Finite Group Databasebeta

← #25251541

Subgroups — #25251541

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145165C211yesmaximal, characteristic, complemented
2C4×#13063347C211yesmaximal, characteristic, complemented
3#19136804C211yesmaximal, characteristic, complemented
4#19136787C211yesmaximal, characteristic, complemented
5#19136760C211yesmaximal, characteristic, complemented
6#19136753C211yesmaximal, characteristic, complemented
7#19136658C211yesmaximal, characteristic, complemented
8#19136651C211yesmaximal, characteristic, complemented
9#19136537C211yesmaximal, characteristic, complemented
10#19136520C211yesmaximal, characteristic
11C4×Dic344C211yesmaximal, characteristic, complemented
12C4×#13063270C211yesmaximal, characteristic, complemented
13C4×#13063270C211yesmaximal, characteristic, complemented
14C4×D688C211yesmaximal, characteristic, complemented
15C43×#2162C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17#14583433—21no—
18C4×#10621898—21no—
19C2×Dic344C2211yescharacteristic
20C2×#13063270C2211yescharacteristic
21C2×#13063270C2211yescharacteristic
22C2×D688C2211yescharacteristic
23#14583301C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583254—21no—
26#14583140C2211yescharacteristic
27#14583135C2211yescharacteristic
28#14583128—21no—
29C4×Dic172C2211yescharacteristic
30C4×Dic172C2211yescharacteristic
31C4×Dic172C2211yescharacteristic
32C4×#10621873—21no—
33C4×#10621873—21no—
34C4×#10621873—21no—
35C4×D344C2211yescharacteristic
36C4×D344C2211yescharacteristic
37C4×D344C2211yescharacteristic
38#14582937C2211yescharacteristic
39#14582896—21no—
40#14582727C2211yescharacteristic
41#14582727C2211yescharacteristic
42#14582725C2211yescharacteristic
43#14582725C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582704C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582701C2211yescharacteristic
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic
52C2×C4×C8×C43C2211yescharacteristic
53C43×C4⋊C16C2211yescharacteristic
54C43×C4⋊C16C2211yescharacteristic
55C43×C22⋊C16C2211yescharacteristic
56C43×C22⋊C16C2211yescharacteristic
57C4×C16×C43C2211yescharacteristic
58C4×C16×C43C2211yescharacteristic
59C2×#10621898—21no—
60#13063347—22no—
61#13063347—22no—
62C2×Dic172C2311yescharacteristic
63C2×Dic172C2311yescharacteristic
64C2×#10621873—21no—
65C2×#10621873—21no—
66C2×D344C2311yescharacteristic
67C2×D344C2311yescharacteristic
68#13063319—41no—
69#13063317—21no—
70#13063313—21no—
71#13063308—41no—
72#13063304—21no—
73#13063299—21no—
74C4×Dic86—21no—
75C4×Dic86—21no—
76C4×Dic86—21no—
77C4×D172—21no—
78C4×D172—21no—
79C4×D172—21no—
80C4×C22⋊D43—41no—
81C4×C22⋊D43—41no—
82C4×C22⋊D43—41no—
83#13063284—21no—
84#13063282—41no—
85#13063282—41no—
86C42×D43—41no—
87Dic344—22no—
88#13063270—22no—
89#13063270—22no—
90D688—22no—
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063259C2311yescharacteristic
94#13063259C2311yescharacteristic
95#13063257—21no—
96#13063257—21no—
97#13063250—21no—
98#13063250—21no—
99#13063250—21no—
100#13063250—21no—
101#13063247—21no—
102#13063247—21no—
103#13063247—21no—
104#13063247—21no—
105C22×C8×C43D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C42×C43D411yescharacteristic
108C2×C16×C43C2311yescharacteristic
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111C2×C16×C43C2311yescharacteristic
112C4×C8×C43D411yescharacteristic
113C4×C8×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C22×C4×C43D811yescharacteristic
117C22×C4×C43D811yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121#10621898—24no—
122#10621898—42no—
123C2×D172—21no—
124C2×D172—21no—
125C2×C4×D43—41no—
126C2×C4×D43—41no—
127C2×C4×D43—41no—
128C2×C4×D43—41no—
