Finite Group Databasebeta

← #25253592

Subgroups — #25253592

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146338C211yesmaximal, characteristic, complemented
2#19136834C211yesmaximal, characteristic, complemented
3#19136797C211yesmaximal, characteristic, complemented
4#19136775C211yesmaximal, characteristic, complemented
5#19136744C211yesmaximal, characteristic, complemented
6#19136706C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136516C211yesmaximal, characteristic, complemented
10#19136511C211yesmaximal, characteristic, complemented
11#19136459C211yesmaximal, characteristic, complemented
12#19136421C211yesmaximal, characteristic, complemented
13#19136305C211yesmaximal, characteristic, complemented
14C2×#14582702C211yesmaximal, characteristic, complemented
15C43×#3334C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18#14583558—21no—
19C2×#13063269C2211yescharacteristic
20C2×#13063269C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22C2×#13063265C2211yescharacteristic
23C22×C43⋊C16C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583122—21no—
28#14583063—21no—
29#14583040—21no—
30C4×Dic172C2211yescharacteristic
31#14582724C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582702C2211yescharacteristic
36#14582702C2211yescharacteristic
37#14582702C2211yescharacteristic
38#14582702C2211yescharacteristic
39#14582702C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47#14582675C2211yescharacteristic
48C43×#547—21no—
49C43×#500C2211yescharacteristic
50C43×#480—21no—
51C43×#480—21no—
52C43×#474—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C8×D4×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×#10621898—21no—
60C22×Dic86—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172—22no—
64C2×Dic172—21no—
65C2×Dic172—41no—
66C2×Dic172C2311yescharacteristic
67C2×Dic172C2311yescharacteristic
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×D344C2311yescharacteristic
71#13063313—21no—
72#13063311—41no—
73#13063304—21no—
74#13063303—41no—
75#13063299—21no—
76#13063297—41no—
77C4×Dic86—21no—
78(C22⋊D43)⋊C4—41no—
79#13063269—22no—
80#13063269—41no—
81#13063266—41no—
82#13063265—41no—
83C2×C43⋊C16—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063250—21no—
91#13063247—21no—
92C2×#41×C43—41no—
93C2×D8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C4⋊Q8×C43—21no—
97#123×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—41no—
100#121×C43—21no—
101#121×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43D411yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#102×C43—21no—
114#102×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119#41×C43—84no—
120C2×Q8×C43—41no—
121C2×D4×C43—21no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C2×D4×C43D811yescharacteristic
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C2×C22⋊D43—41no—
131C2×C22⋊D43—41no—
132C22×Dic43—41no—
133#10621898—42no—
134#10621898—81no—
135C2×D172—21no—
136C2×C4×D43—41no—
137C2×Dic86—21no—
138C2×Dic86—21no—
139C2×Dic86—42no—
140C2×Dic86—41no—
141C2×Dic86—81no—
142D8×C43—21no—
143D8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43C2×D411yescharacteristic
149C2×C8×C43C2×D411yescharacteristic
150C2×C8×C43C2×D411yescharacteristic
151C2×C8×C43C2411yescharacteristic
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43—41no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43D811yescharacteristic
159C22⋊C4×C43—41no—
160C22⋊C4×C43—41no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43D811yescharacteristic
