Finite Group Databasebeta

← #24988275

Subgroups — #24988275

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134685C212yesmaximal, complemented
2#19134583C211yesmaximal, characteristic, complemented
3#19133163C212yesmaximal, complemented
4#19132913C211yesmaximal, characteristic, complemented
5C2×C43×#553C211yesmaximal, characteristic
6C2×#13063240—21no—
7C2×C22⋊(C43⋊C8)C2212yes—
8#14582759C2212yes—
9#14582666—21no—
10#14582661—24no—
11#14582633—24no—
12#14582625—21no—
13#14582623—21no—
14C43×#553—24no—
15C43×#553—24no—
16C2×#126×C43—21no—
17C2×#125×C43C411yescharacteristic, complemented
18C2×#123×C43—21no—
19C2×#121×C43—21no—
20C2×#121×C43C411yescharacteristic, complemented
21C2×#121×C43C2211yescharacteristic
22C2×C4×D4×C43—21no—
23C2×C4×D4×C43C411yescharacteristic, complemented
24C2×C4×D4×C43C2211yescharacteristic
25C2×#117×C43C411yescharacteristic, complemented
26C22×C4⋊C4×C43C2211yescharacteristic
27C22×C43⋊C8—22no—
28C2×C4⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30#13063240—42no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33C43⋊#95—22no—
34C22×D4×C43—21no—
35C22×D4×C43—21no—
36C22×D4×C43C2×C411yescharacteristic
37C22×D4×C43D411yescharacteristic
38C23×C4×C43—21no—
39C23×C4×C43—21no—
40C23×C4×C43C2×C411yescharacteristic
41C23×C4×C43C2311yescharacteristic
42#126×C43—28no—
43#125×C43—22no—
44#125×C43—22no—
45#123×C43—28no—
46#121×C43—28no—
47#121×C43—22no—
48#121×C43—22no—
49#121×C43—22no—
50#121×C43D414yes—
51C4×D4×C43—28no—
52C4×D4×C43—22no—
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C4×D4×C43—22no—
56#117×C43—22no—
57#117×C43—22no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43C2×C411yescharacteristic
63C2×C4⋊C4×C43C2×C411yescharacteristic
64C2×C4⋊C4×C43C2×C411yescharacteristic
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C4⋊C4×C43D414yes—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2×C411yescharacteristic
75C24×C43—21no—
76C24×C43C22⋊C411yescharacteristic
77C24×C43C2×D411yescharacteristic
78C2×D4×C43—24no—
79C2×D4×C43—21no—
80C2×D4×C43—22no—
81C2×D4×C43—24no—
82C2×D4×C43—22no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—42no—
86C2×D4×C43—42no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—82no—
90C2×D4×C43C22⋊C412yes—
91C22×C4×C43—24no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—24no—
98C22×C4×C43—42no—
99C22×C4×C43—42no—
100C22×C4×C43—82no—
101C22×C4×C43—82no—
102C22×C4×C43C22⋊C411yescharacteristic
103C22×C4×C43C22⋊C411yescharacteristic
104C22×C4×C43C22⋊C411yescharacteristic
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D412yes—
108C22×C4×C43C2×D412yes—
109C22×Dic43—42no—
110C4⋊C4×C43—24no—
111C4⋊C4×C43—24no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—24no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43C22⋊C412yes—
118C4⋊C4×C43C22⋊C412yes—
119C4⋊C4×C43C22⋊C412yes—
120C22⋊C4×C43—24no—
121C22⋊C4×C43—24no—
122C22⋊C4×C43—24no—
123C22⋊C4×C43—24no—
124C22⋊C4×C43—22no—
125C22⋊C4×C43—22no—
126C42×C43—24no—
127C42×C43—21no—
128C42×C43—21no—
129C22⋊Dic43—42no—
130C22⋊Dic43—42no—
131C4⋊Dic43—44no—
132C2×C43⋊C8—44no—
133C2×C43⋊C8—42no—
134C23×C43—21no—
135C23×C43—22no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—42no—
141C23×C43—42no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43C2×C22⋊C411yescharacteristic
147C23×C43#12012yes—
148C23×C43#13512yes—
149C23×C43AGL(1,ℤ/8)11yescharacteristic
150C23×C43#13711yescharacteristic
151D4×C43—42no—
152D4×C43—42no—
153D4×C43—44no—
154D4×C43—42no—
155D4×C43—44no—
156D4×C43—42no—
157D4×C43—84no—
158C2×C4×C43—24no—
159C2×C4×C43—22no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—22no—
163C2×C4×C43—21no—
164C2×C4×C43—22no—
165C2×C4×C43—22no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—42no—
172C2×C4×C43—42no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—42no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—84no—
179C2×C4×C43—84no—
180C2×C4×C43C2×C22⋊C411yescharacteristic
181C2×C4×C43C2×C22⋊C411yescharacteristic
182C2×C4×C43#12012yes—
183C2×Dic43—82no—
184C2×Dic43—82no—
185C2×Dic43—82no—
186C43⋊C8—82no—
187#8378—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—22no—
190C22×C43—21no—
191C22×C43—22no—
192C22×C43—42no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—42no—
196C22×C43—41no—
197C22×C43—42no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43—42no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43—82no—
204C22×C43—82no—
205C22×C43#37911yescharacteristic
206C22×C43#41611yescharacteristic
207C22×C43#41711yescharacteristic
208C22×C43#44912yes—
209C22×C43#45212yes—
210C4×C43—22no—
211C4×C43—21no—
212C4×C43—42no—
213C4×C43—42no—
214C4×C43—41no—
215C4×C43—41no—
