Finite Group Databasebeta

← #25080033

Subgroups — #25080033

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145770C212yesmaximal
2#19145181C211yesmaximal, characteristic, complemented
3#19134123C211yesmaximal, characteristic, complemented
4#19134118C211yesmaximal, characteristic, complemented
5#19134089C211yesmaximal, characteristic, complemented
6#19134084C211yesmaximal, characteristic, complemented
7#19134053C212yesmaximal, complemented
8#19134046C212yesmaximal, complemented
9#19133343C211yesmaximal, characteristic, complemented
10#19133306C212yesmaximal, complemented
11C43×#2966C211yesmaximal, characteristic
12#14583456C2212yes—
13#14583304C2211yescharacteristic
14#14583298—22no—
15#14583279C2211yescharacteristic
16#14583253—22no—
17#14583250C2212yes—
18#14583237—22no—
19#14583220—22no—
20#14583194C2212yes—
21#14583189C2212yes—
22#14583184C2212yes—
23#14583179C2212yes—
24#14583140—21no—
25#14583140—21no—
26C4×Dic172—21no—
27C4×Dic172—21no—
28#14582952C2212yes—
29#14582652C2212yes—
30#14582650C2211yescharacteristic
31#14582650C2211yescharacteristic
32#14582647C2212yes—
33#14582647C2212yes—
34#14582646C2212yes—
35#14582646C2212yes—
36C43×#529C2211yescharacteristic
37C43×#446C2211yescharacteristic
38C8×Q8×C43C2211yescharacteristic
39C43×#436C2211yescharacteristic
40C43×#435—21no—
41C8×D4×C43—21no—
42C8×D4×C43C2211yescharacteristic
43C43×#433—21no—
44C43×#432C2211yescharacteristic
45C43×#405—21no—
46C2×C4×C8×C43C2211yescharacteristic
47C2×Dic172—21no—
48C2×Dic172—21no—
49#13063325C2312yes—
50#13063325C2312yes—
51#13063317—22no—
52#13063304—22no—
53#13063304—22no—
54C4×Dic86—22no—
55C4×Dic86—22no—
56#13063284—22no—
57#13063259—21no—
58#13063259—21no—
59#13063258—22no—
60#13063258—22no—
61#13063256—22no—
62#13063256—22no—
63C4⋊(C43⋊C8)C2312yes—
64C4⋊(C43⋊C8)C2312yes—
65#13063250—22no—
66#13063250—22no—
67#13063249—22no—
68#13063249—22no—
69#13063246—22no—
70#13063246—22no—
71C22⋊(C43⋊C8)—22no—
72C4×C43⋊C8—22no—
73C2×M16×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43D411yescharacteristic
76C22×C8×C43D411yescharacteristic
77#126×C43—21no—
78#125×C43D411yescharacteristic
79#124×C43D411yescharacteristic
80#123×C43—21no—
81C22⋊Q8×C43D411yescharacteristic
82#121×C43D411yescharacteristic
83C4×Q8×C43C2311yescharacteristic
84C4×D4×C43—21no—
85C4×D4×C43C2311yescharacteristic
86#117×C43—21no—
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43C2311yescharacteristic
91C4⋊C8×C43C2311yescharacteristic
92C22⋊C8×C43—21no—
93C22⋊C8×C43—21no—
94C22⋊C8×C43—21no—
95#97×C43—21no—
96#97×C43—21no—
97C4×C8×C43—21no—
98C4×C8×C43D411yescharacteristic
99C4×C8×C43D411yescharacteristic
100C4×C8×C43C2311yescharacteristic
101C4×C8×C43C2311yescharacteristic
102C2×Q8×C43C2×D411yescharacteristic
103C2×D4×C43—21no—
104C2×D4×C43C2×D411yescharacteristic
105C22×C4×C43—21no—
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C2×Dic86—22no—
110C2×Dic86—22no—
111M16×C43—42no—
112C2×C8×C43—22no—
113C2×C8×C43—21no—
114C2×C8×C43—21no—
115C2×C8×C43—41no—
116C2×C8×C43—42no—
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43C2×D411yescharacteristic
