Finite Group Databasebeta

← #25079281

Subgroups — #25079281

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144920C211yesmaximal, characteristic
2#19144626C211yesmaximal, characteristic
3C2×#14583030C211yesmaximal, characteristic, complemented
4#19134179C212yesmaximal, complemented
5#19134165C212yesmaximal, complemented
6#19134151C212yesmaximal, complemented
7#19134137C212yesmaximal, complemented
8#19133341C211yesmaximal, characteristic, complemented
9#19133252C211yesmaximal, characteristic, complemented
10#19133242C211yesmaximal, characteristic
11C43×#3104C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13#14583256—21no—
14#14583256—21no—
15#14583251C2211yescharacteristic
16#14583251C2211yescharacteristic
17#14583247C2211yescharacteristic
18#14583247C2211yescharacteristic
19#14583217—21no—
20#14583184C2212yes—
21#14583099C2212yes—
22#14583038—21no—
23#14583030—21no—
24#14583030—21no—
25#14583030C2212yes—
26#14583030C2212yes—
27C4×#10621884—22no—
28#14582952C2211yescharacteristic
29C2×C4⋊(C43⋊C8)—21no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31#14582893—21no—
32#14582893—21no—
33C2×#13063236—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yes—
36#14582649C2212yes—
37#14582648C2212yes—
38#14582645C2212yes—
39#14582644C2212yes—
40#14582642C2212yes—
41C43×#533C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C43×#484—21no—
44C43×#477C2212yes—
45C43×#462C2212yes—
46C43×#451—21no—
47C4×Q16×C43—22no—
48C43×#431C2211yescharacteristic
49C2×#10621898—21no—
50C2×#10621884—22no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8D411yescharacteristic
53C22×C43⋊C8D411yescharacteristic
54#13063325C2311yescharacteristic
55#13063322C2311yescharacteristic
56#13063313—21no—
57#13063299—21no—
58#13063299—21no—
59C4×D172—21no—
60C4×D172—21no—
61#13063256—22no—
62C4⋊(C43⋊C8)—21no—
63C4⋊(C43⋊C8)—22no—
64C4⋊(C43⋊C8)—22no—
65C4⋊(C43⋊C8)C2312yes—
66C4⋊(C43⋊C8)C2312yes—
67#13063249—22no—
68#13063248—21no—
69#13063248—21no—
70#13063248—21no—
71#13063248—21no—
72#13063245—22no—
73#13063245—21no—
74#13063245—21no—
75#13063245—21no—
76#13063245—21no—
77C22⋊(C43⋊C8)—21no—
78#13063236—22no—
79#13063236—22no—
80C4×C43⋊C8—21no—
81C4×C43⋊C8D411yescharacteristic
82C4×C43⋊C8D411yescharacteristic
83C4×C43⋊C8C2311yescharacteristic
84C4×C43⋊C8C2311yescharacteristic
85C22×Q8×C43D411yescharacteristic
86C2×Q16×C43—22no—
87C4⋊Q8×C43C2311yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89#125×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43D412yes—
97C4×Q8×C43C2312yes—
98#117×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104C4⋊C8×C43C2312yes—
105#103×C43—22no—
106#103×C43—22no—
107C22⋊C8×C43—21no—
108C4×C8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—42no—
113C2×Q8×C43C2×D412yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C2×C22⋊D43—41no—
120#10621898—42no—
121#10621898—42no—
122C2×D172—21no—
123C2×D172—21no—
124C2×D172—21no—
125C2×C4×D43—41no—
126C2×Dic86—21no—
127Q16×C43—44no—
128C2×C8×C43—22no—
129C4⋊C4×C43—22no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C4⋊C4×C43C2×D412yes—
139C22⋊C4×C43—41no—
140C42×C43—22no—
141C42×C43—22no—
142C42×C43—41no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43#4111yescharacteristic
146C42×C43C2411yescharacteristic
147#10621884—44no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C2×C43⋊C8—22no—
153C2×C43⋊C8—22no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—42no—
157C2×C43⋊C8C2×D411yescharacteristic
158C2×C43⋊C8C2×D411yescharacteristic
159C2×C43⋊C8C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C23×C43#12111yescharacteristic
162C22×D43—41no—
163Q8×C43—22no—
164Q8×C43—22no—
165Q8×C43—42no—
166Q8×C43—42no—
167Q8×C43—81no—
168C2×C4×C43—22no—
169C2×C4×C43—22no—
170C2×C4×C43—22no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#13512yes—
180C2×C4×C43#13712yes—
181C2×C4×C43C22×D411yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C2×C4×C43C2×#4111yescharacteristic
184C22⋊D43—82no—
185C2×Dic43—41no—
186D172—41no—
187D172—41no—
188D172—42no—
189D172—81no—
190C4×D43—82no—
191Dic86—41no—
192Dic86—41no—
193C8×C43—42no—
194C43⋊C8—21no—
195C43⋊C8—21no—
196C43⋊C8—21no—
197C43⋊C8—21no—
198C43⋊C8—42no—
199C43⋊C8—42no—
200#19155—431nomaximal, Sylow
201C22×C43—21no—
202C22×C43—21no—
203C22×C43#46412yes—
204C22×C43C2×#12111yescharacteristic
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—81no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—42no—
212C4×C43—42no—
213C4×C43—81no—
214C4×C43—81no—
215C4×C43#46412yes—
216C4×C43C2×#13511yescharacteristic
217C4×C43C2×#13711yescharacteristic
218C4×C43#57512yes—
219Dic43—81no—
220#3131—431no—
221#3104D4311yescharacteristic, complemented
