Finite Group Databasebeta

← #24984730

Subgroups — #24984730

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D43C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic
3#19134287C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×C4⋊C4×D43—21no—
10C2×C4⋊C4×D43C411yescharacteristic
11C2×C4⋊C4×D43C411yescharacteristic
12C2×C42×D43C2211yescharacteristic
13C2×(C2×D43)⋊C8—21no—
14#14582798C411yescharacteristic
15#14582797C2211yescharacteristic
16#14582796—21no—
17#14582795C411yescharacteristic
18#14582794—21no—
19#95×D43—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C4×D43—21no—
28C22×C4×D43—21no—
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C2×#10621872—24no—
33C2×#10621872—42no—
34C2×#10621872—42no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C4⋊C4×D43—22no—
45C4⋊C4×D43—22no—
46C4⋊C4×D43—42no—
47C4⋊C4×D43—42no—
48C4⋊C4×D43—42no—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C42×D43—42no—
53(C2×D43)⋊C8—42no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C42×C43C2311yescharacteristic
63#95×C43—21no—
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—22no—
78C2×C4×D43—24no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—22no—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×C4×D43—41no—
86C2×C4×D43—42no—
87C2×C4×D43—42no—
88C2×C4×D43—42no—
89C2×C4×D43—42no—
90C2×C4×D43—42no—
91C2×C4×D43SD1612yes—
92C2×C4×D43Q1612yes—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43M1612yescomplemented
104C42×C43—41no—
105C4⋊Dic43—21no—
106C4⋊Dic43—42no—
107C4⋊Dic43—41no—
108C4⋊Dic43M1612yescomplemented
109Dic43⋊C4—24no—
110Dic43⋊C4—42no—
111Dic43⋊C4—42no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—41no—
115C4×Dic43—41no—
116C4×Dic43—41no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123#10621872—48no—
124C23×C43C2×C22⋊C411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43#9912yes—
130C22×D43#10312yes—
131C22×D43#10412yes—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43C2×M1611yescharacteristic
145C2×C4×C43C2×M1611yescharacteristic
146C2×C4×C43C2×SD1611yescharacteristic
147C2×C4×C43C2×Q1611yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—22no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43#10112yes—
164C2×Dic43#10312yes—
165C4×D43—24no—
166C4×D43—24no—
167C4×D43—24no—
168C4×D43—24no—
169C4×D43—42no—
170C4×D43—42no—
171C4×D43—48no—
172C4×D43—84no—
173C8×C43—42no—
174C8×C43—81no—
175C43⋊C8—42no—
176C43⋊C8—81no—
177#7607—431nomaximal, Sylow
178C22×C43#40711yescharacteristic
179C22×C43C2×#9911yescharacteristic
180C22×C43C2×#10111yescharacteristic
181C22×C43C2×#10311yescharacteristic
182C22×C43#41811yescharacteristic
183C22×C43C2×#10411yescharacteristic
184C22×C43#42111yescharacteristic
185C2×D43—22no—
186C2×D43—22no—
187C2×D43—22no—
188C2×D43—22no—
189C2×D43—22no—
190C2×D43—22no—
191C2×D43#32814yes—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—42no—
199C4×C43—81no—
200Dic43—22no—
201Dic43—22no—
202Dic43—42no—
203Dic43—41no—
204Dic43—81no—
205C2×#389—431no—
206#1817—431no—
207#1728—431no—
208#1271—431no—
209#1271—431no—
210#1271—431no—
211#1271D4311yescharacteristic, complemented
212C2×C43#146311yescharacteristic
213C2×C43#148711yescharacteristic
214C2×C43#149011yescharacteristic
215C2×C43C2×#32811yescharacteristic
216C2×C43#151011yescharacteristic
217C2×C43#152811yescharacteristic
218C2×C43#154911yescharacteristic
219D43—24no—
220C22×M16—861no—
221C22×C4⋊C4—431no—
222C22×C4⋊C4—431no—
223C22×C4⋊C4—861no—
224C22×C42—431no—
225C2×C22⋊C8—861no—
226#389—431no—
227#389—431no—
228#389—431no—
229#389—861no—
230#389—861no—
231#389C2×D4311yescharacteristic
232C2×#95—861no—
233#336—431no—
234#336—431no—
235#336—861no—
236#336—861no—
