Finite Group Databasebeta

← #14648347

Subgroups — #14648347

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D88C211yesmaximal, characteristic
2C2×C8×D44C211yesmaximal, characteristic, complemented
3#13069410C211yesmaximal, characteristic, complemented
4C2×#10622097C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C11×#1273C211yesmaximal, characteristic, complemented
8C22×D88C411yescharacteristic
9C22×C8×D11—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66885C411yescharacteristic
16C2×#66885C411yescharacteristic
17C2×(C2×D11)⋊C8—21no—
18C2×(C2×D11)⋊C8—21no—
19C2×(C2×D11)⋊C8—21no—
20C2×#66882C411yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C4×D88—22no—
24C4×D88—22no—
25C8×D44—22no—
26C8×D44—22no—
27#10622097—22no—
28#10622097—22no—
29C22×D44C2×C411yescharacteristic
30C22×D44C2×C411yescharacteristic
31C22×C4×D11—21no—
32C22×C4×D11—21no—
33C22×C8×C11—21no—
34C22×C8×C11C2×C411yescharacteristic
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45C2×D88—22no—
46C2×D88—22no—
47C2×D88C814yescomplemented
48C2×C8×D11—24no—
49C2×C8×D11—42no—
50C2×C8×D11—42no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44D412yes—
58C4×D44D412yes—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64C4×C8×C11—21no—
65#66885—22no—
66#66885—22no—
67(C2×D11)⋊C8—24no—
68(C2×D11)⋊C8—42no—
69(C2×D11)⋊C8—42no—
70#66882—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75#8947—111nomaximal, Sylow
76C23×D11—21no—
77C23×D11—21no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44C22⋊C412yes—
92C2×D44C2×C812yes—
93C2×D44C2×C812yescomplemented
94C2×D44M1612yes—
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C8×C11—22no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11C2×C812yescomplemented
121C2×C8×C11D812yescomplemented
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126(C2×D11)⋊C4—22no—
127(C2×D11)⋊C4—22no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11C22⋊C412yes—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140D88—28no—
141C8×D11—48no—
142C2×C4×D8—111no—
143C2×C8×D4—111no—
144#1954—111no—
145C2×D4⋊C8—111no—
146C2×D4⋊C8—111no—
147#1277—111no—
148#1273D1111yescharacteristic, complemented
149C23×C11C4×D411yescharacteristic
150C22×D11—22no—
151C22×D11—22no—
152C22×D11—22no—
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11C2×C22⋊C411yescharacteristic
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11C22×C811yescharacteristic
173C2×C4×C11C2×M1611yescharacteristic
174C2×C4×C11#13111yescharacteristic
175C2×C4×C11#13111yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11#13511yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186D44—22no—
187D44—22no—
188D44—22no—
189D44—22no—
190D44—22no—
191D44—41no—
192D44—41no—
193D44C22⋊C814yescomplemented
194C4×D11—42no—
195C4×D11—42no—
196C4×D11—42no—
197C4×D11—42no—
198C4×D11—81no—
199C4×D11—81no—
200C4×D11—81no—
201C4×D11—81no—
202C8×C11—22no—
203C8×C11—22no—
204C8×C11—42no—
205C8×C11—41no—
206C8×C11—41no—
207C11⋊C8—42no—
208C11⋊C8—81no—
209C22×D8—111no—
210C23×C8—221no—
211C2×C4×D4—111no—
212C2×C4×D4—111no—
213C4×D8—222no—
214C4×D8—222no—
215C8×D4—222no—
216C8×D4—222no—
217C2×#107—111no—
218C2×C4⋊C8—111no—
219C2×C4⋊C8—111no—
220C2×#102—111no—
221C2×#102—111no—
222C2×C22⋊C8—221no—
223C2×C22⋊C8—221no—
224C2×C22⋊C8—221no—
225C2×C4×C8C2×D1111yescharacteristic
226C2×C4×C8C2×D1111yescharacteristic
227C2×C4×C8C2×D1111yescharacteristic
228D4⋊C8—222no—
229D4⋊C8—222no—
230C22×C11#38611yescharacteristic
231C22×C11C8×D411yescharacteristic
232C22×C11#43511yescharacteristic
233C22×C11C4×D811yescharacteristic
234C22×C11#44211yescharacteristic
235C22×C11#44311yescharacteristic
236C22×C11#44411yescharacteristic
237C2×D11—24no—
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11C2×C22⋊C811yescharacteristic
254C4×C11#40811yescharacteristic
255C4×C11C8×D411yescharacteristic
256C4×C11#43511yescharacteristic
257C4×C11#44711yescharacteristic
258C4×C11#44911yescharacteristic
259C4×C11#45911yescharacteristic
260C4×C11#46311yescharacteristic
261Dic11—42no—
262Dic11—81no—
263C22×D4—111no—
264C22×D4—111no—
265C23×C4—221no—
266C23×C4—221no—
267C2×D8—114no—
268C2×D8—222no—
269C2×D8—222no—
270C22×C8—21no—
271C22×C8—224no—
272C22×C8—221no—
273C22×C8—221no—
274C22×C8—442no—
275C22×C8—442no—
276C22×C8C4×D1111yescharacteristic
277C22×C8C4×D1111yescharacteristic
278C22×C8D4411yescharacteristic
279C22×C8D4411yescharacteristic
280C4×D4—112no—
281C4×D4—112no—
282C4×D4—221no—
283C4×D4—221no—
