Finite Group Databasebeta

← #24994348

Subgroups — #24994348

Order 11008.

726 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 97 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#19138254C211yesmaximal, characteristic
2#19137180C211yesmaximal, characteristic, complemented
3#19134518C211yesmaximal, characteristic, complemented
4#19133124C211yesmaximal, characteristic
5#19132449C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#1510C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9C2×#13063312C412yescomplemented
10C2×#13063281—21no—
11C2×#13063243—22no—
12#14582863C2211yescharacteristic
13#14582811—22no—
14#14582804C412yescomplemented
15#14582803—22no—
16#14582803—22no—
17#14582779—21no—
18#14582779—21no—
19#14582762C2211yescharacteristic
20#14582760—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582633—22no—
23C2×#121×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C43×#381C2211yescharacteristic
26C43×#327—22no—
27C22×Dic86—21no—
28C22×Dic86—21no—
29C22×Dic86—21no—
30C22×Dic86—21no—
31C22×Dic86—44no—
32C22×Dic86C2×C412yes—
33C22×Dic86D412yes—
34C23×Dic43D411yescharacteristic
35C23×Dic43D411yescharacteristic
36C2×#10621877—21no—
37#13063312—44no—
38#13063281—44no—
39C2×Dic43⋊C4—22no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43C2×C412yes—
46#13063243—44no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C43⋊#95—24no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95D412yes—
55C22×D4×C43—21no—
56C22×D4×C43C2×C411yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59#121×C43—21no—
60#121×C43—21no—
61#121×C43—21no—
62#121×C43—21no—
63C2×C4⋊C4×C43C2×C411yescharacteristic
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68#95×C43—21no—
69#95×C43D412yes—
70C24×C43—21no—
71C24×C43C2×D411yescharacteristic
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—44no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—42no—
78C22×C4×C43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—42no—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×Dic43—24no—
88C22×Dic43—22no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—42no—
95C22×Dic43C22⋊C412yes—
96C22×Dic43C22⋊C412yes—
97C2×Dic86—22no—
98C2×Dic86—22no—
99C2×Dic86—22no—
100C2×Dic86—22no—
101C2×Dic86—24no—
102C2×Dic86—24no—
103C2×Dic86—42no—
104C2×Dic86—42no—
105C2×Dic86—42no—
106C2×Dic86—42no—
107C2×Dic86—42no—
108C2×Dic86—42no—
109C2×Dic86—44no—
110C2×Dic86—44no—
111M16×C43—42no—
112C2×C8×C43—41no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C22⋊C4×C43—42no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊Dic43—42no—
119C22⋊Dic43—42no—
120C22⋊Dic43—44no—
121C22⋊Dic43—44no—
122Dic43⋊C4—44no—
123C4×Dic43—44no—
124C4×Dic43—42no—
125#10621877—42no—
126C2×C43⋊C8—41no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—41no—
130C23×C43—42no—
131C23×C43—42no—
132C23×C43—41no—
133C23×C43—42no—
134C23×C43C2×C22⋊C411yescharacteristic
135C23×C43#12011yescharacteristic
136C23×C43#12311yescharacteristic
137D4×C43—81no—
138D4×C43—81no—
139D4×C43—82no—
140D4×C43—82no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×Dic43—22no—
157C2×Dic43—22no—
158C2×Dic43—24no—
159C2×Dic43—22no—
160C2×Dic43—22no—
161C2×Dic43—22no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43#9914yes—
174Dic86—44no—
175Dic86—44no—
176Dic86—44no—
177Dic86—44no—
178C8×C43—81no—
179C43⋊C8—81no—
180#9466—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—44no—
189C22×C43—84no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43#38611yescharacteristic
194C22×C43C2×#9912yes—
195C22×C43#45412yes—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—82no—
201C4×C43—81no—
202Dic43—24no—
203Dic43—42no—
204Dic43—82no—
205Dic43—82no—
206#2436—431no—
207#2310—431no—
208#1784—431no—
209#1510—431no—
210#1510D4311yescharacteristic
211#1284—431no—
212#1284—431no—
213C2×C43—22no—
214C2×C43—22no—
215C2×C43—41no—
216C2×C43—161no—
217C2×C43#188811yescharacteristic
218C2×C43#189811yescharacteristic
219C2×C43#191211yescharacteristic
220C23×Q8—431no—
