Finite Group Databasebeta

← #24991811

Subgroups — #24991811

Order 11008.

488 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144638C211yesmaximal, characteristic
2#19135392C211yesmaximal, characteristic, complemented
3#19133183C211yesmaximal, characteristic, complemented
4#19133037C211yesmaximal, characteristic, complemented
5#19132493C211yesmaximal, characteristic, complemented
6#19132445C211yesmaximal, characteristic, complemented
7C43×#2992C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9#14583232C411yescharacteristic
10#14583215C411yescharacteristic
11#14583196—21no—
12#14583111—21no—
13#14583049C411yescharacteristic
14#14583032C411yescharacteristic
15C4×#10621884—21no—
16C4×#10621882—21no—
17#14582952C2211yescharacteristic
18C2×(C2×D43)⋊C8—21no—
19C2×(C2×D43)⋊C8—21no—
20C4×#10621877C2211yescharacteristic
21C2×#13063236C2211yescharacteristic
22#14582641—21no—
23#14582639—21no—
24#14582626—21no—
25#14582626—21no—
26C43×#529C2211yescharacteristic
27C43×#446—21no—
28C43×#435—21no—
29C43×#435—21no—
30C8×D4×C43—21no—
31C43×#433—21no—
32C43×#432C2211yescharacteristic
33C43×#424—21no—
34C2×C4⋊C8×C43C2211yescharacteristic
35C22×D172C2×C411yescharacteristic
36C22×C4×D43—21no—
37C2×#10621884—21no—
38C2×#10621882—21no—
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C4×D172—21no—
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×(C2×D43)⋊C4—21no—
47#13063258—21no—
48#13063256—21no—
49C4⋊(C43⋊C8)—21no—
50#13063249—21no—
51#13063246—21no—
52#13063245—21no—
53#13063245—21no—
54C22⋊(C43⋊C8)C2×C411yescharacteristic
55C22⋊(C43⋊C8)C2×C411yescharacteristic
56(C2×D43)⋊C8—42no—
57(C2×D43)⋊C8—42no—
58#13063236—21no—
59#13063236—21no—
60#13063236—21no—
61C4×C43⋊C8—21no—
62C4×C43⋊C8—21no—
63C2×M16×C43—21no—
64C22×C8×C43—21no—
65C22×C8×C43D411yescharacteristic
66C22×C8×C43D411yescharacteristic
67#126×C43—21no—
68#125×C43D411yescharacteristic
69#124×C43D411yescharacteristic
70#123×C43—21no—
71C22⋊Q8×C43C2×C411yescharacteristic
72#121×C43C2×C411yescharacteristic
73C4×Q8×C43D411yescharacteristic
74C4×D4×C43—21no—
75C4×D4×C43D411yescharacteristic
76#117×C43—21no—
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—21no—
79C4⋊C8×C43—21no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43D411yescharacteristic
83C4⋊C8×C43D411yescharacteristic
84C22⋊C8×C43—21no—
85C22⋊C8×C43—21no—
86C22⋊C8×C43—21no—
87#97×C43—21no—
88#97×C43—21no—
89C4×C8×C43—21no—
90C23×D43—21no—
91C2×Q8×C43C22⋊C411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43C22⋊C411yescharacteristic
94C22×C4×C43—21no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×Dic43—21no—
99C2×D172—21no—
100C2×D172—21no—
101C2×D172—42no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C4×D43—41no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108M16×C43—81no—
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—81no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43C22⋊C411yescharacteristic
121C4⋊C4×C43C22⋊C411yescharacteristic
122C22⋊C4×C43—21no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43—21no—
127C42×C43—21no—
128C42×C43C2×D411yescharacteristic
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43#4111yescharacteristic
132#10621884—42no—
133#10621882—42no—
134(C2×D43)⋊C4—41no—
135(C2×D43)⋊C4—41no—
136C4⋊Dic43—21no—
137C4⋊Dic43—21no—
138#10621877—22no—
139#10621877—41no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—21no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C23×C43—21no—
147C23×C43C4×D411yescharacteristic
148C22×D43—22no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154C22×D43—41no—
155Q8×C43—41no—
156D4×C43—41no—
157D4×C43—41no—
158D4×C43—41no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43C2×C22⋊C411yescharacteristic
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12311yescharacteristic
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178D172—22no—
179D172—22no—
180D172—41no—
181D172—41no—
182C4×D43—81no—
183C4×D43—81no—
184C4×D43—81no—
185C4×D43—81no—
186C8×C43—41no—
187C8×C43—41no—
188C8×C43—41no—
189C8×C43—41no—
190C43⋊C8—42no—
191C43⋊C8—41no—
192C43⋊C8—41no—
193C43⋊C8—42no—
194#9052—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43#38611yescharacteristic
201C22×C43#44311yescharacteristic
202C22×C43#44411yescharacteristic
203C2×D43—42no—
204C2×D43—42no—
205C2×D43—42no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—41no—
216C4×C43—41no—
217C4×C43—41no—
218C4×C43#45311yescharacteristic
219C4×C43#45411yescharacteristic
220Dic43—81no—
221#3105—431no—
222#2992D4311yescharacteristic, complemented
