Finite Group Databasebeta

← #14907317

Subgroups — #14907317

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077593C211yesmaximal, characteristic
2#13070525C211yesmaximal, characteristic, complemented
3#13070449C211yesmaximal, characteristic, complemented
4#13070447C211yesmaximal, characteristic, complemented
5#13070443C211yesmaximal, characteristic, complemented
6#13070443C211yesmaximal, characteristic, complemented
7#13070440C211yesmaximal, characteristic, complemented
8#13070440C211yesmaximal, characteristic, complemented
9#13070422C211yesmaximal, characteristic, complemented
10#13070422C211yesmaximal, characteristic, complemented
11#13070418C211yesmaximal, characteristic, complemented
12#13070214C211yesmaximal, characteristic, complemented
13#13070211C211yesmaximal, characteristic, complemented
14#13070209C211yesmaximal, characteristic, complemented
15C11×#2183C211yesmaximal, characteristic, complemented
16#10623111C411yescharacteristic
17C8×Q8×C11C2211yescharacteristic
18#10622637C411yescharacteristic
19C2×#66862C2211yescharacteristic
20C2×#66862C2211yescharacteristic
21C2×#66862C2211yescharacteristic
22C2×#66862C2211yescharacteristic
23C2×C16×D11C2211yescharacteristic
24C2×C16×D11C2211yescharacteristic
25#10622453C411yescharacteristic
26#10622453C411yescharacteristic
27#10622451C411yescharacteristic
28#10622449C411yescharacteristic
29#10622449C411yescharacteristic
30#10622448C411yescharacteristic
31#10622302C2211yescharacteristic
32#10622302C2211yescharacteristic
33C8×D44C2211yescharacteristic
34C8×D44C2211yescharacteristic
35C8×D44C2211yescharacteristic
36C4×C8×D11C2211yescharacteristic
37C11×C4⋊C16C2211yescharacteristic
38C11×C4⋊C16C2211yescharacteristic
39C11×C4⋊C16C2211yescharacteristic
40C11×#346C2211yescharacteristic
41C11×#346C2211yescharacteristic
42C4×C11×C16C2211yescharacteristic
43(C2×D11)⋊C16C2211yescharacteristic
44(C2×D11)⋊C16C2211yescharacteristic
45(C2×D11)⋊C16C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622140C2211yescharacteristic
50#10622140C2211yescharacteristic
51C16×Dic11C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C4⋊(C11⋊C16)C2211yescharacteristic
54C4⋊(C11⋊C16)C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56#10622099C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C4×Q8×C11C2×C411yescharacteristic
60#67000C811yescharacteristic
61#66999C811yescharacteristic
62C2×#4313C2×C411yescharacteristic
63C2×#4313C2×C411yescharacteristic
64C2×C8×D11C2×C411yescharacteristic
65C2×C8×D11C2311yescharacteristic
66C2×C8×D11C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66951C811yescharacteristic
69#66951C811yescharacteristic
70#66948C811yescharacteristic
71#66947C811yescharacteristic
72#66947C811yescharacteristic
73#66943C811yescharacteristic
74C4×D44C2×C411yescharacteristic
75C4×D44C2×C411yescharacteristic
76C4×D44C2×C411yescharacteristic
77#66925C2×C411yescharacteristic
78#66925C2×C411yescharacteristic
79C42×D11C2×C411yescharacteristic
80C2×C11×C16C2311yescharacteristic
81C2×C11×C16C2311yescharacteristic
82C2×C11×C16C2311yescharacteristic
83C2×C11×C16C2311yescharacteristic
84C11×C4⋊C8C2×C411yescharacteristic
85C11×C4⋊C8C2×C411yescharacteristic
