Finite Group Databasebeta

← #24992580

Subgroups — #24992580

Order 11008.

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

normal subgroups only

This group has 560 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#19140447C211yesmaximal, characteristic
2C4×#13063242C211yesmaximal, characteristic, complemented
3#19133194C212yesmaximal, complemented
4#19132461C212yesmaximal, complemented
5C43×#2973C211yesmaximal, characteristic, complemented
6C2×#13063313C2211yescharacteristic
7C2×#13063242—21no—
8C4×#10621877C2212yes—
9#14582825—21no—
10#14582811C411yescharacteristic
11#14582811C411yescharacteristic
12#14582808C411yescharacteristic
13#14582808C411yescharacteristic
14#14582807—21no—
15#14582778—21no—
16#14582778—21no—
17#14582767C2211yescharacteristic
18#14582668—21no—
19#14582638—24no—
20C2×C4×D4×C43C2211yescharacteristic
21C43×#435—24no—
22C43×#432C2212yes—
23C43×#407—21no—
24C2×C22⋊C8×C43—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C22⋊D43—21no—
28C22×C22⋊D43—21no—
29C2×#10621877—22no—
30#13063313—22no—
31#13063313—22no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38#13063242—24no—
39#13063236—22no—
40C4×C43⋊C8—22no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95C2×C411yescharacteristic
46C43⋊#95C2×C411yescharacteristic
47C22×D4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C2×M16×C43—22no—
51C22×C8×C43—22no—
52C4×D4×C43—22no—
53C4×D4×C43—22no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—22no—
59C22⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61C22⋊C8×C43—22no—
62#97×C43D414yescomplemented
63C24×C43C22⋊C411yescharacteristic
64C24×C43C22⋊C411yescharacteristic
65C23×D43—21no—
66C2×D4×C43—22no—
67C2×D4×C43—22no—
68C2×D4×C43—41no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—81no—
74C22×C4×C43—81no—
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C2×C22⋊D43—42no—
81C2×C22⋊D43—42no—
82C2×C22⋊D43—81no—
83C2×C22⋊D43—81no—
84C2×C22⋊D43—81no—
85C2×C22⋊D43—81no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C2×D172—22no—
90C2×D172—81no—
91C2×Dic86—22no—
92C2×Dic86—81no—
93M16×C43—82no—
94C2×C8×C43—24no—
95C2×C8×C43—82no—
96C4⋊C4×C43—22no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C42×C43C2×D412yes—
100C42×C43#4112yes—
101C22⋊Dic43—81no—
102C22⋊Dic43—81no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—42no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—81no—
107(C2×D43)⋊C4—81no—
108#10621877—24no—
109#10621877—42no—
110C2×C43⋊C8—42no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43#10412yes—
121C23×C43C2×C22⋊C411yescharacteristic
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129D4×C43—44no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43C4×D412yes—
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12112yes—
145C2×C4×C43#12311yescharacteristic
146C22⋊D43—84no—
147C22⋊D43—84no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—82no—
158Dic86—82no—
159C8×C43—44no—
160C43⋊C8—44no—
161#9187—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—22no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43#38611yescharacteristic
175C22×C43C2×#10411yescharacteristic
176C22×C43#42111yescharacteristic
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C4×C43—22no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—22no—
188C4×C43—41no—
189C4×C43—41no—
190Dic43—81no—
191Dic43—81no—
192Dic43—81no—
193#2973D4311yescharacteristic, complemented
194#2631—431no—
195C4×#100—431no—
196#1527—432no—
197#1288—432no—
198C2×C43—21no—
199C2×C43—21no—
200C2×C43—42no—
201C2×C43—81no—
202C2×C43#187111yescharacteristic
