Finite Group Databasebeta

← #24988903

Subgroups — #24988903

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135445C211yesmaximal, characteristic, complemented
2#19133325C211yesmaximal, characteristic, complemented
3#19133202C211yesmaximal, characteristic, complemented
4#19133060C211yesmaximal, characteristic, complemented
5#19133016C211yesmaximal, characteristic, complemented
6#19132947C211yesmaximal, characteristic, complemented
7C43×#3561C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9#14582952C2211yescharacteristic
10#14582923C2211yescharacteristic
11C2×#13063244—21no—
12C2×#13063242—21no—
13C4×#10621877C2211yescharacteristic
14#14582648—21no—
15#14582645—21no—
16#14582641—21no—
17#14582639—21no—
18Q8⋊(C43⋊C8)—22no—
19Q8⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—21no—
21#14582623—22no—
22C43×#563—21no—
23C43×#562—21no—
24C43×#556—21no—
25C43×#551—22no—
26D4×Q8×C43—21no—
27C43×#548—21no—
28C43×#546—21no—
29C43×#543C412yes—
30C43×#542—21no—
31C43×#542—22no—
32C43×#538C412yes—
33C43×#536—21no—
34C43×#533C2211yescharacteristic
35C43×#529C2211yescharacteristic
36C2×#124×C43C2211yescharacteristic
37C2×#10621877—21no—
38C2×#10621877—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43#13063244—42no—
44#13063242—42no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47#13063236—21no—
48#13063236—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C2×#41×C43—21no—
52C22×Q8×C43—21no—
53C22×Q8×C43D411yescharacteristic
54C22×D4×C43D411yescharacteristic
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—22no—
57C4⋊Q8×C43D411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59#126×C43—22no—
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—21no—
63#125×C43—21no—
64#125×C43D411yescharacteristic
65#124×C43—21no—
66#124×C43—22no—
67#124×C43—22no—
68#124×C43—21no—
69#124×C43—21no—
70#124×C43—21no—
71#124×C43—21no—
72#124×C43D411yescharacteristic
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—21no—
77#123×C43—22no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43C2×C411yescharacteristic
88C22⋊Q8×C43C2×C412yes—
89#121×C43—21no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43C2×C411yescharacteristic
93#120×C43—22no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43D411yescharacteristic
97C4×Q8×C43D412yes—
98C4×D4×C43—21no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—21no—
102C4×D4×C43D411yescharacteristic
103#117×C43—22no—
104#117×C43—21no—
105#117×C43—21no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43C2×C412yes—
108C2×C22⋊C4×C43D412yes—
109C2×C42×C43C2311yescharacteristic
110C24×C43C22⋊C412yes—
111#41×C43—81no—
112#41×C43—81no—
113C2×Q8×C43—22no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—41no—
118C2×Q8×C43—41no—
119C2×Q8×C43—81no—
120C2×Q8×C43—81no—
121C2×Q8×C43C22⋊C411yescharacteristic
122C2×Q8×C43C22⋊C412yes—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—41no—
129C2×D4×C43—41no—
130C2×D4×C43C22⋊C411yescharacteristic
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43C22⋊C412yes—
136C22×C4×C43C22×C411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43C22⋊C411yescharacteristic
153C4⋊C4×C43C22⋊C411yescharacteristic
154C4⋊C4×C43C22⋊C412yes—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—21no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—21no—
166C22⋊C4×C43—21no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—22no—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—21no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177#10621877—22no—
178#10621877—41no—
179#10621877—41no—
180#10621877—41no—
181C2×C43⋊C8—41no—
182C2×C43⋊C8—41no—
183C2×C43⋊C8—41no—
184C2×C43⋊C8—41no—
185C23×C43—22no—
186C23×C43—21no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43C2×C22⋊C411yescharacteristic
191Q8×C43—41no—
192Q8×C43—42no—
193Q8×C43—41no—
194Q8×C43—41no—
195Q8×C43—41no—
196Q8×C43—41no—
197Q8×C43—81no—
198Q8×C43—82no—
199D4×C43—41no—
200D4×C43—42no—
201D4×C43—41no—
202D4×C43—41no—
203D4×C43—81no—
204D4×C43—82no—
205D4×C43—82no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—82no—
220C2×C4×C43—82no—
221C2×C4×C43—82no—
222C2×C4×C43C2×C22⋊C411yescharacteristic
223C2×C4×C43C2×C22⋊C411yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C43⋊C8—42no—
229C43⋊C8—81no—
230C43⋊C8—81no—
231C43⋊C8—81no—
232#8484—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—42no—
237C22×C43—41no—
238C22×C43—42no—
239C22×C43—41no—
240C22×C43—42no—
241C22×C43—41no—
242C22×C43—162no—
243C22×C43#37911yescharacteristic
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—41no—
250C4×C43—42no—
251C4×C43—42no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—42no—
255C4×C43#45311yescharacteristic
256C4×C43#45511yescharacteristic
257#3561D4311yescharacteristic
258#1967—431no—
259#1559—431no—
260#1529—431no—
261#1495—431no—
262#1485—431no—
