Finite Group Databasebeta

← #24993918

Subgroups — #24993918

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143619C211yesmaximal, characteristic, complemented
2#19134583C211yesmaximal, characteristic, complemented
3#19133163C212yesmaximal, complemented
4#19132474C212yesmaximal, complemented
5C43×#2543C211yesmaximal, characteristic
6D4×C43⋊C8—24no—
7#14582952—21no—
8C2×#13063240—21no—
9C2×C22⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2212yes—
11#14582759C2212yes—
12#14582666—21no—
13#14582633—24no—
14C2×#121×C43—21no—
15C2×#121×C43C2211yescharacteristic
16C2×C4×D4×C43C2211yescharacteristic
17C43×#398C411yescharacteristic, complemented
18C43×#397C411yescharacteristic, complemented
19C43×#394C411yescharacteristic, complemented
20C43×#392C411yescharacteristic, complemented
21C43×#388—21no—
22C43×#386—21no—
23C43×#386—21no—
24C2×#95×C43C2211yescharacteristic
25C22×C43⋊C8—22no—
26C22×C43⋊C8—22no—
27C2×C4⋊Dic43—22no—
28C2×C22⋊Dic43—22no—
29C4⋊(C43⋊C8)—22no—
30#13063240—42no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)D414yescomplemented
34C4×C43⋊C8—22no—
35C43⋊#95—22no—
36C22×D4×C43—21no—
37C22×D4×C43—21no—
38C22×D4×C43C2×C411yescharacteristic
39C22×D4×C43D411yescharacteristic
40C23×C4×C43—21no—
41C23×C4×C43D411yescharacteristic
42C23×C4×C43C2311yescharacteristic
43#121×C43—22no—
44#121×C43—22no—
45#121×C43—42no—
46#121×C43—42no—
47C4×D4×C43—22no—
48C4×D4×C43—22no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64#95×C43C2×C411yescharacteristic
65C24×C43—21no—
66C24×C43C22⋊C411yescharacteristic
67C24×C43C2×D411yescharacteristic
68C2×D4×C43—22no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—42no—
72C2×D4×C43—42no—
73C2×D4×C43—42no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—42no—
77C2×D4×C43—81no—
78C2×D4×C43—81no—
79C2×D4×C43D812yes—
80C2×D4×C43SD1612yes—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—42no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—81no—
90C22×C4×C43—81no—
91C22×C4×C43—81no—
92C22×C4×C43C22⋊C411yescharacteristic
93C22×C4×C43C22⋊C411yescharacteristic
94C22×C4×C43C22⋊C411yescharacteristic
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D412yes—
98C22×C4×C43#4112yes—
99C22×Dic43—42no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—42no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—42no—
106C22⋊C4×C43—42no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—42no—
110C22⋊C4×C43—81no—
111C42×C43—21no—
112C42×C43—21no—
113C22⋊Dic43—42no—
114C22⋊Dic43—42no—
115C4⋊Dic43—82no—
116C2×C43⋊C8—24no—
117C2×C43⋊C8—82no—
118C2×C43⋊C8—82no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43#10212yes—
133C23×C43C2×C22⋊C411yescharacteristic
134C23×C43#12112yes—
135C23×C43C2×D811yescharacteristic
136C23×C43C2×SD1611yescharacteristic
137C23×C43#13512yes—
138D4×C43—24no—
139D4×C43—24no—
140D4×C43—82no—
141D4×C43—84no—
142D4×C43—82no—
143D4×C43—82no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—22no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—81no—
165C2×C4×C43—82no—
166C2×C4×C43—82no—
167C2×C4×C43#10212yes—
168C2×C4×C43C4×D412yes—
169C2×C4×C43#12011yescharacteristic
170C2×C4×C43#12311yescharacteristic
171C2×Dic43—82no—
172C2×Dic43—82no—
173C2×Dic43—82no—
174C43⋊C8—44no—
175#9384—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—22no—
178C22×C43—21no—
179C22×C43—22no—
180C22×C43—22no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—42no—
184C22×C43—42no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43#38611yescharacteristic
196C22×C43C2×#10211yescharacteristic
197C22×C43#41611yescharacteristic
198C22×C43#46512yes—
199C22×C43#46612yes—
200C4×C43—22no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—22no—
204C4×C43—42no—
205C4×C43—41no—
206C4×C43—41no—
207C4×C43—81no—
208C4×C43—81no—
209Dic43—162no—
210#2972—431no—
211#2543D4311yescharacteristic
212#1799—431no—
213#1519—432no—
214#1294—432no—
215C2×C43—22no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—22no—