221C2×#124—432no—
222C2×#121C2×D4311yescharacteristic
223C2×#117—861no—
224C2×#101—862no—
225#407—431no—
226#407C2×D4311yescharacteristic
227#393—862no—
228#391—432no—
229#391—862no—
230#391—862no—
231#386—861no—
232#386—861no—
233#381—431no—
234#381—861no—
235#381C2×D4311yescharacteristic
236C4×C22⋊C4—431no—
237#327—22no—
238#327—862no—
239C43#946611yescharacteristic, complemented, Sylow
240C22×Q8—432no—
241C22×Q8—432no—
242C22×Q8—861no—
243C22×Q8—861no—
244C22×Q8—861no—
245C22×Q8—861no—
246C22×Q8—1724no—
247C22×D4—21no—
248C22×D4C4×D4311yescharacteristic
249C23×C4—431no—
250C23×C4—431no—
251C23×C4C22×D4311yescharacteristic
252C2×M16—21no—
253C2×M16—861no—
254#124—1724no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259#117—1724no—
260C2×C4⋊C4—862no—
261C2×C4⋊C4C4×D4311yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—862no—
265C2×C22⋊C4—862no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C42—432no—
269C2×C42—862no—
270#101—1724no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—861no—
274C22⋊C8—861no—
275#95—21no—
276#95—432no—
277#95—862no—
278#95—862no—
279#95—864no—
280#95—861no—
281#95—861no—
282#95C22⋊D4312yes—
283C24—21no—
284C24D4×D4311yescharacteristic
285C2×Q8—864no—
286C2×Q8—864no—
287C2×Q8—862no—
288C2×Q8—862no—
289C2×Q8—862no—
290C2×Q8—862no—
291C2×Q8—1722no—
292C2×Q8—1722no—
293C2×Q8—1724no—
294C2×Q8—1722no—
295C2×Q8—1722no—
296C2×Q8—1724no—
297C2×Q8—1722no—
298C2×Q8—1722no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—42no—
302C2×D4—44no—
303C2×D4—41no—
304C2×D4—41no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—42no—
308C22×C4—432no—
309C22×C4—432no—
310C22×C4—864no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—862no—
316C22×C4—862no—
317C22×C4—1722no—
318C22×C4C2×C4×D4311yescharacteristic
319C22×C4#1062189811yescharacteristic
320C22×C4D4×D4311yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4#1062190011yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324M16—42no—
325M16—1722no—
326C2×C8—41no—
327C2×C8—1721no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—1724no—
331C22⋊C4—42no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—1724no—
335C22⋊C4—1724no—
336C22⋊C4—1722no—
337C22⋊C4—1722no—
338C42—1722no—
339C42—1724no—
340C23—22no—
341C23—22no—
342C23—41no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23C22⋊C4×D4311yescharacteristic
348C23#1306329311yescharacteristic
349C23#1306330711yescharacteristic
350Q8—1724no—
351Q8—1724no—
352Q8—1724no—
353Q8—1724no—
354D4—81no—
355D4—81no—
356D4—82no—
357D4—82no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—434no—
370C2×C4—862no—
371C2×C4—862no—
372C2×C4—864no—
373C2×C4—862no—
374C2×C4—862no—
375C2×C4—862no—
376C2×C4—862no—
377C2×C4—862no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1722no—
387C2×C4(C22⋊D43)⋊C411yescharacteristic
388C2×C4C4×C22⋊D4311yescharacteristic
389C2×C4#1306329611yescharacteristic
390C2×C4#1306329811yescharacteristic
391C8—81no—
392C8—3441no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—44no—
401C22—84no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#1458277511yescharacteristic
406C22#99×D4312yes—
407C22#1458307012yes—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—82no—
413C4—81no—
414C4—864no—
415C4—3442no—
416C4—3442no—
417C4—1722no—
418C2—22no—
419C2—22no—
420C2—41no—
421C2—161no—
422C2#1913499511yescharacteristic
423C2#1913504511yescharacteristic
424C2#1913512911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1510C2
socleC22×C43#386
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenter#1510D43
hypocenterC43#9466
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #19137180C2semidirect
3. #19134518C2semidirect
5. #19132449C2semidirect
6. #19132447C2semidirect
9. C2×#13063312C4semidirect
14. #14582804C4semidirect
239. C43#9466semidirect

Maximal subgroups

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

subgroupindex
#191382542
#191371802
#191345182
#191331242
#191324492
#191324472
C43×#15102
#946643