Finite Group Databasebeta

← #24992619

Subgroups — #24992619

Order 11008.

524 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143157C211yesmaximal, characteristic
2#19140364C211yesmaximal, characteristic
3#19133268C211yesmaximal, characteristic, complemented
4#19133266C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic
6#19132453C211yesmaximal, characteristic, complemented
7C43×#1286C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063325C2211yescharacteristic
10C2×#13063305—21no—
11C2×#13063282C2211yescharacteristic
12#14582952C2211yescharacteristic
13#14582924—22no—
14#14582924—22no—
15#14582923C2211yescharacteristic
16#14582922—21no—
17#14582831—21no—
18#14582831C412yes—
19#14582826—21no—
20#14582826C412yes—
21#14582804—21no—
22#14582646—22no—
23#14582644—22no—
24#14582624—21no—
25#14582622—21no—
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C43×#382C2211yescharacteristic
29C22×Dic86—21no—
30C22×C4×D43D411yescharacteristic
31C2×#10621877—21no—
32C2×#10621872—22no—
33M16×D43—42no—
34M16×D43—42no—
35C2×C8×D43—22no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325—21no—
40#13063305—42no—
41#13063305—42no—
42#13063282—21no—
43#13063282—21no—
44#13063282—21no—
45#13063282—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43C2×C412yes—
49C2×Dic43⋊C4C2×C411yescharacteristic
50C2×Dic43⋊C4D411yescharacteristic
51C2×(C2×D43)⋊C4—22no—
52C2×(C2×D43)⋊C4C2×C411yescharacteristic
53C2×(C2×D43)⋊C4D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)D412yes—
58Dic43⋊C8—24no—
59C22⋊(C43⋊C8)—21no—
60C4×C43⋊C8—21no—
61C43⋊#95—22no—
62C43⋊#95—22no—
63C2×M16×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43D412yes—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71#95×C43—21no—
72#95×C43C2×C412yes—
73C23×D43C22⋊C411yescharacteristic
74C22×C4×C43—22no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—22no—
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43D812yes—
87C2×C4×D43SD1612yes—
88C2×Dic86—41no—
89C2×Dic86—41no—
90C2×Dic86—41no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94M16×C43—41no—
95M16×C43—41no—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103C42×C43#4111yescharacteristic
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—44no—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113C4⋊Dic43—44no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116Dic43⋊C4—21no—
117Dic43⋊C4—21no—
118C4×Dic43—21no—
119C4×Dic43—21no—
120#10621877—41no—
121#10621877—41no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—41no—
124#10621872—44no—
125C8×D43—44no—
126C23×C43C2×C22⋊C411yescharacteristic
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43#10212yes—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12311yescharacteristic
143C2×C4×C43C2×D811yescharacteristic
144C2×C4×C43C2×SD1611yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43#10212yes—
157C4×D43—22no—
158C4×D43—22no—
159C4×D43—22no—
160C4×D43—22no—
161Dic86—81no—
162Dic86—81no—
163Dic86—81no—
164Dic86—81no—
165C8×C43—42no—
166C8×C43—81no—
167C43⋊C8—42no—
168C43⋊C8—81no—
169#9195—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43C2×#10211yescharacteristic
174C22×C43#41711yescharacteristic
175C2×D43—22no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—42no—
179C2×D43—81no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—82no—
185C4×C43#44711yescharacteristic
186C4×C43#44811yescharacteristic
187C4×C43#48011yescharacteristic
188C4×C43#48111yescharacteristic
189Dic43—22no—
190Dic43—41no—
191Dic43—41no—
192Dic43—82no—
193#2905—431no—
194#2621—431no—
195#1546—431no—
196#1546—431no—
197#1458—431no—
198#1286—431no—
199#1286D4311yescharacteristic, complemented
200C2×C43—21no—
201C2×C43—21no—
202C2×C43#187411yescharacteristic
203C2×C43#190911yescharacteristic
204C2×C43#191511yescharacteristic
