Finite Group Databasebeta

← #24993056

Subgroups — #24993056

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583217C211yesmaximal, characteristic
2#19137472C211yesmaximal, characteristic, complemented
3#19135430C211yesmaximal, characteristic
4#19133164C211yesmaximal, characteristic
5#19132462C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1824C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583217—21no—
10#14583217—21no—
11#14583217—22no—
12C2×#13063256C412yescomplemented
13C2×#13063245C412yescomplemented
14C2×#13063239—21no—
15C2×#13063239—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582798—21no—
18#14582785—22no—
19#14582759—21no—
20#14582759C2211yescharacteristic
21C4⋊C4×Dic43—21no—
22C4×C22⋊Dic43—21no—
23C4×C22⋊Dic43C2211yescharacteristic
24#14582634—22no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#340—22no—
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C22×C43⋊C8C2×C412yes—
32#13063299—21no—
33#13063299—21no—
34#13063299—21no—
35#13063299—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—22no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43D411yescharacteristic
41C2×C22⋊Dic43D411yescharacteristic
42C2×(C2×D43)⋊C4—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—22no—
45#13063256—22no—
46#13063256—22no—
47#13063245—22no—
48#13063245—22no—
49#13063239—42no—
50#13063239—42no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C43⋊#95D412yes—
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43C2×C412yes—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43D412yes—
68C2×C22⋊C4×C43—21no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71#95×C43—21no—
72C24×C43C2×D411yescharacteristic
73C23×D43—21no—
74C22×C4×C43—22no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—22no—
78C22×C4×C43—42no—
79C22×C4×C43—41no—
80C22×C4×C43—82no—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43—41no—
90C2×C22⋊D43—41no—
91C2×C22⋊D43—41no—
92C2×C22⋊D43—41no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—22no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—42no—
100C2×C8×C43—42no—
101C2×C8×C43—41no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—42no—
107C4⋊C4×C43C22⋊C412yes—
108C4⋊C4×C43C22⋊C412yes—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊Dic43—21no—
112C22⋊Dic43—21no—
113C22⋊Dic43—21no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116C22⋊Dic43SD1612yes—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—42no—
122C4⋊Dic43—82no—
123C4×Dic43—42no—
124C4×Dic43—82no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—42no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43C4×D411yescharacteristic
130C23×C43#12011yescharacteristic
131C23×C43#12111yescharacteristic
132C23×C43C2×SD1611yescharacteristic
133C23×C43#13511yescharacteristic
134C23×C43AGL(1,ℤ/8)11yescharacteristic
135C23×C43#13711yescharacteristic
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—81no—
140C22×D43—81no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—82no—
152C2×C4×C43—82no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C22⋊D43—81no—
161C22⋊D43—81no—
162C22⋊D43—81no—
163C22⋊D43—81no—
164C2×Dic43—22no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—42no—
176D172—42no—
177D172—81no—
178C8×C43—81no—
179C43⋊C8—42no—
180#9261—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43#38611yescharacteristic
192C22×C43C4×SD1611yescharacteristic
193C22×C43#44011yescharacteristic
194C22×C43#44811yescharacteristic
195C22×C43#44911yescharacteristic
196C22×C43#46011yescharacteristic
197C22×C43#46411yescharacteristic
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—161no—
202C2×D43—161no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—42no—
207C4×C43—42no—
208C4×C43—161no—
209C4×C43#41012yes—
210Dic43—42no—
211Dic43—81no—
212Dic43—82no—
213Dic43—81no—
214C2×#481—431no—
215#2345—431no—
216#1964—431no—
217#1824D4311yescharacteristic, complemented
218#1519—431no—
219#1289—431no—
220#1282—431no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43#188011yescharacteristic
228C2×C43#189911yescharacteristic
229C2×C43#190411yescharacteristic
230D43—161no—