129C2×Dic86—21no—
130C2×Dic86—21no—
131C2×C8×C43—21no—
132C2×C8×C43—21no—
133C2×C8×C43—41no—
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2411yescharacteristic
138C42×C43D811yescharacteristic
139C42×C43D811yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43C2×D411yescharacteristic
142C22⋊Dic43—41no—
143C22⋊Dic43—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160C4×Dic43—41no—
161C4×Dic43—41no—
162C4×Dic43—41no—
163C4×Dic43—41no—
164Dic172—21no—
165Dic172—21no—
166Dic172—21no—
167Dic172#4112yes—
168D344—21no—
169D344—21no—
170D344—21no—
171D344#4112yes—
172#10621873—24no—
173#10621873—42no—
174C16×C43—21no—
175C16×C43—21no—
176C16×C43—21no—
177C16×C43—21no—
178C23×C43C2×D811yescharacteristic
179C22×D43—41no—
180C22×D43—41no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43C2×D811yescharacteristic
186C2×C4×C43C2×D811yescharacteristic
187C2×C4×C43C2×D811yescharacteristic
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C22⋊D43—44no—
192C22⋊D43—82no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199D172—22no—
200D172—41no—
201D172—41no—
202D172—41no—
203C4×D43—44no—
204C4×D43—82no—
205C4×D43—82no—
206C4×D43—82no—
207Dic86—22no—
208Dic86—41no—
209Dic86—41no—
210Dic86—41no—
211C8×C43—21no—
212C8×C43—21no—
213C8×C43—21no—
214C8×C43C2×#4111yescharacteristic
215C8×C43C2×#4111yescharacteristic
216#33662—431nomaximal, Sylow
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43C22×D811yescharacteristic
221C2×D43—42no—
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43#50812yes—
232C4×C43#52511yescharacteristic
233C4×C43#57511yescharacteristic
234Dic43—42no—
235Dic43—81no—
236Dic43—81no—
237Dic43—81no—
238Dic43—81no—
239Dic43—81no—
240#3168—431no—
241C4×#135—431no—
242#2237—431no—
243#2234—431no—
244#2229—431no—
245#2228—431no—
246#2211—431no—
247#2210—431no—
248#2189—431no—
249#2186—431no—
250C4×Q32—431no—
251C4×SD32—431no—
252C4×SD32—431no—
253C4×D16—431no—
254#2162D4311yescharacteristic, complemented
255C2×C43—41no—
256C2×C43#310011yescharacteristic
257C2×C43C2×#50811yescharacteristic
258C2×C43#341411yescharacteristic
259D43—82no—
260D43—161no—
261C2×#135—431no—
262#529—861no—
263C4×#41—861no—
264C2×Q32—431no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×D16—431no—
268#499—431no—
269#495—431no—
270#488—861no—
271#467—431no—
272#466—431no—
273#465—861no—
274C4×Q16—431no—
275C4×Q16—431no—
276C4×Q16—431no—
277C4×SD16—861no—
278C4×SD16—861no—
279C4×SD16—861no—
280C4×D8—431no—
281C4×D8—431no—
282C4×D8—431no—
283#427—431no—
284#416—861no—
285C2×C4×C8C2×D4311yescharacteristic
286#367—431no—
287#367—431no—
288#366—431no—
289#366—431no—
290C4⋊C16C2×D4311yescharacteristic
291C4⋊C16C2×D4311yescharacteristic
292#358—431no—
293#358—431no—
294#358—431no—
295#358—431no—
296#357—431no—
297#357—431no—
298#357—431no—
299#357—431no—
300C22⋊C16C2×D4311yescharacteristic
301C22⋊C16C2×D4311yescharacteristic
302C4×C16C2×D4311yescharacteristic
303C4×C16C2×D4311yescharacteristic
304C43#3366211yescharacteristic, complemented, Sylow
305C2×#41—861no—
306#135—862no—
307#135—862no—
308C2×Q16—431no—
309C2×Q16—431no—
310C2×SD16—861no—
311C2×SD16—861no—
312C2×D8—431no—
313C2×D8—431no—
314C22×C8D17211yescharacteristic
315C22×C8C22×D4311yescharacteristic
316#126—1721no—
317#125—861no—
318#124—861no—
319#123—1721no—
320C22⋊Q8—861no—
321#121—861no—
322C4×Q8—861no—
323C4×Q8—861no—
324C4×Q8—861no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4—861no—
328C4×D4—1721no—
329C4×D4—1721no—
330C4×D4—1721no—
331#117—861no—
332#117—1721no—
333#117—1721no—
334C2×C42—1721no—
335C2×C42D17211yescharacteristic
336Q32—862no—
337SD32—862no—
338SD32—862no—
339D16—862no—
340C2×C16C22×D4311yescharacteristic
