Finite Group Databasebeta

← #24985068

Subgroups — #24985068

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142946C211yesmaximal, characteristic
2#19134352C211yesmaximal, characteristic
3#19134287C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×#13063324C411yescharacteristic
10C2×#13063303—21no—
11C2×C42×D43C2211yescharacteristic
12C2×(C2×D43)⋊C8—21no—
13C2×C8×Dic43—21no—
14#14582803—21no—
15#14582797C2211yescharacteristic
16#14582794—21no—
17#14582768C411yescharacteristic
18#14582758—21no—
19#14582756C411yescharacteristic
20#14582756C411yescharacteristic
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—24no—
32C2×#10621872—42no—
33C2×#10621872—42no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063324—42no—
37#13063303—42no—
38#13063303—42no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50C42×D43—42no—
51(C2×D43)⋊C8—24no—
52C8×Dic43—42no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C42×C43C2311yescharacteristic
62#95×C43—21no—
63C23×D43C22⋊C411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C2×C4×D43—22no—
75C2×C4×D43—22no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—22no—
81C2×C4×D43—22no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43D812yes—
85C2×C4×D43SD1612yes—
86C2×Dic86—42no—
87C2×Dic86—42no—
88C2×Dic86—42no—
89C2×C8×C43—22no—
90C2×C8×C43—22no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C42×C43—41no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—42no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—41no—
106Dic43⋊C4—42no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—42no—
110Dic43⋊C4—42no—
111C4×Dic43—22no—
112C4×Dic43—22no—
113C4×Dic43—41no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120#10621872—48no—
121C23×C43C2×C22⋊C411yescharacteristic
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43#10212yes—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43#13111yescharacteristic
142C2×C4×C43#13111yescharacteristic
143C2×C4×C43C2×D811yescharacteristic
144C2×C4×C43C2×SD1611yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43#9912yes—
158C2×Dic43#10112yes—
159C2×Dic43#10212yes—
160C2×Dic43#10412yes—
161C2×Dic43#10412yes—
162C4×D43—24no—
163C4×D43—24no—
164C4×D43—42no—
165C4×D43—42no—
166C4×D43—42no—
167C4×D43—42no—
168Dic86—84no—
169C8×C43—42no—
170C8×C43—42no—
171C43⋊C8—42no—
172C43⋊C8—42no—
173#7685—431nomaximal, Sylow
174C22×C43#40811yescharacteristic
175C22×C43C2×#9911yescharacteristic
176C22×C43C2×#10111yescharacteristic
177C22×C43C2×#10211yescharacteristic
178C22×C43#41911yescharacteristic
179C22×C43C2×#10411yescharacteristic
180C22×C43C2×#10411yescharacteristic
181C2×D43—22no—
182C2×D43—22no—
183C2×D43—22no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—81no—
195C4×C43—81no—
196Dic43—22no—
197Dic43—22no—
198Dic43—81no—
199Dic43—81no—
200Dic43#32714yes—
201#2857—431no—
202C4×C22⋊C8—431no—
203#1728—431no—
204#1271—431no—
205#1271—431no—
206#1271—431no—
207#1271D4311yescharacteristic, complemented
208C2×C43#147211yescharacteristic
209C2×C43#148511yescharacteristic
210C2×C43#149211yescharacteristic
211C2×C43C2×#32711yescharacteristic
212C2×C43#150811yescharacteristic
213C2×C43#152611yescharacteristic
214C2×C43#154611yescharacteristic
215D43—42no—
216C22×M16—861no—
217C2×C4⋊Q8—431no—
218C2×C22⋊Q8—861no—
219C22×C42—431no—
220C2×C22⋊C8—861no—
221C2×C4×C8—861no—
222#391—861no—
223#389—431no—
224#389—861no—
225#389C2×D4311yescharacteristic
226#384—431no—
227#380—431no—
228#380—431no—
229#380—861no—
230#336—431no—
231#336—431no—
232#336—861no—
233#336C2×D4311yescharacteristic
234#336C2×D4311yescharacteristic
235C43#768511yescharacteristic, complemented, Sylow
236C22×Q8—861no—
237C23×C4—431no—
238C23×C4—431no—
239C23×C4—431no—
240C2×M16—864no—
241C2×M16—1722no—
242C2×M16—1722no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—861no—
246C22×C8—861no—
247C4⋊Q8—1722no—
248C22⋊Q8—1722no—
249C22⋊Q8—1722no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4C4×D4311yescharacteristic
258C2×C4⋊C4C4×D4311yescharacteristic
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C42—431no—
262C2×C42—431no—
263C2×C42—431no—
264C2×C42—1722no—
265C2×C42C22×D4311yescharacteristic
266C22⋊C8—864no—
267C4×C8—1722no—
268#95—21no—
269#95—861no—
270#95—861no—
271#95—861no—
272C24—431no—
273C2×Q8—1722no—
274C2×Q8—1722no—
275C2×Q8—1722no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—432no—
282C22×C4—432no—
283C22×C4—862no—
284C22×C4—862no—
285C22×C4—862no—
286C22×C4—862no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4C2×C4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298M16—1728no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—1721no—
308C2×C8—1721no—
309C2×C8—1721no—
310C2×C8—1721no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—1721no—
319C4⋊C4—1722no—
320C4⋊C4—1722no—
321C4⋊C4—1722no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C22⋊C4—1722no—
325C22⋊C4—1722no—
326C42—41no—
327C42—862no—
328C42—862no—
329C42—1721no—
330C23—432no—
331C23—861no—
332C23—861no—
333C23—861no—
334C23—861no—
335C23—861no—
336C23—861no—
337C23C22⋊C4×D4311yescharacteristic
338Q8—3444no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—432no—
352C2×C4—432no—
353C2×C4—432no—
354C2×C4—432no—
355C2×C4—432no—
356C2×C4—864no—
357C2×C4—864no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1722no—
365C2×C4—1722no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4#1306333111yescharacteristic
373C2×C4#1306333311yescharacteristic
374C2×C4D8×D4311yescharacteristic
375C2×C4SD16×D4311yescharacteristic
376C2×C4#1306335411yescharacteristic
377C2×C4#1306335711yescharacteristic
378C8—42no—
379C8—42no—
380C8—1722no—
381C8—1722no—
382C22—862no—
383C22—862no—
384C22—862no—
385C22—1721no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22#1458286411yescharacteristic
390C22#99×D4311yescharacteristic
391C22#101×D4311yescharacteristic
392C22#102×D4311yescharacteristic
393C22#1458290611yescharacteristic
394C22#104×D4311yescharacteristic
395C22#104×D4311yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—434no—
405C4—862no—
406C4—862no—
407C4—3441no—
408C4—3441no—
409C2—1722no—
410C2#1913295711yescharacteristic
411C2#1913301411yescharacteristic
412C2#1913304411yescharacteristic
413C2#327×D4311yescharacteristic
414C2#1913311311yescharacteristic
415C2#1913318811yescharacteristic
416C2#1913326511yescharacteristic
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#7685
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
207. #1271D43semidirect
235. C43#7685semidirect

Maximal subgroups

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

subgroupindex
#191429462
#191343522
#191342872
#191324192
#191324182
#191324172
C43×#12712
#768543