Finite Group Databasebeta

← #24989572

Subgroups — #24989572

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143290C211yesmaximal, characteristic
2#19134631C211yesmaximal, characteristic, complemented
3#19134622C211yesmaximal, characteristic, complemented
4#19133138C211yesmaximal, characteristic
5#19132502C211yesmaximal, characteristic, complemented
6#19132501C211yesmaximal, characteristic, complemented
7C43×#1513C211yesmaximal, characteristic
8C2×#13063332C411yescharacteristic, complemented
9C23×C43⋊C8C2211yescharacteristic
10#14582971—21no—
11#14582971—21no—
12D4×C43⋊C8—21no—
13D4×C43⋊C8—21no—
14C2×#13063260—21no—
15C2×#13063258—21no—
16#14582926C411yescharacteristic, complemented
17#14582866C411yescharacteristic, complemented
18#14582863C2211yescharacteristic
19#14582863C2211yescharacteristic
20#14582855C411yescharacteristic, complemented
21#14582759C2211yescharacteristic
22#14582663—21no—
23#14582661—21no—
24#14582636—21no—
25#14582633—21no—
26C43×#525C2211yescharacteristic
27C43×#407C2211yescharacteristic
28C43×#380C2211yescharacteristic
29C43×#328—21no—
30C43×#327—21no—
31#13063332—42no—
32C2×#10621877—21no—
33C2×#10621877—21no—
34C2×#10621877C2×C411yescharacteristic
35C2×#10621877C2×C411yescharacteristic
36C22×C43⋊C8—21no—
37C22×C43⋊C8—42no—
38C22×C43⋊C8C2×C411yescharacteristic
39C22×C43⋊C8C2×C411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42C22×C43⋊C8D411yescharacteristic
43C22×C43⋊C8D411yescharacteristic
44C2×C4⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46#13063260—42no—
47#13063258—42no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56#13063236—21no—
57C4×C43⋊C8—21no—
58C43⋊#95—21no—
59C2×#41×C43C2×C411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×M16×C43—21no—
62#123×C43—21no—
63C22⋊Q8×C43D411yescharacteristic
64C22⋊Q8×C43Q811yescharacteristic
65#121×C43D411yescharacteristic
66#121×C43Q811yescharacteristic
67#120×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70#117×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75#95×C43—21no—
76C24×C43#4111yescharacteristic
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43C4⋊C411yescharacteristic
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43C4⋊C411yescharacteristic
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×Q811yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×Dic43—41no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—41no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43C4⋊C411yescharacteristic
103C4⋊C4×C43C4⋊C411yescharacteristic
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—21no—
107C22⋊C4×C43—21no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43—81no—
110C42×C43—21no—
111C22⋊Dic43—81no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114#10621877—42no—
115#10621877—41no—
116#10621877—41no—
117#10621877—41no—
118#10621877—41no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—42no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8C22⋊C411yescharacteristic
130C2×C43⋊C8C22⋊C411yescharacteristic
131C2×C43⋊C8C22⋊C411yescharacteristic
132C2×C43⋊C8C22⋊C411yescharacteristic
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43#11711yescharacteristic
139C23×C43#12111yescharacteristic
140C23×C43C22⋊Q811yescharacteristic
141Q8×C43—41no—
142D4×C43—41no—
143D4×C43—42no—
144D4×C43—42no—
145D4×C43—41no—
146D4×C43—41no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43C2×C22⋊C411yescharacteristic
165C2×C4×C43C2×C4⋊C411yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43C22⋊Q811yescharacteristic
168C2×Dic43—81no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171C8×C43—81no—
172C43⋊C8—21no—
173C43⋊C8—21no—
174C43⋊C8—21no—
175C43⋊C8—41no—
176C43⋊C8—41no—
177C43⋊C8—81no—
178C43⋊C8#9912yes—
179#8627—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—42no—
189C22×C43—42no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43#38011yescharacteristic
194C22×C43#47211yescharacteristic
195C22×C43#47311yescharacteristic
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43—161no—
203C4×C43C2×#9911yescharacteristic
204C4×C43#41011yescharacteristic
205Dic43—161no—
206#2929—431no—
207#1810—431no—
208#1808—431no—
209#1513—431no—
