Finite Group Databasebeta

← #24994596

Subgroups — #24994596

Order 11008.

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

normal subgroups only

This group has 628 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#19139481C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic, complemented
3#19132921C212yesmaximal, complemented
4#19132502C212yesmaximal, complemented
5C43×#2973C211yesmaximal, characteristic, complemented
6C2×#13063306C411yescharacteristic
7C2×#13063293C411yescharacteristic
8C22×(C2×D43)⋊C4C2211yescharacteristic
9#14582863C2212yes—
10#14582821—21no—
11#14582815—21no—
12#14582790—21no—
13#14582778—21no—
14#14582760C411yescharacteristic
15#14582759C2211yescharacteristic
16#14582754C411yescharacteristic
17#14582625—21no—
18#14582623—21no—
19#14582622—24no—
20C2×C4×D4×C43C2211yescharacteristic
21C43×#435—24no—
22C43×#432—21no—
23C43×#407C2212yes—
24C2×C22⋊C8×C43—21no—
25C24×D43C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C23×Dic43C2×C411yescharacteristic
28C2×#10621877—22no—
29#13063306—42no—
30#13063293—42no—
31C2×C4⋊Dic43—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43C2×C411yescharacteristic
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—22no—
42C2×(C2×D43)⋊C4—21no—
43C22⋊(C43⋊C8)—22no—
44C22⋊(C43⋊C8)—22no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C22×D4×C43C2×C411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C23×C4×C43C2311yescharacteristic
51C2×M16×C43—22no—
52C22×C8×C43—22no—
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C4⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61C22⋊C8×C43—22no—
62C22⋊C8×C43D414yescomplemented
63#97×C43—22no—
64C24×C43C22⋊C411yescharacteristic
65C24×C43C22×C411yescharacteristic
66C23×D43—21no—
67C23×D43—22no—
68C23×D43—42no—
69C23×D43—41no—
70C23×D43—41no—
71C23×D43—81no—
72C2×D4×C43—22no—
73C2×D4×C43—22no—
74C2×D4×C43—41no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—81no—
78C22×C4×C43—81no—
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D412yes—
85C22×C4×C43#4112yes—
86C2×C22⋊D43—42no—
87C2×C22⋊D43—42no—
88C2×C22⋊D43—81no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—22no—
93C22×Dic43—41no—
94C22×Dic43—41no—
95M16×C43—82no—
96C2×C8×C43—24no—
97C2×C8×C43—82no—
98C4⋊C4×C43—22no—
99C22⋊C4×C43—22no—
100C22⋊C4×C43—22no—
101C42×C43—21no—
102C42×C43—21no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105C22⋊Dic43—42no—
106(C2×D43)⋊C4—42no—
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—81no—
112C4⋊Dic43—81no—
113Dic43⋊C4—42no—
114#10621877—82no—
115C2×C43⋊C8—42no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43#10012yes—
125C23×C43C2×C22⋊C411yescharacteristic
126C23×C43C4×D412yes—
127C22×D43—22no—
128C22×D43—24no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—42no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—84no—
137C22×D43—84no—
138C22×D43—82no—
139C22×D43—82no—
140D4×C43—44no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12112yes—
156C2×C4×C43#12311yescharacteristic
157C22⋊D43—84no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—82no—
168C8×C43—44no—
169C43⋊C8—82no—
170#9515—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—22no—
174C22×C43—22no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—81no—
183C22×C43#38611yescharacteristic
184C22×C43C2×#10011yescharacteristic
185C22×C43#41311yescharacteristic
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—42no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—84no—
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—84no—
195C4×C43—22no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201Dic43—81no—
202Dic43—81no—
203Dic43—81no—
204#2973D4311yescharacteristic, complemented
205#2534—431no—
206#1465—431no—
207#1462—432no—
208#1305—432no—
209C2×C43—21no—
210C2×C43—21no—
211C2×C43—42no—
212C2×C43—42no—
213C2×C43#189111yescharacteristic
