Finite Group Databasebeta

← #25253476

Subgroups — #25253476

Order 11008.

548 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146984C211yesmaximal, characteristic
2Q16×C22⋊D43C211yesmaximal, characteristic
3#19136821C211yesmaximal, characteristic, complemented
4#19136798C211yesmaximal, characteristic, complemented
5#19136796C211yesmaximal, characteristic, complemented
6#19136745C211yesmaximal, characteristic, complemented
7#19136684C211yesmaximal, characteristic, complemented
8#19136683C211yesmaximal, characteristic, complemented
9#19136643C211yesmaximal, characteristic, complemented
10#19136527C211yesmaximal, characteristic, complemented
11Q32×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C16C211yesmaximal, characteristic
13C2×#14582703C211yesmaximal, characteristic, complemented
14#358×D43C211yesmaximal, characteristic, complemented
15C43×#2188C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17#14583607—21no—
18Q8×C22⋊D43—21no—
19C2×#13063271C2211yescharacteristic
20C22×C43⋊C16C2211yescharacteristic
21C2×C16×D43C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583277C2211yescharacteristic
24#14583233—21no—
25#14583232—21no—
26#14583192—21no—
27#14583140C2211yescharacteristic
28#14583137C2211yescharacteristic
29#14583137C2211yescharacteristic
30#14583107—21no—
31#14583055—21no—
32#14583053—21no—
33Q16×Dic43C2211yescharacteristic
34Q16×Dic43C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582725C2211yescharacteristic
39#14582725C2211yescharacteristic
40#14582724C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582703C2211yescharacteristic
48#14582703C2211yescharacteristic
49#14582702C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×Q32×C43C2211yescharacteristic
54C2×Q32×C43C2211yescharacteristic
55C43×#467C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×Q8×D43—21no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62C2×#10621885—21no—
63Q16×D43—22no—
64Q16×D43—41no—
65C2×C8×D43C2311yescharacteristic
66#13063324—21no—
67#13063323—21no—
68#13063323—41no—
69#13063315—41no—
70#13063305—41no—
71#13063304—21no—
72#13063304—41no—
73#13063302—41no—
74#13063301—21no—
75#13063301—21no—
76#13063301—41no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79C4×C22⋊D43—41no—
80C4×C22⋊D43D411yescharacteristic
81(C22⋊D43)⋊C4—41no—
82C2×C4⋊Dic43—21no—
83C4⋊C4×D43—21no—
84#13063271—41no—
85C2×C43⋊C16—41no—
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88C16×D43—41no—
89#13063259—21no—
90#13063259C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95Dic43⋊C8D411yescharacteristic
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101C22⋊(C43⋊C8)D411yescharacteristic
102(C2×D43)⋊C8D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C22×Q8×C43—21no—
105C2×Q16×C43—22no—
106C2×Q16×C43—21no—
107C2×Q16×C43—41no—
108C2×Q16×C43C2311yescharacteristic
109C2×Q16×C43C2311yescharacteristic
110C2×Q16×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22⋊Q8×C43—21no—
113Q32×C43—22no—
114Q32×C43—41no—
115C2×C16×C43C2311yescharacteristic
116C2×C16×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43—21no—
122C2×Q8×C43—42no—
123C2×Q8×C43—41no—
124C2×Q8×C43—81no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C2×C22⋊D43D811yescharacteristic
128C22×Dic43—41no—
129Q8×D43—42no—
130Q8×D43—81no—
131C2×C4×D43—41no—
132C2×C4×D43—41no—
133C2×C4×D43C2×D411yescharacteristic
134C2×Dic86—21no—
135C2×Dic86—41no—
136C2×Dic86—41no—
137Q16×C43—21no—
138Q16×C43—21no—
139Q16×C43—21no—
140Q16×C43—21no—
141Q16×C43—21no—
142Q16×C43—42no—
143Q16×C43#4112yes—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2411yescharacteristic
