Finite Group Databasebeta

← #24992679

Subgroups — #24992679

Order 11008.

478 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#19144385C211yesmaximal, characteristic
2C8×#10621898C211yesmaximal, characteristic
3#19134616C211yesmaximal, characteristic
4#19133093C211yesmaximal, characteristic, complemented
5#19133051C211yesmaximal, characteristic, complemented
6#19132492C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583207—21no—
11#14583200—21no—
12#14583195C411yescharacteristic, complemented
13#14583190C411yescharacteristic, complemented
14#14583185C411yescharacteristic, complemented
15#14583180C411yescharacteristic, complemented
16C8×Dic86—21no—
17C8×D172—21no—
18C8×C22⋊D43—22no—
19#14582952C2211yescharacteristic
20#14582950—21no—
21#14582937—21no—
22#14582923C2211yescharacteristic
23C2×#13063253—21no—
24#14582896—21no—
25C4×C8×D43—21no—
26#14582659—21no—
27#14582635—22no—
28#14582631—21no—
29#14582631—21no—
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C4×C4⋊C4×C43C2211yescharacteristic
33C2×#10621898D411yescharacteristic
34C2×#10621877—21no—
35C2×C8×D43—22no—
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×Dic86C2×C411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172C2×C411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284—21no—
50#13063284D411yescharacteristic
51#13063282—21no—
52C42×D43—21no—
53#13063259—21no—
54#13063259—21no—
55#13063257—21no—
56#13063257—21no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60Dic43⋊C8—22no—
61#13063253—42no—
62#13063250—21no—
63#13063250—21no—
64#13063247—21no—
65#13063247—21no—
66C22⋊(C43⋊C8)D412yes—
67(C2×D43)⋊C8—22no—
68C4×C43⋊C8—21no—
69C8×Dic43—22no—
70C22×C8×C43—21no—
71C22×C8×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C4⋊C8×C43C2×C411yescharacteristic
77C4⋊C8×C43C2×C411yescharacteristic
78C4×C8×C43—21no—
79C4×C8×C43D411yescharacteristic
80C4×C8×C43D411yescharacteristic
81#95×C43—21no—
82C22×C4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×C22⋊D43—21no—
87#10621898—21no—
88#10621898—21no—
89#10621898SD1612yes—
90#10621898Q1612yes—
91C2×D172C22⋊C411yescharacteristic
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86C22⋊C411yescharacteristic
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—42no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—41no—
107C42×C43—41no—
108C42×C43—41no—
109C42×C43C22×C411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C22⋊Dic43—21no—
114C22⋊Dic43—41no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43C22⋊C411yescharacteristic
122C4⋊Dic43C22⋊C411yescharacteristic
123Dic43⋊C4—21no—
124Dic43⋊C4—21no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—41no—
131#10621877—41no—
132#10621877—41no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—41no—
135C8×D43—44no—
136C23×C43#12111yescharacteristic
137C22×D43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C2×C4×C43C2×SD1611yescharacteristic
151C2×C4×C43C2×Q1611yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43#13511yescharacteristic
154C22⋊D43—22no—
155C22⋊D43—22no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161D172—21no—
162D172#10312yes—
163C4×D43—22no—
164C4×D43—22no—
165C4×D43—42no—
166C4×D43—41no—
167C4×D43—41no—
168Dic86—21no—
169Dic86—41no—
170Dic86—41no—
171Dic86—81no—
172Dic86#10312yes—
173C8×C43—22no—
174C8×C43—41no—
175C8×C43—41no—
176C8×C43—41no—
177C43⋊C8—42no—
178C43⋊C8—81no—
179#9207—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43#38611yescharacteristic
183C22×C43#46511yescharacteristic
184C22×C43#46711yescharacteristic
185C2×D43—22no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—82no—
192C4×C43C2×#10311yescharacteristic
193C4×C43#41611yescharacteristic
194C4×C43#44311yescharacteristic
195C4×C43#44411yescharacteristic
196C4×C43#46511yescharacteristic
197C4×C43#46711yescharacteristic
198Dic43—22no—
199Dic43—41no—
200Dic43—41no—
201Dic43—81no—
202Dic43—81no—
203#3076—431no—
204C8×#41—431no—
205#1806—431no—
206#1503—431no—
207#1493—431no—
208#1301—431no—
209#1279D4311yescharacteristic, complemented
210C2×C43—21no—
211C2×C43—21no—
212C2×C43#187611yescharacteristic
213C2×C43#189211yescharacteristic