223#1955—431no—
224#1524—431no—
225#1490—431no—
226#1302—431no—
227#1283—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—81no—
231C2×C43#187611yescharacteristic
232C2×C43#188311yescharacteristic
233C2×C43#189111yescharacteristic
234D43—82no—
235#529C2×D4311yescharacteristic
236C2×C4×D4—431no—
237#484—431no—
238#481—431no—
239#478—861no—
240#463—861no—
241#450—431no—
242#447—431no—
243#446—21no—
244C4×SD16—861no—
245C4×D8—861no—
246#435—21no—
247#435—21no—
248C8×D4—21no—
249#433—21no—
250#432C2×D4311yescharacteristic
251#431—431no—
252#424—21no—
253C2×C4⋊C8C2×D4311yescharacteristic
254C2×C22⋊C8—861no—
255C2×C22⋊C8—861no—
256C4×M16—431no—
257C2×#97—431no—
258#330—861no—
259#329—861no—
260D4⋊C8—861no—
261D4⋊C8—861no—
262C43#905211yescharacteristic, complemented, Sylow
263C22×D4—431no—
264C23×C4—861no—
265C2×SD16—861no—
266C2×D8—861no—
267C2×M16—21no—
268C2×M16—861no—
269C22×C8—21no—
270C22×C8—861no—
271C22×C8C22⋊D4311yescharacteristic
272C22×C8C22⋊D4311yescharacteristic
273#126—21no—
274#125D17211yescharacteristic
275#124D17211yescharacteristic
276#123—21no—
277C22⋊Q8C4×D4311yescharacteristic
278#121C4×D4311yescharacteristic
279C4×Q8C22⋊D4311yescharacteristic
280C4×D4—21no—
281C4×D4—861no—
282C4×D4—861no—
283C4×D4—861no—
284C4×D4—861no—
285C4×D4C22⋊D4311yescharacteristic
286#117—21no—
287C2×C4⋊C4—431no—
288C2×C22⋊C4—861no—
289C2×C42C22×D4311yescharacteristic
290#107—861no—
291#106—861no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—861no—
297C4⋊C8C22⋊D4311yescharacteristic
298C4⋊C8C22⋊D4311yescharacteristic
299#103—861no—
300#102—861no—
301#102—861no—
302#102—861no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—431no—
307C22⋊C8—431no—
308C22⋊C8—1722no—
309C22⋊C8—1722no—
310#97—21no—
311#97—21no—
312#97—861no—
313#97—861no—
314#97—861no—
315C4×C8—21no—
316C4×C8—861no—
317C4×C8—861no—
318C24—861no—
319C2×Q8(C2×D43)⋊C411yescharacteristic
320C2×D4—21no—
321C2×D4—861no—
322C2×D4—861no—
323C2×D4—1722no—
324C2×D4(C2×D43)⋊C411yescharacteristic
325C22×C4—21no—
326C22×C4—861no—
327C22×C4—1721no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1721no—
332C22×C4—1721no—
333C22×C4C2×C4×D4311yescharacteristic
334C22×C4#1062189811yescharacteristic
335C22×C4C2×C22⋊D4311yescharacteristic
336SD16—1722no—
337D8—1722no—
338M16—81no—
339M16—862no—
340M16—1721no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—81no—
348C2×C8—862no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4(C2×D43)⋊C411yescharacteristic
361C4⋊C4(C2×D43)⋊C411yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—1721no—
368C22⋊C4—1721no—
369C42—21no—
370C42C2×D17211yescharacteristic
371C42#1062189811yescharacteristic
372C42C2×C22⋊D4311yescharacteristic
373C42C2×C22⋊D4311yescharacteristic
374C23—21no—
375C23—862no—
376C23—1721no—
377C23—1721no—
378C23—1721no—
379C23—1721no—
380C23—1721no—
381C23—1721no—
382C23C4×C22⋊D4311yescharacteristic
383Q8—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—862no—
388D4—862no—
389D4—1721no—
390D4—1721no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4C2×(C2×D43)⋊C411yescharacteristic
409C2×C4C4×C22⋊D4311yescharacteristic
410C2×C4#1306329411yescharacteristic
411C2×C4#1306329911yescharacteristic
412C2×C4#1306329911yescharacteristic
413C2×C4#1306330811yescharacteristic
414C8—41no—
415C8—41no—
416C8—41no—
417C8—41no—
418C8—1722no—
419C8—1721no—
420C8—1721no—
421C8—1722no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22—3441no—
431C22—1722no—
432C22—1722no—
433C22—1722no—
434C22#1458277811yescharacteristic
435C22#1458301411yescharacteristic
436C22#1458301911yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—3441no—
446C4#1458306711yescharacteristic
447C4#1458307211yescharacteristic
448C2—21no—
449C2—21no—
450C2—81no—
451C2—3442no—
452C2#1913492211yescharacteristic
453C2#1913497111yescharacteristic
454C2#1913501311yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2992C2
socleC22×C43#386
prime radical#14583032C4
cosocleC2×C42×C43C23
hypercenter#2992D43
hypocenterC43#9052
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2992

Complements

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

NH ≅ G/Ntype
2. #19135392C2semidirect
3. #19133183C2semidirect
4. #19133037C2semidirect
5. #19132493C2semidirect
6. #19132445C2semidirect
7. C43×#2992C2semidirect
222. #2992D43semidirect
262. C43#9052semidirect

Maximal subgroups

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

subgroupindex
#191446382
#191353922
#191331832
#191330372
#191324932
#191324452
C43×#29922
#905243