148C4⋊C4×C43—21no—
149C4⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43D811yescharacteristic
153#10621885—42no—
154#10621885—81no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4D811yescharacteristic
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—41no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170Dic43⋊C4—41no—
171Dic43⋊C4D811yescharacteristic
172C4×Dic43—41no—
173C4×Dic43—41no—
174C4×Dic43C2×D411yescharacteristic
175C2×C43⋊C8C2×D411yescharacteristic
176C2×C43⋊C8C2×D411yescharacteristic
177Dic172—21no—
178Dic172—21no—
179C8×D43—21no—
180C8×D43—21no—
181C16×C43—21no—
182C16×C43—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43C2×D811yescharacteristic
186C22×D43C2×D811yescharacteristic
187Q8×C43—22no—
188Q8×C43—41no—
189Q8×C43—41no—
190Q8×C43—41no—
191Q8×C43—41no—
192Q8×C43—41no—
193Q8×C43—82no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—82no—
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43Q3214yescomplemented
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—161no—
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211C2×Dic43C2×D811yescharacteristic
212C4×D43—21no—
213C4×D43—21no—
214C4×D43—82no—
215C4×D43—161no—
216Dic86—41no—
217Dic86—41no—
218Dic86—82no—
219Dic86—161no—
220C8×C43—21no—
221C8×C43C2×#4111yescharacteristic
222C8×C43H(5,𝔽2)11yescharacteristic
223C43⋊C8—21no—
224C43⋊C8—21no—
225#33866—431nomaximal, Sylow
226C22×C43—21no—
227C22×C43—21no—
228C22×C43C2×Q3212yes—
229C22×C43C22×D811yescharacteristic
230C2×D43—21no—
231C2×D43—21no—
232C2×D43C2×Q3212yes—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43#54611yescharacteristic
239C4×C43#57711yescharacteristic
240Dic43—21no—
241Dic43—21no—
242Dic43—81no—
243Dic43—81no—
244Dic43—81no—
245Dic43—81no—
246Dic43C2×Q3212yes—
247#3338—431no—
248D4×Q16—431no—
249#2241—431no—
250#2236—431no—
251#2236—431no—
252#2227—431no—
253#2216—431no—
254#2216—431no—
255#2209—431no—
256#2188—431no—
257#2188D4311yescharacteristic, complemented
258C4×Q32—431no—
259D4×C16—431no—
260C2×#358—431no—
261C2×#358—431no—
262C2×C43—22no—
263C2×C43#329411yescharacteristic
264C2×C43C22×Q3211yescharacteristic
265C2×C43#341611yescharacteristic
266D43—22no—
267C22×Q16—431no—
268C22×Q16C2×D4311yescharacteristic
269#554—861no—
270D4×Q8—861no—
271C2×Q32—431no—
272C2×Q32C2×D4311yescharacteristic
273C2×Q32C2×D4311yescharacteristic
274C22×C16—431no—
275C22×C16—431no—
276#500—431no—
277#494—431no—
278#484—861no—
279#484—861no—
280#477—861no—
281#467—431no—
282#467—431no—
283#467—431no—
284#467C2×D4311yescharacteristic
285#462—861no—
286#451—861no—
287#451—861no—
288C4×Q16—431no—
289C4×Q16—431no—
290C8×D4—431no—
291C2×#107—431no—
292C2×#107—431no—
293#366—431no—
294#366—431no—
295#366—431no—
296C4⋊C16—431no—
297#358—431no—
298#358—431no—
299#358—431no—
300#358—431no—
301#358—431no—
302#358—431no—
303#358—431no—
304#358—431no—
305#358C2×D4311yescharacteristic
306#358C2×D4311yescharacteristic
307C22⋊C16—431no—
308C22⋊C16C2×D4311yescharacteristic
309C4×C16—431no—
310C43#3386611yescharacteristic, complemented, Sylow
311C22×Q8—21no—
312C22×Q8—861no—
313C2×Q16—22no—
314C2×Q16—21no—
315C2×Q16—41no—
316C2×Q16—431no—
317C2×Q16—861no—
318C2×Q16—861no—
319C2×Q16—862no—
320C2×Q16—1721no—
321C2×Q16C22×D4311yescharacteristic
322C2×Q16C22×D4311yescharacteristic
323C2×Q16C22×D4311yescharacteristic
324C22×C8—431no—
325C22×C8C22×D4311yescharacteristic
326C4⋊Q8—861no—
327C4⋊Q8—861no—
328C4⋊Q8—1721no—
329#125—1721no—
330C22⋊Q8—21no—
331C22⋊Q8—861no—
332C22⋊Q8—861no—
333C22⋊Q8—861no—
334C22⋊Q8—1721no—
