Finite Group Databasebeta

← #24996982

Subgroups — #24996982

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#19144535C211yesmaximal, characteristic
2#19140075C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic, complemented
4#19133123C211yesmaximal, characteristic
5#19132925C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#2484C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583223—22no—
10#14583217—21no—
11#14583212—21no—
12#14582942—21no—
13#14582903—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582838—21no—
17#14582816—21no—
18#14582789—22no—
19#14582778—21no—
20#14582778—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582658—22no—
23#14582632—22no—
24#14582625—22no—
25C2×#117×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#400—21no—
28C43×#398—21no—
29C43×#387—22no—
30C43×#385—21no—
31C43×#381—21no—
32C43×#381C2211yescharacteristic
33C22×D172D411yescharacteristic
34C22×C22⋊D43—21no—
35C2×#10621877—21no—
36C2×#10621877—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—22no—
46C2×C4×Dic43D412yes—
47#13063258—22no—
48#13063256—22no—
49#13063245—22no—
50#13063245—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C23×C4×C43D411yescharacteristic
59C23×C4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61#117×C43—21no—
62#117×C43—21no—
63#117×C43—21no—
64#117×C43—21no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×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×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C42×C43—21no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43—22no—
80#95×C43—21no—
81#95×C43D412yes—
82C24×C43C2×D411yescharacteristic
83C23×D43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C2×C22⋊D43—44no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—41no—
105C22×Dic43—21no—
106C22×Dic43—22no—
107C2×D172—21no—
108C2×D172—21no—
109C2×D172—42no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—44no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊C4×C43—42no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C42×C43—41no—
123C42×C43—41no—
124C22⋊Dic43—42no—
125(C2×D43)⋊C4—44no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—82no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4×Dic43—42no—
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#12011yescharacteristic
140C23×C43#12011yescharacteristic
141C23×C43#12111yescharacteristic
142C22×D43—42no—
143C22×D43—42no—
144C22×D43—41no—
145C22×D43—42no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
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—42no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43—81no—
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12711yescharacteristic
174C22⋊D43—82no—
175C22⋊D43—82no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—42no—
181D172—42no—
182D172—81no—
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#39211yescharacteristic
195C22×C43#45412yes—
196C22×C43#45812yes—
197C2×D43—84no—
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—42no—
206C4×C43—82no—
207C4×C43—81no—
208C4×C43—81no—
209C4×C43—81no—
210Dic43—82no—
211Dic43—81no—
212#3094—431no—
213#2591—431no—
214#2484D4311yescharacteristic, complemented
215#1826—431no—
216#1510—431no—
217#1463—431no—
218#1284—431no—
219C2×C43—22no—
220C2×C43—22no—
221C2×C43—41no—
222C2×C43#200311yescharacteristic
223C2×C43#201011yescharacteristic
224C2×C43#202211yescharacteristic
225D43—161no—
226C2×#121—431no—
227C2×#117C2×D4311yescharacteristic
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—21no—
239#394—861no—
240#388—862no—
241#387—22no—
242#386—861no—
243#386—861no—
244#385—21no—
245#381—21no—
246#381C2×D4311yescharacteristic
247C4×C22⋊C4—431no—
248#339—862no—
249#327—862no—
250#324—862no—
251C43#994111yescharacteristic, complemented, Sylow
252C22×D4—431no—
253C22×D4—861no—
254C23×C4C22⋊D4311yescharacteristic
255C23×C4C22⋊D4311yescharacteristic
256C23×C4C22×D4311yescharacteristic
257C2×M16—861no—
258C2×M16—861no—
259#121—861no—
260#121—861no—
261#121—861no—
262#121—861no—
263#117—21no—
264#117—21no—
265#117—21no—
266#117—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4C22⋊D4311yescharacteristic
276C2×C4⋊C4C22⋊D4311yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—862no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C42—21no—
284C2×C42—432no—
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—22no—
296#95—21no—
297#95—862no—
298#95—862no—
299#95—861no—
300#95C22⋊D4312yes—
301C24—861no—
302C24C2×C22⋊D4311yescharacteristic
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—1722no—
306C2×D4—1724no—
307C2×D4—1721no—
308C2×D4—1721no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—861no—
322C22×C4—862no—
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—21no—
336C4⋊C4—21no—
337C4⋊C4—44no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C22⋊C4—42no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—3442no—
348C22⋊C4—1724no—
349C22⋊C4—1722no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C42—41no—
353C42—41no—
354C42—1722no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—1722no—
359C23—1722no—
360C23—1721no—
361C23—1722no—
362C23#1306329311yescharacteristic
363C23#1306329411yescharacteristic
364C23#1306329711yescharacteristic
365D4—3441no—
366D4—3442no—
367D4—3442no—
368D4—1722no—
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—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4—1722no—
394C2×C4—1722no—
395C2×C4—1722no—
396C2×C4—1721no—
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—3444no—
413C22—3441no—
414C22—3441no—
415C22—3441no—
416C22#1458280711yescharacteristic
417C22#1458307212yes—
418C22#1458308812yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—81no—
426C4—81no—
427C4—81no—
428C4—3442no—
429C4—3441no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—6881no—
434C2#1913561511yescharacteristic
435C2#1913566011yescharacteristic
436C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2484C2
socleC22×C43#392
prime radicalC2×#13063299C22
hypercenter#2484D43
hypocenterC43#9941
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
3. #19134694C2semidirect
5. #19132925C2semidirect
6. #19132447C2semidirect
7. C43×#2484C2semidirect
214. #2484D43semidirect
251. C43#9941semidirect

Maximal subgroups

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

subgroupindex
#191445352
#191400752
#191346942
#191331232
#191329252
#191324472
C43×#24842
#994143