Finite Group Databasebeta

← #24992341

Subgroups — #24992341

Order 11008.

756 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142927C211yesmaximal, characteristic
2C2×#14582744C211yesmaximal, characteristic, complemented
3#19134661C211yesmaximal, characteristic, complemented
4C2×#14582634C211yesmaximal, characteristic
5C2×#14582632C211yesmaximal, characteristic
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063299C2211yescharacteristic
10C22×C4×Dic43—21no—
11C22×C4×Dic43C2211yescharacteristic
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13#14582800C412yescomplemented
14#14582798C412yescomplemented
15#14582791—22no—
16#14582776—21no—
17#14582744—22no—
18#14582744—22no—
19C2×C43⋊#95—21no—
20C2×C43⋊#95C2211yescharacteristic
21#14582653—22no—
22#14582634—22no—
23#14582632—22no—
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#380C2211yescharacteristic
26C2×#95×C43C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C23×Dic43D411yescharacteristic
32C22×C43⋊C8—21no—
33#13063309—42no—
34#13063309—42no—
35#13063299—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×C4×Dic43—28no—
45C2×C4×Dic43—24no—
46C2×C4×Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43C2×C412yes—
51C2×C4×Dic43D412yes—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C43⋊#95—24no—
55C43⋊#95—21no—
56C43⋊#95—22no—
57C43⋊#95D412yes—
58C23×C4×C43—21no—
59C23×C4×C43C2311yescharacteristic
60C22×C8×C43—21no—
61C2×C4⋊C4×C43C2×C412yes—
62C2×C22⋊C4×C43—21no—
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67#95×C43D412yes—
68C24×C43C2×D411yescharacteristic
69C23×D43—21no—
70C22×C4×C43—24no—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43—42no—
74C22×C4×C43—42no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C22×Dic43—24no—
90C22×Dic43—24no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—22no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—42no—
102C22×Dic43—41no—
103C22×Dic43—41no—
104C22×Dic43C22⋊C412yes—
105C22×Dic43C22⋊C412yes—
106C2×D172—21no—
107C2×D172—21no—
108C2×D172—42no—
109C2×C8×C43—42no—
110C2×C8×C43—41no—
111C4⋊C4×C43—42no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114(C2×D43)⋊C4—44no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—44no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—44no—
121C4×Dic43—216no—
122C4×Dic43—22no—
123C4×Dic43—22no—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C2×C43⋊C8—42no—
127C2×C43⋊C8—41no—
128C23×C43—22no—
129C23×C43—22no—
130C23×C43C2×C22⋊C411yescharacteristic
131C23×C43#12011yescharacteristic
132C23×C43#12311yescharacteristic
133C23×C43#13511yescharacteristic
134C23×C43#13511yescharacteristic
135C23×C43AGL(1,ℤ/8)11yescharacteristic
136C23×C43AGL(1,ℤ/8)11yescharacteristic
137C22×D43—41no—
138C22×D43—42no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—42no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—24no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—44no—
151C2×C4×C43—44no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C22⋊D43—81no—
161C22⋊D43—81no—
162C22⋊D43—81no—
163C22⋊D43—81no—
164C2×Dic43—24no—
165C2×Dic43—24no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—24no—
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—42no—
173C2×Dic43—44no—
174C2×Dic43—44no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43#10414yes—
184D172—81no—
185D172—81no—
186C8×C43—81no—
187C43⋊C8—81no—
188#9149—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—22no—
194C22×C43—22no—
195C22×C43—22no—
196C22×C43—22no—
197C22×C43#38611yescharacteristic
198C22×C43#41012yes—
199C22×C43#41611yescharacteristic
200C22×C43#41811yescharacteristic
201C22×C43C2×#10412yes—
202C22×C43#44911yescharacteristic
203C22×C43#44911yescharacteristic
204C22×C43#48211yescharacteristic
205C22×C43#48211yescharacteristic
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—82no—
210C2×D43—82no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—44no—
216C4×C43—82no—
217Dic43—24no—
218Dic43—44no—
219Dic43—42no—
220Dic43—81no—
221#2854—431no—
222C2×#376—431no—
223#1817—431no—
224C2×#327—431no—
225C2×#327—431no—
226#1294—431no—
227#1294D4311yescharacteristic, complemented
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43#150012yes—
233C2×C43#150512yes—
234C2×C43#187511yescharacteristic
235C2×C43#189611yescharacteristic
