Finite Group Databasebeta

← #24997189

Subgroups — #24997189

Order 11008.

632 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#14583229C211yesmaximal, characteristic
2#19140711C211yesmaximal, characteristic
3C2×#14582637C211yesmaximal, characteristic
4C2×#14582636C211yesmaximal, characteristic
5#19132863C211yesmaximal, characteristic
6#19132437C211yesmaximal, characteristic
7C2×C43×#483C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583229—22no—
10#14583229—22no—
11C2×#13063256—21no—
12C2×#13063248—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582830—21no—
15#14582829—21no—
16#14582819—21no—
17#14582818—21no—
18#14582757—22no—
19C2×C43⋊#95—22no—
20C2×C43⋊#95C2211yescharacteristic
21C2×C43⋊#95C2211yescharacteristic
22#14582637—22no—
23#14582636—22no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#483—22no—
27C43×#483—22no—
28C2×#106×C43—21no—
29C2×#103×C43—21no—
30C2×C22⋊C8×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C23×Dic43—21no—
33C23×Dic43D412yes—
34C22×C43⋊C8—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—22no—
43C2×C22⋊Dic43—21no—
44#13063256—24no—
45#13063248—24no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)D412yes—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—44no—
55C22×Q8×C43D411yescharacteristic
56C23×C4×C43—21no—
57C23×C4×C43C2311yescharacteristic
58C22×C8×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D412yes—
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43—21no—
72#106×C43—24no—
73#103×C43—24no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43D412yes—
76C24×C43C2×D411yescharacteristic
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—42no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×Dic43—22no—
95C22×Dic43—22no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—22no—
99C22×Dic43—42no—
100C22×Dic43—42no—
101C22×Dic43—41no—
102C22×Dic43—42no—
103C22×Dic43—41no—
104C22×Dic43—42no—
105C22×Dic43SD1614yes—
106C2×Dic86—21no—
107C2×Dic86—21no—
108C2×Dic86—42no—
109C2×C8×C43—22no—
110C2×C8×C43—42no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊Dic43—41no—
122C22⋊Dic43—41no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—82no—
128Dic43⋊C4—82no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—22no—
134C23×C43#12011yescharacteristic
135C23×C43#12111yescharacteristic
136C23×C43#12711yescharacteristic
137C23×C43C2×SD1612yes—
138C23×C43#13712yes—
139Q8×C43—42no—
140Q8×C43—81no—
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—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—44no—
154C2×C4×C43—82no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43#12011yescharacteristic
158C2×C4×C43#12011yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×Dic43—24no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—44no—
165C2×Dic43—44no—
166C2×Dic43—42no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—42no—
172C2×Dic43—82no—
173C2×Dic43—82no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176Dic86—42no—
177Dic86—81no—
178C8×C43—42no—
179C43⋊C8—42no—
180#9973—431nomaximal, Sylow
181C22×C43—22no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43#39211yescharacteristic
190C22×C43#44812yes—
191C22×C43#45511yescharacteristic
192C22×C43#45611yescharacteristic
193C22×C43#45812yes—
194C22×C43#46112yes—
195C22×C43#49211yescharacteristic
196C22×C43#49711yescharacteristic
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—81no—
202C4×C43—82no—
203C4×C43—81no—
204Dic43—44no—
205Dic43—82no—
206Dic43—81no—
207Dic43—81no—
208C2×#483—431no—
209C2×#483D4311yescharacteristic
210#2659—431no—
211C2×#328—431no—
212C2×#328—431no—
213#1445—431no—
214#1280—431no—
215C2×C43—21no—
216C2×C43—22no—
217C2×C43—21no—
218C2×C43#160812yes—
