Finite Group Databasebeta

← #25067288

Subgroups — #25067288

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145165C211yesmaximal, characteristic
2#19143746C212yesmaximal, complemented
3#19133499C212yesmaximal, complemented
4#19133493C211yesmaximal, characteristic, complemented
5#19133481C211yesmaximal, characteristic, complemented
6#19133409C212yesmaximal, complemented
7C8×Dic172C211yesmaximal, characteristic, complemented
8C8×D344C211yesmaximal, characteristic, complemented
9#19133354C211yesmaximal, characteristic, complemented
10#19133061C212yesmaximal, complemented
11C43×#1450C211yesmaximal, characteristic, complemented
12#14583433C2212yes—
13#14583301C411yescharacteristic
14#14583283C411yescharacteristic
15#14583254C412yes—
16#14583140C411yescharacteristic
17#14583135C411yescharacteristic
18#14583128C412yes—
19#14583029C2212yes—
20C8×Dic86C2212yes—
21C4×Dic172C2211yescharacteristic
22C4×#10621873C2212yes—
23C4×D344C2211yescharacteristic
24#14582978C2212yes—
25#14582974—22no—
26#14582973—22no—
27C8×D172C2212yes—
28#14582959—22no—
29#14582924—22no—
30#14582923C2212yes—
31#14582652C2211yescharacteristic
32#14582652C2211yescharacteristic
33#14582652C2212yes—
34#14582631C2212yes—
35#14582631C2212yes—
36#14582628C2212yes—
37#14582628C2212yes—
38C43×#431C2211yescharacteristic
39C43×#431C2211yescharacteristic
40C2×C4×C8×C43C2211yescharacteristic
41C43×#322C2211yescharacteristic
42C43×#322C2211yescharacteristic
43C82×C43C2211yescharacteristic
44C82×C43C2211yescharacteristic
45C2×Dic172C2×C411yescharacteristic
46C2×#10621873C2×C412yes—
47C2×D344C2×C411yescharacteristic
48C2×#10621877—22no—
49C2×#10621872—22no—
50C2×C8×D43—22no—
51#13063319—22no—
52#13063317C2×C412yes—
53#13063313C2×C412yes—
54#13063308—22no—
55#13063304C2×C412yes—
56#13063299C2×C412yes—
57C4×Dic86C2312yes—
58C4×D172C2312yes—
59C4×C22⋊D43—22no—
60#13063282—22no—
61#13063259C2×C411yescharacteristic
62#13063259C2×C411yescharacteristic
63#13063257C2×C412yes—
64C4⋊(C43⋊C8)—22no—
65C4⋊(C43⋊C8)C2312yes—
66C4⋊(C43⋊C8)C2312yes—
67Dic43⋊C8—22no—
68Dic43⋊C8—22no—
69#13063250C2×C412yes—
70#13063250C2×C412yes—
71#13063247C2×C412yes—
72#13063247C2×C412yes—
73(C2×D43)⋊C8—22no—
74(C2×D43)⋊C8—22no—
75#13063235—22no—
76C8×Dic43—22no—
77C22×C8×C43C2×C411yescharacteristic
78C22×C8×C43C2×C411yescharacteristic
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43—21no—
81C4⋊C8×C43D411yescharacteristic
82C4⋊C8×C43D411yescharacteristic
83C22⋊C8×C43—21no—
84C22⋊C8×C43D411yescharacteristic
85C22⋊C8×C43D411yescharacteristic
86C4×C8×C43C2×C411yescharacteristic
87C4×C8×C43C2×C411yescharacteristic
88C4×C8×C43C2311yescharacteristic
89C4×C8×C43C2311yescharacteristic
90C4×C8×C43C2311yescharacteristic
91C4×C8×C43C2311yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C4×C8×C43C2311yescharacteristic
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×C22⋊D43—22no—
98C2×D172C22×C412yes—
99C2×C4×D43—22no—
100C2×Dic86C22×C412yes—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C42×C43C22×C411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43#4111yescharacteristic