341C2×C16C22×D4311yescharacteristic
342C2×C16C22×D4311yescharacteristic
343C2×C16C22×D4311yescharacteristic
344#107—431no—
345#107—431no—
346#107—431no—
347#107—431no—
348#106—861no—
349#106—861no—
350#103—861no—
351#103—861no—
352#103—861no—
353#103—861no—
354#102—861no—
355#102—861no—
356#102—861no—
357#102—861no—
358C4×C8D17211yescharacteristic
359C4×C8D17211yescharacteristic
360C4×C8C22×D4311yescharacteristic
361C4×C8C22×D4311yescharacteristic
362#41—864no—
363#41—1722no—
364C2×Q8—861no—
365C2×Q8—861no—
366C2×D4—861no—
367C2×D4—861no—
368C2×D4—1721no—
369C2×D4—1721no—
370C22×C4—1721no—
371C22×C4—1721no—
372C22×C4—1721no—
373C22×C4—1721no—
374C22×C4D34411yescharacteristic
375C22×C4D34411yescharacteristic
376C22×C4C2×D17211yescharacteristic
377Q16—432no—
378Q16—861no—
379Q16—861no—
380Q16—861no—
381SD16—864no—
382SD16—1722no—
383D8—432no—
384D8—861no—
385D8—861no—
386D8—861no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8C2×D17211yescharacteristic
391C2×C8C2×D17211yescharacteristic
392C2×C8C2×D17211yescharacteristic
393C2×C8C23×D4311yescharacteristic
394C4⋊C4—861no—
395C4⋊C4—861no—
396C4⋊C4—861no—
397C4⋊C4—861no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C4⋊C4—1721no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4—1721no—
407C22⋊C4—1721no—
408C22⋊C4—1721no—
409C22⋊C4—1721no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C42—1721no—
413C42—1721no—
414C42—1721no—
415C42—1721no—
416C42D34411yescharacteristic
417C42D34411yescharacteristic
418C42C2×D17211yescharacteristic
419C42C2×D17211yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—1721no—
425C23—1721no—
426C23C2×D34411yescharacteristic
427Q8—862no—
428Q8—1721no—
429Q8—1721no—
430Q8—1721no—
431D4—862no—
432D4—3442no—
433D4—1724no—
434D4—1721no—
435D4—1721no—
436D4—1721no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—3442no—
442C2×C4—3442no—
443C2×C4—3442no—
444C2×C4—1724no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4C2×D34411yescharacteristic
452C2×C4C2×D34411yescharacteristic
453C2×C4C2×D34411yescharacteristic
454C2×C4C2×D34411yescharacteristic
455C2×C4C2×D34411yescharacteristic
456C2×C4C22×D17211yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8#41×D4311yescharacteristic
461C8#41×D4311yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—3441no—
466C22—3441no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—1722no—
471C22C22×D34411yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—3441no—
477C4—3441no—
478C4—3441no—
479C4—3441no—
480C4—3441no—
481C4—1722no—
482C4#1458333112yes—
483C4#1458341111yescharacteristic
484C4#1458369911yescharacteristic
485C2—41no—
486C2—3442no—
487C2—6881no—
488C2#1914459611yescharacteristic
489C2C2×#1458333111yescharacteristic
490C2#1914773111yescharacteristic
subgroupG/H
centerC2×C4C2×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2162C2
socleC22×C43C22×D8
prime radical#19136520C2
hypercenter#2162D43
hypocenterC43#33662
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
1. #19145165C2semidirect
2. C4×#13063347C2semidirect
3. #19136804C2semidirect
4. #19136787C2semidirect
5. #19136760C2semidirect
6. #19136753C2semidirect
7. #19136658C2semidirect
8. #19136651C2semidirect
9. #19136537C2semidirect
11. C4×Dic344C2semidirect
12. C4×#13063270C2semidirect
13. C4×#13063270C2semidirect
14. C4×D688C2semidirect
15. C43×#2162C2semidirect
254. #2162D43semidirect
304. C43#33662semidirect

Maximal subgroups

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

subgroupindex
#191451652
C4×#130633472
#191368042
#191367872
#191367602
#191367532
#191366582
#191366512
#191365372
#191365202
C4×Dic3442
C4×#130632702
C4×D6882
C43×#21622
#3366243