Finite Group Databasebeta

← #14652793

Subgroups — #14652793

Order 2816.

596 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
1#13076971C211yesmaximal, characteristic
2#13068470C211yesmaximal, characteristic, complemented
3#13068364C211yesmaximal, characteristic, complemented
4C2×#10622178C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic, complemented
6C2×#10622102C211yesmaximal, characteristic, complemented
7C2×C11×#329C211yesmaximal, characteristic, complemented
8C2×C11×#124C2211yescharacteristic
9C2×#67000C411yescharacteristic
10C2×#66997C411yescharacteristic
11C2×#66993C411yescharacteristic
12C2×#66989C411yescharacteristic
13C2×#66928C2211yescharacteristic
14C2×C11×#97C2211yescharacteristic
15C2×C11×#97C2211yescharacteristic
16C2×Dic11⋊C8—21no—
17#10622570—21no—
18#10622570—21no—
19#10622570—21no—
20#10622570—21no—
21C42×Dic11C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24C11×#329—22no—
25#10622188—21no—
26#10622188—21no—
27#10622188—21no—
28#10622178—22no—
29#10622102—22no—
30#10622102—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C22×C22⋊D11—21no—
34C22×C22⋊D11—21no—
35C22×D44C2×C411yescharacteristic
36C22×Dic22C2×C411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48#67000—42no—
49#66997—42no—
50#66993—42no—
51#66989—42no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11D411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C22×C11⋊C8—21no—
65C22×C11⋊C8—21no—
66#66928—21no—
67#66928—21no—
68#66928—21no—
69#66928—21no—
70C11×#97—21no—
71C11×#97—21no—
72C11×#97—21no—
73C11×#97D412yescomplemented
74Dic11⋊C8—24no—
75#66867—21no—
76#66867—21no—
77#66867—21no—
78#66867D412yescomplemented
79#9689—111nomaximal, Sylow
80C24×C11—21no—
81C23×D11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C22×C4×C11—21no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C2×C22⋊D11—42no—
97C2×C22⋊D11—42no—
98C2×C22⋊D11—42no—
99C2×C22⋊D11—42no—
100C22×Dic11—21no—
101C22×Dic11C22⋊C411yescharacteristic
102C22×Dic11C22⋊C411yescharacteristic
103C22×Dic11C22⋊C411yescharacteristic
104C22×Dic11C22⋊C411yescharacteristic
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—41no—
108C2×D44—41no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—41no—
112C2×Dic22—41no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11#4111yescharacteristic
127C22⋊Dic11—42no—
128C22⋊Dic11—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135Dic11⋊C4—42no—
136Dic11⋊C4—42no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—41no—
141C4×Dic11—41no—
142C4×Dic11—41no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149#2858—111no—
150#1767—111no—
151#1745—111no—
152C2×#329—111no—
153C2×#329—111no—
154C2×#329—111no—
155C2×#329D1111yescharacteristic, complemented
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11C2×C22⋊C411yescharacteristic
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171Q8×C11—81no—
172Q8×C11—81no—
173D4×C11—81no—
174D4×C11—81no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12411yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C22⋊D11—84no—
191C22⋊D11—84no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11#10012yes—
205C2×Dic11#10012yes—
206C2×Dic11#10412yes—
207D44—81no—
208D44—81no—
209Dic22—81no—
210Dic22—81no—
211C8×C11—42no—
212C8×C11—42no—
213C11⋊C8—42no—
214C11⋊C8—42no—
215C2×C4⋊Q8—111no—
216C2×#127—111no—
217C2×#124—111no—
218C2×#124—111no—
219C2×#124—111no—
220C2×#124C2×D1111yescharacteristic
221C2×C4⋊C8—221no—
222C2×#97—111no—
223C2×#97—111no—
224C2×#97C2×D1111yescharacteristic
225C2×#97C2×D1111yescharacteristic
226#390—221no—
227#390—221no—
228#390—221no—
229#390—221no—
230C43—111no—
231#336—221no—
232#336—221no—
233#336—221no—
234#329—22no—
235#329—222no—
236#329—222no—
237#329—222no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11#39011yescharacteristic
246C22×C11C2×#10011yescharacteristic
247C22×C11C2×#10011yescharacteristic
248C22×C11C2×#10411yescharacteristic
249C22×C11#42111yescharacteristic
250C22×C11#42111yescharacteristic
