Finite Group Databasebeta

← #24996952

Subgroups — #24996952

Order 11008.

526 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144539C211yesmaximal, characteristic
2#19140393C211yesmaximal, characteristic
3#19135581C211yesmaximal, characteristic
4#19134692C211yesmaximal, characteristic
5#19133115C211yesmaximal, characteristic
6#19132500C211yesmaximal, characteristic
7C43×#3195C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583237—22no—
10#14583232—21no—
11#14583227—21no—
12#14582939—21no—
13#14582908—21no—
14#14582863C2211yescharacteristic
15#14582838—21no—
16#14582829—21no—
17#14582827—22no—
18#14582806—21no—
19#14582795—21no—
20#14582759C2211yescharacteristic
21C4×C22⋊Dic43C2211yescharacteristic
22#14582666—22no—
23#14582660—22no—
24#14582636—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C43×#483—21no—
28C43×#483—21no—
29C43×#470—22no—
30C43×#451—21no—
31C43×#451—21no—
32C43×#407C2211yescharacteristic
33C2×#10621877—21no—
34#13063284—21no—
35#13063284—21no—
36#13063284—21no—
37#13063284—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D412yes—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47#13063258—22no—
48#13063256—22no—
49#13063249—22no—
50#13063249—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)D412yes—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C22×Q8×C43D411yescharacteristic
59C22×Q8×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×Q16×C43—22no—
62C2×M16×C43D412yes—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77#106×C43—22no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C24×C43C2×D411yescharacteristic
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—42no—
88C2×Q8×C43—42no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×Dic43—21no—
101C22×Dic43—22no—
102C22×Dic43—21no—
103C22×Dic43—41no—
104Q16×C43—82no—
105M16×C43—42no—
106C2×C8×C43—22no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊Dic43—22no—
120C22⋊Dic43—42no—
121C22⋊Dic43—41no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—42no—
129Dic43⋊C4—82no—
130C4×Dic43—41no—
131C4×Dic43—41no—
132C4×Dic43—42no—
133#10621877—42no—
134C2×C43⋊C8—22no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43#12011yescharacteristic
140C23×C43#12111yescharacteristic
141C23×C43#12711yescharacteristic
142Q8×C43—42no—
143Q8×C43—42no—
144Q8×C43—42no—
145Q8×C43—81no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—42no—
173C2×Dic43—41no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176C8×C43—42no—
177C43⋊C8—42no—
178#9937—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43#39211yescharacteristic
190C22×C43#45511yescharacteristic
191C22×C43#45611yescharacteristic
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—81no—
196C4×C43—81no—
197C4×C43—81no—
198C4×C43—81no—
199C4×C43#45812yes—
200Dic43—82no—
201Dic43—82no—
202Dic43—81no—
203Dic43—81no—
204#3195D4311yescharacteristic
205#3095—431no—
206#2625—431no—
207#1996—431no—
208#1826—431no—
209#1508—431no—
210#1305—431no—
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—41no—
214C2×C43—41no—
215C2×C43#200711yescharacteristic
216C2×C43#200911yescharacteristic
217C2×C43#202211yescharacteristic
218C2×C22⋊Q8C2×D4311yescharacteristic
219C2×C22⋊Q8C2×D4311yescharacteristic
220C2×#117—431no—
221#485—862no—
222#484—861no—
223#483—21no—
224#483—21no—
225#483—861no—
226#470—22no—
227#451—21no—
228#451—21no—
229#428—861no—
230#419—861no—
231#407—431no—
232#407C2×D4311yescharacteristic
233#400—861no—
234#398—861no—
235#397—862no—
236#391—861no—
237#389—861no—
238#380—431no—
239C4×C22⋊C4—431no—
240#342—862no—
241#339—862no—
242#328—862no—
243C43#993711yescharacteristic, complemented, Sylow
244C22×Q8C22⋊D4311yescharacteristic
245C22×Q8C22⋊D4311yescharacteristic
246C23×C4C22×D4311yescharacteristic
247C2×Q16—22no—
248C2×M16—861no—
249C2×M16C22⋊D4312yes—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—861no—
259#117—861no—
260#117—861no—
261#117—861no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—862no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4C22⋊D4311yescharacteristic
269C2×C4⋊C4C22⋊D4311yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—432no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C42—861no—
276C2×C42—861no—
277#107—862no—
278#106—22no—
279#106—862no—
280#103—22no—
281#103—22no—
282#103—862no—
283#103—862no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—432no—
287C22⋊C8—861no—
288#95—862no—
289#95—862no—
290#95—862no—
291#95—861no—
292#95—861no—
293C24D4×D4311yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—861no—
306C22×C4—862no—
307C22×C4—861no—
308C22×C4—1721no—
309C22×C4D4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C22×C4#1062190011yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313C22×C4C2×C22⋊D4311yescharacteristic
314C22×C4C2×C22⋊D4311yescharacteristic
315Q16—82no—
316M16—42no—
317M16—1722no—
318C2×C8—22no—
319C2×C8—862no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C4⋊C4—861no—
331C4⋊C4—861no—
332C4⋊C4—3442no—
333C4⋊C4—1722no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—862no—
339C22⋊C4—1721no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C22⋊C4—1722no—
343C42—1722no—
344C42—1721no—
345C42—1721no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23#1306329311yescharacteristic
351C23#1306329711yescharacteristic
352C23#1306332111yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4—1722no—
377C2×C4—1722no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1722no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4#1306329311yescharacteristic
384C2×C4#1306329411yescharacteristic
385C2×C4#1306329611yescharacteristic
386C2×C4#1306329711yescharacteristic
387C8—42no—
388C8—1722no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22#1458280711yescharacteristic
400C22#1458307511yescharacteristic
401C22#1458308011yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—3442no—
410C4—3442no—
411C4—3441no—
412C4—3441no—
413C4#1458308912yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2#1913564011yescharacteristic
419C2#1913565311yescharacteristic
420C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3195C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#3195D43
hypocenterC43#9937
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
243. C43#9937semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191403932
#191355812
#191346922
#191331152
#191325002
C43×#31952
#993743