Finite Group Databasebeta

← #24990055

Subgroups — #24990055

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136947C211yesmaximal, characteristic
2C2×#14582622C211yesmaximal, characteristic
3C2×#14582622C211yesmaximal, characteristic
4#19132443C211yesmaximal, characteristic, complemented
5#19132442C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1282C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4C2211yescharacteristic
9C2×C22⋊C4×D43C411yescharacteristic
10C2×C22⋊C4×D43C411yescharacteristic
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13C22⋊C4×Dic43C411yescharacteristic
14C22⋊C4×Dic43C411yescharacteristic
15C4×(C2×D43)⋊C4—21no—
16C4×(C2×D43)⋊C4—21no—
17C4×C22⋊Dic43C2211yescharacteristic
18#14582746—21no—
19#14582746—21no—
20#14582622—21no—
21#14582622—21no—
22#14582622—21no—
23#14582622—21no—
24C2×C22⋊C8×C43C2211yescharacteristic
25C2×C22⋊C8×C43C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C24×D43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C22×C4×D43—21no—
30C22×C4×D43—21no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33C2×C22⋊Dic43C2×C411yescharacteristic
34C2×C22⋊Dic43C2×C411yescharacteristic
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4D411yescharacteristic
42C2×(C2×D43)⋊C4D411yescharacteristic
43C2×(C2×D43)⋊C4D411yescharacteristic
44C2×(C2×D43)⋊C4D411yescharacteristic
45C22⋊C4×D43—22no—
46C22⋊C4×D43—22no—
47C22⋊C4×D43—22no—
48C22⋊C4×D43C814yescomplemented
49C2×C4×Dic43—21no—
50C2×C4×Dic43—21no—
51C2×C4×Dic43—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C23×C4×C43C2311yescharacteristic
60C22×C8×C43—21no—
61C22×C8×C43—21no—
62C2×C22⋊C4×C43C2×C411yescharacteristic
63C2×C22⋊C4×C43C2×C411yescharacteristic
64C2×C42×C43—21no—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#95×C43—21no—
70C24×C43C22×C411yescharacteristic
71C23×D43—21no—
72C23×D43—21no—
73C23×D43—21no—
74C23×D43—21no—
75C23×D43—81no—
76C23×D43—81no—
77C23×D43C22⋊C411yescharacteristic
78C23×D43C22⋊C411yescharacteristic
79C23×D43C2×C812yes—
80C23×D43M1612yes—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—81no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—81no—
95C22×Dic43C22⋊C411yescharacteristic
96C22×Dic43C22⋊C411yescharacteristic
97C2×C4×D43—24no—
98C2×C4×D43—24no—
99C2×C4×D43—81no—
100C2×C4×D43—81no—
101C2×C4×D43—81no—
102C2×C4×D43—81no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—81no—
106C2×C8×C43—81no—
107C22⋊C4×C43—21no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43C2×C812yes—
110C22⋊C4×C43M1612yes—
111C42×C43—81no—
112C22⋊Dic43—21no—
113C22⋊Dic43—21no—
114C22⋊Dic43C2×C812yes—
115C22⋊Dic43M1612yes—
116(C2×D43)⋊C4—24no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—21no—
119(C2×D43)⋊C4—21no—
120(C2×D43)⋊C4—21no—
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—24no—
126C4×Dic43—81no—
127C4×Dic43—81no—
128C4×Dic43—81no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—81no—
132C2×C43⋊C8—81no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43C2×C22⋊C411yescharacteristic
136C23×C43#11711yescharacteristic
137C23×C43#11711yescharacteristic
138C23×C43C22×C811yescharacteristic
139C23×C43C2×M1611yescharacteristic
140C23×C43C2×M1611yescharacteristic
141C23×C43C2×M1611yescharacteristic
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—22no—