214C2×C43#190011yescharacteristic
215C2×C43#191311yescharacteristic
216D43—82no—
217C2×#123—431no—
218C2×#120—431no—
219C2×C4×D4C2×D4311yescharacteristic
220C22×C22⋊C4—431no—
221#435—24no—
222#432—21no—
223#407—432no—
224#407C2×D4312yes—
225C2×C22⋊C8—21no—
226#396—861no—
227#394—861no—
228#388—861no—
229#386—861no—
230#381—431no—
231#380—431no—
232#379—431no—
233#324—861no—
234#323—861no—
235#323—864no—
236C43#951511yescharacteristic, complemented, Sylow
237C25—431no—
238C22×D4—861no—
239C22×D4C4×D4311yescharacteristic
240C23×C4—431no—
241C23×C4C22⋊D4311yescharacteristic
242C23×C4C22×D4311yescharacteristic
243C2×M16—22no—
244C2×M16—862no—
245C22×C8—22no—
246#123—1722no—
247#120—1722no—
248C4×D4—22no—
249C4×D4—22no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4D17211yescharacteristic
253C2×C22⋊C4—431no—
254C2×C22⋊C4—431no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—862no—
261C2×C22⋊C4—862no—
262C2×C22⋊C4—861no—
263C2×C22⋊C4C4×D4311yescharacteristic
264C2×C22⋊C4D17211yescharacteristic
265C2×C42C22⋊D4311yescharacteristic
266C4⋊C8—22no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8—862no—
270C22⋊C8—862no—
271C22⋊C8C22⋊D4314yescomplemented
272#97—22no—
273#95—861no—
274#95—861no—
275#95—861no—
276C24—862no—
277C24—861no—
278C24—3441no—
279C24—1721no—
280C24—1721no—
281C24—1722no—
282C24(C2×D43)⋊C411yescharacteristic
283C24C2×C4×D4311yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—3441no—
288C2×D4—1722no—
289C2×D4—1722no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4—862no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—1721no—
299C22×C4—1721no—
300C22×C4(C2×D43)⋊C411yescharacteristic
301C22×C4(C2×D43)⋊C411yescharacteristic
302C22×C4(C2×D43)⋊C411yescharacteristic
303C22×C4C2×D17211yescharacteristic
304C22×C4#1062189812yes—
305C22×C4C2×C22⋊D4312yes—
306C22×C4C2×C22⋊D4311yescharacteristic
307M16—82no—
308M16—3442no—
309C2×C8—24no—
310C2×C8—82no—
311C2×C8—1722no—
312C4⋊C4—22no—
313C4⋊C4—3441no—
314C4⋊C4—1722no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—3441no—
318C22⋊C4—1722no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1721no—
322C22⋊C4—1722no—
323C22⋊C4—1721no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C42—21no—
327C42—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—864no—
337C23—862no—
338C23—3442no—
339C23—3442no—
340C23—3444no—
341C23—3444no—
342C23—1721no—
343C23—1721no—
344C23—1721no—
345C23—1722no—
346C23—1721no—
347C23—1721no—
348C23—1721no—
349C23#1306324112yes—
350C23C2×(C2×D43)⋊C411yescharacteristic
351C23C4×C22⋊D4312yes—
352D4—44no—
353D4—3444no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—3442no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4#1306329411yescharacteristic
378C2×C4#1306329912yes—
379C2×C4#1306330811yescharacteristic
380C8—44no—
381C8—3442no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—3441no—
395C22—3441no—
396C22—3444no—
397C22—3444no—
398C22—3441no—
399C22—3441no—
400C22—1722no—
401C22—1722no—
402C22—1722no—
403C22#1458277811yescharacteristic
404C22C2×#1306324111yescharacteristic
405C22#1458288111yescharacteristic
406C4—21no—
407C4—22no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—3441no—
413C4—3441no—
414C4—3441no—
415C2—21no—
416C2—21no—
417C2—42no—
418C2—42no—
419C2—3442no—
420C2#1913501311yescharacteristic
421C2#1913505811yescharacteristic
422C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2973C2
socleC22×C43#386
prime radicalC2×#13063293C4
cosocleC23×C4×C43C23
hypercenter#2973D43
hypocenterC43#9515
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #19132933C2semidirect
3. #19132921C2semidirect
4. #19132502C2semidirect
5. C43×#2973C2semidirect
62. C22⋊C8×C43D4semidirect
204. #2973D43semidirect
236. C43#9515semidirect
271. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191394812
#191329332
#191329212
#191325022
C43×#29732
#951543