203C2×C43#191111yescharacteristic
204C2×C43#191411yescharacteristic
205D43—161no—
206C2×#124—431no—
207C2×C4×D4C2×D4311yescharacteristic
208#435—24no—
209#432C2×D4312yes—
210C2×#100—861no—
211#407—21no—
212C2×C22⋊C8—21no—
213C4×M16—432no—
214#397—861no—
215#393—431no—
216#393—431no—
217#392—431no—
218#392—431no—
219#392—861no—
220#386—861no—
221#386—861no—
222#383—431no—
223#343—861no—
224#329—864no—
225C43#918711yescharacteristic, complemented, Sylow
226C22×Q8—431no—
227C22×D4—431no—
228C22×D4—861no—
229C22×D4—861no—
230C22×D4D17211yescharacteristic
231C23×C4C22⋊D4311yescharacteristic
232C23×C4C22⋊D4311yescharacteristic
233C2×M16—22no—
234C2×M16—862no—
235C22×C8—22no—
236#124—862no—
237#124—862no—
238C4×D4—22no—
239C4×D4—22no—
240C2×C4⋊C4D17211yescharacteristic
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4C4×D4311yescharacteristic
248C2×C22⋊C4C4×D4311yescharacteristic
249C2×C42C22×D4311yescharacteristic
250C4⋊C8—22no—
251#100—864no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254C22⋊C8—22no—
255#97—862no—
256#97C22⋊D4314yescomplemented
257C4×C8—862no—
258#95—431no—
259#95—431no—
260#95—861no—
261#95—861no—
262#95—861no—
263#95—861no—
264C24—861no—
265C24(C2×D43)⋊C411yescharacteristic
266C24(C2×D43)⋊C411yescharacteristic
267C2×Q8—862no—
268C2×Q8—3441no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—862no—
273C2×D4—3441no—
274C2×D4—3441no—
275C2×D4—3441no—
276C2×D4—3441no—
277C2×D4—3441no—
278C2×D4—1722no—
279C2×D4—1722no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4(C2×D43)⋊C411yescharacteristic
290C22×C4(C2×D43)⋊C411yescharacteristic
291C22×C4C2×C4×D4311yescharacteristic
292C22×C4C2×D17211yescharacteristic
293C22×C4C2×C22⋊D4311yescharacteristic
294M16—82no—
295M16—864no—
296M16—1722no—
297C2×C8—24no—
298C2×C8—82no—
299C2×C8—1722no—
300C4⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—3441no—
304C22⋊C4—3441no—
305C22⋊C4—3441no—
306C22⋊C4—3441no—
307C22⋊C4—1721no—
308C22⋊C4—1722no—
309C22⋊C4—1721no—
310C42#1062189812yes—
311C42C2×C22⋊D4312yes—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—1721no—
322C23—1721no—
323C23—1721no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23#1306325112yes—
329C23C2×(C2×D43)⋊C411yescharacteristic
330Q8—3442no—
331D4—44no—
332D4—3442no—
333D4—3444no—
334D4—3444no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4C4×C22⋊D4312yes—
357C2×C4#1306329411yescharacteristic
358C2×C4#1306329912yes—
359C2×C4#1306330811yescharacteristic
360C8—44no—
361C8—1724no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—42no—
366C22—42no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—81no—
374C22—3441no—
375C22—3441no—
376C22—3441no—
377C22—3441no—
378C22—3441no—
379C22—3441no—
380C22—3441no—
381C22#1458277811yescharacteristic
382C22C2×#1306325111yescharacteristic
383C22#1458291511yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—3441no—
391C4—3441no—
392C4—3441no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—81no—
397C2—6881no—
398C2#1913489711yescharacteristic
399C2#1913512711yescharacteristic
400C2#1913514211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2973C2
socleC22×C43#386
prime radical#19140447C2
cosocleC2×C42×C43C23
hypercenter#2973D43
hypocenterC43#9187
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. C4×#13063242C2semidirect
3. #19133194C2semidirect
4. #19132461C2semidirect
5. C43×#2973C2semidirect
62. #97×C43D4semidirect
193. #2973D43semidirect
225. C43#9187semidirect
256. #97C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191404472
C4×#130632422
#191331942
#191324612
C43×#29732
#918743