Finite Group Databasebeta

← #25006933

Subgroups — #25006933

Order 11008.

470 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 73 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#19137880C211yesmaximal, characteristic
2#19134382C211yesmaximal, characteristic
3#19132910C211yesmaximal, characteristic
4#19132617C211yesmaximal, characteristic, complemented
5#19132615C211yesmaximal, characteristic, complemented
6#19132595C211yesmaximal, characteristic, complemented
7C43×#1344C211yesmaximal, characteristic, complemented
8C2×#13063290C411yescharacteristic, complemented
9C2×(C22⋊D43)⋊C4C2211yescharacteristic
10C2×#13063239—21no—
11C22⋊C8×D43—21no—
12#14582840—21no—
13#14582825C411yescharacteristic, complemented
14#14582814—21no—
15#14582812C411yescharacteristic, complemented
16#14582811C2211yescharacteristic
17C22⋊C4×Dic43—21no—
18C22⋊C4×Dic43—21no—
19#14582746—21no—
20#14582744C411yescharacteristic, complemented
21#14582666C2211yescharacteristic
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×C22⋊D43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×C8×D43—41no—
32#13063290—41no—
33#13063290—41no—
34(C22⋊D43)⋊C4—41no—
35(C22⋊D43)⋊C4—41no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4D411yescharacteristic
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4C2×C411yescharacteristic
43C2×C4×Dic43—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—41no—
46C2×C4×Dic43C2×C411yescharacteristic
47#13063239—24no—
48C22⋊(C43⋊C8)—21no—
49(C2×D43)⋊C8—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95C2×C411yescharacteristic
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—41no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—41no—
79C22×Dic43—42no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—42no—
86C2×Dic86—41no—
87C2×Dic86—42no—
88C2×C8×C43—41no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊Dic43—22no—
96C22⋊Dic43—42no—
97C22⋊Dic43—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101Dic43⋊C4—41no—
102Dic43⋊C4—42no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—42no—
106C4×Dic43—41no—
107C4×Dic43—41no—
108C4×Dic43—82no—
109C2×C43⋊C8—41no—
110C8×D43—82no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43#13511yescharacteristic
117C23×C43#13511yescharacteristic
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43#10412yes—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—42no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—42no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155C2×Dic43#9911yescharacteristic
156C2×Dic43#9911yescharacteristic
157C4×D43—42no—
158C4×D43—81no—
159Dic86—42no—
160Dic86—42no—
161C8×C43—81no—
162C43⋊C8—81no—
163#11728—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—81no—
173C22×C43C2×#9911yescharacteristic
174C22×C43#41611yescharacteristic
175C22×C43C2×#10411yescharacteristic
176C2×D43—22no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—42no—
180C2×D43—81no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—81no—
184C4×C43—82no—
185C4×C43—81no—
186Dic43—21no—
187Dic43—42no—
188Dic43—41no—
189Dic43—41no—
190Dic43—81no—
191Dic43—82no—
192Dic43#35412yes—
193#2398—431no—
194C4×#99—431no—
195#1459—431no—
196#1351—431no—
197#1351—431no—
198#1344—431no—
199#1344D4311yescharacteristic, complemented
200C2×C43—21no—
201C2×C43—21no—
202C2×C43—41no—
203C2×C43—41no—
204C2×C43#150111yescharacteristic
205C2×C43#212011yescharacteristic
206C2×C43C2×#35411yescharacteristic
207D43—42no—
208C2×C4×Q8—431no—
209C2×C4×D4—431no—
210C2×#99—861no—
211C2×C22⋊C8—861no—
212#400—861no—
213#397—431no—
214#397C2×D4311yescharacteristic
215#394—861no—
216#393—431no—
217#393—431no—
218C4×C22⋊C4—861no—
219C4×C22⋊C4—861no—
220C4×C22⋊C4—861no—
221#376—431no—
222#342—431no—
223#342C2×D4311yescharacteristic
224#324—861no—
225#323—431no—
226#323C2×D4311yescharacteristic
227C43#1172811yescharacteristic, complemented, Sylow
228C22×Q8—431no—
229C22×D4—431no—
230C23×C4—431no—
231C23×C4—431no—
232C22×C8—1721no—
233C4×Q8—1721no—
234C4×Q8—1721no—
235C4×D4—1721no—
236C4×D4—1721no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4C4×D4311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—431no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4C22×D4311yescharacteristic
248C2×C42—431no—
249C2×C42—861no—
250C2×C42—861no—
251C2×C42—1721no—
252#99—864no—
253C22⋊C8—21no—
254C22⋊C8—861no—
255C22⋊C8—1721no—
256#95—21no—
257#95—431no—
258#95—861no—
259#95—861no—
260#95—861no—
261#95—861no—
262#95—1721no—
263#95C4×D4311yescharacteristic
264C24—431no—
265C24D4×D4311yescharacteristic
266C2×Q8—1721no—
267C2×Q8—1722no—
268C2×D4—862no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—1721no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—1722no—
285C22×C4—1722no—
286C22×C4—1721no—
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C2×C8—41no—
290C2×C8—3442no—
291C2×C8—1721no—
292C4⋊C4—41no—
293C4⋊C4—1721no—
294C4⋊C4—1722no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—862no—
301C22⋊C4—1721no—
302C22⋊C4—1722no—
303C22⋊C4—1722no—
304C22⋊C4—1722no—
305C22⋊C4—1721no—
306C42—861no—
307C42—861no—
308C42—3442no—
309C42—1721no—
310C42—1721no—
311C42—1722no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—432no—
317C23—861no—
318C23—861no—
319C23—1721no—
320C23—1721no—
321C23C22⋊C4×D4311yescharacteristic
322C23#1306334411yescharacteristic
323C23#1306334611yescharacteristic
324Q8—1722no—
325Q8—1722no—
326D4—1722no—
327D4—1722no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—431no—
342C2×C4—431no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1721no—
356C2×C4—1722no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C8—81no—
363C8—3441no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—862no—
374C22—3441no—
375C22—1722no—
376C22—1721no—
377C22—1721no—
378C22#99×D4311yescharacteristic
379C22#1458289211yescharacteristic
380C22#104×D4311yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—82no—
385C4—81no—
386C4—432no—
387C4—861no—
388C4—3441no—
389C4—3442no—
390C4—1721no—
391C4—1722no—
392C4—1721no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—1722no—
398C2#1913308311yescharacteristic
399C2#1913623511yescharacteristic
400C2#354×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1344C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1344D43
hypocenterC43#11728
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #19132617C2semidirect
5. #19132615C2semidirect
6. #19132595C2semidirect
7. C43×#1344C2semidirect
8. C2×#13063290C4semidirect
13. #14582825C4semidirect
15. #14582812C4semidirect
20. #14582744C4semidirect
199. #1344D43semidirect
227. C43#11728semidirect

Maximal subgroups

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

subgroupindex
#191378802
#191343822
#191329102
#191326172
#191326152
#191325952
C43×#13442
#1172843