116C42×C43C2411yescharacteristic
117C22⋊Dic43—22no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—22no—
121(C2×D43)⋊C4—22no—
122C4⋊Dic43C22×C412yes—
123C4⋊Dic43C22×C412yes—
124Dic43⋊C4—22no—
125Dic43⋊C4—22no—
126Dic43⋊C4—22no—
127Dic43⋊C4—22no—
128C4×Dic43—22no—
129#10621877—82no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132Dic172—22no—
133D344—22no—
134#10621873—24no—
135#10621872—82no—
136C8×D43—82no—
137C23×C43C4×D411yescharacteristic
138C22×D43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—41no—
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43C23×C411yescharacteristic
148C2×C4×C43C22×D411yescharacteristic
149C2×C4×C43C2×#4111yescharacteristic
150C22⋊D43—82no—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—22no—
154D172—22no—
155D172—22no—
156C4×D43—42no—
157C4×D43—42no—
158Dic86—22no—
159Dic86—22no—
160C8×C43—21no—
161C8×C43—21no—
162C8×C43—21no—
163C8×C43—21no—
164C8×C43—21no—
165C8×C43—21no—
166C8×C43—41no—
167C8×C43—41no—
168C8×C43#13112yes—
169C8×C43#13112yes—
170C43⋊C8—42no—
171C43⋊C8—42no—
172#17973—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43C2×C4×D411yescharacteristic
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43C2×#13111yescharacteristic
185C4×C43C2×#13111yescharacteristic
186C4×C43#57611yescharacteristic
187C4×C43#57811yescharacteristic
188Dic43—42no—
189Dic43—42no—
190Dic43—42no—
191#3168—431no—
192#2993—432no—
193#1592—432no—
194#1591—431no—
195#1589—431no—
196SD16⋊C8—432no—
197C8×Q16—431no—
198C8×D8—431no—
199#1567—431no—
200#1495—432no—
201#1450D4311yescharacteristic, complemented
202C2×C43—41no—
203C2×C43#293111yescharacteristic
204C2×C43#295111yescharacteristic
205C2×C43#295711yescharacteristic
206D43—82no—
207#529—432no—
208#499—431no—
209#495—431no—
210#488—432no—
211#467—431no—
212#466—431no—
213#465—432no—
214#446—432no—
215C8×Q8—432no—
216C4×Q16—431no—
217C4×SD16—432no—
218C4×D8—431no—
219#436—432no—
220#436—862no—
221#435—862no—
222C8×D4—432no—
223#433—862no—
224#431C2×D4311yescharacteristic
225#431C2×D4311yescharacteristic
226#424—862no—
227#423—432no—
228C2×C4×C8C2×D4311yescharacteristic
229#335—431no—
230#335—431no—
231#335—432no—
232Q8⋊C8—432no—
233Q8⋊C8—432no—
234D4⋊C8—432no—
235D4⋊C8—432no—
236#322C2×D4311yescharacteristic
237#322C2×D4311yescharacteristic
238C82C2×D4311yescharacteristic
239C82C2×D4311yescharacteristic
240C43#1797311yescharacteristic, complemented, Sylow
241C2×Q16—431no—
242C2×SD16—432no—
243C2×D8—431no—
244C2×M16—862no—
245C2×M16—862no—
246C22×C8—862no—
247C22×C8C4×D4311yescharacteristic
248C22×C8C4×D4311yescharacteristic
249#126—862no—
250#125—432no—
251#124—432no—
252#123—862no—
253C22⋊Q8—432no—
254#121—432no—
255C4×Q8—432no—
256C4×D4—432no—
257C4×D4—862no—
258#117—862no—
259C2×C42C22×D4311yescharacteristic
260#107—431no—
261#107—431no—
262#106—432no—
263C4⋊C8—21no—
264C4⋊C8—432no—
265C4⋊C8—432no—
266C4⋊C8—862no—
267C4⋊C8—862no—
268C4⋊C8—862no—
269C4⋊C8D17211yescharacteristic
270C4⋊C8D17211yescharacteristic
271#103—432no—
272#103—432no—
273#102—432no—
274#102—432no—
275C22⋊C8—21no—
276C22⋊C8—862no—
277C22⋊C8—862no—
278C22⋊C8D17211yescharacteristic
