Finite Group Databasebeta

← #24991676

Subgroups — #24991676

Order 11008.

670 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137874C211yesmaximal, characteristic
2C4×#13063242C211yesmaximal, characteristic, complemented
3#19133037C212yesmaximal, complemented
4#19132487C212yesmaximal, complemented
5C43×#2973C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7C2×C4×C22⋊D43—21no—
8C2×C4×C22⋊D43—21no—
9C2×#13063242—21no—
10C4×#10621877C2212yes—
11#14582835C411yescharacteristic
12#14582835C411yescharacteristic
13#14582834—21no—
14#14582808C411yescharacteristic
15#14582808C411yescharacteristic
16#14582807—21no—
17#14582745C2211yescharacteristic
18#14582668—21no—
19#14582626—24no—
20C2×C4×D4×C43C2211yescharacteristic
21C43×#435—24no—
22C43×#432C2212yes—
23C43×#407—21no—
24C2×C22⋊C8×C43—21no—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C22⋊D43—21no—
28C22×C4×D43—21no—
29C2×#10621877—22no—
30C4×D172—22no—
31C4×D172—22no—
32C4×C22⋊D43—44no—
33C4×C22⋊D43—44no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
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—
43#13063242—24no—
44#13063236—22no—
45C4×C43⋊C8—22no—
46C43⋊#95—21no—
47C43⋊#95C2×C411yescharacteristic
48C43⋊#95C2×C411yescharacteristic
49C22×D4×C43D411yescharacteristic
50C23×C4×C43D411yescharacteristic
51C23×C4×C43D411yescharacteristic
52C2×M16×C43—22no—
53C22×C8×C43—22no—
54C4×D4×C43—22no—
55C4×D4×C43—22no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43C2×C411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43D414yescomplemented
61C22⋊C8×C43—22no—
62C22⋊C8×C43—22no—
63C22⋊C8×C43—22no—
64#97×C43—22no—
65C24×C43C22⋊C411yescharacteristic
66C24×C43C22⋊C411yescharacteristic
67C23×D43—21no—
68C2×D4×C43—22no—
69C2×D4×C43—22no—
70C2×D4×C43—41no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×C22⋊D43—42no—
83C2×C22⋊D43—42no—
84C2×C22⋊D43—42no—
85C2×C22⋊D43—42no—
86C2×C22⋊D43—42no—
87C2×C22⋊D43—42no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C2×D172—22no—
92C2×D172—42no—
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97M16×C43—82no—
98C2×C8×C43—24no—
99C2×C8×C43—82no—
100C4⋊C4×C43—22no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—22no—
103C42×C43C2×D412yes—
104C42×C43#4112yes—
105C22⋊Dic43—42no—
106C22⋊Dic43—42no—
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—42no—
109(C2×D43)⋊C4—42no—
110C4⋊Dic43—22no—
111Dic43⋊C4—42no—
112Dic43⋊C4—42no—
113C4×Dic43—24no—
114#10621877—24no—
115#10621877—42no—
116C2×C43⋊C8—42no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43#10412yes—
127C23×C43C2×C22⋊C411yescharacteristic
128C22×D43—22no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135D4×C43—44no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43C4×D412yes—
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12112yes—
151C2×C4×C43#12311yescharacteristic
152C22⋊D43—48no—
153C22⋊D43—48no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163D172—24no—
164D172—42no—
165C4×D43—82no—
166C4×D43—82no—
167C8×C43—44no—
168C43⋊C8—44no—
169#9031—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—22no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43#38611yescharacteristic
183C22×C43C2×#10411yescharacteristic
184C22×C43#42111yescharacteristic
185C2×D43—42no—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C4×C43—22no—
193C4×C43—21no—
194C4×C43—22no—
195C4×C43—41no—
196C4×C43—41no—
197C4×C43#45312yes—
198Dic43—42no—
199Dic43—42no—
200Dic43—81no—
201#2973D4311yescharacteristic, complemented
202#2397—431no—
203C4×#100—431no—
204#1490—432no—
205#1300—432no—
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—42no—
209C2×C43—81no—
210C2×C43#187111yescharacteristic
211C2×C43#188711yescharacteristic
212C2×C43#189111yescharacteristic
