Finite Group Databasebeta

← #24996845

Subgroups — #24996845

Order 11008.

672 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#14583218C211yesmaximal, characteristic
2#19140340C211yesmaximal, characteristic
3C2×#14582839C211yesmaximal, characteristic, complemented
4#19134683C211yesmaximal, characteristic, complemented
5C2×#14582632C211yesmaximal, characteristic
6C2×#14582624C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063299C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4C2211yescharacteristic
12#14583218—22no—
13#14583218—22no—
14C2×#13063257—21no—
15C2×#13063247—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582839—22no—
18#14582839—22no—
19#14582831—21no—
20#14582821—22no—
21#14582817—21no—
22#14582776—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25#14582661—22no—
26#14582632—22no—
27#14582624—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C23×Dic43D411yescharacteristic
35C23×Dic43D411yescharacteristic
36C22×C43⋊C8—21no—
37#13063309—42no—
38#13063309—42no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43D411yescharacteristic
50C2×C4⋊Dic43D412yes—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—21no—
59C2×(C2×D43)⋊C4—22no—
60#13063257—24no—
61#13063247—24no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C43⋊#95—22no—
65C43⋊#95—24no—
66C43⋊#95—24no—
67C23×C4×C43—21no—
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—21no—
70C2×C4⋊C4×C43D412yes—
71C2×C22⋊C4×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43D412yes—
74#95×C43—21no—
75#95×C43—21no—
76#95×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—22no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—42no—
110C22×Dic43—44no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43SD1612yes—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—42no—
117C2×C8×C43—22no—
118C2×C8×C43—42no—
119C4⋊C4×C43—42no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122(C2×D43)⋊C4—44no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—82no—
126C4⋊Dic43—22no—
127C4⋊Dic43—21no—
128C4⋊Dic43—22no—
129C4⋊Dic43—21no—
130C4⋊Dic43—44no—
131C4⋊Dic43—41no—
132C4⋊Dic43—41no—
133Dic43⋊C4—41no—
134Dic43⋊C4—41no—
135Dic43⋊C4—41no—
136Dic43⋊C4—41no—
137C2×C43⋊C8—42no—
138C2×C43⋊C8—41no—
139C23×C43—22no—
140C23×C43—22no—
141C23×C43#12011yescharacteristic
142C23×C43#12011yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43C2×SD1611yescharacteristic
145C23×C43#13511yescharacteristic
146C23×C43AGL(1,ℤ/8)11yescharacteristic
147C23×C43#13711yescharacteristic
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—42no—
152C22×D43—42no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—82no—
166C2×C4×C43—82no—
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12711yescharacteristic
171C22⋊D43—81no—
172C22⋊D43—81no—
173C22⋊D43—81no—
174C22⋊D43—81no—
175C2×Dic43—22no—
176C2×Dic43—22no—
177C2×Dic43—22no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—44no—
183C2×Dic43—42no—
184C2×Dic43—41no—
185C2×Dic43—42no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—42no—
190C2×Dic43—82no—
191C2×Dic43—82no—
192C2×Dic43—81no—
193D172—42no—
194D172—81no—
195C8×C43—42no—
196C43⋊C8—81no—
197#9921—431nomaximal, Sylow
198C22×C43—22no—
199C22×C43—22no—
200C22×C43—22no—
201C22×C43—22no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43#39211yescharacteristic
207C22×C43#44811yescharacteristic
208C22×C43#44911yescharacteristic
209C22×C43#45011yescharacteristic
210C22×C43#45211yescharacteristic
211C22×C43#45412yes—
212C22×C43#45812yes—
213C22×C43#46511yescharacteristic
214C22×C43#46811yescharacteristic
215C2×D43—82no—
216C2×D43—82no—
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—82no—
225C4×C43—82no—
226Dic43—42no—
227Dic43—81no—
228Dic43—82no—
229Dic43—81no—
230C2×#481—431no—
231#2618—431no—
232C2×#400—431no—
233#1824—431no—
234C2×#327—431no—
235C2×#324—431no—
236#1294D4311yescharacteristic, complemented
237C2×C43—21no—
238C2×C43—21no—
239C2×C43—21no—
240C2×C43—21no—
241C2×C43#161512yes—
242C2×C43#161612yes—
243C2×C43#200011yescharacteristic
244C2×C43#200311yescharacteristic
245C2×C43#202211yescharacteristic
246D43—161no—
247C2×#123—861no—
248C2×#121—431no—
249C22×C4⋊C4—431no—
250C22×C4⋊C4—431no—
251#481—862no—
252#481—862no—
253C2×#106—861no—
254C2×#102—861no—
255C2×C22⋊C8—431no—
256C2×C22⋊C8C2×D4311yescharacteristic
257#400—862no—
258#400—862no—
259#398—861no—
260#396—862no—