284C4×D4—221no—
285C4×D4—221no—
286C4×D4—221no—
287C4×D4—221no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C42C22×D1111yescharacteristic
293#107—222no—
294C4⋊C8—112no—
295C4⋊C8—221no—
296C4⋊C8—221no—
297C4⋊C8—221no—
298#102—222no—
299#102—222no—
300C22⋊C8—224no—
301C22⋊C8—442no—
302C22⋊C8—442no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—21no—
306C4×C8—21no—
307C4×C8—21no—
308C4×C8—21no—
309C2×C11C8×D811yescharacteristic
310C2×C11#158011yescharacteristic
311C2×C11#158111yescharacteristic
312C2×C11#158611yescharacteristic
313C2×C11#186911yescharacteristic
314C2×C11#187611yescharacteristic
315C2×C11#187911yescharacteristic
316D11—44no—
317D11—82no—
318C24—221no—
319C24—221no—
320C2×D4—112no—
321C2×D4—112no—
322C2×D4—112no—
323C2×D4—112no—
324C2×D4—221no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—221no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—221no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4C2×C4×D1111yescharacteristic
347C22×C4C2×D4411yescharacteristic
348C22×C4#433911yescharacteristic
349D8—228no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—222no—
364C2×C8—448no—
365C2×C8—441no—
366C2×C8—441no—
367C2×C8—441no—
368C2×C8—441no—
369C2×C8—441no—
370C2×C8C8×D1112yescomplemented
371C2×C8D8812yescomplemented
372C4⋊C4—112no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C22⋊C4—222no—
377C22⋊C4—222no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42D4×D1111yescharacteristic
381C42D4×D1111yescharacteristic
382C42D4×D1111yescharacteristic
383C42#434311yescharacteristic
384C11#894711yescharacteristic, complemented, Sylow
385C23—222no—
386C23—222no—
387C23—222no—
388C23—222no—
389C23—441no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23C4×D4411yescharacteristic
400D4—114no—
401D4—222no—
402D4—222no—
403D4—222no—
404D4—222no—
405D4—222no—
406D4—441no—
407D4—441no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—222no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—881no—
421C2×C4—881no—
422C2×C4—881no—
423C2×C4—881no—
424C2×C4C22⋊C4×D1111yescharacteristic
425C2×C4#6693511yescharacteristic
426C2×C4#6693711yescharacteristic
427C2×C4#6694611yescharacteristic
428C2×C4#6694711yescharacteristic
429C2×C4#6694811yescharacteristic
430C2×C4C2×C8×D1111yescharacteristic
431C2×C4#6695411yescharacteristic
432C2×C4C2×D8811yescharacteristic
433C2×C4#6695711yescharacteristic
434C2×C4M16×D1111yescharacteristic
435C2×C4#6696011yescharacteristic
436C2×C4#6696111yescharacteristic
437C2×C4#6696111yescharacteristic
438C8—22no—
439C8—22no—
440C8—42no—
441C8—41no—
442C8—41no—
443C8—442no—
444C8—881no—
445C22—224no—
446C22—442no—
447C22—442no—
448C22—442no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22—442no—
454C22—442no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22#1062227811yescharacteristic
460C22C8×D4411yescharacteristic
461C22C4×D8811yescharacteristic
462C22#1062231311yescharacteristic
463C22#1062231911yescharacteristic
464C22#1062232411yescharacteristic
465C22#1062233011yescharacteristic
466C4—21no—
467C4—21no—
468C4—442no—
469C4—881no—
470C4D11×C22⋊C811yescharacteristic
471C4#1062234011yescharacteristic
472C4#1062234511yescharacteristic
473C4#1062234711yescharacteristic
474C4#1062244711yescharacteristic
475C4#1062244911yescharacteristic
476C4#1062245611yescharacteristic
477C4#1062245711yescharacteristic
478C2—444no—
479C2—882no—
480C2C8×D8811yescharacteristic
481C2#1306744111yescharacteristic
482C2#1306744711yescharacteristic
483C2#1306748211yescharacteristic
484C2#1306890711yescharacteristic
485C2#1306894211yescharacteristic
486C2#1306896311yescharacteristic
subgroupG/H
centerC22×C4C2×D44
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1273C2
socleC23×C11C4×D4
prime radicalC22×D88C4
cosocleC2×C42×C11C23
hypercenter#1273D11
hypocenterC11#8947
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1273

Complements

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

NH ≅ G/Ntype
2. C2×C8×D44C2semidirect
3. #13069410C2semidirect
4. C2×#10622097C2semidirect
5. C2×#10622097C2semidirect
6. #13066451C2semidirect
7. C11×#1273C2semidirect
47. C2×D88C8semidirect
93. C2×D44C2×C8semidirect
120. C2×C8×C11C2×C8semidirect
121. C2×C8×C11D8semidirect
148. #1273D11semidirect
193. D44C22⋊C8semidirect
370. C2×C8C8×D11semidirect
371. C2×C8D88semidirect
384. C11#8947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D882
C2×C8×D442
#130694102
C2×#106220972
#130664512
C11×#12732
#894711