Finite Group Databasebeta

← #24991490

Subgroups — #24991490

Order 11008.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144052C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic, complemented
3#19133047C211yesmaximal, characteristic, complemented
4#19132993C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic, complemented
6#19132492C211yesmaximal, characteristic, complemented
7C43×#1277C211yesmaximal, characteristic, complemented
8C2×#13063347—21no—
9#14583449C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583122—21no—
12#14583115—21no—
13#14583110C411yescharacteristic
14#14583105C411yescharacteristic
15#14583100C411yescharacteristic
16#14583095C411yescharacteristic
17#14582959—22no—
18#14582955—21no—
19#14582952C2211yescharacteristic
20#14582951—21no—
21#14582923C2211yescharacteristic
22#14582896—21no—
23#14582865—21no—
24#14582854—21no—
25#14582631—21no—
26#14582628—21no—
27#14582628—22no—
28#14582626—21no—
29#14582626—21no—
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621898—21no—
34C2×#10621898D411yescharacteristic
35#13063347—42no—
36#13063347—42no—
37C2×Dic172—21no—
38C2×#10621873—21no—
39C2×#10621873—21no—
40C2×D344—21no—
41C2×#10621877—21no—
42#13063325C2×C411yescharacteristic
43#13063322C2×C411yescharacteristic
44#13063313—21no—
45#13063299—21no—
46#13063299—21no—
47C4×Dic86C2×C411yescharacteristic
48C4×Dic86D411yescharacteristic
49C4×D172—21no—
50C4×D172—21no—
51C4×D172C2×C411yescharacteristic
52C4×D172D411yescharacteristic
53C4×C22⋊D43—21no—
54C4×C22⋊D43—21no—
55#13063284D411yescharacteristic
56#13063282—21no—
57C42×D43—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)D412yes—
61#13063250—21no—
62#13063250—21no—
63#13063247—21no—
64#13063247—21no—
65C22⋊(C43⋊C8)—21no—
66(C2×D43)⋊C8—22no—
67(C2×D43)⋊C8—22no—
68#13063235—22no—
69C4×C43⋊C8—21no—
70C8×Dic43—22no—
71C22×C8×C43—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43C2×C411yescharacteristic
78C4⋊C8×C43C2×C411yescharacteristic
79C4⋊C8×C43D411yescharacteristic
80C4⋊C8×C43D411yescharacteristic
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×C22⋊D43—21no—
87C2×C22⋊D43—41no—
88#10621898—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898—21no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—41no—
104C2×Dic86—21no—
105C2×Dic86C22⋊C411yescharacteristic
106C2×C8×C43—22no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C42×C43C22×C411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C22⋊Dic43—21no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43C22⋊C411yescharacteristic
129C4⋊Dic43C22⋊C411yescharacteristic
130Dic43⋊C4—21no—
131Dic43⋊C4—21no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135#10621877—41no—
136#10621877—41no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—41no—
139Dic172—42no—
140D344—42no—
141#10621873—42no—
142#10621873—42no—
143C23×C43#12311yescharacteristic
144C22×D43—21no—
145C22×D43—41no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#13511yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C22⋊D43—41no—
160C22⋊D43—41no—
161C22⋊D43—81no—
162C22⋊D43—81no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—41no—
167D172—21no—
168D172—21no—
169D172—42no—
170D172—41no—
171D172—41no—
172D172—41no—
173D172—41no—
174C4×D43—41no—
175C4×D43—41no—
176C4×D43—41no—
177C4×D43—41no—
178C4×D43—81no—
179C4×D43—81no—
180C4×D43—81no—
181Dic86—21no—
182Dic86—21no—
183Dic86—41no—
184Dic86—41no—
185C8×C43—42no—
186C8×C43—41no—
187C8×C43—41no—
188C8×C43—41no—
189C8×C43—41no—
190C43⋊C8—42no—
191C43⋊C8—81no—
192#8996—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43#38611yescharacteristic
196C22×C43#48211yescharacteristic
197C22×C43#48211yescharacteristic
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43#41611yescharacteristic
208C4×C43#41811yescharacteristic
209C4×C43#44311yescharacteristic
210C4×C43#44411yescharacteristic
211C4×C43#44911yescharacteristic
212C4×C43#44911yescharacteristic
213Dic43—41no—
214Dic43—41no—
215Dic43—41no—
216Dic43—81no—
217#3035—431no—
218#2925—431no—
219#1492—431no—
220#1480—431no—
221#1476—431no—
222#1301—431no—
223#1277D4311yescharacteristic, complemented
224C2×C43—21no—
225C2×C43—21no—
226C2×C43#187511yescharacteristic
227C2×C43#187611yescharacteristic
228C2×C43#188111yescharacteristic
229D43—81no—
230D43—161no—
231C2×#135—861no—
232#532—431no—
233C4×#41—431no—