335C22⋊Q8—1721no—
336C22⋊Q8—1721no—
337C22⋊Q8—1721no—
338C4×Q8—861no—
339C4×Q8—861no—
340C4×D4—431no—
341C4×D4—1721no—
342C4×D4—1721no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345Q32—22no—
346Q32—41no—
347Q32—1721no—
348C2×C16—431no—
349C2×C16—431no—
350C2×C16—1721no—
351C2×C16—1721no—
352C2×C16C22×D4311yescharacteristic
353C2×C16C22×D4311yescharacteristic
354#107—431no—
355#107—431no—
356#107—431no—
357#107—861no—
358#107—861no—
359#107—861no—
360#107C22×D4311yescharacteristic
361C4⋊C8—431no—
362#103—21no—
363#103—861no—
364#103—861no—
365#103—861no—
366#103—861no—
367#103—861no—
368C22⋊C8—431no—
369C22⋊C8—431no—
370C4×C8—431no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—42no—
375C2×Q8—41no—
376C2×Q8—81no—
377C2×Q8—861no—
378C2×Q8—3441no—
379C2×Q8—1721no—
380C2×Q8—1721no—
381C2×Q8—1722no—
382C2×D4—431no—
383C22×C4—41no—
384C22×C4—431no—
385C22×C4—1721no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4D4×D4311yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—42no—
395Q16—861no—
396Q16—861no—
397Q16—3441no—
398Q16—1722no—
399Q16#1062190012yes—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—431no—
403C2×C8—431no—
404C2×C8—861no—
405C2×C8—861no—
406C2×C8D4×D4311yescharacteristic
407C2×C8C23×D4311yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—431no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C4⋊C4—1721no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C4⋊C4—1721no—
424C22⋊C4—41no—
425C22⋊C4—431no—
426C22⋊C4—431no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C22⋊C4—1721no—
430C42—431no—
431C42—1721no—
432C42—1721no—
433C16—21no—
434C16—21no—
435C16—861no—
436C16—861no—
437C23—431no—
438C23D8×D4311yescharacteristic
439Q8—22no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—82no—
446Q8—3442no—
447Q8—1721no—
448Q8—1721no—
449Q8—6881no—
450D4—434no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—82no—
458C2×C4—431no—
459C2×C4—431no—
460C2×C4—431no—
461C2×C4—861no—
462C2×C4—861no—
463C2×C4—3442no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4—6881no—
469C2×C4—6881no—
470C2×C4D8×D4311yescharacteristic
471C2×C4C2×D4×D4311yescharacteristic
472C8—21no—
473C8—861no—
474C8—861no—
475C8C2×#1062190011yescharacteristic
476C8#1306337011yescharacteristic
477C22—21no—
478C22—21no—
479C22—432no—
480C22—861no—
481C22—861no—
482C22Q32×D4312yes—
483C22C2×D8×D4311yescharacteristic
484C4—21no—
485C4—42no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—432no—
490C4—861no—
491C4—861no—
492C4—3441no—
493C4—3441no—
494C4—3441no—
495C4—3441no—
496C4#1458353611yescharacteristic
497C4#1458370911yescharacteristic
498C2—22no—
499C2—862no—
500C2#1914640111yescharacteristic
501C2C2×Q32×D4311yescharacteristic
502C2#1914774011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2188C2
socleC22×C43C22×D8
prime radicalC2×C22⋊D43D8
hypercenter#2188D43
hypocenterC43#33866
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
3. #19136821C2semidirect
4. #19136798C2semidirect
5. #19136796C2semidirect
6. #19136745C2semidirect
7. #19136684C2semidirect
8. #19136683C2semidirect
9. #19136643C2semidirect
10. #19136527C2semidirect
11. Q32×Dic43C2semidirect
13. C2×#14582703C2semidirect
14. #358×D43C2semidirect
15. C43×#2188C2semidirect
203. C22⋊D43Q32semidirect
257. #2188D43semidirect
310. C43#33866semidirect

Maximal subgroups

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

subgroupindex
#191469842
Q16×C22⋊D432
#191368212
#191367982
#191367962
#191367452
#191366842
#191366832
#191366432
#191365272
Q32×Dic432
(C22⋊D43)⋊C162
C2×#145827032
#358×D432
C43×#21882
#3386643