Finite Group Databasebeta

← #24991491

Subgroups — #24991491

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#19144050C211yesmaximal, characteristic
2#19133045C211yesmaximal, characteristic, complemented
3#19132993C211yesmaximal, characteristic, complemented
4#19132977C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C43×#2925C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9#14583449C2211yescharacteristic
10#14583121—21no—
11#14583114—21no—
12#14583109C411yescharacteristic
13#14583104C411yescharacteristic
14#14583099C411yescharacteristic
15#14583094C411yescharacteristic
16#14582952C2211yescharacteristic
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18#14582893—21no—
19C2×C4×C43⋊C8C2211yescharacteristic
20Q8⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22#14582626—21no—
23#14582626—21no—
24#14582626—22no—
25C4×#41×C43C2211yescharacteristic
26C43×#433—22no—
27C43×#432—21no—
28C43×#431—21no—
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C43×#408—21no—
32C43×#405—21no—
33C2×#10621898—21no—
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621883—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42#13063325C2×C411yescharacteristic
43#13063322C2×C411yescharacteristic
44#13063313—21no—
45#13063299—21no—
46#13063299—21no—
47C4×D172—21no—
48C4×D172—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)C2×C411yescharacteristic
52C4⋊(C43⋊C8)C2×C411yescharacteristic
53#13063248—21no—
54#13063248—21no—
55#13063245—21no—
56#13063245—21no—
57C22⋊(C43⋊C8)—21no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8—21no—
60C4×C43⋊C8—21no—
61C2×#41×C43D411yescharacteristic
62C2×M16×C43—21no—
63C22×C8×C43—21no—
64C4×Q8×C43C2×C411yescharacteristic
65C4×Q8×C43D411yescharacteristic
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43C2×C411yescharacteristic
69C4×D4×C43D411yescharacteristic
70#117×C43—21no—
71#117×C43D411yescharacteristic
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43D411yescharacteristic
77C4⋊C8×C43D411yescharacteristic
78C4⋊C8×C43D412yes—
79C22⋊C8×C43—22no—
80C22⋊C8×C43—22no—
81#97×C43—22no—
82C4×C8×C43—22no—
83#41×C43—21no—
84#41×C43—21no—
85#41×C43—21no—
86#41×C43—21no—
87C2×Q8×C43C22⋊C411yescharacteristic
88C2×D4×C43—21no—
89C2×D4×C43C22⋊C411yescharacteristic
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×C22⋊D43—41no—
97#10621898—41no—
98#10621898—41no—
99#10621898—41no—
100#10621898—41no—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172—21no—
104C2×C4×D43—41no—
105C2×Dic86—21no—
106M16×C43—41no—
107M16×C43—41no—
108C2×C8×C43—21no—
109C2×C8×C43—22no—
110C2×C8×C43—21no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43C22⋊C411yescharacteristic
116C4⋊C4×C43C22⋊C411yescharacteristic
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C22⋊C4×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C42×C43C22×C411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C42×C43C2×D411yescharacteristic
127#10621885—42no—
128#10621884—42no—
129#10621883—42no—
130#10621882—42no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4—41no—
133C4⋊Dic43—21no—
134C4⋊Dic43—21no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C23×C43—21no—
144C23×C43#12311yescharacteristic
145C22×D43—41no—
146Q8×C43—21no—
147Q8×C43—21no—
148D4×C43—21no—
149D4×C43—21no—
150D4×C43—41no—
151D4×C43—41no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—81no—
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#13511yescharacteristic
170C2×C4×C43#13511yescharacteristic
171C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
173C22⋊D43—81no—
174C22⋊D43—81no—
175C2×Dic43—41no—
176D172—42no—
177D172—41no—
178D172—41no—
179D172—41no—
180D172—41no—
181C4×D43—81no—
182C4×D43—81no—
183Dic86—41no—
184Dic86—41no—
185C8×C43—41no—
186C8×C43—41no—
187C8×C43—42no—
188C43⋊C8—42no—
189C43⋊C8—41no—
190C43⋊C8—41no—
191C43⋊C8—81no—
192#8996—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43#38611yescharacteristic
199C22×C43#48211yescharacteristic
200C22×C43#48211yescharacteristic
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43#41611yescharacteristic
211C4×C43#41811yescharacteristic
212C4×C43#44311yescharacteristic
213C4×C43#44411yescharacteristic
214C4×C43#44911yescharacteristic
215C4×C43#44911yescharacteristic
216Dic43—81no—
217#3035—431no—
218#2925D4311yescharacteristic, complemented
219#1492—431no—
220#1480—431no—
221#1476—431no—
222#1301—431no—
223#1277—431no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—81no—
227C2×C43#187511yescharacteristic
228C2×C43#187611yescharacteristic
