Finite Group Databasebeta

← #24991564

Subgroups — #24991564

Order 11008.

784 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143624C211yesmaximal, characteristic, complemented
2#19137810C211yesmaximal, characteristic
3#19134540C212yesmaximal, complemented
4#19132481C212yesmaximal, complemented
5C4×#99×C43C211yesmaximal, characteristic, complemented
6C22×#10621898C2211yescharacteristic
7C2×C4×C22⋊D43—21no—
8#14582971—24no—
9#14582956—21no—
10C2×#13063253—24no—
11#14582863C2212yes—
12C2×C22⋊(C43⋊C8)—21no—
13#14582819C411yescharacteristic, complemented
14#14582816C411yescharacteristic, complemented
15#14582814—21no—
16#14582811C411yescharacteristic, complemented
17#14582808C411yescharacteristic, complemented
18#14582807—21no—
19C4×(C2×D43)⋊C4—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C2×#99×C43—21no—
23C4×C22⋊C4×C43C2212yes—
24C43×#342—21no—
25C2×#10621898—22no—
26C2×#10621898—22no—
27C2×#10621898—44no—
28C22×Dic86C2×C411yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C22×C22⋊D43—21no—
32C22×C4×D43—21no—
33C2×#10621877D414yescomplemented
34C22×C43⋊C8—22no—
35C4×C22⋊D43—44no—
36C2×Dic43⋊C4—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43C4⋊(C43⋊C8)—22no—
44#13063253—48no—
45C22⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—22no—
47C22⋊(C43⋊C8)—22no—
48#13063236—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95C2×C411yescharacteristic
52C43⋊#95C2×C411yescharacteristic
53C22×D4×C43D411yescharacteristic
54C23×C4×C43D411yescharacteristic
55C23×C4×C43C2311yescharacteristic
56C4×D4×C43—22no—
57C4×D4×C43—22no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—22no—
60C2×C22⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43D411yescharacteristic
62C2×C42×C43—22no—
63C2×C42×C43D411yescharacteristic
64#99×C43—24no—
65#95×C43—22no—
66C24×C43C22⋊C411yescharacteristic
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D412yes—
83C22×C4×C43#4112yes—
84C2×C22⋊D43—42no—
85C2×C22⋊D43—42no—
86C2×C22⋊D43—42no—
87C2×C22⋊D43—42no—
88C2×C22⋊D43—42no—
89C2×C22⋊D43—42no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93#10621898—28no—
94#10621898—44no—
95#10621898—44no—
96#10621898—44no—
97C2×D172—22no—
98C2×D172—42no—
99C2×C4×D43—24no—
100C2×C4×D43—42no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×Dic86—22no—
104C2×Dic86—42no—
105C4⋊C4×C43—22no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—24no—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—42no—
110C42×C43—21no—
111C42×C43—21no—
112C42×C43—44no—
113C22⋊Dic43—42no—
114C22⋊Dic43—42no—
115(C2×D43)⋊C4—42no—
116(C2×D43)⋊C4—42no—
117(C2×D43)⋊C4—42no—
118Dic43⋊C4—42no—
119C4×Dic43—42no—
120#10621877—44no—
121C2×C43⋊C8—24no—
122C2×C43⋊C8—82no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43#10412yescomplemented
132C23×C43C2×C22⋊C411yescharacteristic
133C23×C43#12112yes—
134C22×D43—22no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141D4×C43—44no—
142C2×C4×C43—24no—
143C2×C4×C43—22no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—44no—
155C2×C4×C43—81no—
156C2×C4×C43—82no—
157C2×C4×C43—82no—
158C2×C4×C43C4×D412yes—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C22⋊D43—48no—
162C22⋊D43—48no—
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172D172—24no—
173D172—42no—
174C4×D43—44no—
175C4×D43—44no—
176Dic86—24no—
177Dic86—42no—
178C43⋊C8—44no—
179#9009—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—42no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#38611yescharacteristic
193C22×C43C2×#10411yescharacteristic
194C22×C43#42111yescharacteristic
195C2×D43—42no—
196C2×D43—42no—
197C2×D43—42no—
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—81no—
202C4×C43—22no—
203C4×C43—21no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43—41no—
207C4×C43—84no—
208C4×C43B(4,𝔽2)12yes—
209Dic43—42no—
210Dic43—42no—
211Dic43—81no—
212#2973—431no—
213#2388—431no—
214#1789—432no—
215C4×#99D4311yescharacteristic, complemented
216#1297—432no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—42no—
220C2×C43—42no—
221C2×C43#187111yescharacteristic
222C2×C43#188411yescharacteristic
223C2×C43#188911yescharacteristic
224D43—82no—
225C22×#41—431no—
226C2×C4×D4—861no—
