Finite Group Databasebeta

← #24992425

Subgroups — #24992425

Order 11008.

458 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144717C211yesmaximal, characteristic
2#19143684C211yesmaximal, characteristic, complemented
3#19133205C211yesmaximal, characteristic
4#19133089C211yesmaximal, characteristic
5#19132494C211yesmaximal, characteristic, complemented
6#19132451C211yesmaximal, characteristic, complemented
7C43×#1763C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583212—21no—
10#14583194C411yescharacteristic, complemented
11#14583194C411yescharacteristic, complemented
12#14583099C411yescharacteristic, complemented
13#14583099C411yescharacteristic, complemented
14#14583038—21no—
15#14583030—22no—
16#14583030—21no—
17Q8×C43⋊C8—21no—
18#14582997—21no—
19#14582997—21no—
20#14582956—21no—
21#14582956C2211yescharacteristic
22#14582956C2211yescharacteristic
23#14582952—21no—
24#14582952C2211yescharacteristic
25#14582638—22no—
26#14582632—21no—
27#14582632—21no—
28C2×C4×Q8×C43C2211yescharacteristic
29C2×#103×C43—21no—
30C2×#97×C43C2211yescharacteristic
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#340—21no—
33C2×#10621898—21no—
34C2×#10621884—21no—
35C2×#10621884—21no—
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063313—21no—
39#13063299—21no—
40#13063299—21no—
41C4×D172—21no—
42C4×D172—21no—
43#13063258—21no—
44#13063258—21no—
45C4⋊(C43⋊C8)—22no—
46C4⋊(C43⋊C8)—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51#13063249—21no—
52#13063249—21no—
53#13063245—21no—
54#13063245—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D411yescharacteristic
58C22⋊(C43⋊C8)D411yescharacteristic
59#13063236—22no—
60#13063236—21no—
61#13063236D412yes—
62C4×C43⋊C8—22no—
63C4×C43⋊C8—21no—
64C22×Q8×C43D411yescharacteristic
65C22×C8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43C2×C411yescharacteristic
69C4×Q8×C43C2×C411yescharacteristic
70C4×Q8×C43D411yescharacteristic
71C4×Q8×C43D411yescharacteristic
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C42×C43—21no—
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78#103×C43—24no—
79#97×C43—21no—
80#97×C43—21no—
81#95×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—22no—
84C2×Q8×C43—41no—
85C2×Q8×C43C22⋊C411yescharacteristic
86C2×Q8×C43C22⋊C411yescharacteristic
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—41no—
94#10621898—81no—
95#10621898—81no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—21no—
101C2×C8×C43—22no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43C22⋊C411yescharacteristic
112C4⋊C4×C43C22⋊C411yescharacteristic
113C42×C43—21no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43—81no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122#10621884—42no—
123#10621884—42no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—22no—
133C23×C43#12111yescharacteristic
134C22×D43—41no—
135Q8×C43—21no—
136Q8×C43—21no—
137Q8×C43—21no—
138Q8×C43—42no—
139Q8×C43#10412yes—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43C2×C22⋊C411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43#12011yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C22⋊D43—81no—
162C22⋊D43—81no—
163C2×Dic43—41no—
164D172—41no—
165D172—41no—
166D172—81no—
167D172—81no—
168C4×D43—82no—
169Dic86—81no—
170C8×C43—42no—
171C43⋊C8—41no—
172C43⋊C8—41no—
173C43⋊C8—42no—
174C43⋊C8—41no—
175C43⋊C8—41no—
176#9164—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—21no—
179C22×C43#38611yescharacteristic
180C22×C43#47111yescharacteristic
181C22×C43#47211yescharacteristic
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—22no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43—82no—
195C4×C43C2×#10411yescharacteristic
196C4×C43#42111yescharacteristic
197Dic43—81no—
198#3112—431no—
199#2984—431no—
200#1763D4311yescharacteristic, complemented
201#1530—431no—
202#1502—431no—
203#1302—431no—
204#1285—431no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43#187111yescharacteristic
