Finite Group Databasebeta

← #24997251

Subgroups — #24997251

Order 11008.

544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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, complemented
2#19144531C211yesmaximal, characteristic
3#19134670C211yesmaximal, characteristic, complemented
4#19133128C211yesmaximal, characteristic, complemented
5#19133124C211yesmaximal, characteristic
6#19132503C211yesmaximal, characteristic, complemented
7C43×#2816C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583237—22no—
10#14583232—21no—
11#14583227—21no—
12#14583220—22no—
13#14583215—21no—
14#14583210—21no—
15#14582939—21no—
16#14582939—21no—
17#14582908—21no—
18#14582904—21no—
19#14582863C2211yescharacteristic
20#14582863C2211yescharacteristic
21#14582762C2211yescharacteristic
22#14582665—22no—
23#14582636—22no—
24#14582633—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C43×#399—21no—
28C43×#398—21no—
29C43×#394—21no—
30C43×#394—22no—
31C43×#393—21no—
32C43×#381C2211yescharacteristic
33C2×#10621877—21no—
34C2×#10621877—21no—
35#13063284—21no—
36#13063284—21no—
37#13063284—21no—
38#13063284—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C4×Dic43—21no—
44#13063258—22no—
45#13063258—22no—
46#13063256—22no—
47#13063256—22no—
48#13063249—22no—
49#13063249—22no—
50#13063246—22no—
51#13063246—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C22⋊(C43⋊C8)D412yes—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C22×Q8×C43D411yescharacteristic
59C22×D4×C43—21no—
60C22×D4×C43D411yescharacteristic
61C23×C4×C43C2311yescharacteristic
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69#121×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43D412yes—
79#95×C43—22no—
80#95×C43—21no—
81#95×C43—21no—
82C24×C43—21no—
83C24×C43C2×D411yescharacteristic
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C2×D4×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—42no—
92C2×D4×C43—82no—
93C22×C4×C43—22no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—42no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—41no—
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—82no—
114C22⋊C4×C43—42no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—82no—
120C22⋊C4×C43—82no—
121C22⋊Dic43—42no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4×Dic43—41no—
129C4×Dic43—41no—
130#10621877—42no—
131#10621877—42no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—22no—
134C23×C43—22no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—42no—
138C23×C43—42no—
139C23×C43—41no—
140C23×C43—42no—
141C23×C43#12011yescharacteristic
142C23×C43#12111yescharacteristic
143C23×C43#12711yescharacteristic
144Q8×C43—42no—
145Q8×C43—81no—
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—82no—
149D4×C43—82no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—81no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C43⋊C8—42no—
178C43⋊C8—42no—
179#9984—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—82no—
189C22×C43—84no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43#39211yescharacteristic
194C22×C43#45812yes—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—82no—
200C4×C43—81no—
201C4×C43—81no—
202C4×C43—81no—
203Dic43—81no—
204Dic43—81no—
205Dic43—161no—
206#3095—431no—
207#3094—431no—
208#2816D4311yescharacteristic
209#1820—431no—
210#1511—431no—
211#1510—431no—
212#1306—431no—
213C2×C43—22no—
214C2×C43—41no—
215C2×C43—41no—
216C2×C43—161no—
217C2×C43#200811yescharacteristic
218C2×C43#200911yescharacteristic
219C2×C43#202211yescharacteristic
220C2×C22⋊Q8C2×D4311yescharacteristic
221C2×#121C2×D4311yescharacteristic
222C2×#117—431no—
223#485—862no—
224#484—861no—
225#483—861no—
226#482—862no—
227#481—861no—
228#480—861no—
229#428—861no—
230#428—861no—
231#419—861no—
232#418—861no—
233#407—431no—
234#407—431no—
235#399—21no—
236#398—21no—
237#394—21no—
238#394—22no—
239#393—21no—
240#381—431no—
241#381C2×D4311yescharacteristic
242#342—862no—
243#328—862no—
244#327—862no—
245C43#998411yescharacteristic, complemented, Sylow
246C22×Q8C22⋊D4311yescharacteristic
247C22×D4—21no—
248C22×D4C22⋊D4311yescharacteristic
249C23×C4C22×D4311yescharacteristic
250C2×M16—861no—
251C2×M16—861no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259#121—21no—
260#117—861no—
261#117—861no—
262#117—861no—
263#117—861no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4C22⋊D4311yescharacteristic
269C2×C4⋊C4C22⋊D4311yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4C22⋊D4312yes—
277C2×C42—861no—
278#107—862no—
279#107—862no—
280#106—862no—
281#106—862no—
282#103—862no—
283#103—862no—
284#102—862no—
285#102—862no—
286C22⋊C8—432no—
287C22⋊C8—432no—
288C22⋊C8—861no—
289C22⋊C8—861no—
290#95—22no—
291#95—21no—
292#95—21no—
293#95—861no—
294#95—861no—
295C24—21no—
296C24C2×C22⋊D4311yescharacteristic
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—42no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—42no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—82no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—1721no—
314C22×C4D4×D4311yescharacteristic
315C22×C4D4×D4311yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4#1062190011yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320M16—1722no—
321M16—1722no—
322C2×C8—862no—
323C2×C8—862no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—82no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C22⋊C4—82no—
341C22⋊C4—82no—
342C22⋊C4—1722no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—1721no—
346C42—1721no—
347C23—22no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—42no—
354C23#1306329411yescharacteristic
355C23#1306329611yescharacteristic
356C23#1306332111yescharacteristic
357Q8—42no—
358Q8—81no—
359D4—42no—
360D4—81no—
361D4—82no—
362D4—82no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—3441no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—3441no—
383C2×C4—3441no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4#1306329311yescharacteristic
387C2×C4#1306329311yescharacteristic
388C2×C4#1306329711yescharacteristic
389C2×C4#1306329711yescharacteristic
390C8—1722no—
391C8—1722no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—82no—
401C22—84no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#1458280711yescharacteristic
406C22#1458308912yes—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—3441no—
416C4—3441no—
417C4—6881no—
418C2—22no—
419C2—41no—
420C2—41no—
421C2—161no—
422C2#1913564811yescharacteristic
423C2#1913565511yescharacteristic
424C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2816C2
socleC22×C43#392
prime radicalC2×#121×C43C22
hypercenter#2816D43
hypocenterC43#9984
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2816

Complements

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

NH ≅ G/Ntype
1. #19144539C2semidirect
3. #19134670C2semidirect
4. #19133128C2semidirect
6. #19132503C2semidirect
245. C43#9984semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191445312
#191346702
#191331282
#191331242
#191325032
C43×#28162
#998443