Finite Group Databasebeta

← #24988173

Subgroups — #24988173

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135390C211yesmaximal, characteristic, complemented
2#19134587C211yesmaximal, characteristic, complemented
3#19133285C211yesmaximal, characteristic, complemented
4#19133272C211yesmaximal, characteristic, complemented
5#19133050C211yesmaximal, characteristic, complemented
6#19133046C211yesmaximal, characteristic, complemented
7C43×#3506C211yesmaximal, characteristic
8#14582923C2211yescharacteristic
9#14582923C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063242—21no—
12C2×C22⋊(C43⋊C8)—22no—
13C2×C4×C43⋊C8C2211yescharacteristic
14#14582668—21no—
15#14582648—21no—
16#14582645—21no—
17#14582645—21no—
18#14582643—21no—
19Q8⋊(C43⋊C8)—22no—
20D4⋊(C43⋊C8)—22no—
21C43×#559—22no—
22C43×#556—21no—
23C43×#555—21no—
24C43×#553—22no—
25C43×#550—21no—
26C43×#547—21no—
27C43×#538C414yes—
28C43×#535—21no—
29C43×#533C2211yescharacteristic
30C43×#532C2211yescharacteristic
31C43×#525—22no—
32C43×#520—21no—
33C2×C4×D4×C43C2211yescharacteristic
34C2×#10621877—21no—
35C2×#10621877—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063242—42no—
45C22⋊(C43⋊C8)—44no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8—21no—
48C2×#41×C43—22no—
49C2×#41×C43—21no—
50C22×D4×C43D411yescharacteristic
51C23×C4×C43D412yes—
52C4⋊Q8×C43D411yescharacteristic
53C4⋊Q8×C43D411yescharacteristic
54C4⋊Q8×C43D411yescharacteristic
55#127×C43—22no—
56#127×C43D411yescharacteristic
57#126×C43—24no—
58#125×C43—21no—
59#124×C43—22no—
60#124×C43—24no—
61#124×C43—21no—
62#123×C43—24no—
63#123×C43—24no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43C2×C412yes—
67#121×C43—22no—
68#121×C43—22no—
69#121×C43—22no—
70#121×C43—24no—
71#121×C43—21no—
72#121×C43C2×C412yes—
73#120×C43—24no—
74C4×Q8×C43—22no—
75C4×Q8×C43—21no—
76C4×Q8×C43D412yes—
77C4×D4×C43—22no—
78C4×D4×C43—24no—
79C4×D4×C43—24no—
80C4×D4×C43—21no—
81C4×D4×C43—21no—
82C4×D4×C43—21no—
83C4×D4×C43—21no—
84C4×D4×C43—21no—
85C4×D4×C43D412yes—
86#117×C43—22no—
87#117×C43—22no—
88#117×C43—21no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C22⋊C4×C43C2×C412yes—
92C2×C42×C43C2311yescharacteristic
93C24×C43C22⋊C412yes—
94#41×C43—41no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—82no—
99#41×C43—82no—
100C2×Q8×C43—21no—
101C2×Q8×C43—21no—
102C2×Q8×C43C22⋊C412yes—
103C2×D4×C43—24no—
104C2×D4×C43—24no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—22no—
114C2×D4×C43C22⋊C412yes—
115C22×C4×C43—24no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43C22⋊C412yes—
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C4⋊C4×C43—24no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43C22⋊C412yes—
135C4⋊C4×C43C22⋊C412yes—
136C22⋊C4×C43—24no—
137C22⋊C4×C43—24no—
138C22⋊C4×C43—24no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—22no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C42×C43—24no—
145C42×C43—22no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150#10621877—41no—
151#10621877—41no—
152#10621877—41no—
153#10621877—41no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—41no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—42no—
158C2×C43⋊C8—41no—
159C2×C43⋊C8—41no—
160C2×C43⋊C8—41no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—42no—
166C23×C43—42no—
167C23×C43C2×C22⋊C411yescharacteristic
168Q8×C43—42no—
169Q8×C43—41no—
170Q8×C43—41no—
171Q8×C43—41no—
172Q8×C43—41no—
173D4×C43—42no—
174D4×C43—42no—
175D4×C43—42no—
176D4×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—41no—
180D4×C43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—84no—
185D4×C43—84no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—82no—
199C2×C4×C43—84no—
200C2×C4×C43C2×C22⋊C411yescharacteristic
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#12011yescharacteristic
206C2×C4×C43#13511yescharacteristic
207C2×C4×C43#13511yescharacteristic
208C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
209C2×C4×C43#13711yescharacteristic
210C43⋊C8—42no—
211C43⋊C8—81no—
212C43⋊C8—81no—
213C43⋊C8—81no—
214#8358—431nomaximal, Sylow
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—44no—
218C22×C43—42no—
219C22×C43—42no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—82no—
225C22×C43#37911yescharacteristic
226C22×C43#41611yescharacteristic
227C22×C43#41711yescharacteristic
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—42no—
233C4×C43—42no—
234C4×C43—42no—
235C4×C43#44911yescharacteristic
236C4×C43#44911yescharacteristic
237C4×C43#45211yescharacteristic
238C4×C43#45211yescharacteristic
239C4×C43#45311yescharacteristic