219C2×C43#161112yes—
220C2×C43#200711yescharacteristic
221C2×C43#201311yescharacteristic
222C2×C43#202211yescharacteristic
223C2×C22⋊Q8—431no—
224C2×C22⋊Q8C2×D4311yescharacteristic
225C22×C4⋊C4C2×D4311yescharacteristic
226#483—22no—
227#483—22no—
228#483—862no—
229#483—862no—
230C2×#106—21no—
231C2×#106—861no—
232C2×#103—21no—
233C2×#103—861no—
234C2×C22⋊C8—431no—
235C2×C22⋊C8C2×D4311yescharacteristic
236#398—861no—
237#398—861no—
238#395—861no—
239#395—861no—
240#380—862no—
241C2×#95—431no—
242C2×#95—431no—
243C2×#95—862no—
244#328—862no—
245#328—862no—
246C43#997311yescharacteristic, complemented, Sylow
247C22×Q8—431no—
248C22×Q8C22⋊D4311yescharacteristic
249C23×C4—21no—
250C23×C4—432no—
251C23×C4—861no—
252C23×C4C22×D4311yescharacteristic
253C22×C8—21no—
254C22×C8—861no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—861no—
260C22⋊Q8—861no—
261C22⋊Q8—861no—
262C22⋊Q8—861no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4C22⋊D4312yes—
274C2×C4⋊C4C22⋊D4311yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—861no—
277#106—24no—
278#106—864no—
279#103—24no—
280#103—864no—
281C22⋊C8—21no—
282C22⋊C8—432no—
283C22⋊C8—861no—
284C22⋊C8C22⋊D4312yes—
285#95—862no—
286#95—862no—
287#95—861no—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—1724no—
292C24D4×D4311yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C2×Q8—861no—
297C2×Q8—861no—
298C2×Q8—1722no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—434no—
308C22×C4—862no—
309C22×C4—862no—
310C22×C4—862no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—1721no—
314C22×C4—1722no—
315C22×C4—1721no—
316C22×C4—1722no—
317C22×C4—1722no—
318C22×C4—1722no—
319C22×C4D4×D4311yescharacteristic
320C22×C4D4×D4311yescharacteristic
321C22×C4#1062190011yescharacteristic
322C22×C4C2×C22⋊D4311yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324C22×C4C2×C22⋊D4311yescharacteristic
325C2×C8—22no—
326C2×C8—42no—
327C2×C8—862no—
328C2×C8—1722no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—3442no—
340C4⋊C4—3442no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23#1306329311yescharacteristic
351C23#1306329711yescharacteristic
352C23#1306332111yescharacteristic
353C23SD16×D4312yes—
354C23#1306335412yes—
355Q8—42no—
356Q8—81no—
357Q8—3441no—
358Q8—1722no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—82no—
375C2×C4—864no—
376C2×C4—3442no—
377C2×C4—3441no—
378C2×C4—3441no—
379C2×C4—3442no—
380C2×C4—1722no—
381C2×C4—1724no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1722no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1724no—
390C2×C4#1306329311yescharacteristic
391C2×C4#1306329411yescharacteristic
392C2×C4#1306329611yescharacteristic
393C2×C4#1306329711yescharacteristic
394C8—42no—
395C8—1722no—
396C22—22no—
397C22—22no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—22no—
402C22—21no—
403C22—21no—
404C22#1458280711yescharacteristic
405C22#1458303612yes—
406C22#1458307511yescharacteristic
407C22#1458308011yescharacteristic
408C22#1458308812yes—
409C22#1458310212yes—
410C22#1458327011yescharacteristic
411C22#1458329011yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—81no—
417C4—82no—
418C4—81no—
419C4—3442no—
420C4—3441no—
421C4—3441no—
422C4—1724no—
423C2—21no—
424C2—22no—
425C2—21no—
426C2#1913358412yes—
427C2#1913360112yes—
428C2#1913564011yescharacteristic
429C2#1913567611yescharacteristic
430C2#1913572311yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#483C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#483D43
hypocenterC43#9973
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
246. C43#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#145832292
#191407112
C2×#145826372
C2×#145826362
#191328632
#191324372
C2×C43×#4832
#997343