251C22×C11#42111yescharacteristic
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—22no—
267Dic11—22no—
268Dic11—22no—
269Dic11—41no—
270Dic11—81no—
271C22×Q8—111no—
272C22×Q8C4×D1111yescharacteristic
273C22×D4—111no—
274C22×D4—221no—
275C22×D4—221no—
276C22×D4C4×D1111yescharacteristic
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—221no—
280C22×C8—221no—
281C4⋊Q8—442no—
282#127—442no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—221no—
288#124—221no—
289#124—221no—
290#124—221no—
291#124—442no—
292#124—442no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C42—111no—
304C2×C42—111no—
305C2×C42—111no—
306C2×C42—111no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42C22×D1111yescharacteristic
310C4⋊C8—224no—
311#97—21no—
312#97—21no—
313#97—21no—
314#97—112no—
315#97—221no—
316#97—221no—
317#97—221no—
318#97C22⋊D1112yescomplemented
319C2×C11—161no—
320C2×C11#152711yescharacteristic
321C2×C11#153011yescharacteristic
322C2×C11#153311yescharacteristic
323C2×C11#153611yescharacteristic
324C2×C11#196311yescharacteristic
325C2×C11#196511yescharacteristic
326C2×C11#198011yescharacteristic
327D11—161no—
328C24—21no—
329C24—221no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8—221no—
335C2×Q8—221no—
336C2×Q8—441no—
337C2×Q8—441no—
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—442no—
347C2×D4—442no—
348C2×D4—442no—
349C2×D4—442no—
350C2×D4—442no—
351C2×D4—442no—
352C22×C4—21no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—221no—
358C22×C4C2×C4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C4⋊C4—442no—
374C4⋊C4—442no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—442no—
380C22⋊C4—442no—
381C22⋊C4—442no—
382C22⋊C4—442no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—222no—
388C42—222no—
389C42—222no—
390C42—441no—
391C42—441no—
392C42—441no—
393C42#433911yescharacteristic
394C42D4×D1111yescharacteristic
395C42#434111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C11#968911yescharacteristic, complemented, Sylow
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23C22⋊C4×D1111yescharacteristic
413Q8—81no—
414Q8—81no—
415Q8—881no—
416Q8—881no—
417D4—81no—
418D4—81no—
419D4—881no—
420D4—881no—
421D4—884no—
422D4—884no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—112no—
433C2×C4—112no—
434C2×C4—112no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4(C22⋊D11)⋊C411yescharacteristic
448C2×C4#6693711yescharacteristic
449C2×C4#6693811yescharacteristic
450C2×C4C4×C22⋊D1111yescharacteristic
451C2×C4#6699211yescharacteristic
452C2×C4#6699311yescharacteristic
453C8—42no—
454C8—42no—
455C8—442no—
456C8—442no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22D11×#10011yescharacteristic
472C22D11×#10011yescharacteristic
473C22D11×#10411yescharacteristic
474C22#1062243411yescharacteristic
475C22#1062243411yescharacteristic
476C22#1062243411yescharacteristic
477C22#1062257011yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—81no—
485C4—222no—
486C4—222no—
487C4—222no—
488C4—441no—
489C4—881no—
490C2—161no—
491C2—1761no—
492C2#1306721211yescharacteristic
493C2#1306722511yescharacteristic
494C2#1306723811yescharacteristic
495C2#1306724911yescharacteristic
496C2#1306944611yescharacteristic
497C2#1306945411yescharacteristic
498C2#1306953311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#329C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66993C4
cosocleC2×C42×C11C23
hypercenterC2×#329D11
hypocenterC11#9689
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #13068470C2semidirect
3. #13068364C2semidirect
4. C2×#10622178C2semidirect
5. C2×#10622102C2semidirect
6. C2×#10622102C2semidirect
7. C2×C11×#329C2semidirect
73. C11×#97D4semidirect
78. #66867D4semidirect
155. C2×#329D11semidirect
318. #97C22⋊D11semidirect
397. C11#9689semidirect

Maximal subgroups

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

subgroupindex
#130769712
#130684702
#130683642
C2×#106221782
C2×#106221022
C2×C11×#3292
#968911