Finite Group Databasebeta

← #25253468

Subgroups — #25253468

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146940C211yesmaximal, characteristic
2Q16×C22⋊D43C211yesmaximal, characteristic, complemented
3#19136821C211yesmaximal, characteristic, complemented
4#19136792C211yesmaximal, characteristic, complemented
5#19136791C211yesmaximal, characteristic, complemented
6#19136735C211yesmaximal, characteristic, complemented
7#19136694C211yesmaximal, characteristic, complemented
8#19136691C211yesmaximal, characteristic, complemented
9#19136639C211yesmaximal, characteristic, complemented
10#19136513C211yesmaximal, characteristic, complemented
11#19136512C211yesmaximal, characteristic, complemented
12#19136444C211yesmaximal, characteristic, complemented
13C16×C22⋊D43C211yesmaximal, characteristic, complemented
14#358×D43C211yesmaximal, characteristic, complemented
15C2×C43×#358C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17Q8×C22⋊D43—21no—
18#14583550—21no—
19C2×#13063270C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
22C2×C16×D43C2211yescharacteristic
23#14583303C2211yescharacteristic
24#14583277C2211yescharacteristic
25#14583214—21no—
26#14583212—21no—
27#14583178—21no—
28#14583140C2211yescharacteristic
29#14583137C2211yescharacteristic
30#14583136C2211yescharacteristic
31#14583135C2211yescharacteristic
32#14583107—21no—
33#14583055—21no—
34#14583053—21no—
35Q16×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic
37C8×C22⋊D43C2211yescharacteristic
38#107×D43C2211yescharacteristic
39#14582727C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582726C2211yescharacteristic
42Dic43⋊C16C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582702C2211yescharacteristic
48#14582701C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C43×#358C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#358C2211yescharacteristic
59C2×#10621898—41no—
60C2×Q8×D43—21no—
61C2×Dic172C2311yescharacteristic
62C2×#10621885—21no—
63C2×#10621885—21no—
64Q16×D43—22no—
65Q16×D43—41no—
66C2×D344C2311yescharacteristic
67C2×C8×D43C2311yescharacteristic
68#13063324—21no—
69#13063323—21no—
70#13063323—41no—
71#13063310—41no—
72#13063308—41no—
73#13063304—21no—
74#13063304—41no—
75#13063303—41no—
76#13063301—21no—
77#13063301—41no—
78#13063300—21no—
79#13063299—21no—
80Q8×Dic43—21no—
81#13063287—21no—
82C4×C22⋊D43—41no—
83C4×C22⋊D43D411yescharacteristic
84C4⋊C4×D43—21no—
85#13063270—41no—
86#13063268—22no—
87#13063268—41no—
88C2×C43⋊C16C2311yescharacteristic
89C2×C43⋊C16C2311yescharacteristic
90C16×D43—41no—
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95Dic43⋊C8D411yescharacteristic
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063247—21no—
100#13063245—21no—
101#13063245—21no—
102C22⋊(C43⋊C8)D411yescharacteristic
103(C2×D43)⋊C8D411yescharacteristic
104C8×Dic43C2311yescharacteristic
105C22×Q8×C43—21no—
106C2×Q16×C43—22no—
107C2×Q16×C43—21no—
108C2×Q16×C43—41no—
109C2×Q16×C43C2311yescharacteristic
110C2×Q16×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C16×C43—41no—
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43—21no—
117#107×C43C2311yescharacteristic
118#107×C43C2311yescharacteristic
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43—42no—
122C2×Q8×C43—41no—
123C2×Q8×C43—81no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C2×C22⋊D43—41no—
128C2×C22⋊D43D811yescharacteristic
129Q8×D43—42no—
130Q8×D43—81no—
131#10621898—84no—
132C2×D172—21no—
133C2×D172—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43C2×D411yescharacteristic
138C2×Dic86—21no—
139C2×Dic86—41no—
140C2×Dic86—41no—
141Q16×C43—21no—
142Q16×C43—21no—
143Q16×C43—21no—
144Q16×C43—42no—
145Q16×C43#4112yescomplemented
