Finite Group Databasebeta

← #24996115

Subgroups — #24996115

Order 11008.

606 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×#14583133C211yesmaximal, characteristic
2#19135432C211yesmaximal, characteristic, complemented
3#19135430C211yesmaximal, characteristic, complemented
4#19134622C211yesmaximal, characteristic, complemented
5#19134369C211yesmaximal, characteristic, complemented
6#19133164C211yesmaximal, characteristic, complemented
7C43×#1519C211yesmaximal, characteristic, complemented
8C22×#10621882C411yescharacteristic, complemented
9C23×C43⋊C8C2211yescharacteristic
10C2×#13063299C2211yescharacteristic
11#14583133—21no—
12#14583133—21no—
13#14583133—21no—
14#14583133—21no—
15C2×#13063258—21no—
16C2×#13063258C411yescharacteristic, complemented
17C2×#13063246C411yescharacteristic, complemented
18C2×#13063245C411yescharacteristic, complemented
19C2×#13063240—22no—
20C2×#13063239—22no—
21C2×C8×Dic43—21no—
22#14582759C2211yescharacteristic
23C4×C22⋊Dic43C2211yescharacteristic
24#14582661—21no—
25#14582653—21no—
26#14582634—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#327—22no—
31C22×D172C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C2×#10621882—21no—
34C2×#10621882—21no—
35C2×#10621882—42no—
36C22×C43⋊C8—42no—
37C22×C43⋊C8C2×C411yescharacteristic
38C22×C43⋊C8C2×C411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42C22×C43⋊C8D411yescharacteristic
43#13063299—21no—
44#13063299—21no—
45#13063299—21no—
46#13063299—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43D412yes—
51C2×(C2×D43)⋊C4—21no—
52C2×C4×Dic43—21no—
53#13063258—21no—
54#13063258—21no—
55#13063258—42no—
56#13063246—21no—
57#13063246—21no—
58#13063245—21no—
59#13063245—21no—
60#13063240—44no—
61#13063239—44no—
62C8×Dic43—42no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C22×D4×C43—21no—
66C22×D4×C43C2×C411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72#121×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43C2×C411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D412yes—
79#95×C43—21no—
80C24×C43—21no—
81C24×C43C2×D411yescharacteristic
82C23×D43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—42no—
88C2×D4×C43—42no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C22×C4×C43—21no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—42no—
104C2×C22⋊D43—42no—
105C22×Dic43—21no—
106C22×Dic43—22no—
107C22×Dic43—41no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172—41no—
111C2×D172—41no—
112C2×C8×C43—22no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—42no—
122C22⋊Dic43—22no—
123C22⋊Dic43—42no—
124C22⋊Dic43D814yescomplemented
125#10621882—42no—
126#10621882—42no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43—41no—
132C4⋊Dic43—41no—
133C4×Dic43—41no—
134C4×Dic43—41no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8C22⋊C411yescharacteristic
142C2×C43⋊C8C22⋊C411yescharacteristic
143C2×C43⋊C8C22⋊C411yescharacteristic
144C2×C43⋊C8C22⋊C411yescharacteristic
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—42no—
149C23×C43—81no—
150C23×C43—81no—
151C23×C43C4×D411yescharacteristic
152C23×C43#12111yescharacteristic
153C23×C43#12711yescharacteristic
154C23×C43C2×D812yes—
155C23×C43#13512yes—
156C22×D43—41no—
157C22×D43—42no—
158C22×D43—81no—
159C22×D43—81no—
160D4×C43—41no—
161D4×C43—41no—
162D4×C43—81no—
163D4×C43—82no—
164D4×C43—81no—
165D4×C43—81no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—42no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43—81no—
180C2×C4×C43C2×C22⋊C411yescharacteristic
181C2×C4×C43C4×D411yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#12411yescharacteristic
184C22⋊D43—82no—
185C22⋊D43—81no—
186C22⋊D43—81no—
187C2×Dic43—24no—
188C2×Dic43—42no—
189C2×Dic43—42no—
190C2×Dic43—41no—
191C2×Dic43—42no—
192C2×Dic43—81no—
193C2×Dic43—81no—
194C2×Dic43—81no—
195D172—41no—
196D172—41no—
197D172—81no—
198C8×C43—42no—
199C43⋊C8—21no—
200C43⋊C8—21no—
201C43⋊C8—21no—
202C43⋊C8#9912yescomplemented
203#9783—431nomaximal, Sylow
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—42no—
211C22×C43—42no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43—162no—
216C22×C43#39011yescharacteristic
217C22×C43C4×D812yes—
218C22×C43#46612yes—
219C22×C43#49311yescharacteristic
220C22×C43#49511yescharacteristic
221C2×D43—81no—
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—162no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—81no—
229C4×C43—161no—
230C4×C43C2×#9911yescharacteristic
231C4×C43#41011yescharacteristic
232Dic43—44no—
233Dic43—81no—
234Dic43—161no—
235C2×#466—431no—
236#1964—431no—
237#1964—431no—
238#1808—431no—
239C8×C22⋊C4—431no—
240#1519—431no—
241#1519D4311yescharacteristic, complemented
242C2×C43—22no—
