Finite Group Databasebeta

← #24991311

Subgroups — #24991311

Order 11008.

514 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#19143727C211yesmaximal, characteristic, complemented
2#19135424C211yesmaximal, characteristic, complemented
3C4×#13063252C211yesmaximal, characteristic, complemented
4#19133012C211yesmaximal, characteristic, complemented
5#19132486C211yesmaximal, characteristic, complemented
6#19132427C211yesmaximal, characteristic, complemented
7C43×#3106C211yesmaximal, characteristic
8Q8×C43⋊C8—21no—
9#14582977—22no—
10#14582977—21no—
11#14582952—21no—
12#14582952C2211yescharacteristic
13#14582923—21no—
14#14582923C2211yescharacteristic
15C2×#13063252—22no—
16C2×#13063252—21no—
17C4×#10621877C2211yescharacteristic
18C42×Dic43C2211yescharacteristic
19#14582658—21no—
20D4⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C43×#532C2211yescharacteristic
23C4×#41×C43C2211yescharacteristic
24C43×#482—21no—
25C43×#477C411yescharacteristic, complemented
26C43×#476C411yescharacteristic, complemented
27C43×#460C411yescharacteristic, complemented
28C43×#459C411yescharacteristic, complemented
29C43×#449—21no—
30C4×SD16×C43—21no—
31C4×D8×C43—21no—
32C43×#431C2211yescharacteristic
33C2×#10621877—22no—
34C2×#10621877—21no—
35C2×#10621877D412yes—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—21no—
39C4⋊(C43⋊C8)—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43C4⋊(C43⋊C8)D411yescharacteristic
44#13063252—24no—
45#13063252—44no—
46C22⋊(C43⋊C8)—22no—
47C22⋊(C43⋊C8)—21no—
48#13063236—21no—
49C4×C43⋊C8—22no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C2×#41×C43—21no—
53C2×#41×C43D411yescharacteristic
54C2×SD16×C43—21no—
55C2×D8×C43—21no—
56C4⋊Q8×C43C2×C411yescharacteristic
57#127×C43C2×C411yescharacteristic
58#124×C43—21no—
59#121×C43—21no—
60#121×C43—21no—
61C4×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43D411yescharacteristic
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43C2×C411yescharacteristic
68C4×D4×C43D411yescharacteristic
69#117×C43—21no—
70#117×C43D411yescharacteristic
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73#107×C43—21no—
74#106×C43—21no—
75C4⋊C8×C43C2×C411yescharacteristic
76C4⋊C8×C43C2×C411yescharacteristic
77#103×C43—21no—
78#102×C43—21no—
79#102×C43—21no—
80#102×C43—21no—
81C22⋊C8×C43—21no—
82C4×C8×C43—21no—
83#41×C43—22no—
84#41×C43—41no—
85#41×C43—42no—
86#41×C43—42no—
87C2×Q8×C43—21no—
88C2×Q8×C43C22⋊C411yescharacteristic
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—41no—
94C2×D4×C43C22⋊C411yescharacteristic
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—41no—
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C22×Dic43—41no—
103SD16×C43—42no—
104D8×C43—42no—
105C2×C8×C43—21no—
106C2×C8×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43C22⋊C411yescharacteristic
112C4⋊C4×C43C22⋊C411yescharacteristic
113C22⋊C4×C43—21no—
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C42×C43—21no—
119C42×C43—21no—
120C42×C43—21no—
121C42×C43C22×C411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43#4111yescharacteristic
125C4×Dic43—22no—
126C4×Dic43—22no—
127C4×Dic43—22no—
128C4×Dic43—41no—
129C4×Dic43—41no—
130C4×Dic43—41no—
131#10621877—22no—
132#10621877—41no—
133#10621877—42no—
134#10621877—82no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—41no—
139C23×C43—21no—
140C23×C43—41no—
141C23×C43#12111yescharacteristic
142Q8×C43—21no—
143Q8×C43—42no—
144Q8×C43#10412yescomplemented
145D4×C43—21no—
146D4×C43—21no—
147D4×C43—42no—
148D4×C43—42no—
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—41no—
152D4×C43—41no—
153D4×C43—82no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—81no—
170C2×C4×C43—81no—
171C2×C4×C43C2×C22⋊C411yescharacteristic
172C2×C4×C43C4×D411yescharacteristic
173C2×C4×C43C4×D411yescharacteristic
174C2×C4×C43#12011yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43#12311yescharacteristic
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C8×C43—41no—
181C8×C43—41no—
182C43⋊C8—42no—
183C43⋊C8—42no—
184C43⋊C8—41no—
185C43⋊C8—41no—
186#8970—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43#38611yescharacteristic
197C4×C43—21no—
198C4×C43—22no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—41no—
202C4×C43—41no—
203C4×C43—81no—
204C4×C43C2×#10411yescharacteristic
205C4×C43#42111yescharacteristic
206C4×C43#44311yescharacteristic
207C4×C43#44411yescharacteristic
208C4×C43#45311yescharacteristic
209C4×C43#45411yescharacteristic