236C2×C43#189911yescharacteristic
237D43—161no—
238C2×#123—861no—
239C2×#121—431no—
240C22×C42—431no—
241C22×C42—861no—
242C2×C22⋊C8—431no—
243C2×C22⋊C8C2×D4311yescharacteristic
244#390—432no—
245#389—432no—
246#388—862no—
247#386—861no—
248#380C2×D4311yescharacteristic
249#376—862no—
250#376—862no—
251C2×#95—431no—
252C2×#95—861no—
253C2×#95C2×D4311yescharacteristic
254#336—862no—
255#327—862no—
256#327—862no—
257C43#914911yescharacteristic, complemented, Sylow
258C22×D4—431no—
259C22×D4—861no—
260C23×C4—21no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—861no—
264C23×C4C22×D4311yescharacteristic
265C22×C8—21no—
266C22×C8—861no—
267#123—1722no—
268#123—1722no—
269#121—861no—
270#121—861no—
271#121—861no—
272#121—861no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—862no—
275C2×C4⋊C4C4×D4312yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—862no—
279C2×C22⋊C4—861no—
280C2×C42—432no—
281C2×C42—432no—
282C2×C42—864no—
283C2×C42—868no—
284C2×C42—861no—
285C2×C42—861no—
286C2×C42—861no—
287C2×C42—861no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292#95—21no—
293#95—21no—
294#95—432no—
295#95—862no—
296#95—864no—
297#95—861no—
298#95D17212yes—
299C24—861no—
300C24D4×D4311yescharacteristic
301C2×D4—861no—
302C2×D4—861no—
303C2×D4—1722no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—432no—
318C22×C4—432no—
319C22×C4—864no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—864no—
323C22×C4—862no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—1722no—
332C22×C4—1721no—
333C22×C4—1721no—
334C22×C4C2×C4×D4311yescharacteristic
335C22×C4C2×D17211yescharacteristic
336C22×C4#1062189811yescharacteristic
337C22×C4D4×D4311yescharacteristic
338C22×C4D4×D4311yescharacteristic
339C22×C4#1062190211yescharacteristic
340C2×C8—42no—
341C2×C8—41no—
342C2×C8—1722no—
343C2×C8—1721no—
344C4⋊C4—42no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—1724no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—1724no—
351C22⋊C4—1724no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C42—8616no—
355C42—862no—
356C42—862no—
357C42—862no—
358C42—862no—
359C23—22no—
360C23—22no—
361C23—1722no—
362C23—1721no—
363C23—1721no—
364C23—1722no—
365C23—1721no—
366C23C22⋊C4×D4311yescharacteristic
367C23#1306329511yescharacteristic
368C23#1306331011yescharacteristic
369C23#1306334611yescharacteristic
370C23#1306334811yescharacteristic
371C23#1306334911yescharacteristic
372C23#1306335211yescharacteristic
373D4—3441no—
374D4—3441no—
375D4—3441no—
376D4—3441no—
377D4—3441no—
378D4—3441no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—434no—
394C2×C4—864no—
395C2×C4—864no—
396C2×C4—862no—
397C2×C4—862no—
398C2×C4—864no—
399C2×C4—862no—
400C2×C4—862no—
401C2×C4—862no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1722no—
406C2×C4—1724no—
407C2×C4—1724no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1722no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4#1306328711yescharacteristic
414C2×C4C4×D17211yescharacteristic
415C2×C4#1306329811yescharacteristic
416C2×C4#1306330011yescharacteristic
417C8—81no—
418C8—3441no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—3441no—
428C22—3441no—
429C22—3442no—
430C22—3442no—
431C22—3441no—
432C22#1458277711yescharacteristic
433C22#1458287112yes—
434C22#1458289411yescharacteristic
435C22#1458290211yescharacteristic
436C22#104×D4312yes—
437C22#1458304511yescharacteristic
438C22#1458304711yescharacteristic
439C22#1458322511yescharacteristic
440C22#1458322611yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—44no—
446C4—82no—
447C4—864no—
448C4—3441no—
449C4—1724no—
450C4—1722no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—6881no—
456C2#1913308012yes—
457C2#1913310112yes—
458C2#1913491611yescharacteristic
459C2#1913503711yescharacteristic
460C2#1913505211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9149
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#14582744C2semidirect
3. #19134661C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
13. #14582800C4semidirect
14. #14582798C4semidirect
227. #1294D43semidirect
257. C43#9149semidirect

Maximal subgroups

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

subgroupindex
#191429272
C2×#145827442
#191346612
C2×#145826342
C2×#145826322
#191324732
C43×#12942
#914943