86C11×C4⋊C8C2×C411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90(C2×D11)⋊C8C2×C411yescharacteristic
91(C2×D11)⋊C8C2×C411yescharacteristic
92(C2×D11)⋊C8C2×C411yescharacteristic
93(C2×D11)⋊C8C2×C411yescharacteristic
94(C2×D11)⋊C8C2×C411yescharacteristic
95(C2×D11)⋊C8C2×C411yescharacteristic
96#66879C2×C411yescharacteristic
97#66879C2×C411yescharacteristic
98C8×Dic11C2×C411yescharacteristic
99C8×Dic11C2311yescharacteristic
100C2×C11⋊C16C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C4⋊(C11⋊C8)C2×C411yescharacteristic
105C4⋊(C11⋊C8)C2×C411yescharacteristic
106C4⋊(C11⋊C8)C2×C411yescharacteristic
107#66867C2×C411yescharacteristic
108#66867C2×C411yescharacteristic
109C4×C11⋊C8C2×C411yescharacteristic
110#66862—22no—
111#66862—22no—
112#66862—22no—
113#66862—22no—
114C16×D11—22no—
115C16×D11—22no—
116#33481—111nomaximal, Sylow
117C2×Q8×C11C2×C811yescharacteristic
118C2×D44C2×C811yescharacteristic
119C2×D44C2×C811yescharacteristic
120C2×D44C2×C811yescharacteristic
121C2×C4×D11C2×C811yescharacteristic
122C2×C4×D11C2×C811yescharacteristic
123C2×C4×D11C22×C411yescharacteristic
124C2×C4×D11C22×C411yescharacteristic
125C2×C4×D11C22×C411yescharacteristic
126C2×C8×C11C22×C411yescharacteristic
127C2×C8×C11C22×C411yescharacteristic
128C2×C8×C11C22×C411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4C2×C811yescharacteristic
131C11×C4⋊C4C2×C811yescharacteristic
132C11×C4⋊C4C2×C811yescharacteristic
133C42×C11C22×C411yescharacteristic
134C42×C11C22×C411yescharacteristic
135C42×C11C22×C411yescharacteristic
136(C2×D11)⋊C4C2×C811yescharacteristic
137(C2×D11)⋊C4C2×C811yescharacteristic
138(C2×D11)⋊C4C2×C811yescharacteristic
139(C2×D11)⋊C4C2×C811yescharacteristic
140(C2×D11)⋊C4C2×C811yescharacteristic
141(C2×D11)⋊C4C2×C811yescharacteristic
142(C2×D11)⋊C4C2×C811yescharacteristic
143(C2×D11)⋊C4C2×C811yescharacteristic
144(C2×D11)⋊C4C2×C811yescharacteristic
145(C2×D11)⋊C4C2×C811yescharacteristic
146C4⋊Dic11C2×C811yescharacteristic
147C4⋊Dic11C2×C811yescharacteristic
148C4⋊Dic11C2×C811yescharacteristic
149Dic11⋊C4C2×C811yescharacteristic
150Dic11⋊C4C2×C811yescharacteristic
151Dic11⋊C4C2×C811yescharacteristic
152Dic11⋊C4C2×C811yescharacteristic
153C4×Dic11C2×C811yescharacteristic
154C4×Dic11C2×C811yescharacteristic
155C4×Dic11C22×C411yescharacteristic
156C2×C11⋊C8C22×C411yescharacteristic
157C2×C11⋊C8C22×C411yescharacteristic
158C2×C11⋊C8C22×C411yescharacteristic
159C2×C11⋊C8C22×C411yescharacteristic
160#4313—22no—
161#4313—22no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C8×D11—21no—
166C8×D11—21no—
167C8×D11—21no—
168C8×D11—22no—
169C11×C16—21no—
170C11×C16—21no—
171C11×C16—21no—
172C11×C16#4112yes—
173C11⋊C16—21no—
174C11⋊C16—21no—
175C11⋊C16—21no—
176C11⋊C16#4112yes—
177#2966—111no—
178#2183—111no—
179#2183D1111yescharacteristic, complemented
180#2169—111no—
181#2169—111no—
182#2168—111no—
183#2168—111no—
184#2168—111no—
185#2168—111no—
186#2164—111no—
187#2164—111no—
188#2163—111no—
189#2108—111no—
190#2108—111no—
191C4×M32—111no—
192C22×D11C22×C811yescharacteristic
193C22×D11C22×C811yescharacteristic
194C22×D11C22×C811yescharacteristic
195Q8×C11—41no—
196C2×C4×C11C22×C811yescharacteristic
197C2×C4×C11C22×C811yescharacteristic
