Finite Group Databasebeta

← #24997257

Subgroups — #24997257

Order 11008.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#19142630C211yesmaximal, characteristic
3#19134672C211yesmaximal, characteristic
4#19133129C211yesmaximal, characteristic
5#19133128C211yesmaximal, characteristic
6#19132504C211yesmaximal, characteristic
7C43×#3095C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583240—22no—
10#14583234—21no—
11#14583229—21no—
12#14582942—21no—
13#14582907—21no—
14#14582863C2211yescharacteristic
15#14582838—21no—
16#14582837—21no—
17#14582827—22no—
18#14582819—21no—
19#14582818—21no—
20#14582762C2211yescharacteristic
21#14582762C2211yescharacteristic
22#14582666—22no—
23#14582637—22no—
24#14582636—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#485—22no—
28C43×#484—21no—
29C43×#483—21no—
30C43×#428—21no—
31C43×#419—21no—
32C43×#407C2211yescharacteristic
33C22×Dic86D411yescharacteristic
34C2×#10621877—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D412yes—
45#13063258—22no—
46#13063256—22no—
47#13063248—22no—
48#13063248—22no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)D412yes—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C22×Q8×C43D411yescharacteristic
59C23×C4×C43C2311yescharacteristic
60C2×M16×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65#117×C43—21no—
66#117×C43—21no—
67#117×C43—21no—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C42×C43—21no—
76#107×C43—22no—
77#106×C43—22no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43D412yes—
82C24×C43C2×D411yescharacteristic
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—42no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—42no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—22no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—41no—
101C2×Dic86—21no—
102C2×Dic86—21no—
103C2×Dic86—42no—
104M16×C43—42no—
105C2×C8×C43—22no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C42×C43—41no—
119C42×C43—41no—
120C22⋊Dic43—42no—
121C22⋊Dic43—42no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—82no—
129#10621877—42no—
130C2×C43⋊C8—22no—
131C23×C43—22no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43#12011yescharacteristic
135C23×C43#12111yescharacteristic
136C23×C43#12711yescharacteristic
137Q8×C43—42no—
138Q8×C43—81no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—81no—
165C2×Dic43—81no—
166C2×Dic43—81no—
167Dic86—42no—
168Dic86—81no—
169C8×C43—42no—
170C43⋊C8—42no—
171#9985—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—82no—
181C22×C43#39211yescharacteristic
182C22×C43#45812yes—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43—81no—
190C4×C43—81no—
191Dic43—82no—
192Dic43—81no—
193Dic43—81no—
194Dic43—161no—
195#3095—431no—
196#3095D4311yescharacteristic
197#2817—431no—
198#1820—431no—
199#1511—431no—
200#1511—431no—
201#1306—431no—
202C2×C43—22no—
203C2×C43—41no—
204C2×C43—41no—
205C2×C43#200911yescharacteristic
206C2×C43#200911yescharacteristic
207C2×C43#202211yescharacteristic
208C2×C22⋊Q8—431no—
209C2×C22⋊Q8C2×D4311yescharacteristic
210C2×#117C2×D4311yescharacteristic
211#485—22no—
212#485—862no—
213#484—21no—
214#484—861no—
215#483—21no—
216#483—861no—
217#428—21no—
218#428—861no—
219#419—21no—
220#419—861no—
221#407—431no—
222#407C2×D4311yescharacteristic
223#400—861no—
224#400—861no—
225#397—862no—
226#395—861no—
227#395—861no—
228#381—431no—
229#381—431no—
230#342—862no—
231#328—862no—
232#328—862no—
233C43#998511yescharacteristic, complemented, Sylow
234C22×Q8—431no—
235C22×Q8C22⋊D4311yescharacteristic
236C23×C4C22×D4311yescharacteristic
237C2×M16—21no—
238C2×M16—861no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—861no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C22⋊Q8—861no—
247#117—21no—
248#117—21no—
249#117—21no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—862no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4C22⋊D4311yescharacteristic
256C2×C4⋊C4C22⋊D4311yescharacteristic
257C2×C4⋊C4C22⋊D4311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—432no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—861no—
263C2×C42—21no—
264#107—22no—
265#107—862no—
266#106—22no—
267#106—862no—
268#103—22no—
269#103—22no—
270#103—862no—
271#103—862no—
272C22⋊C8—21no—
273C22⋊C8—432no—
274C22⋊C8—861no—
275C22⋊C8C22⋊D4312yes—
276#95—862no—
277#95—862no—
278#95—862no—
279#95—861no—
280#95—861no—
281#95—861no—
282#95—861no—
283C24D4×D4311yescharacteristic
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×Q8—861no—
288C2×Q8—861no—
289C2×Q8—1722no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—862no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—1721no—
299C22×C4D4×D4311yescharacteristic
300C22×C4D4×D4311yescharacteristic
301C22×C4#1062190011yescharacteristic
302C22×C4C2×C22⋊D4311yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304C22×C4C2×C22⋊D4311yescharacteristic
305M16—42no—
306M16—1722no—
307C2×C8—22no—
308C2×C8—862no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—3442no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—1722no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C22⋊C4—1722no—
330C42—41no—
331C42—41no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23#1306329311yescharacteristic
336C23#1306329711yescharacteristic
337C23#1306332111yescharacteristic
338Q8—42no—
339Q8—81no—
340Q8—3441no—
341Q8—1722no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—1722no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1722no—
365C2×C4—1722no—
366C2×C4#1306329311yescharacteristic
367C2×C4#1306329411yescharacteristic
368C2×C4#1306329611yescharacteristic
369C2×C4#1306329711yescharacteristic
370C8—42no—
371C8—1722no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—82no—
381C22#1458280711yescharacteristic
382C22#1458308812yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—3442no—
392C4—3441no—
393C4—3441no—
394C4—6881no—
395C2—22no—
396C2—41no—
397C2—41no—
398C2#1913565211yescharacteristic
399C2#1913565311yescharacteristic
400C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3095C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#3095D43
hypocenterC43#9985
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
233. C43#9985semidirect

Maximal subgroups

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

subgroupindex
#191445432
#191426302
#191346722
#191331292
#191331282
#191325042
C43×#30952
#998543