Finite Group Databasebeta

← #24984852

Subgroups — #24984852

Order 11008.

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

normal subgroups only

This group has 556 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#19137133C211yesmaximal, characteristic
2#19134356C211yesmaximal, characteristic
3#19134287C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic, complemented
5#19132419C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1272C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×#13063301C411yescharacteristic
10C2×Q8×Dic43C411yescharacteristic
11C2×C42×D43C2211yescharacteristic
12C2×(C2×D43)⋊C8—21no—
13C2×#13063235—21no—
14#14582797C2211yescharacteristic
15#14582786—21no—
16#14582773—21no—
17#14582756C411yescharacteristic
18C4⋊C4×Dic43C411yescharacteristic
19#14582750—21no—
20#14582746—21no—
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#391C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621872—24no—
31C2×#10621872—42no—
32C2×#10621872—42no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063301—22no—
36#13063301—22no—
37Q8×Dic43—42no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50C42×D43—42no—
51(C2×D43)⋊C8—24no—
52#13063235—42no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C22×Q8×C43C2×C411yescharacteristic
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61#95×C43—21no—
62#95×C43—21no—
63C23×D43C22⋊C411yescharacteristic
64C2×Q8×C43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43M1612yescomplemented
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—22no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C8×C43—22no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—41no—
97C42×C43—41no—
98(C2×D43)⋊C4—24no—
99(C2×D43)⋊C4—42no—
100C4⋊Dic43—21no—
101C4⋊Dic43—42no—
102C4⋊Dic43—41no—
103C4⋊Dic43M1612yescomplemented
104Dic43⋊C4—24no—
105Dic43⋊C4—41no—
106Dic43⋊C4—41no—
107C4×Dic43—22no—
108C4×Dic43—22no—
109C4×Dic43—41no—
110C4×Dic43—42no—
111C4×Dic43—42no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118#10621872—48no—
119C23×C43C2×C22⋊C411yescharacteristic
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43#10412yes—
127Q8×C43—42no—
128Q8×C43—42no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43C2×M1611yescharacteristic
142C2×C4×C43C2×M1611yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—22no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43#9912yes—
161C2×Dic43#10412yes—
162C4×D43—24no—
163C4×D43—24no—
164C4×D43—42no—
165C4×D43—42no—
166C4×D43—42no—
167C4×D43—42no—
168C8×C43—42no—
169C8×C43—42no—
170C43⋊C8—42no—
171C43⋊C8—42no—
172#7634—431nomaximal, Sylow
173C22×C43#40711yescharacteristic
174C22×C43C2×#9911yescharacteristic
175C22×C43#41311yescharacteristic
176C22×C43#41711yescharacteristic
177C22×C43#41911yescharacteristic
178C22×C43C2×#10411yescharacteristic
179C22×C43C2×#10411yescharacteristic
180C2×D43—22no—
181C2×D43—22no—
182C2×D43—22no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—42no—
194C4×C43—81no—
195Dic43—22no—
196Dic43—22no—
197Dic43—41no—
198Dic43—42no—
199Dic43—81no—
200C4×C22⋊Q8—431no—
201#1749—431no—
202#1728—431no—
203#1272—431no—
204#1272D4311yescharacteristic, complemented
205#1271—431no—
206#1271—431no—
207C2×C43#146511yescharacteristic
208C2×C43#148911yescharacteristic
209C2×C43#149111yescharacteristic
210C2×C43#150411yescharacteristic
211C2×C43#150811yescharacteristic
212C2×C43#152411yescharacteristic
213C2×C43#155911yescharacteristic
214D43—42no—
215C22×M16—861no—
216C2×C22⋊Q8—431no—
217C2×C4×Q8—431no—
218C22×C42—431no—
219C2×C22⋊C8—861no—
220C2×#97—861no—
221#391C2×D4311yescharacteristic
222#389—431no—
223#387—861no—
224#385—861no—
225#380—431no—
226C4×C4⋊C4—431no—
227C4×C4⋊C4—861no—
228C4×C22⋊C4—861no—
229#336—431no—
230#336—431no—
231#336—861no—
232#336C2×D4311yescharacteristic
233#336C2×D4311yescharacteristic
234C43#763411yescharacteristic, complemented, Sylow
235C22×Q8C4×D4311yescharacteristic
236C23×C4—431no—
237C23×C4—431no—
238C23×C4—431no—
239C2×M16—864no—
240C2×M16—1722no—
241C2×M16—1722no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—861no—
245C22×C8—861no—
246C22⋊Q8—862no—
247C22⋊Q8—862no—
248C4×Q8—1722no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4C4×D4311yescharacteristic
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C42—431no—
258C2×C42—431no—
259C2×C42—431no—
260C2×C42—861no—
261C2×C42—861no—
262C2×C42—1722no—
263C2×C42C22×D4311yescharacteristic
264C22⋊C8—864no—
265#97—1722no—
266#95—21no—
267#95—21no—
268#95—861no—
269#95—861no—
270#95—861no—
271C24—431no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8#1062187212yescomplemented
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4—862no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4C2×C4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298M16—1728no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—1721no—
308C2×C8—1721no—
309C2×C8—1721no—
310C2×C8—1721no—
311C4⋊C4—41no—
312C4⋊C4—432no—
313C4⋊C4—864no—
314C4⋊C4—861no—
315C4⋊C4—1721no—
316C4⋊C4—1722no—
317C4⋊C4—1721no—
318C4⋊C4—1721no—
319C22⋊C4—864no—
320C22⋊C4—1722no—
321C42—41no—
322C42—862no—
323C42—862no—
324C42—1721no—
325C42—1722no—
326C42—1722no—
327C23—432no—
328C23—861no—
329C23—861no—
330C23—861no—
331C23—861no—
332C23—861no—
333C23—861no—
334C23C22⋊C4×D4311yescharacteristic
335Q8—42no—
336Q8—42no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—432no—
350C2×C4—432no—
351C2×C4—864no—
352C2×C4—864no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—862no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1722no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4M16×D4311yescharacteristic
371C2×C4C2×#1062187211yescharacteristic
372C2×C4#1306335211yescharacteristic
373C2×C4#1306335411yescharacteristic
374C2×C4#1306335711yescharacteristic
375C2×C4#1306335711yescharacteristic
376C8—42no—
377C8—42no—
378C8—1722no—
379C8—1722no—
380C22—862no—
381C22—862no—
382C22—862no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22#1458286111yescharacteristic
388C22#99×D4311yescharacteristic
389C22#1458288011yescharacteristic
390C22#1458289911yescharacteristic
391C22#1458290611yescharacteristic
392C22#104×D4311yescharacteristic
393C22#104×D4311yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—862no—
403C4—862no—
404C4—3441no—
405C4—1721no—
406C4—1722no—
407C2—1722no—
408C2#1913293011yescharacteristic
409C2#1913303311yescharacteristic
410C2#1913304011yescharacteristic
411C2#1913309811yescharacteristic
412C2#1913311311yescharacteristic
413C2#1913318011yescharacteristic
414C2#1913332211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7634
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #19132421C2semidirect
5. #19132419C2semidirect
6. #19132417C2semidirect
7. C43×#1272C2semidirect
67. C2×Q8×C43M16semidirect
103. C4⋊Dic43M16semidirect
204. #1272D43semidirect
234. C43#7634semidirect
275. C2×Q8#10621872semidirect

Maximal subgroups

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

subgroupindex
#191371332
#191343562
#191342872
#191324212
#191324192
#191324172
C43×#12722
#763443