120C2×C8×C43C2×D411yescharacteristic
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43C2×D411yescharacteristic
126C4⋊C4×C43C2×D411yescharacteristic
127C22⋊C4×C43—21no—
128C22⋊C4×C43—21no—
129C22⋊C4×C43—21no—
130C22⋊C4×C43—21no—
131C22⋊C4×C43—21no—
132C42×C43—21no—
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43#4111yescharacteristic
136C42×C43C2411yescharacteristic
137C22⋊Dic43—42no—
138C4⋊Dic43—22no—
139C4⋊Dic43—22no—
140C4⋊Dic43—22no—
141C4⋊Dic43—22no—
142Dic43⋊C4—42no—
143Dic43⋊C4—42no—
144C4×Dic43—42no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—22no—
147Dic172—42no—
148Dic172—42no—
149C23×C43—21no—
150C23×C43#12111yescharacteristic
151Q8×C43—22no—
152D4×C43—22no—
153D4×C43—42no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—22no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43C22×D411yescharacteristic
167C2×C4×C43C22×D411yescharacteristic
168C2×C4×C43C2×#4111yescharacteristic
169C2×Dic43—42no—
170C2×Dic43—42no—
171Dic86—42no—
172Dic86—42no—
173Dic86—82no—
174C8×C43—21no—
175C8×C43—21no—
176C8×C43—21no—
177C8×C43—41no—
178C8×C43—41no—
179C8×C43#13512yes—
180C43⋊C8—42no—
181C43⋊C8—42no—
182#19226—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43C2×#12111yescharacteristic
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—41no—
195C4×C43—41no—
196C4×C43—41no—
197C4×C43C2×#13511yescharacteristic
198C4×C43#57511yescharacteristic
199C4×C43#57812yes—
200Dic43—82no—
201Dic43—82no—
202#3233—432no—
203#3170—431no—
204#2966D4311yescharacteristic
205#1696—431no—
206#1695—431no—
207#1690—431no—
208#1689—431no—
209#1684—432no—
210#1683—432no—
211#1564—431no—
212#1554—432no—
213C2×C43—41no—
214C2×C43—81no—
215C2×C43#303511yescharacteristic
216C2×C43#305911yescharacteristic
217C2×C43#306711yescharacteristic
218#533—432no—
219#529C2×D4311yescharacteristic
220#500—431no—
221#499—862no—
222#494—431no—
223#488—862no—
224#487—432no—
225#485—862no—
226#482—862no—
227#477—432no—
228#476—432no—
229#475—432no—
230#474—432no—
231#467—861no—
232#467—861no—
233#446C2×D4311yescharacteristic
234C8×Q8C2×D4311yescharacteristic
235C4×Q16—861no—
236C4×Q16—861no—
237#436C2×D4311yescharacteristic
238#435—21no—
239C8×D4—21no—
240C8×D4C2×D4311yescharacteristic
241#433—21no—
242#432C2×D4311yescharacteristic
243#431—432no—
244#405—21no—
245C2×C4×C8C2×D4311yescharacteristic
246#335—432no—
247#334—431no—
248#334—431no—
249#333—432no—
250#333—432no—
251#332—432no—
252#332—432no—
253C43#1922611yescharacteristic, complemented, Sylow
254C2×Q16—861no—
255C2×Q16—861no—
256C2×M16—21no—
257C22×C8—21no—
258C22×C8C22⋊D4311yescharacteristic
259C22×C8C22⋊D4311yescharacteristic
260C4⋊Q8—432no—
261C4⋊Q8—432no—
262#126—21no—
263#125—862no—
264#125D17211yescharacteristic
265#124D17211yescharacteristic
266#123—21no—
267C22⋊Q8—862no—
268C22⋊Q8—862no—
269C22⋊Q8D17211yescharacteristic
270#121D17211yescharacteristic
271C4×Q8—862no—
272C4×Q8—862no—
273C4×Q8C22×D4311yescharacteristic
274C4×D4—21no—
275C4×D4C22×D4311yescharacteristic
276#117—21no—
277#117—862no—
