Finite Group Databasebeta

← #24989971

Subgroups — #24989971

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582759C211yesmaximal, characteristic
2#19132818C211yesmaximal, characteristic
3#19132475C214yesmaximal, complemented
4C43×#1779C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic, complemented
6C22×C4⋊Dic43C411yescharacteristic, complemented
7C22×C22⋊Dic43—21no—
8C22×C22⋊Dic43—21no—
9#14582759—21no—
10#14582759—21no—
11#14582759C412yescomplemented
12#14582759C2212yes—
13C2×C43⋊#95—21no—
14C2×C43⋊#95—21no—
15C2×C43⋊#95C2212yes—
16C24×C4×C43C2211yescharacteristic
17C2×C22⋊C8×C43—21no—
18C2×C22⋊C8×C43—21no—
19C2×C22⋊C8×C43C2212yes—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C23×Dic43—22no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—42no—
26C2×C4⋊Dic43—42no—
27C2×C4⋊Dic43C2×C412yes—
28C2×C4⋊Dic43C2×C412yes—
29C2×C22⋊Dic43—24no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—42no—
33C2×C22⋊Dic43—42no—
34C2×C22⋊Dic43—42no—
35C2×C22⋊Dic43—42no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—24no—
39C43⋊#95—42no—
40C25×C43D411yescharacteristic
41C23×C4×C43—24no—
42C23×C4×C43—42no—
43C23×C4×C43—42no—
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C23×C4×C43C2311yescharacteristic
50C22×C8×C43—22no—
51C22⋊C8×C43—24no—
52C22⋊C8×C43—42no—
53C22⋊C8×C43—42no—
54C24×C43—22no—
55C24×C43—22no—
56C24×C43—22no—
57C24×C43—22no—
58C24×C43—41no—
59C24×C43—41no—
60C24×C43C22⋊C411yescharacteristic
61C24×C43C22⋊C411yescharacteristic
62C24×C43D812yes—
63C24×C43SD1612yes—
64C24×C43C2×D411yescharacteristic
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—416no—
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4114yes—
88C22×Dic43—24no—
89C22×Dic43—22no—
90C22×Dic43—22no—
91C22×Dic43—42no—
92C22×Dic43—42no—
93C22×Dic43—42no—
94C22×Dic43—42no—
95C22×Dic43—42no—
96C22×Dic43—42no—
97C22×Dic43—42no—
98C22×Dic43—42no—
99C22×Dic43—42no—
100C22×Dic43—42no—
101C22×Dic43—42no—
102C22×Dic43—42no—
103C2×C8×C43—42no—
104C2×C8×C43—42no—
105C2×C8×C43—42no—
106C22⋊Dic43—48no—
107C22⋊Dic43—44no—
108C22⋊Dic43—42no—
109C22⋊Dic43—42no—
110C4⋊Dic43—42no—
111C4⋊Dic43—42no—
112C4⋊Dic43—42no—
113C4⋊Dic43—42no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—24no—
123C23×C43—24no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—24no—
131C23×C43—24no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—44no—
135C23×C43—44no—
136C23×C43—44no—
137C23×C43—44no—
138C23×C43#9912yes—
139C23×C43#10212yes—
140C23×C43#10212yes—
141C23×C43#10412yes—
142C23×C43C2×C22⋊C411yescharacteristic
143C23×C43#12312yes—
144C23×C43C2×D811yescharacteristic
145C23×C43C2×SD1611yescharacteristic
146C23×C43#13712yes—
147C2×C4×C43—28no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—44no—
158C2×C4×C43—44no—
159C2×C4×C43—44no—
160C2×C4×C43—44no—
161C2×C4×C43—44no—
162C2×C4×C43#9912yes—
163C2×C4×C43#11712yes—
164C2×C4×C43#12312yes—
165C2×Dic43—44no—
166C2×Dic43—44no—
167C2×Dic43—44no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—82no—
175C2×Dic43—82no—
176C2×Dic43—82no—
177C2×Dic43—84no—
178C2×Dic43—84no—
179C2×Dic43—82no—
180C8×C43—82no—
181#8712—431nomaximal, Sylow
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—22no—
192C22×C43—22no—
193C22×C43—22no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—22no—
197C22×C43—22no—
198C22×C43—22no—
199C22×C43—48no—
200C22×C43—48no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43#32714yes—
206C22×C43#38111yescharacteristic
207C22×C43C2×#9911yescharacteristic
208C22×C43C2×#9911yescharacteristic
209C22×C43C2×#10211yescharacteristic
210C22×C43#41911yescharacteristic
211C22×C43C2×#10411yescharacteristic
212C22×C43#42111yescharacteristic
213C22×C43#48012yes—
214C22×C43#48312yes—
215C4×C43—22no—
216C4×C43—22no—
217C4×C43—22no—
218C4×C43—41no—
219Dic43—84no—
220Dic43—82no—
221Dic43—82no—
222C2×#380—431no—
223#1779D4311yescharacteristic
224C22⋊#95—431no—
225#1294—434no—
226C2×C43—22no—
227C2×C43—24no—
228C2×C43—22no—
229C2×C43—42no—
230C2×C43C2×#32711yescharacteristic
231C2×C43#150811yescharacteristic
232C2×C43#151111yescharacteristic
233C2×C43#151911yescharacteristic
234C2×C43#181911yescharacteristic