234#464—861no—
235#463—861no—
236#462—431no—
237#461—431no—
238#460—431no—
239#459—431no—
240#433—862no—
241#432—861no—
242#431—431no—
243#431—861no—
244#423—431no—
245C2×C4⋊C8C2×D4311yescharacteristic
246C2×C4⋊C8C2×D4311yescharacteristic
247#416—861no—
248#408—861no—
249#405—861no—
250C2×C4×C8C2×D4311yescharacteristic
251Q8⋊C8—861no—
252D4⋊C8—862no—
253D4⋊C8—861no—
254D4⋊C8—861no—
255D4⋊C8—861no—
256C43#899611yescharacteristic, complemented, Sylow
257C2×#41—431no—
258C2×#41—861no—
259#135—1722no—
260#135—1722no—
261C2×Q16—861no—
262C2×SD16—861no—
263C2×SD16—861no—
264C2×D8—861no—
265C2×M16—861no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C4⋊Q8—431no—
270#127—431no—
271#124—861no—
272#121—861no—
273#121—861no—
274C4×Q8—431no—
275C4×Q8—431no—
276C4×D4—431no—
277C4×D4—431no—
278C4×D4—861no—
279C4×D4—861no—
280C4×D4—861no—
281C4×D4—861no—
282#117—431no—
283#117—861no—
284C2×C42—861no—
285C2×C42C22×D4311yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—432no—
289C4⋊C8—861no—
290C4⋊C8—861no—
291C4⋊C8C4×D4311yescharacteristic
292C4⋊C8C4×D4311yescharacteristic
293C4⋊C8D17211yescharacteristic
294C4⋊C8D17211yescharacteristic
295#103—861no—
296#103—861no—
297#102—861no—
298#102—861no—
299C22⋊C8—862no—
300C22⋊C8—862no—
301C22⋊C8—861no—
302#97—862no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—862no—
306C4×C8—861no—
307#41—861no—
308#41—861no—
309#41—861no—
310#41—861no—
311#41—1721no—
312#41—1721no—
313#41—1721no—
314#41—1721no—
315C2×Q8—431no—
316C2×Q8—861no—
317C2×D4—431no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—1721no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—1721no—
327C22×C4#1062189811yescharacteristic
328C22×C4D4×D4311yescharacteristic
329C22×C4#1062190211yescharacteristic
330Q16—1722no—
331SD16—1722no—
332SD16—1722no—
333D8—1722no—
334M16—1721no—
335M16—1721no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—862no—
348C2×C8—1721no—
349C4⋊C4—431no—
350C4⋊C4—431no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4—861no—
354C4⋊C4—861no—
355C22⋊C4—861no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C42—861no—
361C42—861no—
362C42—861no—
363C42C2×C4×D4311yescharacteristic
364C42C2×D17211yescharacteristic
365C42D4×D4311yescharacteristic
366C42D4×D4311yescharacteristic
367C23—861no—
368C23—1721no—
369C23#1306331011yescharacteristic
370Q8—861no—
371Q8—861no—
372Q8—1721no—
373Q8—1721no—
374D4—861no—
375D4—861no—
376D4—3441no—
377D4—3441no—
378D4—1722no—
379D4—1721no—
380D4—1721no—
381D4—1721no—
382D4—1721no—
383D4—1721no—
384D4—1721no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—3441no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4C22⋊C4×D4311yescharacteristic
400C2×C4#1306328711yescharacteristic
401C2×C4C4×D17211yescharacteristic
402C2×C4#1306329511yescharacteristic
403C2×C4#1306329811yescharacteristic
404C2×C4#1306330011yescharacteristic
405C2×C4#1306334611yescharacteristic
406C2×C4#1306334811yescharacteristic
407C2×C4#1306334911yescharacteristic
408C2×C4#1306335211yescharacteristic
409C8—42no—
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—3441no—
415C8—1722no—
416C22—21no—
417C22—21no—
418C22—3441no—
419C22—3441no—
420C22—3441no—
421C22—1721no—
422C22—1721no—
423C22—1721no—
424C22#1458277711yescharacteristic
425C22#1458322511yescharacteristic
426C22#1458322611yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—3441no—
431C4—1721no—
432C4—1721no—
433C4—1721no—
434C4#1458289411yescharacteristic
435C4#1458290211yescharacteristic
436C4#1458301711yescharacteristic
437C4#1458302211yescharacteristic
438C4#1458304511yescharacteristic
439C4#1458304711yescharacteristic
440C2—21no—
441C2—21no—
442C2—3441no—
443C2—6881no—
444C2#1913491611yescharacteristic
445C2#1913492111yescharacteristic
446C2#1913495811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socleC22×C43#386
prime radical#19144052C2
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#8996
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #19143260C2semidirect
3. #19133047C2semidirect
4. #19132993C2semidirect
5. #19132978C2semidirect
6. #19132492C2semidirect
7. C43×#1277C2semidirect
223. #1277D43semidirect
256. C43#8996semidirect

Maximal subgroups

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

subgroupindex
#191440522
#191432602
#191330472
#191329932
#191329782
#191324922
C43×#12772
#899643