Finite Group Databasebeta

← #14647862

Subgroups — #14647862

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071349C211yesmaximal, characteristic
2#13068923C211yesmaximal, characteristic
3#13068809C211yesmaximal, characteristic
4C2×#10622090C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066459C211yesmaximal, characteristic
7C11×#1442C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×C11×#95—21no—
11C2×C11×#95—21no—
12C2×C11×#95C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622823—21no—
16C4×C22⋊Dic11—21no—
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66874—21no—
20C2×#66872—21no—
21#10622268—21no—
22#10622267—21no—
23#10622260—21no—
24#10622259—21no—
25#10622167—21no—
26#10622167—21no—
27#10622090C414yescomplemented
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×Dic22D411yescharacteristic
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—42no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D411yescharacteristic
42#66977—21no—
43#66977—21no—
44#66977C2×C412yes—
45#66977Q812yes—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52C22×C11⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—42no—
57C11×#95—42no—
58C11×#95C2×C412yes—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)C2×C412yes—
68#66874—42no—
69#66872—42no—
70#8872—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11SD1612yes—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C2×Dic22—21no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22C4⋊C412yes—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C22⋊Dic11—22no—
117C22⋊Dic11—22no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11C4⋊C412yes—
124Dic11⋊C4—22no—
125Dic11⋊C4—22no—
126Dic11⋊C4—81no—
127Dic11⋊C4—81no—
128C4×Dic11—81no—
129C4×Dic11—81no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136#2329—111no—
137#1872—111no—
138#1853—111no—
139C2×#328—111no—
140#1442D1111yescharacteristic
141#1294—111no—
142#1280—111no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11C4×D411yescharacteristic
148C23×C11#12011yescharacteristic
149C23×C11C22⋊Q811yescharacteristic
150C23×C11C2×SD1611yescharacteristic
151C23×C11#13511yescharacteristic
152C23×C11#13711yescharacteristic
153C23×C11#13711yescharacteristic
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11C2×C4⋊C411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11C22⋊Q811yescharacteristic
189C2×C4×C11#12311yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202Dic22—42no—
203Dic22—81no—
204C11⋊C8—42no—
205C11⋊C8—81no—
206C2×C22⋊Q8—111no—
207C22×C4⋊C4C2×D1111yescharacteristic
208C2×#106—221no—
209C2×#103—221no—
210C2×C22⋊C8—111no—
211C2×C22⋊C8—111no—
212#391—221no—
213#389—221no—
214#387—221no—
215#387—221no—
216#385—221no—
217#380—111no—
218C4×C22⋊C4—221no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95C2×D1111yescharacteristic
222C2×#95C2×D1111yescharacteristic
223#340—221no—
224#340—221no—
225#328—114no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11#38511yescharacteristic
239C22×C11C4×SD1611yescharacteristic
240C22×C11#44111yescharacteristic
241C22×C11#44811yescharacteristic
242C22×C11#45211yescharacteristic
243C22×C11#45411yescharacteristic
244C22×C11#45511yescharacteristic
245C22×C11B(4,𝔽2)11yescharacteristic
246C22×C11#45811yescharacteristic
247C22×C11#47511yescharacteristic
248C22×C11#47911yescharacteristic
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11—82no—
256C4×C11—81no—
257Dic11—42no—
258Dic11—42no—
259Dic11—81no—
260Dic11—81no—
261C22×Q8—111no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4C22⋊D1111yescharacteristic
265C23×C4C22⋊D1111yescharacteristic
266C23×C4C22×D1111yescharacteristic
267C22×C8—221no—
268C22×C8—221no—
269C22⋊Q8—112no—
270C22⋊Q8—112no—
271C22⋊Q8—221no—
272C22⋊Q8—221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C42—221no—
285C2×C42—221no—
286#106—442no—
287#103—442no—
288C22⋊C8—112no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291C22⋊C8—221no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—42no—
296#95—42no—
297#95—221no—
298#95—221no—
299#95—221no—
300#95—221no—
301#95—221no—
302#95C4×D1112yes—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—21no—
307C2×C11#159911yescharacteristic
308C2×C11#160611yescharacteristic
309C2×C11#160811yescharacteristic
310C2×C11#161511yescharacteristic
311C2×C11#186011yescharacteristic
312C2×C11#186511yescharacteristic
313C2×C11#186711yescharacteristic
314C24C2×C22⋊D1111yescharacteristic
315C2×Q8—112no—
316C2×Q8—221no—
317C2×Q8—441no—
318C2×Q8—441no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4#432412yes—
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4#433911yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353C22×C4Q8×D1111yescharacteristic
354C22×C4#434311yescharacteristic
355C2×C8—222no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8—441no—
359C2×C8—441no—
360C2×C8—441no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—112no—
366C4⋊C4—222no—
367C4⋊C4—221no—
368C4⋊C4—222no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—881no—
372C4⋊C4—881no—
373C22⋊C4—222no—
374C22⋊C4—222no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C42—881no—
378C42—881no—
379C11#887211yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23C4×C22⋊D1111yescharacteristic
385C23C2×#432411yescharacteristic
386C23#6699011yescharacteristic
387C23#6699511yescharacteristic
388C23#6699911yescharacteristic
389C23#6700311yescharacteristic
390C23#6700411yescharacteristic
391Q8—442no—
392Q8—881no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4C4⋊C4×D1111yescharacteristic
438C2×C4#6694611yescharacteristic
439C2×C4#6694711yescharacteristic
440C2×C4#6694911yescharacteristic
441C8—442no—
442C8—881no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22#1062260211yescharacteristic
456C22C4×#432411yescharacteristic
457C22#1062264311yescharacteristic
458C22#1062264511yescharacteristic
459C22#1062265311yescharacteristic
460C22#1062266011yescharacteristic
461C22#1062266611yescharacteristic
462C22#1062267411yescharacteristic
463C22#1062267511yescharacteristic
464C22#1062267611yescharacteristic
465C22#1062270711yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—42no—
471C4—82no—
472C4—82no—
473C4—81no—
474C4—442no—
475C4—442no—
476C4—881no—
477C4—881no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2#1306755511yescharacteristic
483C2#1306759411yescharacteristic
484C2#1306760611yescharacteristic
485C2#1306764511yescharacteristic
486C2#1306884811yescharacteristic
487C2#1306888311yescharacteristic
488C2#1306889511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1442C2
socleC23×C11#120
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1442D11
hypocenterC11#8872
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
27. #10622090C4semidirect
379. C11#8872semidirect

Maximal subgroups

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

subgroupindex
#130713492
#130689232
#130688092
C2×#106220902
#130664952
#130664592
C11×#14422
#887211