Finite Group Databasebeta

← #24991660

Subgroups — #24991660

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582826C211yesmaximal, characteristic
2#19137192C211yesmaximal, characteristic
3#19134682C211yesmaximal, characteristic, complemented
4#19134679C211yesmaximal, characteristic, complemented
5C2×#14582622C211yesmaximal, characteristic
6#19132474C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic43C2211yescharacteristic
9C22×(C2×D43)⋊C4—21no—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582826—22no—
13#14582826C414yescomplemented
14#14582791—22no—
15#14582789—22no—
16#14582759C2211yescharacteristic
17#14582754—21no—
18C22⋊C4×Dic43—21no—
19C2×C43⋊#95—21no—
20#14582662—22no—
21#14582661—22no—
22#14582622—22no—
23C2×C22⋊C8×C43C2211yescharacteristic
24C43×#380C2211yescharacteristic
25C2×#95×C43C2211yescharacteristic
26C24×D43D411yescharacteristic
27C23×Dic43—21no—
28C23×Dic43D411yescharacteristic
29C22×C43⋊C8—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C412yes—
36C2×C4⋊Dic43D412yes—
37C2×C22⋊Dic43—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—24no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—42no—
46C2×(C2×D43)⋊C4—42no—
47C2×(C2×D43)⋊C4C2×C412yes—
48C2×(C2×D43)⋊C4D412yes—
49C2×C4×Dic43—22no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—22no—
53C43⋊#95—21no—
54C43⋊#95—24no—
55C23×C4×C43—21no—
56C23×C4×C43C2311yescharacteristic
57C22×C8×C43—21no—
58C2×C4⋊C4×C43D412yes—
59C2×C22⋊C4×C43—21no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64#95×C43C2×C412yes—
65C24×C43C2×D411yescharacteristic
66C23×D43—21no—
67C23×D43—21no—
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—21no—
72C23×D43—42no—
73C23×D43—42no—
74C23×D43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×Dic43—22no—
89C22×Dic43—21no—
90C22×Dic43—22no—
91C22×Dic43—21no—
92C22×Dic43—42no—
93C22×Dic43—41no—
94C22×Dic43—41no—
95C22×Dic43—41no—
96C22×Dic43—41no—
97C22×Dic43—41no—
98C22×Dic43—41no—
99C22×Dic43C22⋊C412yes—
100C2×C8×C43—42no—
101C2×C8×C43—41no—
102C4⋊C4×C43—42no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—48no—
112(C2×D43)⋊C4—82no—
113(C2×D43)⋊C4—82no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118C4⋊Dic43—42no—
119C4×Dic43—82no—
120C2×C43⋊C8—42no—
121C2×C43⋊C8—41no—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43C2×C22⋊C411yescharacteristic
125C23×C43#12011yescharacteristic
126C23×C43#12311yescharacteristic
127C23×C43#13511yescharacteristic
128C23×C43#13511yescharacteristic
129C23×C43AGL(1,ℤ/8)11yescharacteristic
130C23×C43AGL(1,ℤ/8)11yescharacteristic
131C22×D43—22no—
132C22×D43—22no—
133C22×D43—22no—
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—44no—
137C22×D43—44no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—42no—
141C22×D43—42no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—81no—
145C22×D43—81no—
146C22×D43—82no—
147C22×D43—82no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—82no—
161C2×C4×C43—82no—
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×Dic43—22no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178C2×Dic43—81no—
179C2×Dic43—81no—
180C8×C43—81no—
181C43⋊C8—81no—
182#9028—431nomaximal, Sylow
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43#38611yescharacteristic
192C22×C43#41611yescharacteristic
193C22×C43#41811yescharacteristic
194C22×C43#44911yescharacteristic
195C22×C43#44911yescharacteristic
196C22×C43#45512yes—
197C22×C43#45812yes—
198C22×C43#48211yescharacteristic
199C22×C43#48211yescharacteristic
200C2×D43—44no—
201C2×D43—42no—
202C2×D43—42no—
203C2×D43—42no—
204C2×D43—82no—
205C2×D43—82no—
206C2×D43—82no—
207C2×D43—82no—
208C2×D43—82no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—82no—
214C4×C43—82no—
215Dic43—42no—
216Dic43—82no—
217Dic43—82no—
218C2×#397—431no—
219#2312—431no—
220#1823—431no—
221#1823—431no—
222C2×#323—431no—
223#1294—431no—
224#1294D4311yescharacteristic, complemented
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43#161212yes—
230C2×C43#161212yes—
231C2×C43#187511yescharacteristic
232C2×C43#188511yescharacteristic
233C2×C43#189011yescharacteristic
234D43—82no—
235C22×C4⋊C4—431no—
236C22×C22⋊C4—431no—