231C2×#121—431no—
232C22×C4⋊C4C2×D4311yescharacteristic
233#481—861no—
234#481—861no—
235#481—862no—
236C2×#106—432no—
237C2×#102—432no—
238C2×#99—861no—
239C2×#99—861no—
240C2×C22⋊C8—431no—
241C2×C22⋊C8C2×D4311yescharacteristic
242#389—861no—
243#387—862no—
244#380—431no—
245#380—861no—
246#380C2×D4311yescharacteristic
247C4×C4⋊C4—861no—
248C4×C22⋊C4—431no—
249C4×C22⋊C4—861no—
250#340—22no—
251#327—862no—
252C43#926111yescharacteristic, complemented, Sylow
253C22×D4—431no—
254C22×D4—861no—
255C23×C4—21no—
256C23×C4C22×D4311yescharacteristic
257C22×C8—21no—
258C22×C8—432no—
259#121—861no—
260#121—861no—
261#121—861no—
262#121—861no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—862no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4C4×D4312yes—
271C2×C4⋊C4D17211yescharacteristic
272C2×C4⋊C4D17211yescharacteristic
273C2×C4⋊C4C22⋊D4312yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—431no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C42—862no—
280C2×C42—861no—
281#106—862no—
282#106—862no—
283#102—862no—
284#102—862no—
285#99—1722no—
286#99—1722no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291#95—21no—
292#95—432no—
293#95—862no—
294#95—862no—
295#95—861no—
296C24—861no—
297C24D4×D4311yescharacteristic
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—1722no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—82no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—862no—
317C22×C4—861no—
318C22×C4C2×C4×D4311yescharacteristic
319C22×C4C2×D17211yescharacteristic
320C22×C4D4×D4311yescharacteristic
321C22×C4#1062190011yescharacteristic
322C22×C4#1062190011yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324C2×C8—42no—
325C2×C8—41no—
326C2×C8—862no—
327C2×C8—1722no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—42no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C4⋊C4—3442no—
336C4⋊C4—1722no—
337C4⋊C4(C2×D43)⋊C412yes—
338C4⋊C4(C2×D43)⋊C412yes—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—432no—
342C22⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—3442no—
350C42—1722no—
351C23—41no—
352C23—41no—
353C23—3441no—
354C23—3441no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23(C22⋊D43)⋊C411yescharacteristic
359C23#1306329511yescharacteristic
360C23#1306329711yescharacteristic
361C23SD16×D4311yescharacteristic
362C23#1306334811yescharacteristic
363C23#1306335211yescharacteristic
364C23#1306335711yescharacteristic
365D4—3441no—
366D4—3441no—
367D4—3441no—
368D4—3441no—
369D4—3441no—
370D4—1722no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—862no—
387C2×C4—1722no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1722no—
391C2×C4—1721no—
392C2×C4—1722no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4C2×(C2×D43)⋊C411yescharacteristic
399C2×C4(C22⋊D43)⋊C411yescharacteristic
400C2×C4#1306329711yescharacteristic
401C2×C4#1306330911yescharacteristic
402C8—81no—
403C8—1722no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—3441no—
415C22—3441no—
416C22—3441no—
417C22—6881no—
418C22—6881no—
419C22#1458277611yescharacteristic
420C22#1458298411yescharacteristic
421C22#1458300211yescharacteristic
422C22#1458303911yescharacteristic
423C22#1458304711yescharacteristic
424C22#1458309711yescharacteristic
425C22#1458312311yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—161no—
432C4—3442no—
433C4—3441no—
434C4—3441no—
435C4—1722no—
436C4#1458287212yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—6881no—
444C2#1913494811yescharacteristic
445C2#1913505111yescharacteristic
446C2#1913508011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1824C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1824D43
hypocenterC43#9261
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. #19137472C2semidirect
5. #19132462C2semidirect
6. #19132441C2semidirect
7. C43×#1824C2semidirect
12. C2×#13063256C4semidirect
13. C2×#13063245C4semidirect
217. #1824D43semidirect
252. C43#9261semidirect

Maximal subgroups

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

subgroupindex
C2×#145832172
#191374722
#191354302
#191331642
#191324622
#191324412
C43×#18242
#926143