Finite Group Databasebeta

← #24994553

Subgroups — #24994553

Order 11008.

544 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143622C211yesmaximal, characteristic
2#19138897C211yesmaximal, characteristic
3#19134675C211yesmaximal, characteristic, complemented
4#19132931C211yesmaximal, characteristic
5#19132502C211yesmaximal, characteristic, complemented
6#19132500C211yesmaximal, characteristic, complemented
7C43×#1821C211yesmaximal, characteristic, complemented
8C2×#13063308C412yes—
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582973—22no—
11#14582968—22no—
12#14582953—21no—
13#14582863C2211yescharacteristic
14#14582863C2211yescharacteristic
15C22⋊C8×D43—21no—
16#14582830—21no—
17#14582825—21no—
18#14582795—21no—
19#14582762C412yes—
20#14582759C2211yescharacteristic
21#14582756—21no—
22#14582668—22no—
23#14582624—21no—
24#14582622—21no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#407C2211yescharacteristic
27C43×#407C2211yescharacteristic
28C43×#343—22no—
29C22×C22⋊D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621877—21no—
32C2×#10621877D412yes—
33C2×C8×D43—22no—
34#13063308—44no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C2×C4⋊Dic43—21no—
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4D411yescharacteristic
42C2×C22⋊Dic43C2×C411yescharacteristic
43C2×C22⋊Dic43C2×C412yes—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52(C2×D43)⋊C8—22no—
53#13063235—22no—
54C43⋊#95—21no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C23×C4×C43C2×C412yes—
58C23×C4×C43C2311yescharacteristic
59C2×M16×C43—21no—
60C2×M16×C43D412yes—
61C2×C4⋊C4×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—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71C24×C43C22×C411yescharacteristic
72C23×D43C22⋊C411yescharacteristic
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—22no—
76C22×C4×C43—42no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C2×C22⋊D43—21no—
86C2×C22⋊D43—21no—
87C2×C22⋊D43—22no—
88C2×C22⋊D43—41no—
89C22×Dic43—22no—
90C22×Dic43C22⋊C411yescharacteristic
91C22×Dic43C22⋊C411yescharacteristic
92C22×Dic43C22⋊C411yescharacteristic
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—42no—
96M16×C43—42no—
97M16×C43—42no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C22⋊Dic43—21no—
105C22⋊Dic43—21no—
106C22⋊Dic43—42no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—44no—
110C4⋊Dic43—42no—
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4—44no—
114C4×Dic43—21no—
115C4×Dic43—21no—
116#10621877—42no—
117#10621877—42no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—41no—
120C8×D43—82no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43C2×C22⋊C411yescharacteristic
126C23×C43C4×D411yescharacteristic
127C23×C43C4×D411yescharacteristic
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43#10012yes—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—82no—
143C2×C4×C43—82no—
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12311yescharacteristic
148C22⋊D43—42no—
149C22⋊D43—42no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C4×D43—42no—
161C4×D43—81no—
162C8×C43—42no—
163C8×C43—81no—
164C43⋊C8—42no—
165C43⋊C8—81no—
166#9507—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43#38611yescharacteristic
178C22×C43C2×#10011yescharacteristic
179C22×C43#41311yescharacteristic
180C2×D43—22no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—42no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—82no—
189C4×C43#45812yes—
190Dic43—41no—
191Dic43—41no—
192Dic43—41no—
193Dic43—82no—
194#2973—431no—
195#2486—431no—
196#1821—431no—
197#1821D4311yescharacteristic, complemented
198#1465—431no—
199#1305—431no—
200#1305—431no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—41no—
204C2×C43—41no—
205C2×C43#189011yescharacteristic
206C2×C43#190011yescharacteristic
207C2×C43#191511yescharacteristic
208D43—42no—
209C2×#123—432no—
210C2×C4×D4—431no—
211C22×C4⋊C4C2×D4311yescharacteristic
212#435—862no—
213#435—862no—
214#432—861no—
215#407—431no—
216#407—431no—
217#407C2×D4311yescharacteristic
218#407C2×D4311yescharacteristic
219C2×C22⋊C8—861no—
220#398—861no—
221#397—861no—
222#389—861no—
223#381—432no—
224#380—431no—
225#380—861no—
226#343—22no—
227#343—862no—
228#324—861no—
229#323—861no—
230C43#950711yescharacteristic, complemented, Sylow
231C22×D4—431no—
232C23×C4—431no—
233C23×C4C4×D4312yes—
234C23×C4C22×D4311yescharacteristic
235C2×M16—21no—
236C2×M16—432no—
237C2×M16—861no—
238C2×M16C22⋊D4312yes—
239C22×C8—862no—
240#123—1724no—
241C4×D4—861no—
242C4×D4—861no—
243C4×D4—861no—
244C4×D4—861no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—862no—
253C2×C4⋊C4—861no—
254C2×C22⋊C4—431no—
255C2×C22⋊C4—431no—
256C2×C22⋊C4—432no—
257C2×C22⋊C4—862no—
258C2×C42—431no—
259C4⋊C8—862no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—862no—
265C22⋊C8—861no—
266C22⋊C8—861no—
267C22⋊C8—861no—
268C22⋊C8—861no—
269#97—862no—
270#95—862no—
271#95—862no—
272#95—861no—
273C24—431no—
274C24C2×C4×D4311yescharacteristic
275C2×D4—862no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—1721no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—431no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—862no—
291C22×C4—1722no—
292C22×C4#1062189811yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4#1062190011yescharacteristic
297C22×C4C2×C22⋊D4311yescharacteristic
298M16—42no—
299M16—42no—
300M16—1722no—
301M16—1722no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—862no—
305C2×C8—3442no—
306C2×C8—1721no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1722no—
314C4⋊C4—1724no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—1724no—
320C22⋊C4—1722no—
321C42—861no—
322C42—861no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—432no—
328C23—861no—
329C23—861no—
330C23—1721no—
331C23—1721no—
332C23C22⋊C4×D4311yescharacteristic
333C23(C22⋊D43)⋊C411yescharacteristic
334C23C4×C22⋊D4311yescharacteristic
335D4—1722no—
336D4—1722no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—3441no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4#1306329311yescharacteristic
361C2×C4#1306329611yescharacteristic
362C2×C4#1306329811yescharacteristic
363C2×C4#1306330711yescharacteristic
364C8—42no—
365C8—81no—
366C8—3441no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—862no—
379C22—3441no—
380C22—1722no—
381C22—1721no—
382C22—1721no—
383C22#1458277511yescharacteristic
384C22#100×D4311yescharacteristic
385C22#1458288011yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—3442no—
391C4—1721no—
392C4—1721no—
393C4—1721no—
394C4#1458308812yes—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—1722no—
400C2#1913500511yescharacteristic
401C2#1913505511yescharacteristic
402C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1821C2
socleC22×C43#386
prime radicalC22×C22⋊D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1821D43
hypocenterC43#9507
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #19134675C2semidirect
5. #19132502C2semidirect
6. #19132500C2semidirect
7. C43×#1821C2semidirect
197. #1821D43semidirect
230. C43#9507semidirect

Maximal subgroups

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

subgroupindex
#191436222
#191388972
#191346752
#191329312
#191325022
#191325002
C43×#18212
#950743