229C2×C43#188111yescharacteristic
230D43—161no—
231C2×#135—861no—
232#532—431no—
233C4×#41C2×D4311yescharacteristic
234#464—861no—
235#463—861no—
236#462—431no—
237#461—431no—
238#460—431no—
239#459—431no—
240#433—22no—
241#432—21no—
242#431—21no—
243#431—431no—
244#423C2×D4311yescharacteristic
245C2×C4⋊C8—431no—
246C2×C4⋊C8C2×D4311yescharacteristic
247#416—861no—
248#408—21no—
249#405—21no—
250C2×C4×C8—431no—
251Q8⋊C8—861no—
252D4⋊C8—861no—
253D4⋊C8—861no—
254D4⋊C8—861no—
255D4⋊C8—862no—
256C43#899611yescharacteristic, complemented, Sylow
257C2×#41—861no—
258C2×#41C22⋊D4311yescharacteristic
259#135—1722no—
260#135—1722no—
261C2×Q16—861no—
262C2×SD16—861no—
263C2×SD16—861no—
264C2×D8—861no—
265C2×M16—21no—
266C22×C8—21no—
267C22×C8—861no—
268C22×C8—861no—
269C4⋊Q8—431no—
270#127—431no—
271#124—861no—
272#121—861no—
273#121—861no—
274C4×Q8C4×D4311yescharacteristic
275C4×Q8D17211yescharacteristic
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—861no—
279C4×D4—861no—
280C4×D4C4×D4311yescharacteristic
281C4×D4D17211yescharacteristic
282#117—21no—
283#117C22⋊D4311yescharacteristic
284C2×C42—21no—
285C2×C42C22×D4311yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—431no—
289C4⋊C8—431no—
290C4⋊C8—861no—
291C4⋊C8—861no—
292C4⋊C8C22⋊D4311yescharacteristic
293C4⋊C8C22⋊D4311yescharacteristic
294C4⋊C8C22⋊D4312yes—
295#103—861no—
296#103—861no—
297#102—861no—
298#102—861no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—861no—
302#97—22no—
303C4×C8—22no—
304C4×C8—861no—
305C4×C8—861no—
306C4×C8—861no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—1721no—
312#41—1721no—
313#41—1721no—
314#41—1721no—
315C2×Q8—861no—
316C2×Q8(C2×D43)⋊C411yescharacteristic
317C2×D4—21no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—1721no—
322C2×D4(C2×D43)⋊C411yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—1721no—
327C22×C4#1062189811yescharacteristic
328C22×C4#1062189811yescharacteristic
329C22×C4C2×C22⋊D4311yescharacteristic
330Q16—1722no—
331SD16—1722no—
332SD16—1722no—
333D8—1722no—
334M16—41no—
335M16—41no—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—21no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—862no—
342C2×C8—861no—
343C2×C8—861no—
344C2×C8—1721no—
345C2×C8—1721no—
346C2×C8—1721no—
347C2×C8—1721no—
348C2×C8—1721no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4(C2×D43)⋊C411yescharacteristic
354C4⋊C4(C2×D43)⋊C411yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C2×C4×D4311yescharacteristic
364C42C2×D17211yescharacteristic
365C42C2×C22⋊D4311yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—21no—
368C23—1721no—
369C23#1306330811yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—1721no—
373Q8—1721no—
374D4—21no—
375D4—21no—
376D4—41no—
377D4—41no—
378D4—3441no—
379D4—3441no—
380D4—1722no—
381D4—1721no—
382D4—1721no—
383D4—1721no—
384D4—1721no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—1721no—
399C2×C4C2×(C2×D43)⋊C411yescharacteristic
400C2×C4C4×C22⋊D4311yescharacteristic
401C2×C4C4×C22⋊D4311yescharacteristic
402C2×C4#1306329411yescharacteristic
403C2×C4#1306329911yescharacteristic
404C2×C4#1306329911yescharacteristic
405C2×C4#1306334511yescharacteristic
406C2×C4#1306334511yescharacteristic
407C2×C4#1306335011yescharacteristic
408C2×C4#1306335011yescharacteristic
409C8—41no—
410C8—41no—
411C8—42no—
412C8—3441no—
413C8—1722no—
414C8—1721no—
415C8—1721no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—3441no—
422C22—3441no—
423C22—3441no—
424C22#1458277811yescharacteristic
425C22#1458322311yescharacteristic
426C22#1458322311yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—3441no—
434C4#1458289311yescharacteristic
435C4#1458290311yescharacteristic
436C4#1458301411yescharacteristic
437C4#1458301911yescharacteristic
438C4#1458304411yescharacteristic
439C4#1458304411yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—6881no—
444C2#1913491711yescharacteristic
445C2#1913492211yescharacteristic
446C2#1913495711yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2925C2
socleC22×C43#386
prime radical#19144050C2
cosocleC2×C42×C43C23
hypercenter#2925D43
hypocenterC43#8996
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #19133045C2semidirect
3. #19132993C2semidirect
4. #19132977C2semidirect
5. #19132490C2semidirect
6. #19132429C2semidirect
7. C43×#2925C2semidirect
218. #2925D43semidirect
256. C43#8996semidirect

Maximal subgroups

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

subgroupindex
#191440502
#191330452
#191329932
#191329772
#191324902
#191324292
C43×#29252
#899643