Finite Group Databasebeta

← #24993909

Subgroups — #24993909

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143617C211yesmaximal, characteristic
2#19139777C211yesmaximal, characteristic
3#19134580C211yesmaximal, characteristic
4#19133167C211yesmaximal, characteristic, complemented
5#19132475C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1520C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9C8×C22⋊D43—22no—
10(C22⋊D43)⋊C8—22no—
11#14582949—21no—
12C2×#13063239—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C22⋊C8×D43—21no—
15#14582837C411yescharacteristic, complemented
16#14582834C411yescharacteristic, complemented
17#14582818C411yescharacteristic, complemented
18#14582810C411yescharacteristic, complemented
19#14582780—21no—
20#14582776—21no—
21#14582770—21no—
22#14582759C2211yescharacteristic
23#14582757—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582665—21no—
26#14582636—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#328—22no—
31C22×C22⋊D43D411yescharacteristic
32C23×Dic43—21no—
33C22×C4×D43D411yescharacteristic
34C22×C43⋊C8—21no—
35C2×C8×D43—22no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40C2×C4⋊Dic43—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4C2×C411yescharacteristic
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43D411yescharacteristic
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4C2×C411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50Dic43⋊C8—22no—
51#13063239—42no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54(C2×D43)⋊C8—22no—
55C8×Dic43—22no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95C2×C411yescharacteristic
63C43⋊#95C2×C411yescharacteristic
64C22×Q8×C43C2×C411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43D412yes—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C23×D43C22⋊C411yescharacteristic
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—81no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43—81no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—21no—
95C2×C22⋊D43—21no—
96C2×C22⋊D43—21no—
97C2×C22⋊D43—21no—
98C2×C22⋊D43SD1612yes—
99C2×C22⋊D43Q1612yes—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—42no—
103C22×Dic43—41no—
104C22×Dic43—41no—
105C22×Dic43—41no—
106C22×Dic43—81no—
107C22×Dic43C22⋊C411yescharacteristic
108C22×Dic43C22⋊C411yescharacteristic
109C22×Dic43C22⋊C411yescharacteristic
110C2×C4×D43—21no—
111C2×C4×D43—21no—
112C2×C4×D43—81no—
113C2×C8×C43—22no—
114C2×C8×C43—81no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—81no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128(C2×D43)⋊C4—21no—
129(C2×D43)⋊C4—21no—
130(C2×D43)⋊C4—42no—
131(C2×D43)⋊C4—81no—
132C4⋊Dic43—81no—
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135Dic43⋊C4—42no—
136Dic43⋊C4—81no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—81no—
141C8×D43—82no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43C2×C22⋊C411yescharacteristic
145C23×C43#12111yescharacteristic
146C23×C43#12111yescharacteristic
147C23×C43C2×SD1611yescharacteristic
148C23×C43C2×Q1611yescharacteristic
149C23×C43#13511yescharacteristic
150C23×C43#13511yescharacteristic
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43#10312yes—
156Q8×C43—81no—
157Q8×C43—81no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—81no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43C4×D411yescharacteristic
174C2×C4×C43C4×D411yescharacteristic
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#12311yescharacteristic
177C22⋊D43—22no—
178C22⋊D43—22no—
179C22⋊D43—22no—
180C22⋊D43—22no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—22no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—82no—
194C2×Dic43—82no—
195C2×Dic43—81no—
196C2×Dic43—81no—
197C2×Dic43—81no—
198C2×Dic43#10312yes—
199C4×D43—42no—
200C4×D43—81no—
201C8×C43—42no—
202C43⋊C8—42no—
203#9383—431nomaximal, Sylow
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43#38611yescharacteristic
215C22×C43C2×#10311yescharacteristic
216C22×C43#41611yescharacteristic
217C22×C43#46511yescharacteristic
218C22×C43#46511yescharacteristic
219C22×C43#46711yescharacteristic
220C22×C43#46711yescharacteristic
221C2×D43—22no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—42no—
225C2×D43—81no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—81no—
231C4×C43—81no—
232C4×C43—161no—
233Dic43—22no—
234Dic43—42no—
235Dic43—41no—
236Dic43—41no—
237Dic43—81no—
238Dic43—161no—
239#2972—431no—
240#2564—431no—
241#1799—431no—
242#1520—431no—
243#1520D4311yescharacteristic, complemented
244#1294—431no—
245#1294—431no—
246C2×C43—21no—
247C2×C43—21no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43#188411yescharacteristic
