Finite Group Databasebeta

← #24994563

Subgroups — #24994563

Order 11008.

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

normal subgroups only

This group has 524 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#19138906C211yesmaximal, characteristic
3#19134675C211yesmaximal, characteristic, complemented
4#19132931C211yesmaximal, characteristic
5#19132502C211yesmaximal, characteristic, complemented
6#19132500C211yesmaximal, characteristic, complemented
7C43×#1821C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9#14582973—22no—
10#14582968—22no—
11#14582953—21no—
12#14582863C2211yescharacteristic
13#14582863C2211yescharacteristic
14C22⋊C8×D43—21no—
15#14582837—21no—
16#14582834—21no—
17#14582795—21no—
18#14582778C412yes—
19#14582772C412yes—
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—
34C4×C22⋊D43—21no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C2×C4⋊Dic43—21no—
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4D411yescharacteristic
41C2×C22⋊Dic43C2×C411yescharacteristic
42C2×C22⋊Dic43C2×C412yes—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—22no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51(C2×D43)⋊C8—22no—
52#13063235—22no—
53C43⋊#95—21no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C23×C4×C43C2×C412yes—
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59C2×M16×C43D412yes—
60C2×C4⋊C4×C43—21no—
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—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C24×C43C22×C411yescharacteristic
71C23×D43C22⋊C411yescharacteristic
72C22×C4×C43—22no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—42no—
76C22×C4×C43—82no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C2×C22⋊D43—21no—
84C2×C22⋊D43—21no—
85C2×C22⋊D43—22no—
86C2×C22⋊D43—41no—
87C22×Dic43—22no—
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—42no—
94M16×C43—42no—
95M16×C43—42no—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊Dic43—21no—
103C22⋊Dic43—21no—
104C22⋊Dic43—42no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—82no—
108C4⋊Dic43—42no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—82no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114#10621877—42no—
115#10621877—42no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—41no—
118C8×D43—82no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43C4×D411yescharacteristic
125C23×C43C4×D411yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43#10112yes—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—82no—
141C2×C4×C43—82no—
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C22⋊D43—42no—
147C22⋊D43—42no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C4×D43—42no—
159C4×D43—81no—
160C8×C43—42no—
161C8×C43—81no—
162C43⋊C8—42no—
163C43⋊C8—81no—
164#9509—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43#38611yescharacteristic
176C22×C43C2×#10111yescharacteristic
177C22×C43#41311yescharacteristic
178C2×D43—22no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—42no—
182C2×D43—81no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—82no—
187C4×C43#45812yes—
188Dic43—41no—
189Dic43—41no—
190Dic43—41no—
191Dic43—82no—
192#2973—431no—
193#2487—431no—
194#1821—431no—
195#1821D4311yescharacteristic, complemented
196#1465—431no—
197#1305—431no—
198#1305—431no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43—41no—
202C2×C43—41no—
203C2×C43#189011yescharacteristic
204C2×C43#190111yescharacteristic
205C2×C43#191411yescharacteristic
206D43—42no—
207C2×C4×D4—431no—
208C22×C4⋊C4C2×D4311yescharacteristic
209#435—862no—
210#435—862no—
211#432—861no—
212#407—431no—
213#407—431no—
214#407C2×D4311yescharacteristic
215#407C2×D4311yescharacteristic
216C2×C22⋊C8—861no—
217#400—861no—
218#399—861no—
219#389—861no—
220#386—432no—
221#385—432no—
222#380—431no—
223#380—861no—
224#343—22no—
225#343—862no—
226#324—861no—
227#323—861no—
228C43#950911yescharacteristic, complemented, Sylow
229C22×D4—431no—
230C23×C4—431no—
231C23×C4C4×D4312yes—
232C23×C4C22×D4311yescharacteristic
233C2×M16—21no—
234C2×M16—432no—
235C2×M16—861no—
236C2×M16C22⋊D4312yes—
237C22×C8—862no—
238C4×D4—861no—
239C4×D4—861no—
240C4×D4—861no—
241C4×D4—861no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—862no—
250C2×C4⋊C4—861no—
251C2×C22⋊C4—431no—
252C2×C22⋊C4—431no—
253C2×C22⋊C4—432no—
254C2×C22⋊C4—862no—
255C2×C42—431no—
256C4⋊C8—862no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—862no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264C22⋊C8—861no—
265C22⋊C8—861no—
266#97—862no—
267#95—862no—
268#95—862no—
269#95—861no—
270C24—431no—
271C24C2×C4×D4311yescharacteristic
272C2×D4—862no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—1721no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—82no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—862no—
287C22×C4—1722no—
288C22×C4#1062189811yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4#1062190011yescharacteristic
293C22×C4C2×C22⋊D4311yescharacteristic
294M16—42no—
295M16—42no—
296M16—1722no—
297M16—1722no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—862no—
301C2×C8—3442no—
302C2×C8—1721no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—3442no—
310C4⋊C4—1722no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—3442no—
316C22⋊C4—1722no—
317C42—861no—
318C42—861no—
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—432no—
324C23—861no—
325C23—861no—
326C23—1721no—
327C23—1721no—
328C23C22⋊C4×D4311yescharacteristic
329C23(C22⋊D43)⋊C411yescharacteristic
330C23C4×C22⋊D4311yescharacteristic
331D4—1722no—
332D4—1722no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4#1306329311yescharacteristic
357C2×C4#1306329611yescharacteristic
358C2×C4#1306329811yescharacteristic
359C2×C4#1306330711yescharacteristic
360C8—42no—
361C8—81no—
362C8—3441no—
363C8—1722no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—862no—
375C22—3441no—
376C22—1722no—
377C22—1721no—
378C22—1721no—
379C22#1458277511yescharacteristic
380C22#101×D4311yescharacteristic
381C22#1458288211yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—3442no—
387C4—1721no—
388C4—1721no—
389C4—1721no—
390C4#1458308812yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—1722no—
396C2#1913500511yescharacteristic
397C2#1913506011yescharacteristic
398C2#1913513911yescharacteristic
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#9509
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
195. #1821D43semidirect
228. C43#9509semidirect

Maximal subgroups

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

subgroupindex
#191436222
#191389062
#191346752
#191329312
#191325022
#191325002
C43×#18212
#950943