214C2×C43#190611yescharacteristic
215D43—42no—
216#533—431no—
217C4×#41—431no—
218#479—861no—
219#478—861no—
220#477—431no—
221#476—431no—
222#475—431no—
223#474—431no—
224C8×Q8—861no—
225C8×D4—861no—
226C8×D4—862no—
227#431—431no—
228#431—861no—
229#427—861no—
230#423—431no—
231C2×C4⋊C8C2×D4311yescharacteristic
232C2×#104—861no—
233#416—861no—
234C2×C4×C8—861no—
235C2×C4×C8C2×D4311yescharacteristic
236C4×C4⋊C4C2×D4311yescharacteristic
237#339—861no—
238#328—862no—
239Q8⋊C8—861no—
240Q8⋊C8—861no—
241C43#920711yescharacteristic, complemented, Sylow
242C2×#41—431no—
243C2×M16—861no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—862no—
247C4⋊Q8—431no—
248C4⋊Q8—431no—
249#125—861no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C4×Q8—431no—
253C4×Q8—431no—
254C4×Q8—861no—
255C4×Q8—861no—
256C4×D4—431no—
257C4×D4—431no—
258C4×D4—861no—
259C4×D4—861no—
260#117—431no—
261#117—861no—
262#117—861no—
263C2×C4⋊C4—21no—
264C2×C42—21no—
265C2×C42—861no—
266C2×C42C22×D4311yescharacteristic
267#107—861no—
268#107—861no—
269#106—861no—
270#106—861no—
271C4⋊C8—21no—
272C4⋊C8—862no—
273C4⋊C8—861no—
274C4⋊C8—861no—
275C4⋊C8—861no—
276C4⋊C8C4×D4311yescharacteristic
277C4⋊C8C4×D4311yescharacteristic
278#104—1722no—
279#103—861no—
280#103—861no—
281#102—861no—
282#102—861no—
283C22⋊C8—432no—
284C22⋊C8—862no—
285C4×C8—21no—
286C4×C8—862no—
287C4×C8—861no—
288C4×C8D17211yescharacteristic
289C4×C8D17211yescharacteristic
290#95—21no—
291#41—432no—
292#41—432no—
293#41—861no—
294#41—861no—
295C2×Q8—431no—
296C2×Q8—861no—
297C2×Q8—861no—
298C2×D4—431no—
299C2×D4—861no—
300C22×C4—41no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4#1062189811yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307M16—1721no—
308M16—1721no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—862no—
317C2×C8—1724no—
318C2×C8—1721no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—431no—
322C4⋊C4—431no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—1721no—
335C42—41no—
336C42—41no—
337C42—861no—
338C42—861no—
339C42—861no—
340C42—1721no—
341C42C2×C4×D4311yescharacteristic
342C42C2×D17211yescharacteristic
343C42D4×D4311yescharacteristic
344C42#1062190211yescharacteristic
345C23—861no—
346C23#1306329811yescharacteristic
347Q8—432no—
348Q8—861no—
349Q8—3441no—
350Q8—1721no—
351Q8—1721no—
352D4—432no—
353D4—862no—
354D4—862no—
355D4—861no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—861no—
363C2×C4—862no—
364C2×C4—862no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—1722no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4C22⋊C4×D4311yescharacteristic
373C2×C4#1306328711yescharacteristic
374C2×C4C4×D17211yescharacteristic
375C2×C4#1306329511yescharacteristic
376C2×C4#1306330011yescharacteristic
377C2×C4#1306331011yescharacteristic
378C2×C4SD16×D4311yescharacteristic
379C2×C4Q16×D4311yescharacteristic
380C2×C4#1306334411yescharacteristic
381C2×C4#1306334611yescharacteristic
382C8—22no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—3441no—
387C8—1722no—
388C22—21no—
389C22—21no—
390C22—862no—
391C22—1721no—
392C22—1721no—
393C22#1458277711yescharacteristic
394C22#1458312711yescharacteristic
395C22#1458313911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—862no—
401C4—3441no—
402C4—3441no—
403C4—1721no—
404C4—1721no—
405C4#103×D4311yescharacteristic
406C4#1458289211yescharacteristic
407C4#1458301711yescharacteristic
408C4#1458302211yescharacteristic
409C4#1458312911yescharacteristic
410C4#1458314111yescharacteristic
411C2—21no—
412C2—21no—
413C2—1722no—
414C2#1913492111yescharacteristic
415C2#1913501711yescharacteristic
416C2#1913509511yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#9207
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #19133093C2semidirect
5. #19133051C2semidirect
6. #19132492C2semidirect
7. C43×#1279C2semidirect
12. #14583195C4semidirect
13. #14583190C4semidirect
14. #14583185C4semidirect
15. #14583180C4semidirect
209. #1279D43semidirect
241. C43#9207semidirect

Maximal subgroups

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

subgroupindex
#191443852
C8×#106218982
#191346162
#191330932
#191330512
#191324922
C43×#12792
#920743