240C4×C43#45511yescharacteristic
241#3506D4311yescharacteristic
242#1954—431no—
243#1800—431no—
244#1550—431no—
245#1547—431no—
246#1493—431no—
247#1492—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—82no—
251C2×C43—82no—
252C2×C43#178811yescharacteristic
253C2×C43#179111yescharacteristic
254C2×C43#179211yescharacteristic
255#559—22no—
256#556—21no—
257#555—21no—
258#553—22no—
259#550—21no—
260#547—21no—
261#538Dic4314yes—
262#535—21no—
263#533C2×D4311yescharacteristic
264#532C2×D4311yescharacteristic
265#525—22no—
266#520—21no—
267C2×C4×D4C2×D4311yescharacteristic
268#423—431no—
269#423—431no—
270C2×C4⋊C8—431no—
271C2×#100—861no—
272C2×C22⋊C8—862no—
273C2×C4×C8—431no—
274#343—861no—
275#333—861no—
276#332—861no—
277#332—861no—
278#331—861no—
279Q8⋊C8—862no—
280D4⋊C8—862no—
281C43#835811yescharacteristic, complemented, Sylow
282C2×#41—22no—
283C2×#41—21no—
284C22×D4C22⋊D4311yescharacteristic
285C23×C4C22⋊D4312yes—
286C2×M16—861no—
287C2×M16—861no—
288C22×C8—861no—
289C22×C8—861no—
290C4⋊Q8C22⋊D4311yescharacteristic
291C4⋊Q8C22⋊D4311yescharacteristic
292C4⋊Q8C22⋊D4311yescharacteristic
293#127—22no—
294#127C22⋊D4311yescharacteristic
295#126—24no—
296#125—21no—
297#124—22no—
298#124—24no—
299#124—21no—
300#123—24no—
301#123—24no—
302C22⋊Q8—22no—
303C22⋊Q8—21no—
304C22⋊Q8C2×Dic4312yes—
305#121—22no—
306#121—22no—
307#121—22no—
308#121—24no—
309#121—21no—
310#121C2×Dic4312yes—
311#120—24no—
312C4×Q8—22no—
313C4×Q8—21no—
314C4×Q8C22⋊D4312yes—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4C22⋊D4312yes—
324#117—22no—
325#117—22no—
326#117—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4C22⋊D4311yescharacteristic
329C2×C22⋊C4C2×Dic4312yes—
330C2×C42C22×D4311yescharacteristic
331C4⋊C8—861no—
332C4⋊C8—861no—
333C4⋊C8—861no—
334C4⋊C8—861no—
335C4⋊C8—861no—
336C4⋊C8—861no—
337#100—1722no—
338C22⋊C8—1724no—
339C4×C8—861no—
340C4×C8—861no—
341C24C22⋊Dic4312yes—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—41no—
346#41—82no—
347#41—82no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8C22⋊Dic4312yes—
351C2×D4—22no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C22⋊Dic4312yes—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4C22⋊Dic4312yes—
370C22×C4C22×Dic4311yescharacteristic
371C22×C4C2×C22⋊D4311yescharacteristic
372C22×C4C2×C22⋊D4311yescharacteristic
373M16—1721no—
374M16—1721no—
375M16—1721no—
376M16—1721no—
377C2×C8—862no—
378C2×C8—1722no—
379C2×C8—1721no—
380C2×C8—1721no—
381C2×C8—1721no—
382C2×C8—1721no—
383C2×C8—1721no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4C22⋊Dic4312yes—
394C4⋊C4C22⋊Dic4312yes—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C42—24no—
404C42—22no—
405C42C2×C22⋊D4311yescharacteristic
406C42C2×C22⋊D4311yescharacteristic
407C42C2×C22⋊D4311yescharacteristic
408C42C2×C22⋊D4311yescharacteristic
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23C2×C22⋊Dic4311yescharacteristic
416Q8—42no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—84no—
433D4—84no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—84no—
448C2×C4C2×C22⋊Dic4311yescharacteristic
449C2×C4C2×C22⋊Dic4311yescharacteristic
450C2×C4#1306329411yescharacteristic
451C2×C4#1306329411yescharacteristic
452C2×C4#1306329411yescharacteristic
453C2×C4#1306329411yescharacteristic
454C2×C4#1306334511yescharacteristic
455C2×C4#1306334511yescharacteristic
456C2×C4#1306335011yescharacteristic
457C2×C4#1306335511yescharacteristic
458C8—3441no—
459C8—3441no—
460C8—3441no—
461C8—1722no—
462C22—21no—
463C22—21no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—82no—
472C22#1458275511yescharacteristic
473C22#1458289511yescharacteristic
474C22#1458290011yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4#1458304411yescharacteristic
483C4#1458304411yescharacteristic
484C4#1458306111yescharacteristic
485C4#1458306111yescharacteristic
486C4#1458306711yescharacteristic
487C4#1458307711yescharacteristic
488C2—21no—
489C2—21no—
490C2—82no—
491C2—82no—
492C2#1913453511yescharacteristic
493C2#1913454611yescharacteristic
494C2#1913454911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3506C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3506D43
hypocenterC43#8358
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #19135390C2semidirect
2. #19134587C2semidirect
3. #19133285C2semidirect
4. #19133272C2semidirect
5. #19133050C2semidirect
6. #19133046C2semidirect
281. C43#8358semidirect

Maximal subgroups

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

subgroupindex
#191353902
#191345872
#191332852
#191332722
#191330502
#191330462
C43×#35062
#835843