222#3103—431no—
223C2×#446—431no—
224#1704—432no—
225#1702—432no—
226#1700—432no—
227#1698—432no—
228#1564—431no—
229#1542—431no—
230#1540—431no—
231C2×C43—22no—
232C2×C43C2×#46411yescharacteristic
233C2×C43#305411yescharacteristic
234C2×C43#306711yescharacteristic
235D43—161no—
236#533C2×D4311yescharacteristic
237#532—431no—
238C2×C4×Q8C2×D4311yescharacteristic
239#488—861no—
240#488—861no—
241#487—431no—
242#487—431no—
243#486—431no—
244#486—431no—
245#484—21no—
246#481—861no—
247#477C2×D4312yes—
248#475—432no—
249#462C2×D4312yes—
250#460—432no—
251#451—21no—
252#448—861no—
253#446—432no—
254#446—432no—
255#446—861no—
256#446—861no—
257C4×Q16—22no—
258C4×SD16—862no—
259#431—431no—
260#431C2×D4311yescharacteristic
261C2×C4⋊C8—431no—
262C2×C4⋊C8—861no—
263#416—861no—
264#416—861no—
265C2×#97—861no—
266C2×C4×C8—431no—
267#335—432no—
268#334—432no—
269#333—432no—
270#332—432no—
271#332—432no—
272#331—432no—
273C43#1915511yescharacteristic, complemented, Sylow
274C2×#41—861no—
275C22×Q8C22⋊D4311yescharacteristic
276C2×Q16—22no—
277C2×SD16—862no—
278C22×C8—431no—
279C22×C8—431no—
280C22×C8—861no—
281C4⋊Q8—431no—
282C4⋊Q8C22×D4311yescharacteristic
283C4⋊Q8C22×D4311yescharacteristic
284#127—431no—
285#125—21no—
286#124—861no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289#121—861no—
290#121—861no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8C22⋊D4312yes—
296C4×Q8C22×D4312yes—
297C4×D4—861no—
298C4×D4—861no—
299#117—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C22⋊D4311yescharacteristic
302C2×C42—21no—
303C2×C42C22×D4311yescharacteristic
304#107—22no—
305#106—862no—
306C4⋊C8—432no—
307C4⋊C8—432no—
308C4⋊C8—862no—
309C4⋊C8—862no—
310C4⋊C8—861no—
311C4⋊C8C22×D4312yes—
312#103—22no—
313#103—22no—
314#103—861no—
315#103—861no—
316#103—861no—
317#103—861no—
318#103—862no—
319#102—861no—
320#102—861no—
321#102—861no—
322#102—861no—
323#102—862no—
324C22⋊C8—21no—
325C22⋊C8—861no—
326#97—862no—
327#97—862no—
328C4×C8—21no—
329C4×C8—431no—
330C4×C8—431no—
331C4×C8—431no—
332C4×C8—431no—
333C4×C8—861no—
334#41—1722no—
335#41—1722no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—42no—
340C2×Q8—861no—
341C2×Q8C2×C22⋊D4312yes—
342C2×D4—861no—
343C2×D4—861no—
344C2×D4—861no—
345C2×D4—1721no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—1721no—
349C22×C4D4×D4311yescharacteristic
350C22×C4#1062190011yescharacteristic
351C22×C4C2×C22⋊D4311yescharacteristic
352Q16—44no—
353SD16—1724no—
354C2×C8—22no—
355C2×C8—431no—
356C2×C8—431no—
357C2×C8—431no—
358C2×C8—431no—
359C2×C8—862no—
360C2×C8—862no—
361C2×C8—862no—
362C2×C8—862no—
363C2×C8—1722no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4C2×C22⋊D4312yes—
376C22⋊C4—41no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C42—22no—
380C42—22no—
381C42—41no—
382C42D4×D4311yescharacteristic
383C42#1062190011yescharacteristic
384C42C2×C22⋊D4311yescharacteristic
385C42C23×D4311yescharacteristic
386C23—1721no—
387C23#1306329711yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—42no—
392Q8—81no—
393Q8—1721no—
394Q8—1721no—
395D4—3441no—
396D4—3442no—
397D4—1721no—
398D4—1721no—
399D4—1722no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—3442no—
409C2×C4—1721no—
410C2×C4#1306329711yescharacteristic
411C2×C4#1306329711yescharacteristic
412C2×C4#1306329711yescharacteristic
413C2×C4#1306334812yes—
414C2×C4#1306335712yes—
415C2×C4C2×D4×D4311yescharacteristic
416C2×C4C22×C22⋊D4311yescharacteristic
417C2×C4C2×#1062190011yescharacteristic
418C8—42no—
419C8—861no—
420C8—861no—
421C8—861no—
422C8—861no—
423C8—1722no—
424C8—1722no—
425C22—21no—
426C22—21no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22#1458312312yes—
431C22C2×#1306329711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4—81no—
439C4—3441no—
440C4#1458312312yes—
441C4C2×#1306334811yescharacteristic
442C4C2×#1306335711yescharacteristic
443C4#1458369712yes—
444C2—22no—
445C2—6881no—
446C2C2×#1458312311yescharacteristic
447C2#1914420111yescharacteristic
448C2#1914431211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3104C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenter#3104D43
hypocenterC43#19155
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. C2×#14583030C2semidirect
4. #19134179C2semidirect
5. #19134165C2semidirect
6. #19134151C2semidirect
7. #19134137C2semidirect
8. #19133341C2semidirect
9. #19133252C2semidirect
11. C43×#3104C2semidirect
221. #3104D43semidirect
273. C43#19155semidirect

Maximal subgroups

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

subgroupindex
#191449202
#191446262
C2×#145830302
#191341792
#191341652
#191341512
#191341372
#191333412
#191332522
#191332422
C43×#31042
#1915543