216C4×C43—41no—
217C4×C43—42no—
218C4×C43#41012yes—
219Dic43—162no—
220C2×#553D4311yescharacteristic
221#1824—432no—
222#1799—431no—
223#1519—432no—
224#1459—431no—
225C2×C43—22no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—22no—
229C2×C43—81no—
230C2×C43—82no—
231C2×C43#178211yescharacteristic
232C2×C43#178811yescharacteristic
233C2×C43#179511yescharacteristic
234#553—24no—
235#553—24no—
236C2×#126—21no—
237C2×#125Dic4311yescharacteristic, complemented
238C2×#123—21no—
239C2×#121—21no—
240C2×#121Dic4311yescharacteristic, complemented
241C2×#121C2×D4311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4Dic4311yescharacteristic, complemented
244C2×C4×D4C2×D4311yescharacteristic
245C2×#117Dic4311yescharacteristic, complemented
246C22×C4⋊C4C2×D4311yescharacteristic
247C2×#99—861no—
248C2×C22⋊C8—432no—
249#380—432no—
250#342—861no—
251#340—864no—
252#327—864no—
253#324—861no—
254#323—861no—
255C43#837811yescharacteristic, complemented, Sylow
256C22×D4—21no—
257C22×D4—21no—
258C22×D4C2×Dic4311yescharacteristic
259C22×D4C22⋊D4311yescharacteristic
260C23×C4—21no—
261C23×C4—21no—
262C23×C4C2×Dic4311yescharacteristic
263C23×C4C22×D4311yescharacteristic
264C22×C8—862no—
265#126—28no—
266#125—22no—
267#125—22no—
268#123—28no—
269#121—28no—
270#121—22no—
271#121—22no—
272#121—22no—
273#121C22⋊D4314yes—
274C4×D4—28no—
275C4×D4—22no—
276C4×D4—22no—
277C4×D4—22no—
278C4×D4—22no—
279#117—22no—
280#117—22no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—862no—
286C2×C4⋊C4C2×Dic4311yescharacteristic
287C2×C4⋊C4C2×Dic4311yescharacteristic
288C2×C4⋊C4C2×Dic4311yescharacteristic
289C2×C4⋊C4C22⋊D4311yescharacteristic
290C2×C4⋊C4C22⋊D4314yes—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—862no—
296C2×C22⋊C4C22⋊D4311yescharacteristic
297C2×C22⋊C4C22⋊D4311yescharacteristic
298C2×C42—21no—
299C2×C42C2×Dic4311yescharacteristic
300#99—1722no—
301C22⋊C8—862no—
302C22⋊C8—862no—
303#95—862no—
304C24—21no—
305C24C22⋊Dic4311yescharacteristic
306C24C2×C22⋊D4311yescharacteristic
307C2×D4—22no—
308C2×D4—24no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—24no—
313C2×D4—21no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—82no—
319C2×D4C22⋊Dic4312yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—82no—
330C22×C4—82no—
331C22×C4—1722no—
332C22×C4C22⋊Dic4311yescharacteristic
333C22×C4C22⋊Dic4311yescharacteristic
334C22×C4C22⋊Dic4311yescharacteristic
335C22×C4C22×Dic4311yescharacteristic
336C22×C4C2×C22⋊D4312yes—
337C22×C4C2×C22⋊D4312yes—
338C22×C4C2×C22⋊D4311yescharacteristic
339C2×C8—1724no—
340C2×C8—1722no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—1724no—
349C4⋊C4C22⋊Dic4312yes—
350C4⋊C4C22⋊Dic4312yes—
351C4⋊C4C22⋊Dic4312yes—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—22no—
356C22⋊C4—24no—
357C22⋊C4—22no—
358C22⋊C4—1722no—
359C22⋊C4—1722no—
360C42—24no—
361C42—21no—
362C42—21no—
363C23—21no—
364C23—22no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23C2×C22⋊Dic4311yescharacteristic
376C23#1306329412yes—
377C23#1306334512yes—
378C23#1306335011yescharacteristic
379C23#1306335511yescharacteristic
380D4—42no—
381D4—42no—
382D4—44no—
383D4—42no—
384D4—44no—
385D4—42no—
386D4—84no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—3442no—
410C2×C4—3442no—
411C2×C4—3442no—
412C2×C4C2×C22⋊Dic4311yescharacteristic
413C2×C4C2×C22⋊Dic4311yescharacteristic
414C2×C4#1306329412yes—
415C8—3442no—
416C22—21no—
417C22—22no—
418C22—21no—
419C22—22no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—42no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—82no—
432C22—82no—
433C22#1458275511yescharacteristic
434C22#1458289511yescharacteristic
435C22#1458290011yescharacteristic
436C22#1458304412yes—
437C22#1458306112yes—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—41no—
446C4—6882no—
447C4#1458287312yes—
448C2—22no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—82no—
453C2—81no—
454C2#1913451311yescharacteristic
455C2#1913453511yescharacteristic
456C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#553C2
socleC22×C43#379
cosocleC23×C4×C43C23
hypercenterC2×#553D43
hypocenterC43#8378
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. #19134685C2semidirect
2. #19134583C2semidirect
3. #19133163C2semidirect
4. #19132913C2semidirect
17. C2×#125×C43C4semidirect
20. C2×#121×C43C4semidirect
23. C2×C4×D4×C43C4semidirect
25. C2×#117×C43C4semidirect
237. C2×#125Dic43semidirect
240. C2×#121Dic43semidirect
243. C2×C4×D4Dic43semidirect
245. C2×#117Dic43semidirect
255. C43#8378semidirect

Maximal subgroups

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

subgroupindex
#191346852
#191345832
#191331632
#191329132
C2×C43×#5532
#837843