147C22×D43—22no—
148C22×D43—22no—
149C22×D43—22no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154C22×D43—81no—
155C22×D43—81no—
156C22×D43—81no—
157C22×D43—81no—
158C22×D43—82no—
159C22×D43—82no—
160C22×D43—82no—
161C22×D43—82no—
162C22×D43C22⋊C812yes—
163C22×D43C22⋊C812yes—
164C2×C4×C43—22no—
165C2×C4×C43—22no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43#12311yescharacteristic
177C2×C4×C43#12311yescharacteristic
178C2×C4×C43#12311yescharacteristic
179C2×C4×C43#12311yescharacteristic
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43—22no—
183C2×Dic43—22no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—81no—
191C2×Dic43—81no—
192C4×D43—84no—
193C4×D43—84no—
194C8×C43—81no—
195C8×C43—81no—
196C43⋊C8—81no—
197C43⋊C8—81no—
198#8734—431nomaximal, Sylow
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43#38111yescharacteristic
210C22×C43C2×C22⋊C811yescharacteristic
211C22×C43#40711yescharacteristic
212C22×C43#43111yescharacteristic
213C22×C43#43111yescharacteristic
214C22×C43#43211yescharacteristic
215C22×C43#43211yescharacteristic
216C2×D43—22no—
217C2×D43—22no—
218C2×D43—42no—
219C2×D43—42no—
220C2×D43—41no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—42no—
225C2×D43—42no—
226C2×D43—82no—
227C2×D43—82no—
228C2×D43—82no—
229C2×D43—82no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43—42no—
236Dic43—42no—
237Dic43—42no—
238Dic43—41no—
239Dic43—41no—
240#2273—431no—
241C2×#323—431no—
242C2×#323—431no—
243#1282—431no—
244#1282—431no—
245#1282—431no—
246#1282D4311yescharacteristic, complemented
247C2×C43—21no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43#181711yescharacteristic
254C2×C43#182811yescharacteristic
255C2×C43#182911yescharacteristic
256D43—42no—
257D43—42no—
258C22×C22⋊C4—431no—
259C22×C22⋊C4—431no—
260C22×C22⋊C4—431no—
261C2×C22⋊C8—431no—
262C2×C22⋊C8—431no—
263C2×C22⋊C8C2×D4311yescharacteristic
264C2×C22⋊C8C2×D4311yescharacteristic
265C4×C22⋊C4—431no—
266C4×C22⋊C4—431no—
267C4×C22⋊C4—431no—
268C4×C22⋊C4—861no—
269C4×C22⋊C4—861no—
270C4×C22⋊C4—861no—
271C4×C22⋊C4—861no—
272C4×C22⋊C4C2×D4311yescharacteristic
273#323—861no—
274#323—861no—
275#323—861no—
276#323—861no—
277C43#873411yescharacteristic, complemented, Sylow
278C25—431no—
279C23×C4—431no—
280C23×C4—861no—
281C23×C4—861no—
282C23×C4C22×D4311yescharacteristic
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—861no—
286C22×C8—861no—
287C2×C22⋊C4—431no—
288C2×C22⋊C4—431no—
289C2×C22⋊C4—434no—
290C2×C22⋊C4—431no—
291C2×C22⋊C4—431no—
292C2×C22⋊C4—431no—
293C2×C22⋊C4—431no—
294C2×C22⋊C4—862no—
295C2×C22⋊C4—862no—
296C2×C22⋊C4—861no—
297C2×C22⋊C4—861no—
298C2×C22⋊C4—861no—
299C2×C22⋊C4—861no—
300C2×C22⋊C4—861no—
301C2×C22⋊C4—861no—
302C2×C22⋊C4—862no—
303C2×C22⋊C4C4×D4311yescharacteristic
304C2×C22⋊C4C4×D4311yescharacteristic
305C2×C42—21no—
306C2×C42—861no—
307C2×C42—861no—
308C2×C42—861no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C22⋊C8—861no—
314C22⋊C8—861no—
315C22⋊C8—861no—
316C22⋊C8—861no—
317#95—21no—
318#95—861no—
319#95—861no—
320#95—861no—
321C24—432no—
322C24—432no—
323C24—431no—
324C24—431no—
325C24—861no—
326C24—861no—
327C24—861no—
328C24—861no—
329C24—3441no—
330C24—3441no—
331C24C2×C4×D4311yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—81no—
335C22×C4—431no—