210Dic43—44no—
211#3106D4311yescharacteristic
212#2991—431no—
213#1962—431no—
214C4×#104—431no—
215#1484—431no—
216#1299—431no—
217#1276—431no—
218C2×C43—41no—
219C2×C43—81no—
220C2×C43—161no—
221C2×C43#187111yescharacteristic
222C2×C43#187611yescharacteristic
223C2×C43#188311yescharacteristic
224#532C2×D4311yescharacteristic
225C4×#41C2×D4311yescharacteristic
226#482—21no—
227#477Dic4311yescharacteristic, complemented
228#476Dic4311yescharacteristic, complemented
229#460Dic4311yescharacteristic, complemented
230#459Dic4311yescharacteristic, complemented
231#449—21no—
232C8×Q8—861no—
233C4×SD16—21no—
234C4×D8—21no—
235#436—862no—
236#436—861no—
237#431—431no—
238#431—861no—
239#431C2×D4311yescharacteristic
240#423—431no—
241#423—861no—
242C2×#104—861no—
243C2×#104—862no—
244C4×M16—431no—
245C43—431no—
246#339—861no—
247D4⋊C8—861no—
248D4⋊C8—861no—
249C43#897011yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41C22⋊D4311yescharacteristic
252C2×SD16—21no—
253C2×D8—21no—
254C2×M16—432no—
255C2×M16—862no—
256C2×M16—861no—
257C4⋊Q8C2×Dic4311yescharacteristic
258#127C2×Dic4311yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8C2×Dic4311yescharacteristic
263C4×Q8C22⋊D4311yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C2×Dic4311yescharacteristic
269C4×D4C22⋊D4311yescharacteristic
270#117—21no—
271#117C22⋊D4311yescharacteristic
272C2×C42—21no—
273C2×C42—861no—
274C2×C42—861no—
275C2×C42—861no—
276C2×C42C22×D4311yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—431no—
280C4⋊C8—431no—
281C4⋊C8—862no—
282C4⋊C8—861no—
283C4⋊C8—861no—
284C4⋊C8C2×Dic4311yescharacteristic
285C4⋊C8C2×Dic4311yescharacteristic
286#104—864no—
287#104—1724no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—21no—
293C22⋊C8—862no—
294C22⋊C8—861no—
295#97—861no—
296C4×C8—21no—
297C4×C8—862no—
298C4×C8—861no—
299C4×C8—861no—
300#41—22no—
301#41—41no—
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×Q8C22⋊Dic4311yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊Dic4311yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—1721no—
317C22×C4D4×D4311yescharacteristic
318C22×C4#1062190011yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320SD16—42no—
321D8—42no—
322M16—862no—
323M16—3442no—
324M16—1721no—
325M16—1722no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—861no—
329C2×C8—861no—
330C2×C8—862no—
331C2×C8—1721no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊Dic4311yescharacteristic
337C4⋊C4C22⋊Dic4311yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—862no—
347C42—862no—
348C42—862no—
349C42—1721no—
350C42—1721no—
351C42—1721no—
352C42D4×D4311yescharacteristic
353C42#1062190011yescharacteristic
354C42C22×Dic4311yescharacteristic
355C42C2×C22⋊D4311yescharacteristic
356C23—21no—
357C23—41no—
358C23#1306329711yescharacteristic
359Q8—21no—
360Q8—42no—
361Q8#1306325212yescomplemented
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4C2×C22⋊Dic4311yescharacteristic
392C2×C4D4×Dic4311yescharacteristic
393C2×C4D4×Dic4311yescharacteristic
394C2×C4#1306329311yescharacteristic
395C2×C4#1306329711yescharacteristic
396C2×C4#1306330611yescharacteristic
397C8—41no—
398C8—41no—
399C8—1722no—
400C8—1721no—
401C8—1722no—
402C8—1721no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1458277911yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—1724no—
421C4C2×#1306325211yescharacteristic
422C4#1458291611yescharacteristic
423C4#1458301611yescharacteristic
424C4#1458302111yescharacteristic
425C4#1458306511yescharacteristic
426C4#1458307011yescharacteristic
427C2—41no—
428C2—81no—
429C2—161no—
430C2#1913489811yescharacteristic
431C2#1913492411yescharacteristic
432C2#1913497311yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3106C2
socleC22×C43#386
cosocleC2×C42×C43C23
hypercenter#3106D43
hypocenterC43#8970
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19143727C2semidirect
2. #19135424C2semidirect
3. C4×#13063252C2semidirect
4. #19133012C2semidirect
5. #19132486C2semidirect
6. #19132427C2semidirect
25. C43×#477C4semidirect
26. C43×#476C4semidirect
27. C43×#460C4semidirect
28. C43×#459C4semidirect
144. Q8×C43#104semidirect
227. #477Dic43semidirect
228. #476Dic43semidirect
229. #460Dic43semidirect
230. #459Dic43semidirect
249. C43#8970semidirect
361. Q8#13063252semidirect

Maximal subgroups

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

subgroupindex
#191437272
#191354242
C4×#130632522
#191330122
#191324862
#191324272
C43×#31062
#897043