Finite Group Databasebeta

← #24996980

Subgroups — #24996980

Order 11008.

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

normal subgroups only

This group has 600 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#19144531C211yesmaximal, characteristic
2#19138882C211yesmaximal, characteristic, complemented
3#19134695C211yesmaximal, characteristic, complemented
4#19133124C211yesmaximal, characteristic
5#19132925C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#2591C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583220—22no—
10#14583215—21no—
11#14583210—21no—
12#14582939—21no—
13#14582904—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582838—21no—
17#14582829—21no—
18#14582780—22no—
19#14582772—21no—
20#14582762—21no—
21#14582762C2211yescharacteristic
22#14582659—22no—
23#14582633—22no—
24#14582625—22no—
25C2×#121×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#400—21no—
28C43×#394—21no—
29C43×#388—22no—
30C43×#386—21no—
31C43×#386—21no—
32C4×C22⋊C4×C43C2211yescharacteristic
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×Dic43⋊C4—22no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45#13063258—22no—
46#13063256—22no—
47#13063246—22no—
48#13063246—22no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)D412yes—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95D412yes—
58C22×D4×C43—21no—
59C22×D4×C43D411yescharacteristic
60C23×C4×C43D411yescharacteristic
61C23×C4×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63#121×C43—21no—
64#121×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—22no—
78C2×C42×C43D412yes—
79#95×C43—22no—
80#95×C43—22no—
81#95×C43—21no—
82C24×C43—21no—
83C24×C43C2×D411yescharacteristic
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—44no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—42no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—22no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—42no—
99C22×C4×C43—42no—
100C22×C4×C43—42no—
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×Dic43—22no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C22⋊C4×C43—42no—
117C22⋊C4×C43—44no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—82no—
121C42×C43—42no—
122C22⋊Dic43—42no—
123C22⋊Dic43—41no—
124C22⋊Dic43—41no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129Dic43⋊C4—44no—
130C4×Dic43—41no—
131C4×Dic43—41no—
132#10621877—42no—
133#10621877—42no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—41no—
136C23×C43—22no—
137C23×C43—22no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—41no—
142C23×C43—42no—
143C23×C43#12011yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—82no—
149D4×C43—82no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—42no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—81no—
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43#12711yescharacteristic
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C43⋊C8—42no—
184C43⋊C8—81no—
185#9941—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—44no—
194C22×C43—84no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43#39211yescharacteristic
199C22×C43#45412yes—
200C22×C43#45812yes—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—42no—
206C4×C43—82no—
207C4×C43—81no—
208C4×C43—81no—
209Dic43—82no—
210Dic43—81no—
211Dic43—81no—
212#3094—431no—
213#2591D4311yescharacteristic
214#2484—431no—
215#1826—431no—
216#1510—431no—
217#1463—431no—
218#1284—431no—
219C2×C43—22no—
220C2×C43—22no—
221C2×C43—41no—
222C2×C43—161no—
223C2×C43#200311yescharacteristic
224C2×C43#201011yescharacteristic
225C2×C43#202211yescharacteristic
226C2×#121C2×D4311yescharacteristic
227C2×#117—431no—
228C22×C4⋊C4C2×D4311yescharacteristic
229#482—862no—
230#481—861no—
231#480—861no—
232#428—861no—
233#418—861no—
234#407—431no—
235#407—431no—
236#400—21no—
237#400—861no—
238#398—861no—
239#394—21no—
240#388—22no—
241#387—862no—
242#386—21no—
243#386—21no—
244#385—861no—
245#381—431no—
246#381—861no—
247C4×C22⋊C4C2×D4311yescharacteristic
248#339—862no—
249#327—862no—
250#324—862no—
251C43#994111yescharacteristic, complemented, Sylow
252C22×D4—21no—
253C22×D4C22⋊D4311yescharacteristic
254C23×C4C22⋊D4311yescharacteristic
255C23×C4C22⋊D4311yescharacteristic
256C23×C4C22×D4311yescharacteristic
257C2×M16—861no—
258C2×M16—861no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#117—861no—
264#117—861no—
265#117—861no—
266#117—861no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—862no—
276C2×C4⋊C4C22⋊D4311yescharacteristic
277C2×C22⋊C4—22no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C42—861no—
284C2×C42C22⋊D4312yes—
285#107—862no—
286#106—862no—
287#102—862no—
288#102—862no—
289C22⋊C8—432no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292C22⋊C8—861no—
293#95—22no—
294#95—22no—
295#95—21no—
296#95—432no—
297#95—862no—
298#95—862no—
299#95—862no—
300#95—861no—
301C24—21no—
302C24C2×C22⋊D4311yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—862no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4D4×D4311yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4#1062190011yescharacteristic
327C22×C4C2×C22⋊D4311yescharacteristic
328C22×C4C2×C22⋊D4311yescharacteristic
329M16—1722no—
330M16—1722no—
331C2×C8—862no—
332C2×C8—1721no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—861no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—1724no—
344C22⋊C4—44no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—82no—
349C22⋊C4—1722no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C42—42no—
353C42—1721no—
354C42—1721no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23#1306329311yescharacteristic
363C23#1306329411yescharacteristic
364C23#1306329711yescharacteristic
365D4—42no—
366D4—81no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—1722no—
392C2×C4—1722no—
393C2×C4—1722no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4#1306329311yescharacteristic
399C2×C4#1306329611yescharacteristic
400C2×C4#1306329711yescharacteristic
401C2×C4#1306332111yescharacteristic
402C8—3441no—
403C8—1722no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22#1458280711yescharacteristic
417C22#1458307112yes—
418C22#1458308912yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—81no—
426C4—81no—
427C4—3442no—
428C4—3441no—
429C4—3441no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—161no—
434C2#1913561711yescharacteristic
435C2#1913566011yescharacteristic
436C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2591C2
socleC22×C43#392
prime radicalC2×#121×C43C22
hypercenter#2591D43
hypocenterC43#9941
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
2. #19138882C2semidirect
3. #19134695C2semidirect
5. #19132925C2semidirect
6. #19132448C2semidirect
251. C43#9941semidirect

Maximal subgroups

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

subgroupindex
#191445312
#191388822
#191346952
#191331242
#191329252
#191324482
C43×#25912
#994143