210#1513D4311yescharacteristic
211#1305—431no—
212#1305—431no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—41no—
216C2×C43—41no—
217C2×C43—81no—
218C2×C43#179911yescharacteristic
219C2×C43#181411yescharacteristic
220C2×C43#181611yescharacteristic
221C2×#131—431no—
222C23×C8—431no—
223#525C2×D4311yescharacteristic
224#435—861no—
225#435—861no—
226C8×D4—861no—
227C8×D4—861no—
228C2×#108—861no—
229C2×#107—861no—
230#424—431no—
231#408—431no—
232#407—431no—
233#407—431no—
234#407C2×D4311yescharacteristic
235#405—431no—
236#380—431no—
237#380C2×D4311yescharacteristic
238#341—861no—
239#340—861no—
240#328—21no—
241#328—861no—
242#327—21no—
243#327—861no—
244C43#862711yescharacteristic, complemented, Sylow
245C2×#41C4×D4311yescharacteristic
246C23×C4C22×D4311yescharacteristic
247#131—1722no—
248C2×M16—21no—
249C2×M16—431no—
250C2×M16—431no—
251C2×M16—861no—
252C2×M16—861no—
253C22×C8—431no—
254C22×C8—431no—
255C22×C8—431no—
256C22×C8—431no—
257C22×C8—431no—
258C22×C8—431no—
259C22×C8—861no—
260C22×C8—1722no—
261#123—21no—
262C22⋊Q8Dic8611yescharacteristic
263C22⋊Q8C22⋊D4311yescharacteristic
264#121Dic8611yescharacteristic
265#121C22⋊D4311yescharacteristic
266#120—21no—
267C4×D4—21no—
268C4×D4—21no—
269#117C4×D4311yescharacteristic
270C2×C4⋊C4—21no—
271C2×C4⋊C4—861no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—861no—
274#108—1722no—
275#107—1722no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—861no—
281C22⋊C8—861no—
282C22⋊C8—861no—
283C22⋊C8—861no—
284C22⋊C8—861no—
285C22⋊C8—861no—
286#97—861no—
287C4×C8—861no—
288#95—21no—
289#95—861no—
290C24#1062190011yescharacteristic
291#41—41no—
292#41—41no—
293C2×Q8Dic43⋊C411yescharacteristic
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4Dic43⋊C411yescharacteristic
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—1721no—
303C22×C4C2×Dic8611yescharacteristic
304C22×C4C2×C4×D4311yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307C22×C4#1062190011yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309M16—41no—
310M16—41no—
311M16—1722no—
312M16—1721no—
313M16—1721no—
314M16—1721no—
315M16—1721no—
316C2×C8—41no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—431no—
320C2×C8—431no—
321C2×C8—862no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—861no—
325C2×C8—861no—
326C2×C8—1722no—
327C2×C8—1721no—
328C2×C8—1721no—
329C2×C8—1721no—
330C2×C8—1721no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C4⋊C4Dic43⋊C411yescharacteristic
338C4⋊C4Dic43⋊C411yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—81no—
345C22⋊C4—3441no—
346C42—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23#1306328111yescharacteristic
353C23#1306329711yescharacteristic
354C23#1306330211yescharacteristic
355Q8—41no—
356D4—41no—
357D4—42no—
358D4—42no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—3441no—
379C2×C4—3441no—
380C2×C4—3441no—
381C2×C4C22⋊C4×D4311yescharacteristic
382C2×C4C2×Dic43⋊C411yescharacteristic
383C2×C4#1306329711yescharacteristic
384C2×C4#1306330211yescharacteristic
385C8—81no—
386C8—432no—
387C8—861no—
388C8—861no—
389C8—861no—
390C8—3441no—
391C8—1721no—
392C8—1721no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22#1458275711yescharacteristic
407C22#1458316711yescharacteristic
408C22#1458317211yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—161no—
416C4—6881no—
417C4#99×D4311yescharacteristic
418C4#1458287111yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—81no—
424C2#1913458111yescharacteristic
425C2#1913464711yescharacteristic
426C2#1913465711yescharacteristic
subgroupG/H
centerC22#14582757
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1513C2
socleC22×C43#380
prime radicalC43×#525C22
cosocleC23×C4×C43C23
hypercenter#1513D43
hypocenterC43#8627
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19134631C2semidirect
3. #19134622C2semidirect
5. #19132502C2semidirect
6. #19132501C2semidirect
8. C2×#13063332C4semidirect
16. #14582926C4semidirect
17. #14582866C4semidirect
20. #14582855C4semidirect
244. C43#8627semidirect

Maximal subgroups

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

subgroupindex
#191432902
#191346312
#191346222
#191331382
#191325022
#191325012
C43×#15132
#862743