Finite Group Databasebeta

← #24992490

Subgroups — #24992490

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144075C211yesmaximal, characteristic
2#19133264C211yesmaximal, characteristic, complemented
3C2×#14582642C211yesmaximal, characteristic, complemented
4#19132982C211yesmaximal, characteristic, complemented
5#19132492C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#2906C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C2×#13063322C2211yescharacteristic
10#14583099—21no—
11#14583099C412yes—
12#14583094—21no—
13#14583094C412yes—
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17#14582903—21no—
18#14582642—21no—
19#14582642—21no—
20#14582642—22no—
21Q8⋊(C43⋊C8)—21no—
22D4⋊(C43⋊C8)—21no—
23C2×#131×C43—21no—
24C4×#41×C43C2211yescharacteristic
25C43×#424—21no—
26C43×#424—22no—
27C43×#423—21no—
28C43×#423C2211yescharacteristic
29C2×C4⋊C8×C43—21no—
30C2×C4⋊C8×C43C2211yescharacteristic
31C22×D172—21no—
32C22×D172—21no—
33C22×D172—21no—
34#13063350—42no—
35#13063350—42no—
36C2×#10621884—22no—
37C2×#10621882—22no—
38C2×#10621877—21no—
39C22×C43⋊C8—21no—
40#13063322—21no—
41#13063322—21no—
42#13063322—21no—
43#13063322C2×C412yes—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)C2×C412yes—
49#13063245—22no—
50#13063245—22no—
51C22⋊(C43⋊C8)—21no—
52C4×C43⋊C8—21no—
53C2×#41×C43D411yescharacteristic
54#131×C43—42no—
55#131×C43—42no—
56C2×M16×C43—22no—
57C2×M16×C43—21no—
58C22×C8×C43—22no—
59C22×C8×C43—21no—
60C4×Q8×C43C2×C411yescharacteristic
61C4×Q8×C43D411yescharacteristic
62C4×D4×C43—21no—
63C4×D4×C43—21no—
64C4×D4×C43C2×C411yescharacteristic
65C4×D4×C43D411yescharacteristic
66#117×C43—21no—
67#117×C43D411yescharacteristic
68C2×C42×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—22no—
71C4⋊C8×C43—22no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43D411yescharacteristic
75C4⋊C8×C43D411yescharacteristic
76C4⋊C8×C43D412yes—
77C23×D43—41no—
78#41×C43—21no—
79#41×C43—21no—
80#41×C43D812yes—
81#41×C43SD1612yes—
82C2×Q8×C43C22⋊C411yescharacteristic
83C2×D4×C43—21no—
84C2×D4×C43C22⋊C411yescharacteristic
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×D172—22no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—81no—
102C2×D172—81no—
103C2×D172—82no—
104M16×C43—44no—
105M16×C43—41no—
106M16×C43—41no—
107C2×C8×C43—21no—
108C2×C8×C43—22no—
109C2×C8×C43—21no—
110C2×C8×C43—44no—
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#10621884—44no—
128#10621882—44no—
129#10621877—41no—
130#10621877—41no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—81no—
135C23×C43—21no—
136C23×C43#12311yescharacteristic
137C22×D43—42no—
138C22×D43—82no—
139C22×D43—82no—
140C22×D43—81no—
141C22×D43—81no—
142Q8×C43—21no—
143Q8×C43#10212yes—
144D4×C43—22no—
145D4×C43—22no—
146D4×C43—21no—
147D4×C43#10212yes—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—81no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43C2×D811yescharacteristic
166C2×C4×C43C2×SD1611yescharacteristic
167C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C43#13711yescharacteristic
169D172—42no—
170D172—42no—
171D172—82no—
172D172—82no—
173D172—82no—
174D172—81no—
175D172—81no—
176D172—81no—
177D172—81no—
178C8×C43—41no—
179C8×C43—42no—
180C8×C43—41no—
181C43⋊C8—42no—
182C43⋊C8—81no—
183C43⋊C8—81no—
184#9173—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—22no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43#38611yescharacteristic
191C22×C43#48011yescharacteristic
192C22×C43#48111yescharacteristic
193C2×D43—82no—
194C2×D43—82no—
195C2×D43—82no—
196C2×D43—162no—
197C2×D43—162no—
198C4×C43—22no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—41no—
203C4×C43—41no—
204C4×C43C2×#10211yescharacteristic
205C4×C43#41711yescharacteristic
206C4×C43#44711yescharacteristic
207C4×C43#44811yescharacteristic
208C4×C43#47111yescharacteristic
209C4×C43#47211yescharacteristic
210#3038—431no—
211#2906D4311yescharacteristic, complemented
212#1545—431no—
213C2×#331—431no—
214#1477—431no—
215#1301—431no—
216#1292—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—42no—
220C2×C43#187411yescharacteristic
221C2×C43#190311yescharacteristic
222C2×C43#190711yescharacteristic
223D43—162no—
224C2×AGL(1,ℤ/8)—861no—
225C2×#131—21no—
226C2×#127—431no—
227C4×#41C2×D4311yescharacteristic
228#460—432no—
229#460—861no—
230#459—432no—
231#459—861no—
232#431—431no—