198C2×C4×C11C22×C811yescharacteristic
199C2×C4×C11C22×C811yescharacteristic
200C2×C4×C11C22×C811yescharacteristic
201C2×C4×C11C22×C811yescharacteristic
202C2×C4×C11C23×C411yescharacteristic
203C2×Dic11C22×C811yescharacteristic
204C2×Dic11C22×C811yescharacteristic
205C2×Dic11C22×C811yescharacteristic
206C2×Dic11C22×C811yescharacteristic
207C2×Dic11C22×C811yescharacteristic
208D44—41no—
209D44—41no—
210D44—41no—
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—21no—
214C4×D11—21no—
215C4×D11—21no—
216C4×D11—21no—
217C4×D11—41no—
218C4×D11—41no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11C2×#4111yescharacteristic
223C8×C11C2×#4111yescharacteristic
224C11⋊C8—21no—
225C11⋊C8—21no—
226C11⋊C8—21no—
227C11⋊C8#13112yes—
228#529—111no—
229C2×M32—111no—
230C2×M32—111no—
231C2×M32—111no—
232C2×M32—111no—
233C22×C16—111no—
234C22×C16—111no—
235#446—111no—
236C8×Q8C2×D1111yescharacteristic
237#436—111no—
238#435—111no—
239#435—111no—
240C8×D4—111no—
241C8×D4—111no—
242C8×D4—111no—
243#433—111no—
244#433—111no—
245#432—111no—
246#405—111no—
247#405—111no—
248C2×C4×C8—111no—
249C4⋊C16—111no—
250C4⋊C16—111no—
251C4⋊C16—111no—
252C4⋊C16C2×D1111yescharacteristic
253C4⋊C16C2×D1111yescharacteristic
254C4⋊C16C2×D1111yescharacteristic
255C22⋊C16—111no—
256C22⋊C16—111no—
257C22⋊C16—111no—
258C22⋊C16—111no—
259C22⋊C16—111no—
260C22⋊C16—111no—
261#346—111no—
262#346—111no—
263#346—111no—
264#346—111no—
265#346C2×D1111yescharacteristic
266#346C2×D1111yescharacteristic
267C4×C16—111no—
268C4×C16—111no—
269C4×C16—111no—
270C4×C16C2×D1111yescharacteristic
271C22×C11C23×C811yescharacteristic
272C2×D11—21no—
273C2×D11—21no—
274C2×D11—21no—
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—21no—
278C2×D11—21no—
279C2×D11—21no—
280C2×D11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11C4×#4111yescharacteristic
288C4×C11C2×#13111yescharacteristic
289Dic11—21no—
290Dic11—21no—
291Dic11—21no—
292Dic11—21no—
293Dic11—21no—
294C2×M16—111no—
295C2×M16—111no—
296C22×C8—111no—
297C22×C8—111no—
298C22×C8—111no—
299C22×C8—111no—
300#126—111no—
301#126—111no—
302#125—111no—
303#124—111no—
304#123—111no—
305#123—111no—
306C22⋊Q8—111no—
307#121—111no—
308C4×Q8C4×D1111yescharacteristic
309C4×D4—111no—
310C4×D4—111no—
311C4×D4—111no—
312#117—111no—
313#117—111no—
314C2×C42—111no—
315M32—222no—
316M32—222no—
317M32—222no—
318M32—222no—
319C2×C16—111no—
320C2×C16—111no—
321C2×C16—111no—
322C2×C16—111no—
323C2×C16—222no—
324C2×C16—222no—
325C2×C16C22×D1111yescharacteristic
326C2×C16C22×D1111yescharacteristic
327C2×C16C22×D1111yescharacteristic
328C2×C16C22×D1111yescharacteristic
329C4⋊C8—111no—
330C4⋊C8—111no—
331C4⋊C8—111no—
332C4⋊C8C4×D1111yescharacteristic
333C4⋊C8C4×D1111yescharacteristic
334C4⋊C8C4×D1111yescharacteristic
335C22⋊C8—111no—
336C22⋊C8—111no—
337C22⋊C8—111no—
338C22⋊C8—111no—
339C22⋊C8—111no—
340C22⋊C8—111no—
341#97—111no—
342#97—111no—
343#97—111no—
344#97—111no—
345C4×C8—111no—
346C4×C8—111no—
347C4×C8—111no—
348C4×C8C22×D1111yescharacteristic
349C4×C8C22×D1111yescharacteristic
350C4×C8C22×D1111yescharacteristic
351C2×C11C8×#4111yescharacteristic
352C2×C11#340711yescharacteristic
353C2×C11#340711yescharacteristic
354D11—41no—
355D11—41no—
