Finite Group Databasebeta

← #14656276

Subgroups — #14656276

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622686C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3#13069411C211yesmaximal, characteristic, complemented
4C2×#10622182C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#459C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4323—21no—
12C22×#4323—22no—
13C2×#66927C2211yescharacteristic
14C11×#459—22no—
15C11×#459—22no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622686—22no—
20#10622686—22no—
21#10622628—22no—
22#10622628—22no—
23C2×#66873—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622182—22no—
28#10622123—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44—21no—
37C2×C11×D8—24no—
38C2×C11×D8—42no—
39C2×C11×D8—42no—
40C22×C8×C11—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127D412yes—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4323—24no—
53C2×#4323—28no—
54C2×#4323—44no—
55C2×#4323—42no—
56C2×#4323—42no—
57C2×#4323—44no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8D412yes—
61#66927—21no—
62#66927—21no—
63#66927—21no—
64#66927D412yes—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#102—24no—
68C22⋊(C11⋊C8)—44no—
69#66873—24no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10260—111nomaximal, Sylow
77C24×C11—21no—
78C24×C11—41no—
79C23×D11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—82no—
98C2×D4×C11D812yescomplemented
99C22×C4×C11—21no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—42no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—42no—
117C2×D44—41no—
118C2×D44—41no—
119C2×D44—82no—
120C11×D8—48no—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#4323—48no—
133#4323—416no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—42no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8D814yescomplemented
142C2×#493—111no—
143C2×#459—111no—
144C2×#459D1111yescharacteristic, complemented
145#1954—111no—
146C2×#331—111no—
147C2×#331—111no—
148#1277—111no—
149C23×C11—22no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—41no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—82no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11—82no—
159C23×C11#12111yescharacteristic
160C22×D11—42no—
161C22×D11—82no—
162C22×D11—81no—
163C22×D11—81no—
164C22×D11—82no—
165D4×C11—22no—
166D4×C11—22no—
167D4×C11—44no—
168D4×C11—42no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—42no—
172D4×C11—82no—
173D4×C11—82no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177D4×C11—81no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—82no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11C2×D812yes—
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11#13511yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196D44—44no—
197D44—42no—
198D44—42no—
199D44—82no—
200D44—82no—
201D44—81no—
202D44—81no—
203D44—81no—
204D44—81no—
205C8×C11—42no—
206C11⋊C8—24no—
207C11⋊C8—42no—
208C11⋊C8—81no—
209C22×D8—21no—
210C22×D8—222no—
211C22×D8—221no—
212C2×#127—111no—
213C2×#127C2×D1111yescharacteristic
214C2×C4×D4C2×D1111yescharacteristic
215#493—222no—
216#493—222no—
217#459—22no—
218#459—22no—
219#459—222no—
220#459—222no—
221C2×C4⋊C8—111no—
222C2×C4⋊C8—111no—
223C2×C4⋊C8C2×D1111yescharacteristic
224C2×#102—21no—
225C2×#102—221no—
226C2×C22⋊C8—222no—
227C2×C4×C8—111no—
228#331—222no—
229#331—222no—
230C22×C11—44no—
231C22×C11—42no—
232C22×C11—82no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—162no—
239C22×C11—162no—
240C22×C11#39211yescharacteristic
241C22×C11#45912yes—
242C22×C11#46611yescharacteristic
243C22×C11#46911yescharacteristic
244C22×C11#47212yes—
245C2×D11—82no—
246C2×D11—82no—
247C2×D11—82no—
248C2×D11—162no—
249C2×D11—162no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—81no—
253C4×C11#44712yes—
254C4×C11#44711yescharacteristic
255C4×C11#44711yescharacteristic
256C4×C11#44911yescharacteristic
257C4×C11#44911yescharacteristic
258C4×C11#49311yescharacteristic
259C4×C11#49611yescharacteristic
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—221no—
264C22×D4—221no—
265C22×D4—221no—
266C22×D4C22⋊D1111yescharacteristic
267C23×C4—21no—
268C2×D8—24no—
269C2×D8—42no—
270C2×D8—42no—