279C22⋊C8D17211yescharacteristic
280#97—862no—
281C4×C8—862no—
282C4×C8C4×D4311yescharacteristic
283C4×C8C4×D4311yescharacteristic
284C4×C8C22×D4311yescharacteristic
285C4×C8C22×D4311yescharacteristic
286C4×C8C22×D4311yescharacteristic
287C4×C8C22×D4311yescharacteristic
288C4×C8C22×D4311yescharacteristic
289C4×C8C22×D4311yescharacteristic
290C2×Q8—432no—
291C2×D4—432no—
292C2×D4—862no—
293C22×C4—862no—
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4C2×D17211yescharacteristic
296C22×C4#1062189811yescharacteristic
297Q16—862no—
298SD16—864no—
299D8—862no—
300M16—3442no—
301M16—3442no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—3442no—
309C2×C8C2×C4×D4311yescharacteristic
310C2×C8C2×C4×D4311yescharacteristic
311C2×C8C2×C4×D4311yescharacteristic
312C2×C8C2×C4×D4311yescharacteristic
313C2×C8C2×D17211yescharacteristic
314C2×C8C2×D17211yescharacteristic
315C2×C8C2×D17211yescharacteristic
316C2×C8C2×D17211yescharacteristic
317C4⋊C4—432no—
318C4⋊C4—432no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C4⋊C4—862no—
322C4⋊C4—862no—
323C22⋊C4—862no—
324C22⋊C4—862no—
325C22⋊C4—862no—
326C22⋊C4—862no—
327C22⋊C4—862no—
328C42—862no—
329C42C2×C4×D4311yescharacteristic
330C42C2×D17211yescharacteristic
331C42#1062189811yescharacteristic
332C42C23×D4311yescharacteristic
333C23—862no—
334C23C4×D17211yescharacteristic
335Q8—862no—
336Q8—862no—
337D4—862no—
338D4—862no—
339D4—3442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—862no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4C4×D17211yescharacteristic
351C2×C4C4×D17211yescharacteristic
352C2×C4C4×D17211yescharacteristic
353C2×C4C22×C4×D4311yescharacteristic
354C2×C4C22×D17211yescharacteristic
355C2×C4C2×#1062189811yescharacteristic
356C8—21no—
357C8—21no—
358C8—21no—
359C8—21no—
360C8—21no—
361C8—21no—
362C8—41no—
363C8—41no—
364C8—1722no—
365C8—1722no—
366C8#1306333112yes—
367C8#1306333112yes—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—1722no—
372C22—1722no—
373C22—1722no—
374C22C2×C4×D17211yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—1722no—
380C4—1722no—
381C4—1722no—
382C4C2×#1306333111yescharacteristic
383C4C2×#1306333111yescharacteristic
384C4#1458370411yescharacteristic
385C4#1458371611yescharacteristic
386C2—41no—
387C2—3442no—
388C2#1914330811yescharacteristic
389C2#1914347211yescharacteristic
390C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1450C2
socleC22×C43C2×C4×D4
prime radical#14583135C4
cosocleC42×C43C24
hypercenter#1450D43
hypocenterC43#17973
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
2. #19143746C2semidirect
3. #19133499C2semidirect
4. #19133493C2semidirect
5. #19133481C2semidirect
6. #19133409C2semidirect
7. C8×Dic172C2semidirect
8. C8×D344C2semidirect
9. #19133354C2semidirect
10. #19133061C2semidirect
11. C43×#1450C2semidirect
201. #1450D43semidirect
240. C43#17973semidirect

Maximal subgroups

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

subgroupindex
#191451652
#191437462
#191334992
#191334932
#191334812
#191334092
C8×Dic1722
C8×D3442
#191333542
#191330612
C43×#14502
#1797343