263#1469—431no—
264C2×C43—41no—
265C2×C43—81no—
266C2×C43—82no—
267C2×C43#179111yescharacteristic
268C2×C43#179211yescharacteristic
269C2×C43#179611yescharacteristic
270#563—21no—
271#562—21no—
272#556—21no—
273#551—22no—
274D4×Q8—21no—
275#548—21no—
276#546—21no—
277#543Dic4312yes—
278#542—21no—
279#542—22no—
280#538Dic4312yes—
281#536—21no—
282#533C2×D4311yescharacteristic
283#529C2×D4311yescharacteristic
284C2×#124C2×D4311yescharacteristic
285#432—431no—
286#431—431no—
287#423—431no—
288C2×#101—861no—
289C2×#100—861no—
290C4×M16—431no—
291#333—861no—
292#332—861no—
293#330—861no—
294#329—861no—
295Q8⋊C8—862no—
296Q8⋊C8—861no—
297D4⋊C8—861no—
298#323—862no—
299C43#848411yescharacteristic, complemented, Sylow
300C2×#41—21no—
301C22×Q8—21no—
302C22×Q8C22⋊D4311yescharacteristic
303C22×D4C22⋊D4311yescharacteristic
304C2×M16—861no—
305C2×M16—861no—
306C4⋊Q8—21no—
307C4⋊Q8—22no—
308C4⋊Q8C22⋊D4311yescharacteristic
309C4⋊Q8C22⋊D4311yescharacteristic
310#126—22no—
311#126—22no—
312#126—22no—
313#126—21no—
314#125—21no—
315#125C22⋊D4311yescharacteristic
316#124—21no—
317#124—22no—
318#124—22no—
319#124—21no—
320#124—21no—
321#124—21no—
322#124—21no—
323#124C22⋊D4311yescharacteristic
324#123—22no—
325#123—22no—
326#123—22no—
327#123—21no—
328#123—22no—
329C22⋊Q8—22no—
330C22⋊Q8—21no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—21no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8C2×Dic4311yescharacteristic
339C22⋊Q8C2×Dic4312yes—
340#121—21no—
341#121—22no—
342#121—22no—
343#121C2×Dic4311yescharacteristic
344#120—22no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C22⋊D4311yescharacteristic
348C4×Q8C22⋊D4312yes—
349C4×D4—21no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—21no—
353C4×D4C22⋊D4311yescharacteristic
354#117—22no—
355#117—21no—
356#117—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4C2×Dic4312yes—
359C2×C22⋊C4C22⋊D4312yes—
360C2×C42C22×D4311yescharacteristic
361C4⋊C8—861no—
362C4⋊C8—861no—
363C4⋊C8—861no—
364C4⋊C8—861no—
365#101—1722no—
366#100—1722no—
367C22⋊C8—861no—
368C22⋊C8—861no—
369#97—861no—
370#97—861no—
371C4×C8—861no—
372C4×C8—861no—
373C24C22⋊Dic4312yes—
374#41—81no—
375#41—81no—
376C2×Q8—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—81no—
383C2×Q8—81no—
384C2×Q8C22⋊Dic4311yescharacteristic
385C2×Q8C22⋊Dic4312yes—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4C22⋊Dic4311yescharacteristic
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4C22⋊Dic4312yes—
399C22×C4C22×Dic4311yescharacteristic
400C22×C4C2×C22⋊D4311yescharacteristic
401C22×C4C2×C22⋊D4311yescharacteristic
402M16—862no—
403M16—1721no—
404M16—1721no—
405M16—1721no—
406C2×C8—1721no—
407C2×C8—1721no—
408C2×C8—1721no—
409C2×C8—1721no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4C22⋊Dic4311yescharacteristic
424C4⋊C4C22⋊Dic4311yescharacteristic
425C4⋊C4C22⋊Dic4312yes—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—21no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—21no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C42—22no—
442C42—22no—
443C42—21no—
444C42C2×C22⋊D4311yescharacteristic
445C42C2×C22⋊D4311yescharacteristic
446C42C2×C22⋊D4311yescharacteristic
447C42C2×C22⋊D4311yescharacteristic
448C23—22no—
449C23—21no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23C2×C22⋊Dic4311yescharacteristic
454Q8—41no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—41no—
460Q8—81no—
461Q8—82no—
462D4—41no—
463D4—42no—
464D4—41no—
465D4—41no—
466D4—81no—
467D4—82no—
468D4—82no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4C2×C22⋊Dic4311yescharacteristic
486C2×C4C2×C22⋊Dic4311yescharacteristic
487C2×C4#1306329411yescharacteristic
488C2×C4#1306329411yescharacteristic
489C2×C4#1306329411yescharacteristic
490C2×C4#1306329411yescharacteristic
491C8—3441no—
492C8—3441no—
493C8—3441no—
494C8—1722no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—162no—
505C22#1458275511yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—41no—
512C4—42no—
513C4—41no—
514C4—42no—
515C4—42no—
516C4—41no—
517C4#1458306711yescharacteristic
518C4#1458307711yescharacteristic
519C2—41no—
520C2—82no—
521C2—81no—
522C2#1913454611yescharacteristic
523C2#1913454911yescharacteristic
524C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3561C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3561D43
hypocenterC43#8484
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3561

Complements

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

NH ≅ G/Ntype
1. #19135445C2semidirect
2. #19133325C2semidirect
3. #19133202C2semidirect
4. #19133060C2semidirect
5. #19133016C2semidirect
6. #19132947C2semidirect
299. C43#8484semidirect

Maximal subgroups

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

subgroupindex
#191354452
#191333252
#191332022
#191330602
#191330162
#191329472
C43×#35612
#848443