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43C2×D411yescharacteristic
149C2×C8×C43C2411yescharacteristic
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C22⋊Dic43—41no—
154C22⋊Dic43D811yescharacteristic
155#10621885—42no—
156#10621885—81no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4D811yescharacteristic
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—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×Dic43C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175C2×C43⋊C8C2×D411yescharacteristic
176Dic172—21no—
177Dic172—21no—
178D344—21no—
179D344—21no—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43C2×D811yescharacteristic
187C22×D43—41no—
188C22×D43C2×D811yescharacteristic
189Q8×C43—22no—
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×C43—82no—
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—82no—
205C22⋊D43SD3214yescomplemented
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211C2×Dic43C2×D811yescharacteristic
212D172—41no—
213D172—41no—
214D172—82no—
215C4×D43—21no—
216C4×D43—21no—
217C4×D43—82no—
218C4×D43—82no—
219C4×D43—82no—
220Dic86—41no—
221Dic86—41no—
222Dic86—82no—
223Dic86—82no—
224C8×C43—21no—
225C8×C43C2×#4111yescharacteristic
226C8×C43H(5,𝔽2)11yescharacteristic
227C43⋊C8—21no—
228C43⋊C8—21no—
229#33865—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43C2×SD3212yes—
233C22×C43C22×D811yescharacteristic
234C2×D43—21no—
235C2×D43—21no—
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—81no—
239C2×D43C2×SD3212yes—
240C4×C43—21no—
241C4×C43—42no—
242C4×C43—81no—
243C4×C43—81no—
244C4×C43—81no—
245C4×C43#54611yescharacteristic
246C4×C43#57711yescharacteristic
247Dic43—21no—
248Dic43—21no—
249Dic43—81no—
250Dic43—81no—
251Dic43—81no—
252Dic43C2×SD3212yes—
253#3334—431no—
254D4×Q16—431no—
255#2241—431no—
256#2235—431no—
257#2235—431no—
258#2225—431no—
259#2217—431no—
260#2217—431no—
261#2208—431no—
262#2185—431no—
263#2185—431no—
264C4×SD32—431no—
265D4×C16—431no—
266C2×#358—431no—
267C2×#358D4311yescharacteristic, complemented
268C2×C43—22no—
269C2×C43#329411yescharacteristic
270C2×C43C22×SD3211yescharacteristic
271C2×C43#341711yescharacteristic
272D43—22no—
273D43—161no—
274C22×Q16—431no—
275C22×Q16C2×D4311yescharacteristic
276D4×Q8—861no—
277#547—861no—
278C2×SD32—431no—
279C2×SD32—431no—
280C2×SD32—431no—
281C22×C16—431no—
282C22×C16C2×D4311yescharacteristic
283#500—431no—
284#494—431no—
285#480—861no—
286#480—861no—
287#474—861no—
288#467—431no—
289#467—431no—
290#466—431no—
291#466—431no—
292#462—861no—
293#451—861no—
294#451—861no—
295C4×Q16—431no—
296C4×D8—431no—
297C8×D4—431no—
298C2×#107—431no—
299C2×#107C2×D4311yescharacteristic
300#367—431no—
301#367—431no—
302#367—431no—
303C4⋊C16—431no—
304#358—431no—
305#358—431no—
306#358—431no—
307#358—431no—
308#358—431no—
309#358C2×D4311yescharacteristic
310#358C2×D4311yescharacteristic
311#358C2×D4311yescharacteristic
312#358C2×D4311yescharacteristic
313#357—431no—
314C22⋊C16—431no—
315C22⋊C16—431no—
316C4×C16—431no—
317C43#3386511yescharacteristic, complemented, Sylow
318C2×#41—1721no—
319C22×Q8—21no—
320C22×Q8—861no—
321C2×Q16—22no—
322C2×Q16—21no—
323C2×Q16—41no—
324C2×Q16—431no—
325C2×Q16—861no—
326C2×Q16—861no—
327C2×Q16—862no—
328C2×Q16—1721no—
329C2×Q16C22×D4311yescharacteristic
330C2×Q16C22×D4311yescharacteristic
331C2×D8—431no—
332C22×C8—431no—
333C22×C8C22×D4311yescharacteristic
334C4⋊Q8—861no—
335C4⋊Q8—861no—
336C4⋊Q8—1721no—
337#123—1721no—
338#123—1721no—
339C22⋊Q8—861no—
340C22⋊Q8—861no—
341C22⋊Q8—1721no—
342C22⋊Q8—1721no—
343C22⋊Q8—1721no—
344#121—861no—
345#121—861no—
346C4×Q8—861no—
347C4×D4—431no—
348C4×D4—861no—