219C2×C43—42no—
220C2×C43—161no—
221C2×C43#188411yescharacteristic
222C2×C43#189311yescharacteristic
223C2×C43#191311yescharacteristic
224C2×#121—21no—
225C2×#121C2×D4311yescharacteristic
226C2×C4×D4C2×D4311yescharacteristic
227C8×D4—864no—
228#431—861no—
229C2×#99—861no—
230C2×C22⋊C8—432no—
231C2×C22⋊C8—861no—
232#398Dic4311yescharacteristic, complemented
233#397Dic4311yescharacteristic, complemented
234#394Dic4311yescharacteristic, complemented
235#392Dic4311yescharacteristic, complemented
236#388—21no—
237#386—21no—
238#386—21no—
239#380—432no—
240C2×#95C2×D4311yescharacteristic
241#342—861no—
242#327—864no—
243C43#938411yescharacteristic, complemented, Sylow
244C22×D4—21no—
245C22×D4—21no—
246C22×D4C2×Dic4311yescharacteristic
247C22×D4C22⋊D4311yescharacteristic
248C23×C4—21no—
249C23×C4C22⋊D4311yescharacteristic
250C23×C4C22×D4311yescharacteristic
251C22×C8—862no—
252C22×C8—862no—
253#121—22no—
254#121—22no—
255#121—42no—
256#121—42no—
257C4×D4—22no—
258C4×D4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—862no—
261C2×C4⋊C4C2×Dic4311yescharacteristic
262C2×C4⋊C4C2×Dic4311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—862no—
269C2×C22⋊C4C2×Dic4311yescharacteristic
270C2×C22⋊C4C22⋊D4311yescharacteristic
271C2×C42C22⋊D4311yescharacteristic
272C4⋊C8—862no—
273#99—1722no—
274C22⋊C8—434no—
275C22⋊C8—862no—
276C22⋊C8—862no—
277C4×C8—862no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—862no—
282#95C2×Dic4311yescharacteristic
283#95C2×Dic4311yescharacteristic
284C24—21no—
285C24C22⋊Dic4311yescharacteristic
286C24C2×C22⋊D4311yescharacteristic
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4#1062188212yes—
299C2×D4#1062188312yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—1722no—
312C22×C4C22⋊Dic4311yescharacteristic
313C22×C4C22⋊Dic4311yescharacteristic
314C22×C4C22⋊Dic4311yescharacteristic
315C22×C4D4×D4312yes—
316C22×C4#1062190012yes—
317C22×C4C22×Dic4311yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319C2×C8—864no—
320C2×C8—3442no—
321C2×C8—3442no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—42no—
325C4⋊C4—3442no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C22⋊C4—1722no—
335C22⋊C4—1722no—
336C42—21no—
337C42—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#1306324612yes—
352C23C2×C22⋊Dic4311yescharacteristic
353C23#1306329712yes—
354C23C2×#1062188211yescharacteristic
355C23C2×#1062188311yescharacteristic
356C23#1306334512yes—
357D4—24no—
358D4—24no—
359D4—82no—
360D4—84no—
361D4—82no—
362D4—82no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—3442no—
387C2×C4—3442no—
388C2×C4—3442no—
389C2×C4#1306324612yes—
390C2×C4D4×Dic4312yes—
391C2×C4#1306329311yescharacteristic
392C2×C4#1306330611yescharacteristic
393C8—1724no—
394C22—21no—
395C22—22no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22#1458277911yescharacteristic
414C22C2×#1306324611yescharacteristic
415C22#1458289511yescharacteristic
416C22#1458312612yes—
417C22#1458313312yes—
418C4—22no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—42no—
423C4—41no—
424C4—41no—
425C4—81no—
426C4—81no—
427C4—6882no—
428C2—21no—
429C2—22no—
430C2—21no—
431C2—22no—
432C2—42no—
433C2—161no—
434C2#1913497911yescharacteristic
435C2#1913502411yescharacteristic
436C2#1913513811yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#2543C2
socleC22×C43#386
cosocleC23×C4×C43C23
hypercenter#2543D43
hypocenterC43#9384
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. #19143619C2semidirect
2. #19134583C2semidirect
3. #19133163C2semidirect
4. #19132474C2semidirect
17. C43×#398C4semidirect
18. C43×#397C4semidirect
19. C43×#394C4semidirect
20. C43×#392C4semidirect
33. C22⋊(C43⋊C8)D4semidirect
232. #398Dic43semidirect
233. #397Dic43semidirect
234. #394Dic43semidirect
235. #392Dic43semidirect
243. C43#9384semidirect

Maximal subgroups

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

subgroupindex
#191436192
#191345832
#191331632
#191324742
C43×#25432
#938443