243C2×C43—21no—
244C2×C43—22no—
245C2×C43—21no—
246C2×C43—161no—
247C2×C43#196411yescharacteristic
248C2×C43#197011yescharacteristic
249C2×C43#197611yescharacteristic
250D43—161no—
251C22×D8—431no—
252C23×C8—431no—
253C2×#121—431no—
254C2×#121C2×D4311yescharacteristic
255#466—861no—
256#466—861no—
257#466—861no—
258#466—861no—
259C2×#107—431no—
260C2×#107—861no—
261C2×#102—431no—
262C2×#102—431no—
263C2×#99—862no—
264C2×#99—862no—
265C2×C22⋊C8C2×D4311yescharacteristic
266C2×C4×C8—861no—
267#380—431no—
268#380C2×D4311yescharacteristic
269C4×C22⋊C4—431no—
270#340—861no—
271#336—861no—
272#327—22no—
273#327—862no—
274C43#978311yescharacteristic, complemented, Sylow
275C22×D4—21no—
276C22×D4—431no—
277C22×D4—861no—
278C22×D4C4×D4311yescharacteristic
279C23×C4C22×D4311yescharacteristic
280C2×D8—861no—
281C2×D8—861no—
282C2×D8—1722no—
283C22×C8—21no—
284C22×C8—431no—
285C22×C8—431no—
286C22×C8—431no—
287C22×C8—431no—
288C22×C8—431no—
289C22×C8—431no—
290C22×C8—1722no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—861no—
296#121—861no—
297#121—861no—
298#121—861no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—431no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4C4×D4311yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—432no—
306C2×C22⋊C4—861no—
307C2×C22⋊C4—861no—
308C2×C42—861no—
309#107—861no—
310#107—861no—
311#107—1722no—
312#102—861no—
313#102—861no—
314#102—861no—
315#102—861no—
316#99—1724no—
317#99—1724no—
318C22⋊C8—21no—
319C22⋊C8C22⋊D4312yes—
320C4×C8—1722no—
321#95—21no—
322#95—861no—
323#95—861no—
324C24—21no—
325C24—861no—
326C24D4×D4311yescharacteristic
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—1721no—
338C2×D4—1721no—
339C2×D4—1721no—
340C2×D4—1721no—
341C2×D4—1722no—
342C2×D4—1722no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—862no—
348C22×C4—861no—
349C22×C4—1721no—
350C22×C4C2×C4×D4311yescharacteristic
351C22×C4#1062189811yescharacteristic
352C22×C4D4×D4311yescharacteristic
353C22×C4D4×D4311yescharacteristic
354C22×C4#1062190011yescharacteristic
355C22×C4C2×C22⋊D4311yescharacteristic
356D8—1722no—
357D8—1722no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—431no—
362C2×C8—431no—
363C2×C8—431no—
364C2×C8—431no—
365C2×C8—862no—
366C2×C8—862no—
367C2×C8—862no—
368C2×C8—1721no—
369C2×C8—1721no—
370C2×C8—1721no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—42no—
382C22⋊C4—434no—
383C22⋊C4—862no—
384C22⋊C4—1722no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C42—1721no—
388C42—1721no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—81no—
394C23—81no—
395C23—3441no—
396C23—3441no—
397C23—1721no—
398C23—1722no—
399C23(C22⋊D43)⋊C411yescharacteristic
400C23#1306329811yescharacteristic
401C23#1306332111yescharacteristic
402C23D8×D4312yes—
403C23#1306334612yes—
404D4—41no—
405D4—41no—
406D4—81no—
407D4—82no—
408D4—81no—
409D4—81no—
410D4—3441no—
411D4—3442no—
412D4—3441no—
413D4—3441no—
414D4—1721no—
415D4—1721no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—864no—
431C2×C4—3441no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—1721no—
435C2×C4—1722no—
436C2×C4—1722no—
437C2×C4—1722no—
438C2×C4C22⋊C4×D4311yescharacteristic
439C2×C4C4×C22⋊D4311yescharacteristic
440C2×C4#1306329711yescharacteristic
441C2×C4#1306331111yescharacteristic
442C8—42no—
443C8—432no—
444C8—861no—
445C8—861no—
446C8—861no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—162no—
459C22—3441no—
460C22—3441no—
461C22—3441no—
462C22—6882no—
463C22#1458279911yescharacteristic
464C22#1458297912yes—
465C22#1458313412yes—
466C22#1458327411yescharacteristic
467C22#1458328011yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—81no—
472C4—161no—
473C4—3441no—
474C4—1724no—
475C4—6881no—
476C4#99×D4311yescharacteristic
477C4#1458287111yescharacteristic
478C2—21no—
479C2—22no—
480C2—22no—
481C2—21no—
482C2—161no—
483C2—6881no—
484C2#1913542911yescharacteristic
485C2#1913545811yescharacteristic
486C2#1913549211yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1519C2
socleC22×C43#390
prime radicalC2×#14583133C2
cosocleC23×C4×C43C23
hypercenter#1519D43
hypocenterC43#9783
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #19135432C2semidirect
3. #19135430C2semidirect
4. #19134622C2semidirect
5. #19134369C2semidirect
6. #19133164C2semidirect
7. C43×#1519C2semidirect
8. C22×#10621882C4semidirect
16. C2×#13063258C4semidirect
17. C2×#13063246C4semidirect
18. C2×#13063245C4semidirect
124. C22⋊Dic43D8semidirect
202. C43⋊C8#99semidirect
241. #1519D43semidirect
274. C43#9783semidirect

Maximal subgroups

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

subgroupindex
C2×#145831332
#191354322
#191354302
#191346222
#191343692
#191331642
C43×#15192
#978343