237#336C2×D4311yescharacteristic
238#336C2×D4311yescharacteristic
239C43#760711yescharacteristic, complemented, Sylow
240C23×C4—431no—
241C23×C4—431no—
242C23×C4—431no—
243C23×C4—861no—
244C23×C4—861no—
245C2×M16—864no—
246C2×M16—1722no—
247C2×M16—1722no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—861no—
251C22×C8—861no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—862no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4—862no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—1722no—
263C2×C4⋊C4—1722no—
264C2×C4⋊C4—1722no—
265C2×C4⋊C4C4×D4311yescharacteristic
266C2×C4⋊C4C4×D4311yescharacteristic
267C2×C42—431no—
268C2×C42—431no—
269C2×C42—431no—
270C2×C42—1722no—
271C2×C42C22×D4311yescharacteristic
272C22⋊C8—1722no—
273#95—21no—
274#95—861no—
275#95—861no—
276#95—861no—
277C24—431no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—432no—
283C22×C4—432no—
284C22×C4—431no—
285C22×C4—862no—
286C22×C4—862no—
287C22×C4—862no—
288C22×C4—862no—
289C22×C4—862no—
290C22×C4—864no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—1721no—
298C22×C4—1722no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4—1722no—
302C22×C4—1722no—
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305C22×C4D4×D4311yescharacteristic
306M16—1728no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—862no—
314C2×C8—1721no—
315C2×C8—1721no—
316C2×C8—1721no—
317C2×C8—1721no—
318C2×C8—1721no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—432no—
324C4⋊C4—864no—
325C4⋊C4—861no—
326C4⋊C4—1721no—
327C4⋊C4—1722no—
328C4⋊C4—1722no—
329C4⋊C4—1722no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C4⋊C4#1062187212yescomplemented
333C42—41no—
334C42—1721no—
335C42—1721no—
336C42—1721no—
337C23—432no—
338C23—432no—
339C23—432no—
340C23—861no—
341C23—861no—
342C23—861no—
343C23—861no—
344C23C22⋊C4×D4311yescharacteristic
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—432no—
358C2×C4—432no—
359C2×C4—864no—
360C2×C4—864no—
361C2×C4—864no—
362C2×C4—864no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—862no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—3444no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4—1728no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4M16×D4311yescharacteristic
381C2×C4C2×#1062187211yescharacteristic
382C2×C4SD16×D4311yescharacteristic
383C2×C4Q16×D4311yescharacteristic
384C2×C4#1306334911yescharacteristic
385C2×C4#1306335211yescharacteristic
386C8—42no—
387C8—81no—
388C8—3441no—
389C8—1722no—
390C22—434no—
391C22—862no—
392C22—862no—
393C22—862no—
394C22—862no—
395C22—862no—
396C22—862no—
397C22#1458286111yescharacteristic
398C22#99×D4311yescharacteristic
399C22#101×D4311yescharacteristic
400C22#103×D4311yescharacteristic
401C22#1458290211yescharacteristic
402C22#104×D4311yescharacteristic
403C22#1458291411yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—862no—
413C4—862no—
414C4—3441no—
415C4—1722no—
416C4—1721no—
417C2—864no—
418C2#1913292311yescharacteristic
419C2#1913302211yescharacteristic
420C2#1913303611yescharacteristic
421C2#328×D4311yescharacteristic
422C2#1913312211yescharacteristic
423C2#1913319511yescharacteristic
424C2#1913327811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7607
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #19132419C2semidirect
5. #19132418C2semidirect
6. #19132417C2semidirect
7. C43×#1271C2semidirect
103. C4⋊C4×C43M16semidirect
108. C4⋊Dic43M16semidirect
211. #1271D43semidirect
239. C43#7607semidirect
332. C4⋊C4#10621872semidirect

Maximal subgroups

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

subgroupindex
#389×D432
#191346622
#191342872
#191324192
#191324182
#191324172
C43×#12712
#760743