336C22×C4—431no—
337C22×C4—864no—
338C22×C4—864no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—3441no—
344C22×C4—3441no—
345C22×C4—3441no—
346C22×C4—3441no—
347C22×C4—3441no—
348C22×C4#1062189811yescharacteristic
349C22×C4#1062189811yescharacteristic
350C22×C4D4×D4311yescharacteristic
351C22×C4D4×D4311yescharacteristic
352C22×C4#1062190011yescharacteristic
353C22×C4#1062190211yescharacteristic
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—81no—
357C2×C8—81no—
358C2×C8—3441no—
359C2×C8—3441no—
360C2×C8—1721no—
361C2×C8—1721no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—432no—
365C22⋊C4—432no—
366C22⋊C4—864no—
367C22⋊C4—864no—
368C22⋊C4—861no—
369C22⋊C4—861no—
370C22⋊C4—861no—
371C22⋊C4—861no—
372C22⋊C4—861no—
373C22⋊C4—861no—
374C22⋊C4—861no—
375C22⋊C4—861no—
376C22⋊C4—861no—
377C22⋊C4—861no—
378C22⋊C4C8×D4312yes—
379C22⋊C4#1062187212yes—
380C42—81no—
381C42—3441no—
382C42—3441no—
383C42—3441no—
384C23—41no—
385C23—41no—
386C23—432no—
387C23—432no—
388C23—862no—
389C23—862no—
390C23—862no—
391C23—862no—
392C23—861no—
393C23—861no—
394C23—861no—
395C23—861no—
396C23—3441no—
397C23—3441no—
398C23—3441no—
399C23—3441no—
400C23—3442no—
401C23—3442no—
402C23—3442no—
403C23—3442no—
404C23—1721no—
405C23—1721no—
406C23—1721no—
407C23—1721no—
408C23C22⋊C4×D4311yescharacteristic
409C23#1306328211yescharacteristic
410C23#1306328311yescharacteristic
411C23C2×C8×D4311yescharacteristic
412C23M16×D4311yescharacteristic
413C23M16×D4311yescharacteristic
414C23C2×#1062187211yescharacteristic
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—862no—
428C2×C4—862no—
429C2×C4—861no—
430C2×C4—861no—
431C2×C4—3444no—
432C2×C4—3444no—
433C2×C4—3441no—
434C2×C4—3441no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4#1306330711yescharacteristic
442C2×C4#1306330711yescharacteristic
443C2×C4#1306331011yescharacteristic
444C2×C4#1306331011yescharacteristic
445C8—81no—
446C8—81no—
447C8—3441no—
448C8—3441no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—862no—
460C22—862no—
461C22—3442no—
462C22—3442no—
463C22—3442no—
464C22—3442no—
465C22—1722no—
466C22—1722no—
467C22—1722no—
468C22—1722no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22#1458276111yescharacteristic
474C22C22⋊C8×D4311yescharacteristic
475C22#1458286111yescharacteristic
476C22#1458295011yescharacteristic
477C22#1458295111yescharacteristic
478C22#1458295411yescharacteristic
479C22#1458295511yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—42no—
486C4—1722no—
487C4—1722no—
488C4—1721no—
489C4—1721no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—1722no—
497C2—1722no—
498C2#1913466211yescharacteristic
499C2#1913470211yescharacteristic
500C2#1913470511yescharacteristic
subgroupG/H
centerC22#14582761
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43#381
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1282D43
hypocenterC43#8734
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
4. #19132443C2semidirect
5. #19132442C2semidirect
6. #19132441C2semidirect
7. C43×#1282C2semidirect
48. C22⋊C4×D43C8semidirect
246. #1282D43semidirect
277. C43#8734semidirect

Maximal subgroups

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

subgroupindex
#191369472
C2×#145826222
#191324432
#191324422
#191324412
C43×#12822
#873443