233#424—21no—
234#424—22no—
235#423—21no—
236#423—431no—
237#423C2×D4311yescharacteristic
238C2×C4⋊C8—21no—
239C2×C4⋊C8—431no—
240C2×C4⋊C8C2×D4311yescharacteristic
241#418—861no—
242#331—861no—
243#331—861no—
244#331—862no—
245Q8⋊C8—861no—
246D4⋊C8—861no—
247C43#917311yescharacteristic, complemented, Sylow
248C2×#41C22⋊D4311yescharacteristic
249C22×D4—861no—
250C22×D4—861no—
251C22×D4—861no—
252AGL(1,ℤ/8)—1722no—
253AGL(1,ℤ/8)—1722no—
254C2×SD16—862no—
255C2×D8—862no—
256#131—42no—
257#131—42no—
258C2×M16—22no—
259C2×M16—21no—
260C2×M16—861no—
261C22×C8—22no—
262C22×C8—21no—
263C22×C8—861no—
264#127—432no—
265#127—861no—
266#127—861no—
267#127—861no—
268C4×Q8C4×D4311yescharacteristic
269C4×Q8D17211yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4C4×D4311yescharacteristic
273C4×D4D17211yescharacteristic
274#117—21no—
275#117C22⋊D4311yescharacteristic
276C2×C42—21no—
277C2×C42C22×D4311yescharacteristic
278C4⋊C8—22no—
279C4⋊C8—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—432no—
283C4⋊C8—861no—
284C4⋊C8—861no—
285C4⋊C8—861no—
286C4⋊C8—861no—
287C4⋊C8C22⋊D4311yescharacteristic
288C4⋊C8C22⋊D4311yescharacteristic
289C4⋊C8C22⋊D4312yes—
290#102—862no—
291#102—862no—
292C22⋊C8—861no—
293C4×C8—861no—
294C24—1721no—
295#41—21no—
296#41—21no—
297#41#1062188212yes—
298#41#1062188412yes—
299C2×Q8(C2×D43)⋊C411yescharacteristic
300C2×D4—21no—
301C2×D4—862no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—3441no—
305C2×D4—3441no—
306C2×D4—3442no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4(C2×D43)⋊C411yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4#1062189811yescharacteristic
319C22×C4#1062189811yescharacteristic
320C22×C4C2×C22⋊D4311yescharacteristic
321SD16—1724no—
322D8—1724no—
323M16—44no—
324M16—41no—
325M16—41no—
326M16—1721no—
327M16—1721no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—21no—
331C2×C8—44no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—862no—
335C2×C8—3441no—
336C2×C8—1721no—
337C2×C8—1721no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4(C2×D43)⋊C411yescharacteristic
341C4⋊C4(C2×D43)⋊C411yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42C2×C4×D4311yescharacteristic
349C42C2×D17211yescharacteristic
350C42C2×C22⋊D4311yescharacteristic
351C42C2×C22⋊D4311yescharacteristic
352C23—21no—
353C23—3442no—
354C23—3442no—
355C23—3441no—
356C23—3441no—
357C23—1722no—
358C23#1306330811yescharacteristic
359Q8—21no—
360Q8#1306324512yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—3442no—
365D4—3442no—
366D4—3442no—
367D4—3441no—
368D4—3441no—
369D4—3441no—
370D4—3441no—
371D4—1722no—
372D4—1722no—
373D4#1306324512yes—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×(C2×D43)⋊C411yescharacteristic
386C2×C4C4×C22⋊D4311yescharacteristic
387C2×C4C4×C22⋊D4311yescharacteristic
388C2×C4#1306329411yescharacteristic
389C2×C4#1306329911yescharacteristic
390C2×C4#1306329911yescharacteristic
391C2×C4C2×#1062188211yescharacteristic
392C2×C4C2×#1062188411yescharacteristic
393C2×C4#1306335111yescharacteristic
394C2×C4#1306335611yescharacteristic
395C8—41no—
396C8—42no—
397C8—41no—
398C8—3441no—
399C8—3441no—
400C8—1722no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—3442no—
407C22—3442no—
408C22—3442no—
409C22—6882no—
410C22—6882no—
411C22#1458277811yescharacteristic
412C22#1458321211yescharacteristic
413C22#1458321711yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4C2×#1306324511yescharacteristic
421C4#1458289811yescharacteristic
422C4#1458303311yescharacteristic
423C4#1458303811yescharacteristic
424C4#1458316211yescharacteristic
425C4#1458316911yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—6882no—
430C2#1913491211yescharacteristic
431C2#1913507511yescharacteristic
432C2#1913510311yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2906C2
socleC22×C43#386
prime radical#19144075C2
cosocleC2×C42×C43C23
hypercenter#2906D43
hypocenterC43#9173
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #19133264C2semidirect
3. C2×#14582642C2semidirect
4. #19132982C2semidirect
5. #19132492C2semidirect
6. #19132469C2semidirect
7. C43×#2906C2semidirect
211. #2906D43semidirect
247. C43#9173semidirect

Maximal subgroups

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

subgroupindex
#191440752
#191332642
C2×#145826422
#191329822
#191324922
#191324692
C43×#29062
#917343