213D43—82no—
214C2×C4×D4—431no—
215C2×C4×D4—861no—
216C2×C4×D4—861no—
217C2×C4×D4C2×D4311yescharacteristic
218#435—24no—
219#432C2×D4312yes—
220C2×#100—861no—
221#407—21no—
222C2×C22⋊C8—21no—
223C4×M16—432no—
224#399—431no—
225#399—431no—
226#399—861no—
227#392—431no—
228#392—431no—
229#392—861no—
230#376—431no—
231#343—861no—
232D4⋊C8—864no—
233C43#903111yescharacteristic, complemented, Sylow
234C22×D4—431no—
235C22×D4—861no—
236C22×D4—861no—
237C22×D4D17211yescharacteristic
238C23×C4—861no—
239C23×C4C22⋊D4311yescharacteristic
240C23×C4C22⋊D4311yescharacteristic
241C2×M16—22no—
242C2×M16—862no—
243C22×C8—22no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—862no—
247C4×D4—862no—
248C4×D4—1724no—
249C4×D4—1724no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4D17211yescharacteristic
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4C4×D4311yescharacteristic
260C2×C22⋊C4C4×D4311yescharacteristic
261C2×C42—861no—
262C2×C42C22×D4311yescharacteristic
263C4⋊C8C22⋊D4314yescomplemented
264#100—864no—
265C22⋊C8—22no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268#97—22no—
269#97—862no—
270C4×C8—862no—
271#95—431no—
272#95—431no—
273#95—861no—
274C24—861no—
275C24(C2×D43)⋊C411yescharacteristic
276C24(C2×D43)⋊C411yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—862no—
281C2×D4—1722no—
282C2×D4—1722no—
283C2×D4—1722no—
284C2×D4—1722no—
285C2×D4—1722no—
286C2×D4—1722no—
287C2×D4—1722no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—1722no—
298C22×C4—1722no—
299C22×C4—1721no—
300C22×C4—1721no—
301C22×C4(C2×D43)⋊C411yescharacteristic
302C22×C4(C2×D43)⋊C411yescharacteristic
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4C2×D17211yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306M16—82no—
307M16—864no—
308M16—1722no—
309C2×C8—24no—
310C2×C8—82no—
311C2×C8—1722no—
312C4⋊C4—22no—
313C4⋊C4—862no—
314C4⋊C4—1722no—
315C4⋊C4—1722no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—1722no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1722no—
322C22⋊C4—1722no—
323C42—864no—
324C42#1062189812yes—
325C42C2×C22⋊D4312yes—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—862no—
336C23—1721no—
337C23—1721no—
338C23—1721no—
339C23—1721no—
340C23—1721no—
341C23—1721no—
342C23#1306325112yes—
343C23C2×(C2×D43)⋊C411yescharacteristic
344D4—44no—
345D4—864no—
346D4—1722no—
347D4—1728no—
348D4—1728no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—3442no—
364C2×C4—3442no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4C4×C22⋊D4312yes—
373C2×C4#1306329411yescharacteristic
374C2×C4#1306329912yes—
375C2×C4#1306330811yescharacteristic
376C8—44no—
377C8—1724no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—3441no—
391C22—3441no—
392C22—3441no—
393C22—3441no—
394C22—1722no—
395C22—1722no—
396C22—1722no—
397C22#1458277811yescharacteristic
398C22C2×#1306325111yescharacteristic
399C22#1458291511yescharacteristic
400C4—21no—
401C4—22no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—3441no—
406C4—1722no—
407C4—1722no—
408C4#1458306712yes—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—81no—
413C2—3442no—
414C2#1913489711yescharacteristic
415C2#1913499311yescharacteristic
416C2#1913501311yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2973C2
socleC22×C43#386
prime radical#19137874C2
cosocleC2×C42×C43C23
hypercenter#2973D43
hypocenterC43#9031
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. C4×#13063242C2semidirect
3. #19133037C2semidirect
4. #19132487C2semidirect
5. C43×#2973C2semidirect
60. C4⋊C8×C43D4semidirect
201. #2973D43semidirect
233. C43#9031semidirect
263. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191378742
C4×#130632422
#191330372
#191324872
C43×#29732
#903143