163C22⋊C4×C43D811yescharacteristic
164C42×C43C2×D411yescharacteristic
165C22⋊Dic43—41no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4—41no—
169C4⋊Dic43—21no—
170Dic43⋊C4—41no—
171Dic43⋊C4—41no—
172C4×Dic43—41no—
173Dic172—21no—
174Dic172—21no—
175Dic172—21no—
176Dic172—42no—
177Dic172#4112yescomplemented
178D344—21no—
179D344—21no—
180#10621873—42no—
181#10621873—81no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C23×C43C2×D811yescharacteristic
189C22×D43—41no—
190Q8×C43—82no—
191D4×C43—22no—
192D4×C43—41no—
193D4×C43—41no—
194D4×C43—82no—
195D4×C43—82no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—82no—
204C2×C4×C43—82no—
205C2×C4×C43—82no—
206C2×C4×C43C2×D811yescharacteristic
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C2×D811yescharacteristic
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C22⋊D43—82no—
212C22⋊D43—82no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—82no—
217D172—41no—
218D172—41no—
219C4×D43—82no—
220Dic86—22no—
221Dic86—41no—
222Dic86—41no—
223Dic86—41no—
224Dic86—82no—
225C8×C43—21no—
226C8×C43—21no—
227C8×C43—21no—
228C8×C43C2×#4111yescharacteristic
229C8×C43H(5,𝔽2)11yescharacteristic
230#33875—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43#50912yes—
240C22×C43C22×D811yescharacteristic
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—81no—
249C4×C43—81no—
250C4×C43—81no—
251C4×C43#54611yescharacteristic
252C4×C43#57711yescharacteristic
253Dic43—42no—
254Dic43—81no—
255Dic43—81no—
256#3334D4311yescharacteristic, complemented
257#3285—431no—
258#2243—431no—
259#2236—431no—
260#2232—431no—
261#2227—431no—
262#2220—431no—
263#2215—431no—
264#2210—431no—
265#2186—431no—
266#2185—431no—
267#2175—431no—
268#2168—431no—
269#2139—431no—
270C2×#358—431no—
271C2×C43—22no—
272C2×C43—41no—
273C2×C43—161no—
274C2×C43#329411yescharacteristic
275C2×C43C2×#50911yescharacteristic
276C2×C43#341711yescharacteristic
277D43—161no—
278C2×#135—431no—
279C22×Q16—431no—
280#548—861no—
281#547—21no—
282C2×SD32—431no—
283C2×SD32—431no—
284C2×D16—431no—
285C2×M32—431no—
286C22×C16—431no—
287#500C2×D4311yescharacteristic
288#495—431no—
289#480—21no—
290#480—21no—
291#474—21no—
292#467—431no—
293#466—431no—
294#466C2×D4311yescharacteristic
295#466C2×D4311yescharacteristic
296#464—861no—
297#452—861no—
298#448—861no—
299C4×Q16—431no—
300C4×D8C2×D4311yescharacteristic
301C8×D4C2×D4311yescharacteristic
302C2×#107C2×D4311yescharacteristic
303C2×#107C2×D4311yescharacteristic
304#366—431no—
305#366—431no—
306#366—431no—
307C4⋊C16—431no—
308#358—431no—
309#358—431no—
310#358—431no—
311#358—431no—
312#358—431no—
313#358—431no—
314#357—431no—
315#357—431no—
316#357—431no—
317#357—431no—
318C22⋊C16—431no—
319C22⋊C16—431no—
320#346—431no—
321C43#3387511yescharacteristic, complemented, Sylow
322C2×#41—41no—
323C2×#41—861no—
324C22×Q8—861no—
325#135—862no—
326#135—1721no—
327C2×Q16—431no—
328C2×Q16—431no—
329C2×Q16—862no—
330C2×Q16—861no—
331C2×Q16—1721no—
332C2×SD16—861no—
333C2×SD16—861no—
334C2×D8—431no—
335C2×D8C22×D4311yescharacteristic
336C22×C8C22×D4311yescharacteristic
337C22×C8C22×D4311yescharacteristic
338C4⋊Q8—21no—
339#124—861no—
340#124—1721no—
341#123—41no—
342#123—41no—
343C22⋊Q8—41no—
344C22⋊Q8—861no—
345C22⋊Q8—1721no—
346#121—21no—
347#121—21no—
348#121—861no—
349#121—1721no—
350C4×Q8—861no—
351C4×D4—21no—
352C4×D4—1721no—
353C4×D4C22⋊D4311yescharacteristic
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356SD32—862no—
