Finite Group Databasebeta

← #24992706

Subgroups — #24992706

Order 11008.

536 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144655C211yesmaximal, characteristic
2C4×#13063332C211yesmaximal, characteristic, complemented
3#19133186C211yesmaximal, characteristic, complemented
4#19133045C211yesmaximal, characteristic, complemented
5#19132484C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1489C211yesmaximal, characteristic, complemented
8C2×#13063332—21no—
9#14583449C2211yescharacteristic
10#14583223—21no—
11#14583194C411yescharacteristic
12#14583189C411yescharacteristic
13#14583099C411yescharacteristic
14#14583094C411yescharacteristic
15#14583044—21no—
16C4×#10621884—21no—
17C4×#10621882—21no—
18#14582952C2211yescharacteristic
19#14582855—22no—
20#14582855—21no—
21C4×#10621877—21no—
22C4×#10621877C2211yescharacteristic
23C2×C4×C43⋊C8—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582638—22no—
26#14582626—21no—
27#14582626—21no—
28C4×#41×C43C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×M16×C43C2211yescharacteristic
31C43×Q8⋊C8—21no—
32C43×D4⋊C8—21no—
33C2×#10621898—21no—
34C2×#10621884—21no—
35C2×#10621882—21no—
36#13063332—24no—
37#13063332—24no—
38C2×#10621877—22no—
39C2×#10621877—21no—
40C22×C43⋊C8—22no—
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—
49#13063258—21no—
50#13063256—21no—
51C4⋊(C43⋊C8)C2×C411yescharacteristic
52C4⋊(C43⋊C8)C2×C411yescharacteristic
53#13063249—21no—
54#13063246—21no—
55#13063245—21no—
56#13063245—21no—
57C22⋊(C43⋊C8)—21no—
58#13063236—22no—
59#13063236D412yes—
60C4×C43⋊C8—22no—
61C4×C43⋊C8—21no—
62C4×C43⋊C8—21no—
63C4×C43⋊C8—21no—
64C4×C43⋊C8D411yescharacteristic
65C4×C43⋊C8D411yescharacteristic
66C2×#41×C43D411yescharacteristic
67C2×M16×C43—21no—
68C2×M16×C43—21no—
69C4×Q8×C43C2×C411yescharacteristic
70C4×Q8×C43D411yescharacteristic
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43C2×C411yescharacteristic
74C4×D4×C43D411yescharacteristic
75#117×C43—21no—
76#117×C43D411yescharacteristic
77C2×C42×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43—21no—
81#97×C43—21no—
82C4×C8×C43—21no—
83#41×C43—22no—
84#41×C43—22no—
85C2×Q8×C43C22⋊C411yescharacteristic
86C2×D4×C43—21no—
87C2×D4×C43C22⋊C411yescharacteristic
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—41no—
95#10621898—81no—
96#10621898—81no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×C4×D43—41no—
101C2×Dic86—21no—
102M16×C43—22no—
103M16×C43—41no—
104M16×C43—81no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43C22⋊C411yescharacteristic
110C4⋊C4×C43C22⋊C411yescharacteristic
111C22⋊C4×C43—21no—
112C22⋊C4×C43—21no—
113C22⋊C4×C43—21no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43C22×C411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121#10621884—42no—
122#10621882—42no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127#10621877—28no—
128#10621877—22no—
129#10621877—22no—
130C2×C43⋊C8—28no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C23×C43—21no—
139C23×C43#12311yescharacteristic
140C22×D43—41no—
141Q8×C43—21no—
142Q8×C43#10412yes—
143D4×C43—24no—
144D4×C43—21no—
145D4×C43#10412yes—
146C2×C4×C43—24no—
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×C43C2×C22⋊C411yescharacteristic
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C22⋊D43—82no—
167C2×Dic43—41no—
168D172—41no—
169D172—41no—
170D172—41no—
171D172—41no—
172D172—81no—
173C4×D43—81no—
174C4×D43—81no—
175Dic86—81no—
176C8×C43—42no—
177C8×C43—81no—
178C43⋊C8—22no—
179C43⋊C8—24no—
180C43⋊C8—22no—
181C43⋊C8—41no—
182C43⋊C8—41no—
183#9211—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—22no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43#38611yescharacteristic
191C2×D43—81no—
192C2×D43—81no—
193C2×D43—81no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—22no—
197C4×C43—21no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43C2×#10411yescharacteristic
201C4×C43C2×#10411yescharacteristic
202C4×C43#44311yescharacteristic
203C4×C43#44411yescharacteristic
204C4×C43#47111yescharacteristic
205C4×C43#47211yescharacteristic
206Dic43—81no—
207#3106—431no—
208C4×#131—431no—
209#1525—431no—
210#1492—431no—
211#1489D4311yescharacteristic, complemented
212#1299—431no—
213#1278—431no—
214C2×C43—41no—
215C2×C43—42no—
216C2×C43#187611yescharacteristic