237C22×C22⋊C4—861no—
238C2×C22⋊C8—431no—
239C2×C22⋊C8C2×D4311yescharacteristic
240#397—434no—
241#397—862no—
242#388—862no—
243#388—862no—
244#380—431no—
245#380C2×D4311yescharacteristic
246#379—861no—
247C4×C22⋊C4—861no—
248C2×#95—861no—
249C2×#95C2×D4311yescharacteristic
250#340—862no—
251#340—862no—
252#323—862no—
253C43#902811yescharacteristic, complemented, Sylow
254C25—431no—
255C23×C4—21no—
256C23×C4—431no—
257C23×C4—861no—
258C23×C4C22×D4311yescharacteristic
259C22×C8—21no—
260C22×C8—861no—
261C2×C4⋊C4—432no—
262C2×C4⋊C4—432no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4D17212yes—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—432no—
271C2×C22⋊C4—432no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—864no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—1722no—
281C2×C22⋊C4—1722no—
282C2×C42—862no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—861no—
286C22⋊C8—861no—
287#95—21no—
288#95—21no—
289#95—864no—
290#95—862no—
291#95—861no—
292#95C4×D4312yes—
293C24—432no—
294C24—861no—
295C24—861no—
296C24—861no—
297C24—861no—
298C24—861no—
299C24—861no—
300C24—1722no—
301C24—1722no—
302C24D4×D4311yescharacteristic
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—432no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4—1721no—
318C22×C4—1721no—
319C22×C4—1721no—
320C22×C4—1721no—
321C22×C4—1722no—
322C22×C4C2×C4×D4311yescharacteristic
323C22×C4C2×D17211yescharacteristic
324C22×C4#1062189811yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4#1062190211yescharacteristic
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—1722no—
331C2×C8—1721no—
332C4⋊C4—42no—
333C4⋊C4—862no—
334C4⋊C4—862no—
335C4⋊C4—1722no—
336C4⋊C4—1721no—
337C4⋊C4—1721no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—862no—
341C22⋊C4—862no—
342C22⋊C4—862no—
343C22⋊C4—862no—
344C22⋊C4—3442no—
345C22⋊C4—3442no—
346C22⋊C4—1728no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—3442no—
350C23—22no—
351C23—22no—
352C23—862no—
353C23—862no—
354C23—862no—
355C23—3442no—
356C23—3442no—
357C23—3441no—
358C23—3441no—
359C23—1724no—
360C23—1724no—
361C23—1722no—
362C23—1722no—
363C23—1721no—
364C23—1721no—
365C23—1722no—
366C23—1722no—
367C23—1721no—
368C23—1721no—
369C23C22⋊C4×D4311yescharacteristic
370C23#1306329511yescharacteristic
371C23#1306331011yescharacteristic
372C23#1306334611yescharacteristic
373C23#1306334811yescharacteristic
374C23#1306334911yescharacteristic
375C23#1306335211yescharacteristic
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—862no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—3441no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1722no—
401C2×C4—1722no—
402C2×C4—1722no—
403C2×C4—1722no—
404C2×C4#1306328711yescharacteristic
405C2×C4C4×D17211yescharacteristic
406C2×C4#1306329811yescharacteristic
407C2×C4#1306330011yescharacteristic
408C8—81no—
409C8—3441no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—3442no—
419C22—3442no—
420C22—3442no—
421C22—3442no—
422C22—3442no—
423C22—1724no—
424C22—1722no—
425C22—1722no—
426C22—1722no—
427C22#1458277711yescharacteristic
428C22#1458289411yescharacteristic
429C22#1458290211yescharacteristic
430C22#1458304511yescharacteristic
431C22#1458304711yescharacteristic
432C22#1458307812yes—
433C22#1458309012yes—
434C22#1458322511yescharacteristic
435C22#1458322611yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—82no—
442C4—3442no—
443C4—3442no—
444C4—1722no—
445C2—21no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—3442no—
450C2#1913361012yes—
451C2#1913361212yes—
452C2#1913491611yescharacteristic
453C2#1913498211yescharacteristic
454C2#1913500711yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43#120
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9028
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
3. #19134682C2semidirect
4. #19134679C2semidirect
6. #19132474C2semidirect
7. C43×#1294C2semidirect
13. #14582826C4semidirect
224. #1294D43semidirect
253. C43#9028semidirect

Maximal subgroups

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

subgroupindex
C2×#145828262
#191371922
#191346822
#191346792
C2×#145826222
#191324742
C43×#12942
#902843