208C2×C43#190511yescharacteristic
209C2×C43#190711yescharacteristic
210D43—161no—
211#532—431no—
212C2×C4×Q8C2×D4311yescharacteristic
213#480—861no—
214#477—431no—
215#477—431no—
216#460—431no—
217#460—431no—
218#448—861no—
219#446—862no—
220#446—861no—
221C8×Q8—861no—
222#440—861no—
223#440—861no—
224#432—431no—
225#432—431no—
226#432—861no—
227#431—431no—
228#431—861no—
229C2×#103—21no—
230C2×#97C2×D4311yescharacteristic
231C4×C4⋊C4C2×D4311yescharacteristic
232#340—21no—
233#329—862no—
234#327—861no—
235#327—861no—
236C43#916411yescharacteristic, complemented, Sylow
237C2×#41—861no—
238C22×Q8C22⋊D4311yescharacteristic
239C2×SD16—861no—
240C2×SD16—861no—
241C22×C8—21no—
242C4⋊Q8—431no—
243#127—431no—
244#124—861no—
245#121—861no—
246#121—861no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8C4×D4311yescharacteristic
250C4×Q8C4×D4311yescharacteristic
251C4×Q8D17211yescharacteristic
252C4×Q8D17211yescharacteristic
253C4×D4—861no—
254C4×D4—861no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C22⋊D4311yescharacteristic
258C2×C42—21no—
259C2×C42—21no—
260C2×C42C22×D4311yescharacteristic
261#107—861no—
262#107—861no—
263C4⋊C8—431no—
264C4⋊C8—431no—
265C4⋊C8—862no—
266C4⋊C8—862no—
267C4⋊C8—861no—
268C4⋊C8—861no—
269#103—24no—
270#103—861no—
271#103—861no—
272#102—861no—
273#102—861no—
274C22⋊C8—431no—
275C22⋊C8—431no—
276C22⋊C8—861no—
277C22⋊C8—861no—
278#97—21no—
279#97—21no—
280#97—432no—
281#97—862no—
282#97—861no—
283C4×C8—862no—
284C4×C8—861no—
285#95—21no—
286#41—3441no—
287#41—3441no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—861no—
292C2×Q8(C2×D43)⋊C411yescharacteristic
293C2×Q8(C2×D43)⋊C411yescharacteristic
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—1721no—
302C22×C4D4×D4311yescharacteristic
303C22×C4#1062190011yescharacteristic
304C22×C4C2×C22⋊D4311yescharacteristic
305SD16—1722no—
306SD16—1722no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—861no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—862no—
314C2×C8—861no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4(C2×D43)⋊C411yescharacteristic
325C4⋊C4(C2×D43)⋊C411yescharacteristic
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—81no—
333C42C2×C4×D4311yescharacteristic
334C42C2×D17211yescharacteristic
335C42D4×D4311yescharacteristic
336C42#1062190011yescharacteristic
337C23—1721no—
338C23#1306329711yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—21no—
342Q8—42no—
343Q8—3441no—
344Q8#1306325312yes—
345D4—3441no—
346D4—3441no—
347D4—3441no—
348D4—3441no—
349D4—1721no—
350D4—1721no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—3442no—
367C2×C4—1721no—
368C2×C4C2×(C2×D43)⋊C411yescharacteristic
369C2×C4(C22⋊D43)⋊C411yescharacteristic
370C2×C4(C22⋊D43)⋊C411yescharacteristic
371C2×C4#1306329511yescharacteristic
372C2×C4#1306329711yescharacteristic
373C2×C4#1306330911yescharacteristic
374C8—42no—
375C8—1721no—
376C8—1722no—
377C8—1721no—
378C8—1721no—
379C8—1721no—
380C22—21no—
381C22—21no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22#1458277611yescharacteristic
386C22#1458316411yescharacteristic
387C22#1458316711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—3441no—
399C4C2×#1306325311yescharacteristic
400C4#1458291711yescharacteristic
401C2—21no—
402C2—21no—
403C2—6881no—
404C2#1913489511yescharacteristic
405C2#1913508711yescharacteristic
406C2#1913510111yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1763C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1763D43
hypocenterC43#9164
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. #19143684C2semidirect
5. #19132494C2semidirect
6. #19132451C2semidirect
7. C43×#1763C2semidirect
10. #14583194C4semidirect
11. #14583194C4semidirect
12. #14583099C4semidirect
13. #14583099C4semidirect
200. #1763D43semidirect
236. C43#9164semidirect

Maximal subgroups

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

subgroupindex
#191447172
#191436842
#191332052
#191330892
#191324942
#191324512
C43×#17632
#916443