235C2×C43#182311yescharacteristic
236C2×C43#182611yescharacteristic
237C24×C4C2×D4311yescharacteristic
238C22×C4⋊C4—431no—
239C22×C4⋊C4—431no—
240C22×C22⋊C4—861no—
241C22×C22⋊C4—861no—
242C2×C22⋊C8—21no—
243C2×C22⋊C8—21no—
244C2×C22⋊C8C2×D4312yes—
245#380—432no—
246#380—432no—
247#380—861no—
248#380—861no—
249C2×#95—432no—
250C2×#95—861no—
251C2×#95—861no—
252C43#871211yescharacteristic, complemented, Sylow
253C25D17211yescharacteristic
254C23×C4—24no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—861no—
258C23×C4—861no—
259C23×C4—862no—
260C23×C4C4×D4311yescharacteristic
261C23×C4C4×D4311yescharacteristic
262C23×C4D17211yescharacteristic
263C23×C4C22⋊D4311yescharacteristic
264C23×C4C22⋊D4311yescharacteristic
265C23×C4C22×D4311yescharacteristic
266C22×C8—22no—
267C2×C4⋊C4—432no—
268C2×C4⋊C4—432no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—1722no—
272C2×C4⋊C4—1722no—
273C2×C22⋊C4—864no—
274C2×C22⋊C4—862no—
275C2×C22⋊C4—862no—
276C2×C22⋊C4—1722no—
277C2×C22⋊C4—1722no—
278C2×C22⋊C4—1722no—
279C2×C22⋊C4—1722no—
280C22⋊C8—24no—
281C22⋊C8—42no—
282C22⋊C8—42no—
283#95—862no—
284#95—862no—
285#95—864no—
286#95—1722no—
287C24—22no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—41no—
292C24—41no—
293C24#1062187312yes—
294C24D34412yes—
295C24(C2×D43)⋊C411yescharacteristic
296C24(C2×D43)⋊C411yescharacteristic
297C24C2×D17211yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—416no—
316C22×C4—864no—
317C22×C4—862no—
318C22×C4—862no—
319C22×C4—1722no—
320C22×C4—1722no—
321C22×C4—1722no—
322C22×C4—1722no—
323C22×C4—1722no—
324C22×C4—1722no—
325C22×C4—1722no—
326C22×C4—1722no—
327C22×C4—1722no—
328C22×C4—1722no—
329C22×C4—1722no—
330C22×C4—1722no—
331C22×C4(C2×D43)⋊C411yescharacteristic
332C22×C4(C2×D43)⋊C411yescharacteristic
333C22×C4C2×C4×D4311yescharacteristic
334C22×C4#1062190014yes—
335C22×C4C2×C22⋊D4311yescharacteristic
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C4⋊C4—1722no—
340C4⋊C4—1722no—
341C4⋊C4—1722no—
342C4⋊C4—1722no—
343C22⋊C4—1728no—
344C22⋊C4—1724no—
345C22⋊C4—1722no—
346C22⋊C4—1722no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—24no—
358C23—24no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—24no—
363C23—24no—
364C23—21no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23#1306323912yes—
372C23#1306324712yes—
373C23#1306324712yes—
374C23#1306325112yes—
375C23C2×(C2×D43)⋊C411yescharacteristic
376C23#1306330912yes—
377C23C2×D34411yescharacteristic
378C23C2×#1062187311yescharacteristic
379C23#1306335812yes—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—3442no—
396C2×C4—3442no—
397C2×C4—3442no—
398C2×C4—3444no—
399C2×C4—3444no—
400C2×C4—3442no—
401C2×C4—1724no—
402C2×C4—1724no—
403C2×C4—1724no—
404C2×C4—1722no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4#1306323912yes—
411C2×C4#1306328112yes—
412C2×C4#1306330612yes—
413C8—82no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—48no—
432C22—48no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22#1458263414yes—
438C22#1458276011yescharacteristic
439C22C2×#1306323911yescharacteristic
440C22C2×#1306323911yescharacteristic
441C22C2×#1306324711yescharacteristic
442C22#1458290911yescharacteristic
443C22C2×#1306325111yescharacteristic
444C22#1458291511yescharacteristic
445C22#1458321312yes—
446C22#1458323012yes—
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—3444no—
452C4—3442no—
453C4—3442no—
454C2—22no—
455C2—24no—
456C2—22no—
457C2—42no—
458C2C2×#1458263411yescharacteristic
459C2#1913311611yescharacteristic
460C2#1913312911yescharacteristic
461C2#1913316411yescharacteristic
462C2#1913466711yescharacteristic
463C2#1913468211yescharacteristic
464C2#1913469211yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1779C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43D4
cosocleC23×C4×C43C23
hypercenter#1779D43
hypocenterC43#8712
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. #19132475C2semidirect
5. C22×C4⋊Dic43C4semidirect
6. C22×C4⋊Dic43C4semidirect
11. #14582759C4semidirect
252. C43#8712semidirect

Maximal subgroups

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

subgroupindex
C2×#145827592
#191328182
#191324752
C43×#17792
#871243