278C2×C42C22×D4311yescharacteristic
279#107—861no—
280#107—861no—
281#107—862no—
282#107—862no—
283#106—862no—
284#106—862no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—432no—
288C4⋊C8—432no—
289C4⋊C8C22×D4311yescharacteristic
290C4⋊C8C22×D4311yescharacteristic
291#103—862no—
292#103—862no—
293#103—862no—
294#103—862no—
295#102—862no—
296#102—862no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—862no—
301#97—21no—
302#97—21no—
303C4×C8—21no—
304C4×C8—862no—
305C4×C8C22⋊D4311yescharacteristic
306C4×C8C22⋊D4311yescharacteristic
307C4×C8C22×D4311yescharacteristic
308C4×C8C22×D4311yescharacteristic
309C2×Q8—862no—
310C2×Q8—862no—
311C2×Q8C2×D17211yescharacteristic
312C2×D4—21no—
313C2×D4C2×D17211yescharacteristic
314C22×C4—21no—
315C22×C4C2×D17211yescharacteristic
316C22×C4#1062189811yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318Q16—1722no—
319Q16—1722no—
320M16—42no—
321C2×C8—22no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8—42no—
326C2×C8—862no—
327C2×C8—862no—
328C2×C8C2×C22⋊D4311yescharacteristic
329C2×C8C2×C22⋊D4311yescharacteristic
330C2×C8C2×C22⋊D4311yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—862no—
337C4⋊C4—862no—
338C4⋊C4—862no—
339C4⋊C4—862no—
340C4⋊C4—1722no—
341C4⋊C4—1722no—
342C4⋊C4C2×D17211yescharacteristic
343C4⋊C4C2×D17211yescharacteristic
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—1722no—
350C42—21no—
351C42—1722no—
352C42C2×D17211yescharacteristic
353C42#1062189811yescharacteristic
354C42C2×C22⋊D4311yescharacteristic
355C42C23×D4311yescharacteristic
356C23—21no—
357C23#1306329911yescharacteristic
358Q8—22no—
359Q8—3442no—
360Q8—1722no—
361Q8—1722no—
362D4—22no—
363D4—42no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4#1306329911yescharacteristic
376C2×C4#1306329911yescharacteristic
377C2×C4#1306329911yescharacteristic
378C2×C4C22×C22⋊D4311yescharacteristic
379C2×C4C22×D17211yescharacteristic
380C2×C4C2×#1062189811yescharacteristic
381C8—21no—
382C8—21no—
383C8—21no—
384C8—41no—
385C8—41no—
386C8—1722no—
387C8—1722no—
388C8#1306334512yes—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22C2×#1306329911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—3442no—
404C4—3442no—
405C4C2×#1306334511yescharacteristic
406C4#1458369711yescharacteristic
407C4#1458371612yes—
408C2—41no—
409C2—81no—
410C2#1914405011yescharacteristic
411C2#1914425011yescharacteristic
412C2#1914431511yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2966C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#2966D43
hypocenterC43#19226
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #19145181C2semidirect
3. #19134123C2semidirect
4. #19134118C2semidirect
5. #19134089C2semidirect
6. #19134084C2semidirect
7. #19134053C2semidirect
8. #19134046C2semidirect
9. #19133343C2semidirect
10. #19133306C2semidirect
253. C43#19226semidirect

Maximal subgroups

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

subgroupindex
#191457702
#191451812
#191341232
#191341182
#191340892
#191340842
#191340532
#191340462
#191333432
#191333062
C43×#29662
#1922643