1111yescharacteristic
220C2×C4×Q8—111no—
221#423—221no—
222C2×#101—111no—
223C2×#101—111no—
224C2×#101C2×D1111yescharacteristic
225C2×#101C2×D1111yescharacteristic
226C4×M16—221no—
227#394—221no—
228#394—221no—
229#390—111no—
230#390—111no—
231#390—221no—
232#390—221no—
233C4×C4⋊C4—111no—
234#355—22no—
235#355—222no—
236#355—222no—
237#355—222no—
238#343—221no—
239#343—221no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11#39011yescharacteristic
250C22×C11C2×#9911yescharacteristic
251C22×C11#41011yescharacteristic
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—81no—
266Dic11—21no—
267Dic11—41no—
268Dic11—41no—
269Dic11—41no—
270Dic11—81no—
271Dic11#35512yescomplemented
272C22×Q8C22×D1111yescharacteristic
273C22×D4—111no—
274C22×D4—221no—
275C22×D4—221no—
276C22×D4C4×D1111yescharacteristic
277C2×M16—21no—
278C2×M16—21no—
279C2×M16—221no—
280C2×M16—221no—
281#127—441no—
282#127—441no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—221no—
288#124—221no—
289#124—221no—
290#124—221no—
291C4×Q8—441no—
292C4×Q8—441no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—221no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C22⋊C4—221no—
304C2×C22⋊C4—221no—
305C2×C42—111no—
306C2×C42—111no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42C4×D1111yescharacteristic
310C4⋊C8—441no—
311C4⋊C8—441no—
312#101—21no—
313#101—21no—
314#101—21no—
315#101—112no—
316#101—221no—
317#101—221no—
318#101—221no—
319#101C22⋊D1112yescomplemented
320#97—441no—
321C4×C8—441no—
322#95—221no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—161no—
326C2×C11#196411yescharacteristic
327C2×C11C2×#35511yescharacteristic
328C2×C11#213411yescharacteristic
329D11—161no—
330C24—21no—
331C24—221no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8#433911yescharacteristic
335C2×Q8D4×D1111yescharacteristic
336C2×Q8#434111yescharacteristic
337C2×Q8C2×C22⋊D1111yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—442no—
349C2×D4—442no—
350C2×D4—442no—
351C2×D4—881no—
352C2×D4—881no—
353C22×C4—21no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—221no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4D4×D1111yescharacteristic
362M16—22no—
363M16—41no—
364M16—41no—
365M16—41no—
366M16—222no—
367M16—441no—
368M16—441no—
369M16—441no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—441no—
373C2×C8—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—442no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—881no—
387C22⋊C4—881no—
388C22⋊C4—881no—
389C22⋊C4—881no—
390C42—21no—
391C42—21no—
392C42—221no—
393C42—221no—
394C42—221no—
395C42—221no—
396C42—221no—
397C42—221no—
398C42—221no—
399C42—221no—
400C11#1322611yescharacteristic, complemented, Sylow
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23C22⋊C4×D1111yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420D4—81no—
421D4—81no—
422D4—881no—
423D4—881no—
424D4—882no—
425D4—882no—
426D4—884no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—222no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4(C22⋊D11)⋊C411yescharacteristic
449C2×C4#6693711yescharacteristic
450C2×C4#6693811yescharacteristic
451C2×C4C4×C22⋊D1111yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4#6699311yescharacteristic
454C8—42no—
455C8—81no—
456C8—442no—
457C8—881no—
458C22—21no—
459C22—21no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22#1062235311yescharacteristic
475C22D11×#9911yescharacteristic
476C22#1062257011yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—112no—
485C4—221no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—881no—
490C2—21no—
491C2—21no—
492C2—161no—
493C2—1761no—
494C2#1306945011yescharacteristic
495C2D11×#35511yescharacteristic
496C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#355C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC22×Q8×C11C23
hypercenterC2×#355D11
hypocenterC11#13226
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
2. C2×#10622180C2semidirect
3. C2×#10622115C2semidirect
4. C2×#10622115C2semidirect
5. #13068610C2semidirect
6. #101×Dic11C2semidirect
7. C2×C11×#355C2semidirect
72. C11×#101D4semidirect
76. #66900D4semidirect
157. C2×#355D11semidirect
271. Dic11#355semidirect
319. #101C22⋊D11semidirect
400. C11#13226semidirect

Maximal subgroups

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

subgroupindex
#130736162
C2×#106221802
C2×#106221152
#130686102
#101×Dic112
C2×C11×#3552
#1322611