Finite Group Databasebeta

← #24997259

Subgroups — #24997259

Order 11008.

502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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#19144544C211yesmaximal, characteristic
2#19144539C211yesmaximal, characteristic
3#19142630C211yesmaximal, characteristic
4#19134670C211yesmaximal, characteristic
5#19133127C211yesmaximal, characteristic
6#19132504C211yesmaximal, characteristic
7C43×#1511C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14583241—22no—
11#14583237—22no—
12#14583235—21no—
13#14583232—21no—
14#14583230—21no—
15#14583227—21no—
16#14582941—21no—
17#14582939—21no—
18#14582909—21no—
19#14582908—21no—
20#14582863C2211yescharacteristic
21#14582838—21no—
22#14582837—21no—
23#14582827—22no—
24#14582819—21no—
25#14582818—21no—
26#14582762C2211yescharacteristic
27#14582665—22no—
28#14582635—22no—
29C2×C22⋊Q8×C43C2211yescharacteristic
30C43×#407C2211yescharacteristic
31C43×#381C2211yescharacteristic
32C43×#328—22no—
33C22×Dic86D411yescharacteristic
34C2×#10621877—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063284—21no—
40#13063284—21no—
41#13063284—21no—
42#13063284—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×C4⋊Dic43D411yescharacteristic
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—22no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43D412yes—
51C2×C4×Dic43—21no—
52#13063259—22no—
53#13063258—22no—
54#13063257—22no—
55#13063256—22no—
56#13063250—22no—
57#13063250—22no—
58#13063249—22no—
59#13063249—22no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)D412yes—
62C43⋊#95—22no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C22×Q8×C43D411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C22⋊Q8×C43—21no—
71C22⋊Q8×C43—21no—
72C22⋊Q8×C43—21no—
73C22⋊Q8×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43D411yescharacteristic
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D412yes—
80#95×C43—21no—
81#95×C43—21no—
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—42no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C22×Dic43—22no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
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—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—42no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊Dic43—42no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—82no—
127C4×Dic43—41no—
128C4×Dic43—41no—
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—42no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—42no—
164C2×Dic43—42no—
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—161no—
190Dic43—82no—
191Dic43—81no—
192Dic43—81no—
193Dic43—81no—
194Dic43—81no—
195#3095—431no—
196#3095—431no—
197#2817—431no—
198#1820—431no—
199#1511—431no—
200#1511D4311yescharacteristic
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×#117—431no—
211#485—862no—
212#485—862no—
213#484—861no—
214#484—861no—
215#483—861no—
216#483—861no—
217#428—861no—
218#428—861no—
219#419—861no—
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#381C2×D4311yescharacteristic
230#342—862no—
231#328—22no—
232#328—862no—
233C43#998511yescharacteristic, complemented, Sylow
234C22×Q8—431no—
235C22×Q8D17211yescharacteristic
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—861no—
248#117—861no—
249#117—861no—
250#117—861no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—862no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4D17211yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—432no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—861no—
263C2×C42—861no—
264#107—862no—
265#107—862no—
266#106—862no—
267#106—862no—
268#103—862no—
269#103—862no—
270#103—862no—
271#103—862no—
272C22⋊C8—21no—
273C22⋊C8—432no—
274C22⋊C8—861no—
275C22⋊C8C22⋊D4312yes—
276#95—21no—
277#95—21no—
278#95—862no—
279#95—862no—
280#95—862no—
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—42no—
293C22×C4—41no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—862no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4C2×D17211yescharacteristic
300C22×C4#1062189811yescharacteristic
301C22×C4D4×D4311yescharacteristic
302C22×C4D4×D4311yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4C2×C22⋊D4311yescharacteristic
305M16—42no—
306M16—1722no—
307C2×C8—22no—
308C2×C8—862no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—3442no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—1721no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C22⋊C4—1722no—
330C42—1721no—
331C42—1721no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23#1306329511yescharacteristic
336C23#1306329811yescharacteristic
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—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1722no—
365C2×C4—1722no—
366C2×C4#1306329311yescharacteristic
367C2×C4#1306329511yescharacteristic
368C2×C4#1306329811yescharacteristic
369C2×C4#1306329911yescharacteristic
370C8—42no—
371C8—1722no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—82no—
381C22#1458280811yescharacteristic
382C22#1458309012yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—81no—
388C4—81no—
389C4—161no—
390C4—3442no—
391C4—3441no—
392C4—3441no—
393C4—3441no—
394C4—3441no—
395C2—22no—
396C2—41no—
397C2—41no—
398C2#1913565611yescharacteristic
399C2#1913565711yescharacteristic
400C2#1913572511yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1511C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#1511D43
hypocenterC43#9985
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

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
#191445442
#191445392
#191426302
#191346702
#191331272
#191325042
C43×#15112
#998543