349C4×D4—1721no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—861no—
352SD32—862no—
353SD32—1721no—
354SD32—1721no—
355C2×C16—41no—
356C2×C16—431no—
357C2×C16—431no—
358C2×C16—1721no—
359C2×C16C22×D4311yescharacteristic
360C2×C16C22×D4311yescharacteristic
361#107—21no—
362#107—431no—
363#107—431no—
364#107—861no—
365#107—861no—
366#107C22×D4311yescharacteristic
367#107C22×D4311yescharacteristic
368C4⋊C8—431no—
369#103—861no—
370#103—861no—
371#103—861no—
372#102—861no—
373#102—861no—
374#102—861no—
375C22⋊C8—431no—
376C22⋊C8—431no—
377C4×C8—431no—
378#41—3444no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—42no—
382C2×Q8—41no—
383C2×Q8—81no—
384C2×Q8—861no—
385C2×Q8—3441no—
386C2×Q8—1721no—
387C2×Q8—1721no—
388C2×Q8—1722no—
389C2×D4—431no—
390C2×D4—861no—
391C2×D4—1721no—
392C2×D4—1721no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—431no—
396C22×C4—1721no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4D4×D4311yescharacteristic
400Q16—21no—
401Q16—21no—
402Q16—21no—
403Q16—42no—
404Q16—861no—
405Q16—861no—
406Q16—3441no—
407Q16—1722no—
408Q16#1062189812yescomplemented
409D8—861no—
410D8—861no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—431no—
414C2×C8—431no—
415C2×C8—861no—
416C2×C8—861no—
417C2×C8D4×D4311yescharacteristic
418C2×C8C23×D4311yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—431no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C22⋊C4—431no—
433C22⋊C4—431no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—431no—
440C42—1721no—
441C16—21no—
442C16—21no—
443C16—861no—
444C16—861no—
445C23—431no—
446C23—1721no—
447C23D8×D4311yescharacteristic
448Q8—22no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452Q8—82no—
453Q8—3442no—
454Q8—3442no—
455Q8—1721no—
456Q8—1721no—
457D4—434no—
458D4—3442no—
459D4—3442no—
460D4—1721no—
461D4—1721no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—431no—
471C2×C4—431no—
472C2×C4—431no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—3442no—
476C2×C4—3442no—
477C2×C4—3442no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4D8×D4311yescharacteristic
482C2×C4C2×D4×D4311yescharacteristic
483C8—21no—
484C8—861no—
485C8—861no—
486C8C2×#1062189811yescharacteristic
487C8#1306337011yescharacteristic
488C22—21no—
489C22—21no—
490C22—432no—
491C22—861no—
492C22—861no—
493C22—3441no—
494C22—3441no—
495C22—3441no—
496C22SD32×D4312yes—
497C22C2×D8×D4311yescharacteristic
498C4—21no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—432no—
504C4—861no—
505C4—861no—
506C4—3441no—
507C4—3441no—
508C4—3441no—
509C4#1458353911yescharacteristic
510C4#1458370511yescharacteristic
511C2—22no—
512C2—862no—
513C2—6881no—
514C2#1914640411yescharacteristic
515C2C2×SD32×D4311yescharacteristic
516C2#1914774411yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#358C2
socleC22×C43C22×D8
prime radical#19146940C2
hypercenterC2×#358D43
hypocenterC43#33865
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. Q16×C22⋊D43C2semidirect
3. #19136821C2semidirect
4. #19136792C2semidirect
5. #19136791C2semidirect
6. #19136735C2semidirect
7. #19136694C2semidirect
8. #19136691C2semidirect
9. #19136639C2semidirect
10. #19136513C2semidirect
11. #19136512C2semidirect
12. #19136444C2semidirect
13. C16×C22⋊D43C2semidirect
14. #358×D43C2semidirect
15. C2×C43×#358C2semidirect
145. Q16×C43#41semidirect
205. C22⋊D43SD32semidirect
267. C2×#358D43semidirect
317. C43#33865semidirect
408. Q16#10621898semidirect

Maximal subgroups

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

subgroupindex
#191469402
Q16×C22⋊D432
#191368212
#191367922
#191367912
#191367352
#191366942
#191366912
#191366392
#191365132
#191365122
#191364442
C16×C22⋊D432
#358×D432
C2×C43×#3582
#3386543