261#394—861no—
262#386—861no—
263#380C2×D4311yescharacteristic
264C2×#95—861no—
265C2×#95—861no—
266C2×#95C2×D4311yescharacteristic
267#340—862no—
268#327—862no—
269#324—862no—
270C43#992111yescharacteristic, complemented, Sylow
271C22×D4—431no—
272C22×D4—861no—
273C23×C4—21no—
274C23×C4—431no—
275C23×C4—431no—
276C23×C4—861no—
277C23×C4C22×D4311yescharacteristic
278C22×C8—21no—
279C22×C8—861no—
280#123—1722no—
281#123—1722no—
282#121—861no—
283#121—861no—
284#121—861no—
285#121—861no—
286C2×C4⋊C4—432no—
287C2×C4⋊C4—431no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—861no—
291C2×C4⋊C4—861no—
292C2×C4⋊C4—862no—
293C2×C4⋊C4—861no—
294C2×C4⋊C4—861no—
295C2×C4⋊C4—861no—
296C2×C4⋊C4—861no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4—861no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4D17212yes—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—862no—
303C2×C22⋊C4—862no—
304C2×C22⋊C4—861no—
305#106—864no—
306#102—864no—
307C22⋊C8—21no—
308C22⋊C8—861no—
309C22⋊C8—861no—
310C22⋊C8D17212yes—
311#95—21no—
312#95—21no—
313#95—864no—
314#95—864no—
315#95—862no—
316#95D17212yes—
317C24—861no—
318C24D4×D4311yescharacteristic
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—1722no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4—1721no—
327C2×D4—1721no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—432no—
336C22×C4—861no—
337C22×C4—861no—
338C22×C4—861no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—862no—
344C22×C4—861no—
345C22×C4—861no—
346C22×C4—861no—
347C22×C4—1724no—
348C22×C4—1721no—
349C22×C4—1721no—
350C22×C4—1722no—
351C22×C4C2×D17211yescharacteristic
352C22×C4C2×D17211yescharacteristic
353C22×C4C2×D17211yescharacteristic
354C22×C4D4×D4311yescharacteristic
355C22×C4D4×D4311yescharacteristic
356C22×C4#1062190211yescharacteristic
357C2×C8—22no—
358C2×C8—42no—
359C2×C8—1722no—
360C2×C8—1721no—
361C4⋊C4—42no—
362C4⋊C4—862no—
363C4⋊C4—861no—
364C4⋊C4—862no—
365C4⋊C4—861no—
366C4⋊C4—1724no—
367C4⋊C4—1721no—
368C4⋊C4—1721no—
369C4⋊C4—1721no—
370C4⋊C4—1721no—
371C4⋊C4—1721no—
372C4⋊C4—1721no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—3442no—
376C22⋊C4—1724no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C23—22no—
380C23—22no—
381C23—1721no—
382C23—1721no—
383C23—1721no—
384C23—1722no—
385C23—1722no—
386C23#1306329511yescharacteristic
387C23#1306329511yescharacteristic
388C23#1306330011yescharacteristic
389C23SD16×D4311yescharacteristic
390C23#1306334611yescharacteristic
391C23#1306334911yescharacteristic
392C23#1306335711yescharacteristic
393D4—3441no—
394D4—3441no—
395D4—3441no—
396D4—3441no—
397D4—3441no—
398D4—1722no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—862no—
414C2×C4—862no—
415C2×C4—862no—
416C2×C4—3442no—
417C2×C4—3442no—
418C2×C4—3441no—
419C2×C4—1724no—
420C2×C4—1722no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1722no—
425C2×C4—1721no—
426C2×C4—1722no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4#1306329511yescharacteristic
432C2×C4#1306330011yescharacteristic
433C2×C4#1306330011yescharacteristic
434C2×C4#1306332211yescharacteristic
435C8—42no—
436C8—3441no—
437C22—21no—
438C22—21no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—21no—
444C22—21no—
445C22—3441no—
446C22—3441no—
447C22—3442no—
448C22—3442no—
449C22—3441no—
450C22#1458280911yescharacteristic
451C22#1458303911yescharacteristic
452C22#1458304511yescharacteristic
453C22#1458305111yescharacteristic
454C22#1458306411yescharacteristic
455C22#1458307312yes—
456C22#1458309012yes—
457C22#1458312911yescharacteristic
458C22#1458314611yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—82no—
464C4—82no—
465C4—3441no—
466C4—3442no—
467C4—3441no—
468C4—1722no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—6881no—
474C2#1913362912yes—
475C2#1913363312yes—
476C2#1913560111yescharacteristic
477C2#1913562011yescharacteristic
478C2#1913572711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenter#1294D43
hypocenterC43#9921
LCSG ▷ C23×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. C2×#14582839C2semidirect
4. #19134683C2semidirect
6. C2×#14582624C2semidirect
7. C43×#1294C2semidirect
236. #1294D43semidirect
270. C43#9921semidirect

Maximal subgroups

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

subgroupindex
C2×#145832182
#191403402
C2×#145828392
#191346832
C2×#145826322
C2×#145826242
C43×#12942
#992143