227C2×C4×D4C2×D4311yescharacteristic
228#435—864no—
229#432—861no—
230C2×#104—864no—
231C2×#99—21no—
232#407—432no—
233C2×C22⋊C8—861no—
234#395—431no—
235#394—431no—
236#394—861no—
237#393—431no—
238#392—431no—
239#392—861no—
240C4×C22⋊C4—431no—
241C4×C22⋊C4—861no—
242C4×C22⋊C4C2×D4312yes—
243#342—21no—
244C43#900911yescharacteristic, complemented, Sylow
245C2×#41—862no—
246C2×#41—862no—
247C2×#41—1724no—
248C22×Q8—431no—
249C22×D4—431no—
250C22×D4—861no—
251C22×D4—861no—
252C22×D4C22⋊D4311yescharacteristic
253C23×C4—861no—
254C23×C4D17211yescharacteristic
255C23×C4C22×D4311yescharacteristic
256C2×M16—434no—
257C22×C8—862no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—1724no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4C4×D4311yescharacteristic
263C2×C22⋊C4—22no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4C4×D4311yescharacteristic
270C2×C22⋊C4C22⋊D4311yescharacteristic
271C2×C42—22no—
272C2×C42—861no—
273C2×C42D17211yescharacteristic
274C4⋊C8—862no—
275#104—1728no—
276#99—24no—
277C22⋊C8—862no—
278C22⋊C8—862no—
279C22⋊C8—862no—
280#97—862no—
281#95—22no—
282#95—431no—
283#95—431no—
284#95—861no—
285#95—861no—
286C24—861no—
287C24(C2×D43)⋊C411yescharacteristic
288C24C2×C22⋊D4311yescharacteristic
289#41—868no—
290#41—1724no—
291#41—1724no—
292#41—1724no—
293C2×Q8—862no—
294C2×Q8—1722no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—862no—
299C2×D4—1722no—
300C2×D4—1722no—
301C2×D4—1722no—
302C2×D4—1722no—
303C2×D4—1722no—
304C2×D4—1722no—
305C2×D4—1722no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—864no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—1722no—
316C22×C4—1721no—
317C22×C4—1721no—
318C22×C4(C2×D43)⋊C411yescharacteristic
319C22×C4(C2×D43)⋊C411yescharacteristic
320C22×C4(C2×D43)⋊C411yescharacteristic
321C22×C4C2×C4×D4311yescharacteristic
322C22×C4C2×D17211yescharacteristic
323C22×C4D4×D4312yes—
324C22×C4#1062190012yes—
325M16—1724no—
326C2×C8—864no—
327C2×C8—3442no—
328C4⋊C4—22no—
329C4⋊C4—1722no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—24no—
333C22⋊C4—42no—
334C22⋊C4—1722no—
335C22⋊C4—1722no—
336C22⋊C4—1722no—
337C22⋊C4—1722no—
338C22⋊C4—1722no—
339C42—21no—
340C42—21no—
341C42—44no—
342C42—1722no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—862no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23#1306325312yescomplemented
359C23C2×(C2×D43)⋊C411yescharacteristic
360C23#1306329712yes—
361Q8—864no—
362Q8—1722no—
363D4—44no—
364D4—864no—
365D4—1722no—
366D4—1728no—
367D4—1728no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—44no—
381C2×C4—81no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—862no—
385C2×C4—862no—
386C2×C4—1724no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1724no—
395C2×C4(C22⋊D43)⋊C412yes—
396C2×C4#1306329511yescharacteristic
397C2×C4#1306330911yescharacteristic
398C8—1724no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—42no—
406C22—41no—
407C22—41no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—3441no—
412C22—3441no—
413C22—3441no—
414C22—3441no—
415C22—1722no—
416C22—1722no—
417C22—1722no—
418C22#1458277611yescharacteristic
419C22C2×#1306325311yescharacteristic
420C22#1458291711yescharacteristic
421C4—21no—
422C4—22no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—84no—
427C4—3441no—
428C4—1722no—
429C4—1722no—
430C4#1458308712yes—
431C2—21no—
432C2—21no—
433C2—42no—
434C2—42no—
435C2—3442no—
436C2#1913489511yescharacteristic
437C2#1913497611yescharacteristic
438C2#1913500111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC4×#99×C43C2
socleC22×C43#386
prime radical#19137810C2
cosocleC23×C4×C43C23
hypercenterC4×#99D43
hypocenterC43#9009
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
1. #19143624C2semidirect
3. #19134540C2semidirect
4. #19132481C2semidirect
5. C4×#99×C43C2semidirect
13. #14582819C4semidirect
14. #14582816C4semidirect
16. #14582811C4semidirect
17. #14582808C4semidirect
33. C2×#10621877D4semidirect
131. C23×C43#104semidirect
215. C4×#99D43semidirect
244. C43#9009semidirect
358. C23#13063253semidirect

Maximal subgroups

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

subgroupindex
#191436242
#191378102
#191345402
#191324812
C4×#99×C432
#900943