271C2×D8—224no—
272C2×D8—228no—
273C2×D8—444no—
274C2×D8—444no—
275C2×D8—442no—
276C2×D8—442no—
277C22×C8—21no—
278C22×C8—112no—
279C22×C8—221no—
280C22×C8—221no—
281#127—21no—
282#127—21no—
283#127—21no—
284#127—112no—
285#127—221no—
286#127—221no—
287#127—221no—
288#127C22⋊D1112yes—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C2×C4⋊C4C22⋊D1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C42C22×D1111yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—112no—
298C4⋊C8—221no—
299C4⋊C8—221no—
300C4⋊C8—221no—
301C4⋊C8C22⋊D1112yes—
302#102—24no—
303#102—224no—
304C22⋊C8—444no—
305C4×C8—221no—
306C4×C8—221no—
307C2×C11—82no—
308C2×C11—162no—
309C2×C11#166712yes—
310C2×C11#168712yes—
311C2×C11#199911yescharacteristic
312C2×C11#201111yescharacteristic
313C2×C11#201811yescharacteristic
314D11—162no—
315C24—21no—
316C24—41no—
317C24—441no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—82no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—222no—
339C2×D4—442no—
340C2×D4—442no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—882no—
349C2×D4#432312yescomplemented
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4D4×D1111yescharacteristic
356C22×C4#434111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358D8—48no—
359D8—4416no—
360D8—448no—
361C2×C8—22no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—114no—
365C2×C8—222no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—441no—
369C2×C8—441no—
370C2×C8—442no—
371C2×C8—441no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C42D4×D1111yescharacteristic
377C42D4×D1111yescharacteristic
378C42C2×C22⋊D1111yescharacteristic
379C42C2×C22⋊D1111yescharacteristic
380C11#1026011yescharacteristic, complemented, Sylow
381C23—22no—
382C23—42no—
383C23—42no—
384C23—41no—
385C23—41no—
386C23—42no—
387C23—82no—
388C23—82no—
389C23—81no—
390C23—81no—
391C23—442no—
392C23—882no—
393C23—882no—
394C23—881no—
395C23—881no—
396C23#6699211yescharacteristic
397D4—22no—
398D4—22no—
399D4—44no—
400D4—42no—
401D4—41no—
402D4—42no—
403D4—41no—
404D4—82no—
405D4—82no—
406D4—81no—
407D4—81no—
408D4—81no—
409D4—81no—
410D4—444no—
411D4—442no—
412D4—442no—
413D4—882no—
414D4—882no—
415D4—881no—
416D4—881no—
417D4—881no—
418D4—881no—
419C2×C4—22no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4D8×D1112yes—
426C2×C4#6696412yes—
427C2×C4C2×#432311yescharacteristic
428C2×C4#6698511yescharacteristic
429C2×C4#6699011yescharacteristic
430C2×C4#6699011yescharacteristic
431C2×C4#6699111yescharacteristic
432C2×C4#6699211yescharacteristic
433C2×C4#6699311yescharacteristic
434C2×C4#6700211yescharacteristic
435C2×C4#6700311yescharacteristic
436C2×C4#6700611yescharacteristic
437C8—42no—
438C8—224no—
439C8—442no—
440C8—881no—
441C22—42no—
442C22—44no—
443C22—82no—
444C22—81no—
445C22—81no—
446C22—82no—
447C22—82no—
448C22—82no—
449C22—162no—
450C22—162no—
451C22—882no—
452C22—882no—
453C22—882no—
454C22—1762no—
455C22—1762no—
456C22#1062265111yescharacteristic
457C22#1062265211yescharacteristic
458C22#1062276312yes—
459C22#1062281212yes—
460C22#1062283611yescharacteristic
461C4—21no—
462C4—21no—
463C4—81no—
464C4#1062264911yescharacteristic
465C4#1062265011yescharacteristic
466C4#1062276411yescharacteristic
467C4#1062276711yescharacteristic
468C4#1062276912yes—
469C4#1062283011yescharacteristic
470C4#1062285111yescharacteristic
471C2—82no—
472C2—162no—
473C2—1762no—
474C2#1306796912yes—
475C2#1306809312yes—
476C2#1306961211yescharacteristic
477C2#1306968511yescharacteristic
478C2#1306972211yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#459C2
socleC23×C11#121
hypercenterC2×#459D11
hypocenterC11#10260
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622686C2semidirect
2. C2×#10622628C2semidirect
3. #13069411C2semidirect
4. C2×#10622182C2semidirect
5. C2×#10622123C2semidirect
6. #13066450C2semidirect
7. C2×C11×#459C2semidirect
98. C2×D4×C11D8semidirect
141. C2×C11⋊C8D8semidirect
144. C2×#459D11semidirect
349. C2×D4#4323semidirect
380. C11#10260semidirect

Maximal subgroups

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

subgroupindex
C2×#106226862
C2×#106226282
#130694112
C2×#106221822
C2×#106221232
#130664502
C2×C11×#4592
#1026011