Finite Group Databasebeta

← #24997103

Subgroups — #24997103

Order 11008.

594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145352C211yesmaximal, characteristic
2C2×#14583235C211yesmaximal, characteristic, complemented
3#19139088C211yesmaximal, characteristic
4#19135579C211yesmaximal, characteristic, complemented
5#19134683C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1519C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14583235—22no—
11#14583235—22no—
12#14583229—21no—
13#14583215—21no—
14#14583126—22no—
15#14583050—21no—
16#14583037—21no—
17C2×#13063259—21no—
18C2×#13063250—21no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20#14582824—22no—
21#14582802—21no—
22#14582779—22no—
23#14582764—21no—
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—22no—
26#14582661—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#327—22no—
31C22×Dic86D411yescharacteristic
32C23×Dic43—21no—
33C2×#10621883—22no—
34C22×C43⋊C8D412yes—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43D412yes—
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—24no—
49C2×C22⋊Dic43D412yes—
50C2×C4×Dic43—21no—
51#13063259—24no—
52#13063256—22no—
53#13063250—24no—
54#13063248—22no—
55#13063246—22no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C43⋊#95—24no—
59C43⋊#95—21no—
60C22×D4×C43—21no—
61C22×D4×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64#121×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43D412yes—
74#95×C43—21no—
75C24×C43—21no—
76C24×C43C2×D411yescharacteristic
77C2×D4×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—42no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—42no—
83C2×D4×C43—42no—
84C22×C4×C43—21no—
85C22×C4×C43—42no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×Dic43—22no—
94C22×Dic43—22no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—41no—
98C22×Dic43—41no—
99C22×Dic43—82no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86—42no—
103C2×C8×C43—22no—
104C2×C8×C43—42no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—42no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—42no—
111C22⋊Dic43—22no—
112C22⋊Dic43—22no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115C22⋊Dic43—84no—
116#10621883—82no—
117C4⋊Dic43—21no—
118C4⋊Dic43—22no—
119C4⋊Dic43—21no—
120C4⋊Dic43—22no—
121C4⋊Dic43—41no—
122C4⋊Dic43—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125C4×Dic43—42no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—42no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—42no—
131C23×C43—42no—
132C23×C43—41no—
133C23×C43—42no—
134C23×C43#12011yescharacteristic
135C23×C43#12111yescharacteristic
136C23×C43#12711yescharacteristic
137C23×C43#13512yes—
138C23×C43#13712yes—
139D4×C43—42no—
140D4×C43—81no—
141D4×C43—82no—
142D4×C43—81no—
143D4×C43—81no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—44no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—82no—
167C2×Dic43—82no—
168C2×Dic43—81no—
169C2×Dic43—81no—
170Dic86—42no—
171Dic86—42no—
172C8×C43—42no—
173C43⋊C8—42no—
174#9958—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—42no—
182C22×C43—42no—
183C22×C43—84no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43#39211yescharacteristic
188C22×C43#45212yes—
189C22×C43#46412yes—
190C22×C43#49511yescharacteristic
191C22×C43#49711yescharacteristic
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—81no—
196C4×C43—161no—
197C4×C43#45812yes—
198Dic43—82no—
199Dic43—82no—
200Dic43—81no—
201Dic43—81no—
202#3187—431no—
203C2×#484—431no—
204#2504—431no—
205#1996—431no—
206#1824—431no—
207#1519D4311yescharacteristic
208#1282—431no—
209C2×C43—22no—
210C2×C43—21no—
211C2×C43—22no—
212C2×C43—21no—
213C2×C43—161no—
214C2×C43#200811yescharacteristic
215C2×C43#201511yescharacteristic
216C2×C43#202211yescharacteristic
217C2×C22⋊Q8—431no—
218C2×#121C2×D4311yescharacteristic
219C22×C4⋊C4—431no—
220#484—862no—
221#484—862no—
222#483—861no—
223#481—861no—
224#465—862no—
225#450—861no—
226#448—861no—
227C2×#107—861no—
228C2×#103—861no—
229C2×C22⋊C8—431no—
230C2×C22⋊C8C2×D4311yescharacteristic
231#397—862no—
232#390—861no—
233#386—862no—
234#382—861no—
235#380C2×D4311yescharacteristic
236C4×C22⋊C4—431no—
237#342—862no—
238#340—862no—
239#327—22no—
240C43#995811yescharacteristic, complemented, Sylow
241C22×Q8—431no—
242C22×D4—21no—
243C22×D4D17211yescharacteristic
244C23×C4—861no—
245C23×C4C22×D4311yescharacteristic
246C2×SD16—862no—
247C22×C8—21no—
248C22×C8—432no—
249C22⋊Q8—861no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C22⋊Q8—861no—
253#121—21no—
254#121—21no—
255#121—21no—
256#121—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—432no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4D17211yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—432no—
270C2×C22⋊C4—864no—
271C2×C22⋊C4—861no—
272C2×C42—861no—
273#107—864no—
274#106—862no—
275#103—862no—
276#103—864no—
277#102—862no—
278C22⋊C8—21no—
279C22⋊C8—861no—
280C22⋊C8—861no—
281C22⋊C8C22⋊D4312yes—
282#95—21no—
283#95—864no—
284#95—861no—
285C24—21no—
286C24D4×D4311yescharacteristic
287C2×Q8—861no—
288C2×Q8—861no—
289C2×Q8—1722no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—862no—
303C22×C4—862no—
304C22×C4—3442no—
305C22×C4—1721no—
306C22×C4—1721no—
307C22×C4C2×D17211yescharacteristic
308C22×C4#1062189811yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C22×C4D4×D4311yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313SD16—3442no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—862no—
317C2×C8—1722no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—42no—
321C4⋊C4—862no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—862no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—862no—
333C22⋊C4—862no—
334C22⋊C4—3444no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C42—1722no—
338C23—41no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—41no—
344C23#1306329511yescharacteristic
345C23#1306329811yescharacteristic
346C23#1306332111yescharacteristic
347C23#1306334412yes—
348C23#1306335412yes—
349Q8—1722no—
350Q8—1722no—
351D4—42no—
352D4—81no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—3442no—
368C2×C4—3442no—
369C2×C4—3441no—
370C2×C4—3441no—
371C2×C4—1722no—
372C2×C4—1722no—
373C2×C4—1724no—
374C2×C4—1722no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1722no—
378C2×C4#1306329311yescharacteristic
379C2×C4#1306329511yescharacteristic
380C2×C4#1306329811yescharacteristic
381C2×C4#1306329911yescharacteristic
382C8—42no—
383C8—1722no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—84no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#1458280811yescharacteristic
397C22#1458306212yes—
398C22#1458312012yes—
399C22#1458328211yescharacteristic
400C22#1458329011yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—161no—
406C4—3442no—
407C4—3442no—
408C4—3441no—
409C4—3441no—
410C4#1458309012yes—
411C2—21no—
412C2—22no—
413C2—22no—
414C2—21no—
415C2—161no—
416C2#1913564911yescharacteristic
417C2#1913569111yescharacteristic
418C2#1913572511yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1519C2
socleC22×C43#392
prime radicalC2×#121×C43C22
hypercenter#1519D43
hypocenterC43#9958
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. C2×#14583235C2semidirect
4. #19135579C2semidirect
5. #19134683C2semidirect
6. #19132441C2semidirect
240. C43#9958semidirect

Maximal subgroups

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

subgroupindex
#191453522
C2×#145832352
#191390882
#191355792
#191346832
#191324412
C43×#15192
#995843