217C2×C43#189611yescharacteristic
218C2×C43#190711yescharacteristic
219D43—161no—
220C2×#131—861no—
221#532—431no—
222C4×#41C2×D4311yescharacteristic
223#482—861no—
224#477—431no—
225#476—431no—
226#460—431no—
227#459—431no—
228#449—861no—
229C4×SD16—861no—
230C4×D8—861no—
231#431—431no—
232#423C2×D4311yescharacteristic
233#405—862no—
234#405—861no—
235C4×M16—431no—
236C4×M16—861no—
237C4×M16C2×D4311yescharacteristic
238C2×C4×C8—431no—
239C2×C4×C8—861no—
240#329—862no—
241Q8⋊C8—21no—
242D4⋊C8—21no—
243D4⋊C8—861no—
244D4⋊C8—861no—
245C43#921111yescharacteristic, complemented, Sylow
246C2×#41—861no—
247C2×#41D17211yescharacteristic
248C2×SD16—861no—
249C2×D8—861no—
250#131—864no—
251#131—864no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—862no—
255C2×M16—861no—
256C22×C8—862no—
257C22×C8—861no—
258C4⋊Q8—431no—
259#127—431no—
260#124—861no—
261#121—861no—
262#121—861no—
263C4×Q8C4×D4311yescharacteristic
264C4×Q8C22⋊D4311yescharacteristic
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—861no—
268C4×D4—861no—
269C4×D4C4×D4311yescharacteristic
270C4×D4C22⋊D4311yescharacteristic
271#117—21no—
272#117D17211yescharacteristic
273C2×C42—21no—
274C2×C42C22×D4311yescharacteristic
275#107—861no—
276#106—861no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—431no—
280C4⋊C8—431no—
281#103—861no—
282#102—861no—
283#102—861no—
284#102—861no—
285C22⋊C8—861no—
286#97—21no—
287#97—432no—
288#97—862no—
289C4×C8—21no—
290C4×C8—431no—
291C4×C8—431no—
292C4×C8—862no—
293C4×C8—861no—
294C4×C8—861no—
295C4×C8—861no—
296#41—22no—
297#41—22no—
298#41—3441no—
299#41—3441no—
300C2×Q8—861no—
301C2×Q8(C2×D43)⋊C411yescharacteristic
302C2×D4—21no—
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—861no—
306C2×D4—1721no—
307C2×D4(C2×D43)⋊C411yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—1721no—
312C22×C4C2×D17211yescharacteristic
313C22×C4#1062190011yescharacteristic
314C22×C4#1062190011yescharacteristic
315SD16—1722no—
316D8—1722no—
317M16—22no—
318M16—41no—
319M16—81no—
320M16—868no—
321M16—862no—
322M16—862no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—868no—
326C2×C8—862no—
327C2×C8—862no—
328C2×C8—861no—
329C2×C8—861no—
330C2×C8—862no—
331C2×C8—861no—
332C2×C8—861no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—861no—
336C4⋊C4—861no—
337C4⋊C4(C2×D43)⋊C411yescharacteristic
338C4⋊C4(C2×D43)⋊C411yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42C2×C4×D4311yescharacteristic
348C42D4×D4311yescharacteristic
349C42D4×D4311yescharacteristic
350C42C2×C22⋊D4311yescharacteristic
351C23—21no—
352C23—1721no—
353C23#1306330911yescharacteristic
354Q8—21no—
355Q8—3441no—
356Q8#1306325112yes—
357D4—24no—
358D4—21no—
359D4—3441no—
360D4—3442no—
361D4—1721no—
362D4—1721no—
363D4—1721no—
364D4—1721no—
365D4#1306325112yes—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—1721no—
383C2×C4C2×(C2×D43)⋊C411yescharacteristic
384C2×C4(C22⋊D43)⋊C411yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4#1306329511yescharacteristic
387C2×C4#1306329711yescharacteristic
388C2×C4#1306329711yescharacteristic
389C8—42no—
390C8—81no—
391C8—862no—
392C8—862no—
393C8—864no—
394C8—1721no—
395C8—1721no—
396C22—21no—
397C22—22no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22#1458277611yescharacteristic
406C4—21no—
407C4—22no—
408C4—21no—
409C4—21no—
410C4—41no—
411C4—41no—
412C4—3441no—
413C4C2×#1306325111yescharacteristic
414C4C2×#1306325111yescharacteristic
415C4#1458301311yescharacteristic
416C4#1458301811yescharacteristic
417C4#1458316411yescharacteristic
418C4#1458316711yescharacteristic
419C2—41no—
420C2—42no—
421C2—6881no—
422C2#1913492011yescharacteristic
423C2#1913503611yescharacteristic
424C2#1913510111yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1489C2
socleC22×C43#386
prime radical#19144655C2
cosocleC2×C42×C43C23
hypercenter#1489D43
hypocenterC43#9211
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. C4×#13063332C2semidirect
3. #19133186C2semidirect
4. #19133045C2semidirect
5. #19132484C2semidirect
6. #19132433C2semidirect
7. C43×#1489C2semidirect
211. #1489D43semidirect
245. C43#9211semidirect

Maximal subgroups

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

subgroupindex
#191446552
C4×#130633322
#191331862
#191330452
#191324842
#191324332
C43×#14892
#921143