356D11—41no—
357C2×Q8C8×D1111yescharacteristic
358C2×D4—111no—
359C2×D4—111no—
360C2×D4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366M16—222no—
367M16—222no—
368C2×C8—111no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—222no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8C2×C4×D1111yescharacteristic
380C2×C8C2×C4×D1111yescharacteristic
381C2×C8C2×C4×D1111yescharacteristic
382C2×C8C23×D1111yescharacteristic
383C4⋊C4—111no—
384C4⋊C4—111no—
385C4⋊C4—111no—
386C4⋊C4—111no—
387C4⋊C4—111no—
388C4⋊C4—111no—
389C4⋊C4—111no—
390C4⋊C4C8×D1111yescharacteristic
391C4⋊C4C8×D1111yescharacteristic
392C4⋊C4C8×D1111yescharacteristic
393C22⋊C4—111no—
394C22⋊C4—111no—
395C22⋊C4—111no—
396C22⋊C4—111no—
397C22⋊C4—111no—
398C22⋊C4—111no—
399C22⋊C4—111no—
400C22⋊C4—111no—
401C22⋊C4—111no—
402C22⋊C4—111no—
403C42—111no—
404C42—111no—
405C42—111no—
406C42C2×C4×D1111yescharacteristic
407C42C2×C4×D1111yescharacteristic
408C42C2×C4×D1111yescharacteristic
409C16—21no—
410C16—21no—
411C16—21no—
412C16—112no—
413C16—221no—
414C16—221no—
415C16—221no—
416C16#434312yes—
417C11#3348111yescharacteristic, complemented, Sylow
418C23—111no—
419C23—111no—
420C23—111no—
421Q8—41no—
422D4—441no—
423D4—441no—
424D4—441no—
425C2×C4—111no—
426C2×C4—111no—
427C2×C4—111no—
428C2×C4—111no—
429C2×C4—111no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4C2×C8×D1111yescharacteristic
439C2×C4C2×C8×D1111yescharacteristic
440C2×C4C2×C8×D1111yescharacteristic
441C2×C4C2×C8×D1111yescharacteristic
442C2×C4C2×C8×D1111yescharacteristic
443C2×C4C2×C8×D1111yescharacteristic
444C2×C4C22×C4×D1111yescharacteristic
445C8—21no—
446C8—21no—
447C8—21no—
448C8—112no—
449C8—221no—
450C8—221no—
451C8—221no—
452C8C2×#434311yescharacteristic
453C8#41×D1111yescharacteristic
454C22—221no—
455C22—221no—
456C22—221no—
457C22—221no—
458C22—221no—
459C22—221no—
460C22—221no—
461C22—221no—
462C22—221no—
463C22C22×C8×D1111yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—221no—
471C4—221no—
472C4—221no—
473C4—221no—
474C4—221no—
475C4C4×#434311yescharacteristic
476C4D11×#13111yescharacteristic
477C2—441no—
478C2—441no—
479C2—441no—
480C2C8×#434311yescharacteristic
481C2#1308171711yescharacteristic
482C2#1308171811yescharacteristic
subgroupG/H
center, FrattiniC2×C8C23×D11
commutator, socleC22×C11C23×C8
FittingC11×#2183C2
prime radical#66948C8
cosocleC2×C8×C11C24
hypercenter#2183D11
hypocenterC11#33481
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ #2183

Complements

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

NH ≅ G/Ntype
2. #13070525C2semidirect
3. #13070449C2semidirect
4. #13070447C2semidirect
5. #13070443C2semidirect
6. #13070443C2semidirect
7. #13070440C2semidirect
8. #13070440C2semidirect
9. #13070422C2semidirect
10. #13070422C2semidirect
11. #13070418C2semidirect
12. #13070214C2semidirect
13. #13070211C2semidirect
14. #13070209C2semidirect
15. C11×#2183C2semidirect
179. #2183D11semidirect
417. C11#33481semidirect

Maximal subgroups

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

subgroupindex
#130775932
#130705252
#130704492
#130704472
#130704432
#130704402
#130704222
#130704182
#130702142
#130702112
#130702092
C11×#21832
#3348111