Finite Group Databasebeta

← #25080559

Subgroups — #25080559

Order 11008.

670 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
1C2×#14583249C211yesmaximal, characteristic, complemented
2#19144404C211yesmaximal, characteristic
3#19144083C211yesmaximal, characteristic
4#19143551C211yesmaximal, characteristic
5#19134024C214yesmaximal, complemented
6#19134017C214yesmaximal, complemented
7#19133350C211yesmaximal, characteristic, complemented
8#19133266C211yesmaximal, characteristic, complemented
9C43×#1549C211yesmaximal, characteristic, complemented
10C2×#13063358—21no—
11C2×#13063325C2211yescharacteristic
12C4×#10621898C2211yescharacteristic
13#14583249—21no—
14#14583249—21no—
15#14583249C2214yes—
16#14583191—21no—
17#14583186—21no—
18#14583181C2212yes—
19#14583176C2212yes—
20#14583110—21no—
21#14583110C2212yes—
22#14583105—21no—
23#14583105C2212yes—
24#14583023C2212yes—
25#14582964C2212yes—
26(C22⋊D43)⋊C8—22no—
27#14582950—21no—
28#14582939—21no—
29#14582923C2211yescharacteristic
30#14582909—21no—
31#14582898—21no—
32C2×#13063249—22no—
33C2×C4×C43⋊C8C2211yescharacteristic
34C4×C8×D43—21no—
35#14582649C2214yes—
36#14582644C2214yes—
37C2×C4⋊Q8×C43C2211yescharacteristic
38C43×#431C2211yescharacteristic
39C43×#423C2211yescharacteristic
40C43×#332C2214yes—
41C2×#10621898D411yescharacteristic
42C22×Dic86—21no—
43#13063358—44no—
44C2×Dic172—22no—
45C2×#10621873—22no—
46C2×#10621877—21no—
47C22×C43⋊C8D412yes—
48C2×C8×D43—22no—
49#13063325—21no—
50#13063325—21no—
51#13063325—21no—
52#13063325C2312yes—
53C4×Dic86D411yescharacteristic
54C4×Dic86C2311yescharacteristic
55C4×D172D411yescharacteristic
56C4×D172C2311yescharacteristic
57C4×C22⋊D43—21no—
58C4×C22⋊D43—21no—
59#13063284D411yescharacteristic
60#13063282—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C42×D43—21no—
64#13063258—22no—
65#13063256—22no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)C2312yes—
68Dic43⋊C8—22no—
69#13063250—22no—
70#13063250—22no—
71#13063249—24no—
72#13063249—24no—
73#13063248—22no—
74#13063245—22no—
75(C2×D43)⋊C8—22no—
76C4×C43⋊C8D411yescharacteristic
77C4×C43⋊C8D411yescharacteristic
78C4×C43⋊C8C2312yes—
79C8×Dic43—22no—
80C22×Q8×C43—21no—
81C2×M16×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43C2312yes—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C42×C43C2311yescharacteristic
89C4⋊C8×C43—21no—
90C4⋊C8×C43C2312yes—
91C4⋊C8×C43C2312yes—
92C22⋊C8×C43—21no—
93C4×C8×C43—21no—
94C2×Q8×C43—22no—
95C2×Q8×C43—44no—
96C2×Q8×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C2×C22⋊D43—21no—
102C22×Dic43—41no—
103#10621898—22no—
104#10621898SD1614yes—
105C2×D172C2×D411yescharacteristic
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×C4×D43—21no—
109C2×Dic86—22no—
110C2×Dic86—42no—
111C2×Dic86—42no—
112C2×Dic86—41no—
113C2×Dic86C2×D411yescharacteristic
114M16×C43—42no—
115C2×C8×C43—22no—
116C2×C8×C43—22no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—22no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C42×C43C2411yescharacteristic
125C22⋊Dic43—21no—
126(C2×D43)⋊C4—21no—
127(C2×D43)⋊C4—21no—
128C4⋊Dic43—22no—
129C4⋊Dic43—22no—
130C4⋊Dic43—41no—
131C4⋊Dic43—41no—
132C4⋊Dic43C2×D411yescharacteristic
133C4⋊Dic43C2×D411yescharacteristic
134Dic43⋊C4—21no—
135Dic43⋊C4—21no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139#10621877—42no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—42no—
142C2×C43⋊C8C2×D412yes—
143C2×C43⋊C8C2×D412yes—
144Dic172—44no—
145#10621873—44no—
146C8×D43—44no—
147C23×C43#12111yescharacteristic
148C22×D43—21no—
149Q8×C43—44no—
150Q8×C43—82no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—42no—
154C2×C4×C43—82no—
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43C2×SD1612yes—
159C2×C4×C43#13512yes—
160C2×C4×C43C22×D411yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C2×#4111yescharacteristic
163C22⋊D43—24no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—42no—
168C2×Dic43—82no—
169D172—21no—
170D172C2×SD1612yes—
171C4×D43—24no—
172C4×D43—42no—
173C4×D43—42no—
174Dic86—21no—
175Dic86—42no—
176Dic86—42no—
177Dic86—82no—
178Dic86C2×SD1612yes—
179C8×C43—42no—
180C8×C43—42no—
181C43⋊C8—22no—
182C43⋊C8—22no—
183C43⋊C8—42no—
184#19275—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43#46512yes—
188C22×C43C2×#12111yescharacteristic
189C2×D43—22no—
190C2×D43—41no—
191C2×D43—41no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43#46512yes—
196C4×C43#47312yes—
197C4×C43C22×SD1611yescharacteristic
198C4×C43C2×#13511yescharacteristic
199C4×C43#57512yes—
200Dic43—22no—
201Dic43—41no—