253C2×C43#189211yescharacteristic
254C2×C43#191311yescharacteristic
255D43—42no—
256C2×C22⋊Q8C2×D4311yescharacteristic
257C2×C4×D4—431no—
258C8×D4—862no—
259C8×D4—862no—
260#431—861no—
261C2×#99—861no—
262C2×C22⋊C8—431no—
263C2×C22⋊C8—861no—
264C2×C22⋊C8C2×D4311yescharacteristic
265#400—431no—
266#399—431no—
267#395—431no—
268#393—431no—
269#387—861no—
270#386—861no—
271#385—861no—
272#380—431no—
273#380—861no—
274#380C2×D4311yescharacteristic
275C2×#95—431no—
276#342—861no—
277#328—22no—
278#328—862no—
279C43#938311yescharacteristic, complemented, Sylow
280C22×Q8C4×D4311yescharacteristic
281C22×D4—431no—
282C23×C4—431no—
283C23×C4—861no—
284C23×C4C22×D4311yescharacteristic
285C22×C8—21no—
286C22×C8—862no—
287C22×C8—861no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C4×D4—861no—
293C4×D4—861no—
294C4×D4—861no—
295C4×D4—861no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—431no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4C4×D4311yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C42—431no—
311C4⋊C8—862no—
312#99—1722no—
313C22⋊C8—21no—
314C22⋊C8—432no—
315C22⋊C8—862no—
316C22⋊C8—861no—
317C22⋊C8C22⋊D4312yes—
318C4×C8—862no—
319#95—21no—
320#95—431no—
321#95—431no—
322#95—861no—
323#95—861no—
324#95—861no—
325#95—861no—
326#95—861no—
327#95—861no—
328C24—431no—
329C24D4×D4311yescharacteristic
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—81no—
333C2×D4—432no—
334C2×D4—432no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—861no—
338C2×D4—861no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—81no—
343C22×C4—431no—
344C22×C4—431no—
345C22×C4—431no—
346C22×C4—861no—
347C22×C4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—3441no—
351C22×C4—3441no—
352C22×C4—1722no—
353C22×C4—1721no—
354C22×C4—1721no—
355C22×C4—1721no—
356C22×C4C2×C4×D4311yescharacteristic
357C22×C4#1062189811yescharacteristic
358C22×C4D4×D4311yescharacteristic
359C22×C4D4×D4311yescharacteristic
360C22×C4#1062190011yescharacteristic
361C22×C4C2×C22⋊D4311yescharacteristic
362C2×C8—22no—
363C2×C8—81no—
364C2×C8—862no—
365C2×C8—3442no—
366C2×C8—3441no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—81no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C4⋊C4—3441no—
375C4⋊C4—3441no—
376C4⋊C4—1722no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—861no—
382C22⋊C4—861no—
383C22⋊C4—861no—
384C22⋊C4—861no—
385C22⋊C4—3441no—
386C22⋊C4—1722no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C42—861no—
390C42—861no—
391C23—41no—
392C23—41no—
393C23—432no—
394C23—861no—
395C23—861no—
396C23—1721no—
397C23—1721no—
398C23C22⋊C4×D4311yescharacteristic
399C23#1306329611yescharacteristic
400C23#1306329811yescharacteristic
401C23SD16×D4311yescharacteristic
402C23Q16×D4311yescharacteristic
403C23#1306334611yescharacteristic
404C23#1306334811yescharacteristic
405Q8—81no—
406Q8—81no—
407D4—862no—
408D4—862no—
409D4—862no—
410D4—862no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—432no—
427C2×C4—861no—
428C2×C4—861no—
429C2×C4—862no—
430C2×C4—861no—
431C2×C4—861no—
432C2×C4—3441no—
433C2×C4—3442no—
434C2×C4—3442no—
435C2×C4—3441no—
436C2×C4—3441no—
437C2×C4—3441no—
438C2×C4—1722no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4(C22⋊D43)⋊C411yescharacteristic
447C2×C4C4×C22⋊D4311yescharacteristic
448C2×C4#1306329311yescharacteristic
449C2×C4#1306330711yescharacteristic
450C8—42no—
451C8—1722no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—862no—
463C22—3441no—
464C22—1722no—
465C22—1721no—
466C22—1721no—
467C22#1458277511yescharacteristic
468C22#103×D4311yescharacteristic
469C22#1458289411yescharacteristic
470C22#1458312511yescharacteristic
471C22#1458313111yescharacteristic
472C22#1458313711yescharacteristic
473C22#1458313911yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—81no—
479C4—81no—
480C4—161no—
481C4—862no—
482C4—3441no—
483C4—1722no—
484C4—1721no—
485C4—1721no—
486C4—6881no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—1722no—
494C2#1913497511yescharacteristic
495C2#1913501511yescharacteristic
496C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1520C2
socleC22×C43#386
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1520D43
hypocenterC43#9383
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
4. #19133167C2semidirect
5. #19132475C2semidirect
6. #19132473C2semidirect
7. C43×#1520C2semidirect
15. #14582837C4semidirect
16. #14582834C4semidirect
17. #14582818C4semidirect
18. #14582810C4semidirect
243. #1520D43semidirect
279. C43#9383semidirect

Maximal subgroups

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

subgroupindex
#191436172
#191397772
#191345802
#191331672
#191324752
#191324732
C43×#15202
#938343