205D43—42no—
206C22×M16—861no—
207C2×C4⋊Q8—431no—
208C2×C22⋊Q8—861no—
209C2×#117—431no—
210#431—431no—
211#431C2×D4311yescharacteristic
212#424—862no—
213#424—862no—
214#423—431no—
215#423—861no—
216#423C2×D4311yescharacteristic
217#398—432no—
218#398—861no—
219#397—432no—
220#397—861no—
221#391—861no—
222#382C2×D4311yescharacteristic
223#332—862no—
224#332—862no—
225#324—861no—
226#323—861no—
227C43#919511yescharacteristic, complemented, Sylow
228C22×Q8—861no—
229C23×C4—431no—
230C2×M16—21no—
231C2×M16—862no—
232C2×M16—861no—
233C2×M16—1722no—
234C2×M16—1722no—
235C22×C8—862no—
236C4⋊Q8—861no—
237C4⋊Q8—861no—
238C4⋊Q8—861no—
239C4⋊Q8—861no—
240C22⋊Q8—1722no—
241C22⋊Q8—1722no—
242#117—861no—
243#117—861no—
244#117—861no—
245#117—861no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—432no—
250C2×C4⋊C4—862no—
251C2×C4⋊C4—861no—
252C2×C22⋊C4—431no—
253C2×C22⋊C4—431no—
254C2×C22⋊C4—862no—
255C2×C42—431no—
256C2×C42C22×D4311yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—432no—
260C4⋊C8—864no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263C4⋊C8D17212yes—
264C22⋊C8—21no—
265C22⋊C8—861no—
266C4×C8—21no—
267C4×C8—861no—
268#95—21no—
269#95—862no—
270#95—862no—
271#95C4×D4312yes—
272C24—431no—
273C2×Q8—1721no—
274C2×Q8—1721no—
275C2×Q8—1721no—
276C2×Q8—1721no—
277C2×Q8—1721no—
278C2×Q8—1721no—
279C22×C4—22no—
280C22×C4—431no—
281C22×C4—432no—
282C22×C4—432no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—862no—
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4D4×D4311yescharacteristic
293M16—41no—
294M16—41no—
295M16—1724no—
296M16—1721no—
297M16—1721no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—862no—
301C2×C8—1724no—
302C2×C8—1721no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—862no—
310C4⋊C4—862no—
311C4⋊C4—1724no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—1724no—
319C42—861no—
320C42—861no—
321C42C2×D17211yescharacteristic
322C42#1062189811yescharacteristic
323C42D4×D4311yescharacteristic
324C42#1062190211yescharacteristic
325C23—432no—
326C23—861no—
327C23—861no—
328C23—1721no—
329C23—1721no—
330C23C22⋊C4×D4311yescharacteristic
331Q8—3441no—
332Q8—3441no—
333Q8—3441no—
334Q8—3441no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—432no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4#1306328711yescharacteristic
355C2×C4C4×D17211yescharacteristic
356C2×C4#1306329511yescharacteristic
357C2×C4#1306329811yescharacteristic
358C2×C4#1306330011yescharacteristic
359C2×C4#1306331011yescharacteristic
360C2×C4D8×D4311yescharacteristic
361C2×C4SD16×D4311yescharacteristic
362C2×C4#1306335211yescharacteristic
363C2×C4#1306335711yescharacteristic
364C8—42no—
365C8—81no—
366C8—3441no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—862no—
371C22—3441no—
372C22—1722no—
373C22—1721no—
374C22—1721no—
375C22#1458277711yescharacteristic
376C22#102×D4311yescharacteristic
377C22#1458289911yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—862no—
384C4—3442no—
385C4—1721no—
386C4—1721no—
387C4#1458303411yescharacteristic
388C4#1458303911yescharacteristic
389C4#1458321411yescharacteristic
390C4#1458321911yescharacteristic
391C2—21no—
392C2—21no—
393C2—1722no—
394C2#1913491111yescharacteristic
395C2#1913511611yescharacteristic
396C2#1913514611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1286C2
socleC22×C43#386
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1286D43
hypocenterC43#9195
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
3. #19133268C2semidirect
4. #19133266C2semidirect
6. #19132453C2semidirect
7. C43×#1286C2semidirect
199. #1286D43semidirect
227. C43#9195semidirect

Maximal subgroups

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

subgroupindex
#191431572
#191403642
#191332682
#191332662
#191329072
#191324532
C43×#12862
#919543