202Dic43—41no—
203Dic43—82no—
204C2×#487—431no—
205#3079—431no—
206#3039—431no—
207C8×#41—431no—
208#1680—434no—
209#1679—434no—
210#1566—431no—
211#1549D4311yescharacteristic, complemented
212#1546—431no—
213C2×C43—22no—
214C2×C43#304011yescharacteristic
215C2×C43C2×#46511yescharacteristic
216C2×C43C2×#47311yescharacteristic
217D43—42no—
218C2×#137—861no—
219C2×C4⋊Q8—431no—
220C2×C4⋊Q8C2×D4311yescharacteristic
221C4×#41—431no—
222#487—434no—
223#487—861no—
224#487—861no—
225#477—861no—
226#476—861no—
227#475—432no—
228#474—432no—
229#462—432no—
230#462—861no—
231#461—432no—
232#461—861no—
233C8×Q8—432no—
234C8×D4—432no—
235C8×D4—862no—
236#431—861no—
237#431C2×D4311yescharacteristic
238#428—861no—
239#423—431no—
240#423C2×D4311yescharacteristic
241#419—861no—
242#417—861no—
243C2×#103—862no—
244C2×C4×C8—431no—
245C2×C4×C8—861no—
246#334—434no—
247#332—434no—
248#332C2×D4314yes—
249C43#1927511yescharacteristic, complemented, Sylow
250C2×#41—431no—
251C22×Q8—21no—
252C22×Q8—861no—
253#137—1724no—
254C2×Q16—862no—
255C2×SD16—862no—
256C2×M16—21no—
257C2×M16—861no—
258C22×C8—432no—
259C22×C8—862no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—432no—
264C4⋊Q8—861no—
265C4⋊Q8—861no—
266C4⋊Q8—861no—
267C4⋊Q8C22×D4312yes—
268C4×Q8—431no—
269C4×Q8—431no—
270C4×D4—431no—
271C4×D4—431no—
272C4×D4—861no—
273C4×D4—861no—
274#117—431no—
275#117—861no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—861no—
280C2×C42—861no—
281C2×C42C22×D4311yescharacteristic
282#107—862no—
283#106—862no—
284C4⋊C8—21no—
285C4⋊C8—432no—
286C4⋊C8—862no—
287C4⋊C8—861no—
288C4⋊C8C22×D4312yes—
289C4⋊C8C22×D4312yes—
290#103—862no—
291#103—862no—
292#103—862no—
293#103—864no—
294#103—864no—
295#102—862no—
296C22⋊C8—21no—
297C22⋊C8—862no—
298C4×C8—21no—
299C4×C8—431no—
300C4×C8—431no—
301C4×C8—432no—
302C4×C8—862no—
303#41—434no—
304#41—862no—
305C2×Q8—22no—
306C2×Q8—44no—
307C2×Q8—41no—
308C2×Q8—431no—
309C2×Q8—862no—
310C2×Q8—1722no—
311C2×Q8—1722no—
312C2×Q8—1721no—
313C2×D4—431no—
314C2×D4—861no—
315C22×C4—41no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—1721no—
320C22×C4#1062189811yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323Q16—1724no—
324SD16—1724no—
325M16—42no—
326M16—1722no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—432no—
330C2×C8—432no—
331C2×C8—862no—
332C2×C8—1724no—
333C2×C8—1722no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—431no—
339C4⋊C4—431no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—862no—
343C4⋊C4—862no—
344C4⋊C4—1721no—
345C4⋊C4—1721no—
346C22⋊C4—861no—
347C22⋊C4—861no—
348C22⋊C4—861no—
349C42—861no—
350C42—861no—
351C42—861no—
352C42#1062189811yescharacteristic
353C42D4×D4311yescharacteristic
354C42D4×D4311yescharacteristic
355C42C23×D4311yescharacteristic
356C23—861no—
357C23#1306329811yescharacteristic
358Q8—44no—
359Q8—82no—
360Q8—432no—
361Q8—861no—
362Q8—3442no—
363Q8—1722no—
364Q8—1722no—
365D4—432no—
366D4—864no—
367D4—861no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—861no—
373C2×C4—864no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—3442no—
377C2×C4—1722no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4#1306329811yescharacteristic
381C2×C4#1306329811yescharacteristic
382C2×C4#1306329811yescharacteristic
383C2×C4SD16×D4312yes—
384C2×C4#1306334812yes—
385C2×C4C2×D4×D4311yescharacteristic
386C2×C4C2×D4×D4311yescharacteristic
387C2×C4C2×#1062189811yescharacteristic
388C8—42no—
389C8—42no—
390C8—862no—
391C8—862no—
392C8—1722no—
393C22—21no—
394C22—21no—
395C22—862no—
396C22—1721no—
397C22—1721no—
398C22#1458313112yes—
399C22C2×#1306329811yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—862no—
404C4—3442no—
405C4—1721no—
406C4—1721no—
407C4#1458313112yes—
408C4#1458317312yes—
409C4C2×SD16×D4311yescharacteristic
410C4C2×#1306334811yescharacteristic
411C4#1458369512yes—
412C2—22no—
413C2—1722no—
414C2#1914408811yescharacteristic
415C2C2×#1458313111yescharacteristic
416C2C2×#1458317311yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1549C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1549D43
hypocenterC43#19275
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. C2×#14583249C2semidirect
5. #19134024C2semidirect
6. #19134017C2semidirect
7. #19133350C2semidirect
8. #19133266C2semidirect
9. C43×#1549C2semidirect
211. #1549D43semidirect
249. C43#19275semidirect

Maximal subgroups

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

subgroupindex
C2×#145832492
#191444042
#191440832
#191435512
#191340242
#191340172
#191333502
#191332662
C43×#15492
#1927543