Finite Group Databasebeta

← #24992381

Subgroups — #24992381

Order 11008.

648 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#19142927C211yesmaximal, characteristic
2C2×#14582766C211yesmaximal, 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×Dic43C2211yescharacteristic
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582800C412yescomplemented
13#14582798C412yescomplemented
14#14582791—22no—
15#14582776—21no—
16#14582766—22no—
17#14582766—22no—
18C2×C43⋊#95—21no—
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—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43C2×C412yes—
49C2×C4×Dic43D412yes—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—24no—
53C43⋊#95—24no—
54C43⋊#95—21no—
55C43⋊#95—22no—
56C43⋊#95D412yes—
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60C2×C4⋊C4×C43C2×C412yes—
61C2×C22⋊C4×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43D412yes—
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—42no—
72C22×C4×C43—42no—
73C22×C4×C43—42no—
74C22×C4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—42no—
99C22×Dic43—42no—
100C22×Dic43—42no—
101C22×Dic43—41no—
102C22×Dic43—41no—
103C22×Dic43C22⋊C412yes—
104C22×Dic43C22⋊C412yes—
105C2×D172—21no—
106C2×D172—21no—
107C2×D172—42no—
108C2×C8×C43—42no—
109C2×C8×C43—41no—
110C4⋊C4×C43—42no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113(C2×D43)⋊C4—44no—
114(C2×D43)⋊C4—44no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—44no—
120C4×Dic43—22no—
121C4×Dic43—22no—
122C4×Dic43—22no—
123C4×Dic43—22no—
124C2×C43⋊C8—42no—
125C2×C43⋊C8—41no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43C2×C22⋊C411yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12311yescharacteristic
131C23×C43#13511yescharacteristic
132C23×C43#13511yescharacteristic
133C23×C43AGL(1,ℤ/8)11yescharacteristic
134C23×C43AGL(1,ℤ/8)11yescharacteristic
135C22×D43—41no—
136C22×D43—42no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—42no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—82no—
153C2×C4×C43—82no—
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C22⋊D43—81no—
159C22⋊D43—81no—
160C22⋊D43—81no—
161C22⋊D43—81no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—82no—
181C2×Dic43—82no—
182D172—81no—
183D172—81no—
184C8×C43—81no—
185C43⋊C8—81no—
186#9157—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—22no—
192C22×C43—22no—
193C22×C43—22no—
194C22×C43—22no—
195C22×C43#38611yescharacteristic
196C22×C43#41012yes—
197C22×C43#41611yescharacteristic
198C22×C43#41811yescharacteristic
199C22×C43#42112yes—
200C22×C43#44911yescharacteristic
201C22×C43#44911yescharacteristic
202C22×C43#48211yescharacteristic
203C22×C43#48211yescharacteristic
204C2×D43—81no—
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—82no—
208C2×D43—82no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—82no—
214C4×C43—82no—
215Dic43—42no—
216Dic43—42no—
217Dic43—82no—
218Dic43—81no—
219#2854—431no—
220C2×#383—431no—
221#1817—431no—
222C2×#327—431no—
223C2×#327—431no—
224#1294—431no—
225#1294D4311yescharacteristic, complemented
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43#151412yes—
231C2×C43#152112yes—
232C2×C43#187511yescharacteristic
233C2×C43#189711yescharacteristic
234C2×C43#189911yescharacteristic
235D43—161no—
236C2×#123—861no—
237C2×#121—431no—
238C22×C42—431no—
239C2×C22⋊C8—431no—
240C2×C22⋊C8C2×D4311yescharacteristic
241#390—432no—
242#389—432no—
243#388—862no—
244#386—861no—
245#383—862no—
246#383—862no—
247#380C2×D4311yescharacteristic
248C2×#95—431no—
249C2×#95—861no—
250C2×#95—861no—
251C2×#95C2×D4311yescharacteristic
252#336—862no—
253#327—862no—
254#327—862no—
255C43#915711yescharacteristic, complemented, Sylow
256C22×D4—431no—
257C22×D4—861no—
258C23×C4—21no—
259C23×C4—431no—
260C23×C4—431no—
261C23×C4—861no—
262C23×C4C22×D4311yescharacteristic
263C22×C8—21no—
264C22×C8—861no—
265#123—1722no—
266#123—1722no—
267#121—861no—
268#121—861no—
269#121—861no—
270#121—861no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4—862no—
273C2×C4⋊C4C4×D4312yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—862no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—861no—
278C2×C42—432no—
279C2×C42—432no—
280C2×C42—861no—
281C2×C42—861no—
282C2×C42—861no—
283C2×C42—861no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—861no—
287C22⋊C8—861no—
288#95—21no—
289#95—21no—
290#95—432no—
291#95—862no—
292#95—864no—
293#95—864no—
294#95—861no—
295#95D17212yes—
296C24—861no—
297C24D4×D4311yescharacteristic
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—1722no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—432no—
315C22×C4—432no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—862no—
326C22×C4—1722no—
327C22×C4—1722no—
328C22×C4—1722no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4C2×C4×D4311yescharacteristic
332C22×C4C2×D17211yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190211yescharacteristic
337C2×C8—42no—
338C2×C8—41no—
339C2×C8—1722no—
340C2×C8—1721no—
341C4⋊C4—42no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—1724no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—1724no—
348C22⋊C4—1724no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C42—862no—
352C42—862no—
353C42—862no—
354C42—862no—
355C23—22no—
356C23—22no—
357C23—1722no—
358C23—1721no—
359C23—1721no—
360C23—1722no—
361C23—1721no—
362C23C22⋊C4×D4311yescharacteristic
363C23#1306329511yescharacteristic
364C23#1306331011yescharacteristic
365C23#1306334611yescharacteristic
366C23#1306334811yescharacteristic
367C23#1306334911yescharacteristic
368C23#1306335211yescharacteristic
369D4—3441no—
370D4—3441no—
371D4—3441no—
372D4—3441no—
373D4—3441no—
374D4—3441no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—862no—
390C2×C4—862no—
391C2×C4—862no—
392C2×C4—862no—
393C2×C4—862no—
394C2×C4—862no—
395C2×C4—3442no—
396C2×C4—3442no—
397C2×C4—1722no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1722no—
404C2×C4—1722no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4#1306328711yescharacteristic
410C2×C4C4×D17211yescharacteristic
411C2×C4#1306329811yescharacteristic
412C2×C4#1306330011yescharacteristic
413C8—81no—
414C8—3441no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—3441no—
424C22—3441no—
425C22—3441no—
426C22—3442no—
427C22—3442no—
428C22#1458277711yescharacteristic
429C22#1458287112yes—
430C22#1458289411yescharacteristic
431C22#1458290211yescharacteristic
432C22#1458291412yes—
433C22#1458304511yescharacteristic
434C22#1458304711yescharacteristic
435C22#1458322511yescharacteristic
436C22#1458322611yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—82no—
443C4—3442no—
444C4—3441no—
445C4—1722no—
446C4—1722no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—6881no—
452C2#1913314012yes—
453C2#1913317112yes—
454C2#1913491611yescharacteristic
455C2#1913504211yescharacteristic
456C2#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#9157
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×#14582766C2semidirect
3. #19134661C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
12. #14582800C4semidirect
13. #14582798C4semidirect
225. #1294D43semidirect
255. C43#9157semidirect

Maximal subgroups

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

subgroupindex
#191429272
C2×#145827662
#191346612
C2×#145826342
C2×#145826322
#191324732
C43×#12942
#915743