357SD32—1721no—
358D16—1721no—
359M32—1721no—
360C2×C16—431no—
361C2×C16—431no—
362C2×C16—431no—
363C2×C16—431no—
364C2×C16—1721no—
365#107—21no—
366#107—21no—
367#107—21no—
368#107—431no—
369#107C22×D4311yescharacteristic
370#107C22×D4311yescharacteristic
371#107C22×D4311yescharacteristic
372C4⋊C8C22⋊D4311yescharacteristic
373#103—861no—
374#103—861no—
375#102—21no—
376#102—21no—
377#102—21no—
378#102—861no—
379C22⋊C8C22⋊D4311yescharacteristic
380C22⋊C8C22⋊D4311yescharacteristic
381C4×C8C22×D4311yescharacteristic
382#41—84no—
383#41—3441no—
384#41—1722no—
385C2×Q8—41no—
386C2×Q8—861no—
387C2×Q8—861no—
388C2×Q8—3441no—
389C2×Q8—1722no—
390C2×Q8—1721no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—861no—
395C2×D4—1721no—
396C2×D4—1721no—
397C2×D4#1062188211yescharacteristic
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4C2×C22⋊D4311yescharacteristic
404C22×C4C2×C22⋊D4311yescharacteristic
405Q16—432no—
406Q16—861no—
407Q16—861no—
408Q16—861no—
409Q16—1722no—
410SD16—3441no—
411SD16—1722no—
412D8—21no—
413D8—21no—
414D8—861no—
415D8—861no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8C2×C22⋊D4311yescharacteristic
421C2×C8C2×C22⋊D4311yescharacteristic
422C2×C8C2×C22⋊D4311yescharacteristic
423C2×C8C23×D4311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4#1062188211yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C22⋊C4#1062188211yescharacteristic
442C22⋊C4#1062188211yescharacteristic
443C42—1721no—
444C42C2×C22⋊D4311yescharacteristic
445C16—861no—
446C16—861no—
447C16—861no—
448C16—861no—
449C23—41no—
450C23—1721no—
451C23C2×#1062188211yescharacteristic
452C23C2×#1062188211yescharacteristic
453Q8—82no—
454Q8—862no—
455Q8—3442no—
456Q8—1721no—
457Q8—1721no—
458Q8—1721no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—3442no—
465D4—3442no—
466D4—1721no—
467D4—1721no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4C2×#1062188211yescharacteristic
484C2×C4C2×#1062188211yescharacteristic
485C2×C4C2×#1062188211yescharacteristic
486C2×C4C2×#1062188211yescharacteristic
487C2×C4C22×C22⋊D4311yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8#41×D4311yescharacteristic
492C8#1306337111yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—3441no—
502C22—3441no—
503C22—3441no—
504C22#1458333512yes—
505C22C22×#1062188211yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—3441no—
514C4—3441no—
515C4—1722no—
516C4#1458353711yescharacteristic
517C4#1458370711yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—6881no—
522C2#1914640211yescharacteristic
523C2C2×#1458333511yescharacteristic
524C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3334C2
socleC22×C43C22×D8
hypercenter#3334D43
hypocenterC43#33875
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #19146338C2semidirect
2. #19136834C2semidirect
3. #19136797C2semidirect
4. #19136775C2semidirect
5. #19136744C2semidirect
6. #19136706C2semidirect
7. #19136679C2semidirect
8. #19136650C2semidirect
9. #19136516C2semidirect
10. #19136511C2semidirect
11. #19136459C2semidirect
12. #19136421C2semidirect
13. #19136305C2semidirect
14. C2×#14582702C2semidirect
15. C43×#3334C2semidirect
177. Dic172#41semidirect
256. #3334D43semidirect
321. C43#33875semidirect

Maximal subgroups

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

subgroupindex
#191463382
#191368342
#191367972
#191367752
#191367442
#191367062
#191366792
#191366502
#191365162
#191365112
#191364592
#191364212
#191363052
C2×#145827022
C43×#33342
#3387543