Finite Group Databasebeta

← #24997098

Subgroups — #24997098

Order 11008.

594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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#19145348C211yesmaximal, characteristic
2#19139083C211yesmaximal, characteristic
3#19135581C211yesmaximal, characteristic, complemented
4#19134685C211yesmaximal, characteristic, complemented
5#19133164C211yesmaximal, characteristic
6#19132441C211yesmaximal, characteristic, complemented
7C2×C43×#484C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583227—21no—
10#14583217—21no—
11#14583130—22no—
12#14583049—21no—
13#14583038—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15#14582825—22no—
16#14582800—21no—
17#14582778—22no—
18#14582764—21no—
19#14582759C2211yescharacteristic
20C4×C22⋊Dic43C2211yescharacteristic
21#14582666—22no—
22#14582661—22no—
23#14582634—22no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#484—22no—
27C43×#484—22no—
28C2×#107×C43—21no—
29C2×#103×C43—21no—
30C2×C22⋊C8×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C2×#10621884—22no—
34C22×C43⋊C8D412yes—
35#13063299—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43D412yes—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—24no—
45C2×C4×Dic43—21no—
46#13063256—22no—
47#13063249—22no—
48#13063245—22no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C43⋊#95—24no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×Q8×C43D411yescharacteristic
55C23×C4×C43—21no—
56C23×C4×C43C2311yescharacteristic
57C22×C8×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D412yes—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71#107×C43—24no—
72#103×C43—24no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43D412yes—
75C24×C43C2×D411yescharacteristic
76C23×D43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—42no—
80C22×C4×C43—22no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—82no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C2×C22⋊D43—42no—
96C2×C22⋊D43—42no—
97C22×Dic43—21no—
98C22×Dic43—22no—
99C22×Dic43—41no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—42no—
103C2×C8×C43—22no—
104C2×C8×C43—42no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊Dic43—22no—
116C22⋊Dic43—22no—
117C22⋊Dic43—42no—
118#10621884—82no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—84no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—42no—
125C4×Dic43—42no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—42no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43#12011yescharacteristic
131C23×C43#12111yescharacteristic
132C23×C43#12711yescharacteristic
133C23×C43#13512yes—
134C23×C43#13712yes—
135C22×D43—42no—
136C22×D43—42no—
137C22×D43—41no—
138C22×D43—42no—
139Q8×C43—42no—
140Q8×C43—42no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—44no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—82no—
152C2×C4×C43—82no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C22⋊D43—82no—
160C22⋊D43—81no—
161C22⋊D43—81no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—41no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—81no—
168C2×Dic43—81no—
169C2×Dic43—81no—
170D172—42no—
171D172—81no—
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#39211yescharacteristic
184C22×C43#45212yes—
185C22×C43#46412yes—
186C22×C43#49511yescharacteristic
187C22×C43#49711yescharacteristic
188C2×D43—84no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—82no—
196C4×C43—81no—
197C4×C43—81no—
198C4×C43#45812yes—
199Dic43—82no—
200Dic43—81no—
201Dic43—161no—
202#3187—431no—
203C2×#484D4311yescharacteristic, complemented
204#2504—431no—
205#1996—431no—
206#1824—431no—
207#1519—431no—
208#1282—431no—
209C2×C43—22no—
210C2×C43—21no—
211C2×C43—22no—
212C2×C43—21no—
213C2×C43#200811yescharacteristic
214C2×C43#201511yescharacteristic
215C2×C43#202211yescharacteristic
216D43—161no—
217C2×C22⋊Q8C2×D4311yescharacteristic
218C2×#121—431no—
219C22×C4⋊C4C2×D4311yescharacteristic
220#484—22no—
221#484—22no—
222#483—861no—
223#481—861no—
224#465—862no—
225#450—861no—
226#448—861no—
227C2×#107—21no—
228C2×#103—21no—
229C2×C22⋊C8—431no—
230C2×C22⋊C8C2×D4311yescharacteristic
231#397—862no—
232#390—861no—
233#386—862no—
234#382—861no—
235#380—431no—
236C4×C22⋊C4—431no—
237#342—862no—
238#340—862no—
239#327—862no—
240C43#995811yescharacteristic, complemented, Sylow
241C22×Q8C22⋊D4311yescharacteristic
242C22×D4—431no—
243C22×D4—861no—
244C23×C4—21no—
245C23×C4C22×D4311yescharacteristic
246C2×SD16—862no—
247C22×C8—21no—
248C22×C8—432no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#121—861no—
254#121—861no—
255#121—861no—
256#121—861no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C22⋊D4312yes—
266C2×C4⋊C4C22⋊D4311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—432no—
269C2×C22⋊C4—864no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C42—861no—
273#107—24no—
274#106—862no—
275#103—24no—
276#103—862no—
277#102—862no—
278C22⋊C8—21no—
279C22⋊C8—861no—
280C22⋊C8—861no—
281C22⋊C8C22⋊D4312yes—
282#95—864no—
283#95—861no—
284#95—861no—
285C24—861no—
286C24D4×D4311yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—1722no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1722no—
296C2×D4—1722no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—82no—
304C22×C4—861no—
305C22×C4—862no—
306C22×C4—1721no—
307C22×C4D4×D4311yescharacteristic
308C22×C4D4×D4311yescharacteristic
309C22×C4#1062190011yescharacteristic
310C22×C4C2×C22⋊D4311yescharacteristic
311C22×C4C2×C22⋊D4311yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313SD16—3442no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—862no—
317C2×C8—1722no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—1722no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—862no—
332C22⋊C4—862no—
333C22⋊C4—3444no—
334C22⋊C4—1722no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C42—1722no—
338C23—41no—
339C23—41no—
340C23—1722no—
341C23—1722no—
342C23—1722no—
343C23—1721no—
344C23#1306329311yescharacteristic
345C23#1306329711yescharacteristic
346C23#1306332111yescharacteristic
347C23#1306334812yes—
348C23#1306335712yes—
349Q8—42no—
350Q8—42no—
351D4—3441no—
352D4—3442no—
353D4—3441no—
354D4—3441no—
355D4—1722no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—3441no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4—1722no—
377C2×C4—1721no—
378C2×C4#1306329311yescharacteristic
379C2×C4#1306329411yescharacteristic
380C2×C4#1306329611yescharacteristic
381C2×C4#1306329711yescharacteristic
382C8—42no—
383C8—1722no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—3444no—
393C22—3441no—
394C22—3441no—
395C22—3441no—
396C22#1458280711yescharacteristic
397C22#1458306012yes—
398C22#1458312312yes—
399C22#1458328411yescharacteristic
400C22#1458329211yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—81no—
407C4—3442no—
408C4—3441no—
409C4—6881no—
410C4#1458308812yes—
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—6881no—
416C2#1913564611yescharacteristic
417C2#1913568611yescharacteristic
418C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#484C2
socleC22×C43#392
prime radicalC2×#13063299C22
hypercenterC2×#484D43
hypocenterC43#9958
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #19135581C2semidirect
4. #19134685C2semidirect
6. #19132441C2semidirect
7. C2×C43×#484C2semidirect
203. C2×#484D43semidirect
240. C43#9958semidirect

Maximal subgroups

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

subgroupindex
#191453482
#191390832
#191355812
#191346852
#191331642
#191324412
C2×C43×#4842
#995843