Finite Group Databasebeta

← #24994668

Subgroups — #24994668

Order 11008.

482 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 89 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#19144543C211yesmaximal, characteristic
2#19137348C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic
4#19133127C211yesmaximal, characteristic
5#19132503C211yesmaximal, characteristic
6#19132447C211yesmaximal, characteristic
7C43×#1820C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583240—22no—
10#14583234C412yescomplemented
11#14583229C412yescomplemented
12#14582942—21no—
13#14582907—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582803—21no—
17#14582793—21no—
18#14582787—21no—
19#14582782—21no—
20#14582781—21no—
21#14582750—21no—
22C4×C22⋊Dic43C2211yescharacteristic
23#14582658—21no—
24#14582658—21no—
25#14582635—22no—
26C2×#117×C43C2211yescharacteristic
27C43×#381C2211yescharacteristic
28C43×#381C2211yescharacteristic
29C43×#342—21no—
30C43×#342—21no—
31C22×Dic86D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621877—21no—
34#13063304—21no—
35#13063304—21no—
36#13063304C2×C412yes—
37#13063304D412yes—
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48#13063258—22no—
49#13063256—22no—
50#13063248—22no—
51#13063248—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)C2×C412yes—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C23×C4×C43C2311yescharacteristic
62#117×C43—21no—
63#117×C43—21no—
64#117×C43—21no—
65#117×C43—21no—
66C2×C4⋊C4×C43C2×C411yescharacteristic
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43D411yescharacteristic
72C2×C42×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75#95×C43—21no—
76#95×C43—21no—
77C24×C43C2×D411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C2×Dic86—21no—
96C2×Dic86—41no—
97C2×Dic86—41no—
98C2×Dic86C22⋊C412yes—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C22⋊Dic43—22no—
112C22⋊Dic43—22no—
113C22⋊Dic43—42no—
114C4⋊Dic43—21no—
115C4⋊Dic43C22⋊C412yes—
116Dic43⋊C4—22no—
117Dic43⋊C4—22no—
118Dic43⋊C4—42no—
119Dic43⋊C4—81no—
120C4×Dic43—42no—
121C4×Dic43—41no—
122C4×Dic43—41no—
123C4×Dic43—81no—
124#10621877—41no—
125#10621877—41no—
126#10621877—41no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43C4×D411yescharacteristic
135C23×C43#12011yescharacteristic
136C23×C43#12111yescharacteristic
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
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—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174Dic86—42no—
175Dic86—81no—
176C43⋊C8—42no—
177C43⋊C8—81no—
178#9526—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#38611yescharacteristic
190C22×C43#45811yescharacteristic
191C22×C43#45811yescharacteristic
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—81no—
197C4×C43—81no—
198C4×C43—81no—
199C4×C43—81no—
200C4×C43—161no—
201Dic43—42no—
202Dic43—42no—
203Dic43—42no—
204Dic43—81no—
205#3095—431no—
206#2332—431no—
207#1826—431no—
208#1820D4311yescharacteristic
209#1511—431no—
210#1306—431no—
211#1284—431no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—41no—
215C2×C43—41no—
216C2×C43#189011yescharacteristic
217C2×C43#190511yescharacteristic
218C2×C43#190611yescharacteristic
219C2×C22⋊Q8—431no—
220C2×#117C2×D4311yescharacteristic
221#485—862no—
222#484—432no—
223#483—432no—
224#428—861no—
225#419—861no—
226#407—431no—
227#407—431no—
228#391—861no—
229#388—861no—
230#388—861no—
231#387—861no—
232#387—861no—
233#381C2×D4311yescharacteristic
234#381C2×D4311yescharacteristic
235C4×C4⋊C4—861no—
236C4×C22⋊C4—431no—
237#342—21no—
238#342—21no—
239#339—861no—
240#339—861no—
241#328—862no—
242C43#952611yescharacteristic, complemented, Sylow
243C22×Q8—431no—
244C23×C4C22×D4311yescharacteristic
245C2×M16—861no—
246C2×M16—861no—
247C22⋊Q8—432no—
248C22⋊Q8—432no—
249C22⋊Q8—861no—
250C22⋊Q8—861no—
251#117—21no—
252#117—21no—
253#117—21no—
254#117—21no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4—861no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4C4×D4311yescharacteristic
260C2×C4⋊C4C4×D4311yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4C22⋊D4311yescharacteristic
266C2×C22⋊C4C22⋊D4311yescharacteristic
267C2×C42—21no—
268C2×C42—431no—
269C2×C42—431no—
270C2×C42—861no—
271C2×C42—861no—
272#107—862no—
273#106—862no—
274#103—862no—
275#103—862no—
276C22⋊C8—432no—
277C22⋊C8—861no—
278C22⋊C8—861no—
279C22⋊C8—861no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—861no—
285#95—861no—
286#95—861no—
287#95—861no—
288#95—861no—
289C24C2×C22⋊D4311yescharacteristic
290C2×Q8—432no—
291C2×Q8—861no—
292C2×Q8—1721no—
293C2×Q8—1721no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4C2×C4×D4311yescharacteristic
306C22×C4#1062189811yescharacteristic
307C22×C4D4×D4311yescharacteristic
308C22×C4D4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4#1062190011yescharacteristic
311M16—1721no—
312M16—1721no—
313M16—1721no—
314M16—1721no—
315C2×C8—862no—
316C2×C8—1721no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—432no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—861no—
325C4⋊C4—3441no—
326C4⋊C4—1722no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—862no—
334C22⋊C4—862no—
335C22⋊C4—1722no—
336C42—41no—
337C42—41no—
338C42—3441no—
339C42—1721no—
340C42—1721no—
341C42—1722no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23C4×C22⋊D4311yescharacteristic
347C23#1306329311yescharacteristic
348C23#1306329611yescharacteristic
349Q8—3441no—
350Q8—1722no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—862no—
373C2×C4—862no—
374C2×C4—862no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4#1306329811yescharacteristic
387C2×C4#1306330711yescharacteristic
388C8—3441no—
389C8—1722no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1458277511yescharacteristic
401C22#1458308811yescharacteristic
402C22#1458308811yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—161no—
412C4—3441no—
413C4—1722no—
414C4—1722no—
415C4—1722no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1913500511yescharacteristic
421C2#1913509211yescharacteristic
422C2#1913509311yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1820C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1820D43
hypocenterC43#9526
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
10. #14583234C4semidirect
11. #14583229C4semidirect
242. C43#9526semidirect

Maximal subgroups

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

subgroupindex
#191445432
#191373482
#191346942
#191331272
#191325032
#191324472
C43×#18202
#952643